gsw-3.6.21/0000755000175000017500000000000015147371330012571 5ustar alastairalastairgsw-3.6.21/gsw.egg-info/0000755000175000017500000000000015147371330015063 5ustar alastairalastairgsw-3.6.21/gsw.egg-info/SOURCES.txt0000644000175000017500000000176615147371330016761 0ustar alastairalastairLICENSE.txt MANIFEST.in README.md pyproject.toml requirements-dev.txt setup.py gsw/__init__.py gsw/_fixed_wrapped_ufuncs.py gsw/_utilities.py gsw/_version.py gsw/_wrapped_ufuncs.py gsw/conversions.py gsw/density.py gsw/energy.py gsw/freezing.py gsw/geostrophy.py gsw/ice.py gsw/interpolation.py gsw/stability.py gsw/utility.py gsw/tests/_WIP_test_ufuncs.py gsw/tests/check_functions.py gsw/tests/geo_strf_dyn_height.npy gsw/tests/geo_strf_steric_height.npy gsw/tests/geo_strf_velocity.npy gsw/tests/gsw_check_functions_save.m gsw/tests/gsw_cv_v3_0.npz gsw/tests/list_check_functions.py gsw/tests/test_check_functions.py gsw/tests/test_dll_export.py gsw/tests/test_geostrophy.py gsw/tests/test_gibbs.py gsw/tests/test_interpolation.py gsw/tests/test_utility.py gsw/tests/test_xarray.py gsw/tests/write_geo_npyfiles.py src/_ufuncs.c src/method_bodies.c src/method_def_entries.c src/c_gsw/gsw_internal_const.h src/c_gsw/gsw_oceanographic_toolbox.c src/c_gsw/gsw_saar.c src/c_gsw/gsw_saar_data.h src/c_gsw/gswteos-10.hgsw-3.6.21/PKG-INFO0000644000175000017500000001551115147371330013671 0ustar alastairalastairMetadata-Version: 2.4 Name: gsw Version: 3.6.21 Summary: Gibbs Seawater Oceanographic Package of TEOS-10 Author-email: "Eric Firing, Filipe Fernandes" License-Expression: BSD-3-Clause Project-URL: documentation, https://teos-10.github.io/GSW-Python/ Project-URL: homepage, https://www.teos-10.org/ Project-URL: repository, https://github.com/TEOS-10/GSW-python Classifier: Development Status :: 5 - Production/Stable Classifier: Intended Audience :: Science/Research Classifier: Operating System :: OS Independent Classifier: Programming Language :: Python Classifier: Programming Language :: Python :: 3 :: Only Classifier: Programming Language :: Python :: 3.11 Classifier: Programming Language :: Python :: 3.12 Classifier: Programming Language :: Python :: 3.13 Classifier: Programming Language :: Python :: 3.14 Classifier: Topic :: Scientific/Engineering Requires-Python: >=3.11 Description-Content-Type: text/markdown License-File: LICENSE.txt Requires-Dist: numpy>=2 Dynamic: license-file # GSW-Python [![Tests](https://github.com/TEOS-10/GSW-Python/actions/workflows/tests.yml/badge.svg)](https://github.com/TEOS-10/GSW-Python/actions/workflows/tests.yml) [![Wheels](https://github.com/TEOS-10/GSW-Python/actions/workflows/cibuildwheel.yml/badge.svg)](https://github.com/TEOS-10/GSW-Python/actions/workflows/cibuildwheel.yml) [![DOI](https://zenodo.org/badge/86503067.svg)](https://zenodo.org/badge/latestdoi/86503067) This Python implementation of the Thermodynamic Equation of Seawater 2010 (TEOS-10) is based primarily on numpy ufunc wrappers of the GSW-C implementation. This library replaces the original [python-gsw](https://github.com/TEOS-10/python-gsw) pure-python implementation. The primary reasons for this change are that by building on the C implementation we reduce code duplication and we gain an immediate update to the 75-term equation. Additional benefits include a major increase in speed, a reduction in memory usage, and the inclusion of more functions. The penalty is that a C (or MSVC C++ for Windows) compiler is required to build the package from source. **Warning: this is for Python >=3.8 only.** Documentation is provided at https://teos-10.github.io/GSW-Python/. For the core functionality, we use an auto-generated C extension module to wrap the C functions as numpy [ufuncs](https://docs.scipy.org/doc/numpy/reference/ufuncs.html), and then use an autogenerated Python module to add docstrings and handle masked arrays. 165 scalar C functions with only double-precision arguments and return values are wrapped as ufuncs, and 158 of these are exposed in the ``gsw`` namespace with an additional wrapper in Python. A hand-written wrapper is used for one C function, and others are re-implemented directly in Python instead of being wrapped. Additional functions present in GSW-Matlab but not in GSW-C may be re-implemented in Python, but there is no expectation that all such functions will be provided. ## Installation Pip users can install the pre-built wheels with: ```shell pip install gsw ``` conda users will find binaries on conda-forge, ```shell conda install gsw --channel conda-forge ``` The development version of the package can be installed from a clone of the repo using ```shell pip install . ``` ## Citation If you use GSW-Python, please cite: McDougall, T.J. and P.M. Barker, 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox, 28pp., SCOR/IAPSO WG127, ISBN 978-0-646-55621-5 ```bibtex @book{mcdougall2011getting, author = {McDougall, T. J. and Barker, P. M.}, title = {Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox}, year = {2011}, pages = {28}, publisher = {SCOR/IAPSO WG127}, isbn = {978-0-646-55621-5} } ``` ## Note for xarray users A wrapper around gsw called [gsw-xarray](https://github.com/DocOtak/gsw-xarray) exists for xarray. It adds CF compliant attributes when possible, units, and name. ## Note on generating the docstrings The autogenerated docstrings are checked with codespell in the CIs. When autogenerating them we need to run ``pre-commit run --all-files`` and fix the documentation issues found. ## Development notes You will need a suitable compiler: gcc or clang for unix-like systems, or the MSVC compiler set used for Python itself on Windows. For Windows, some of the source code has been modified to C++ because the MSVC C compiler does not support the C99 complex data type used in original GSW-C. The subdirectory ('tools') contains modules and scripts for maintaining the code that is autogenerated from the upstream GSW-Matlab and GSW-C repos. The scripts are to be run from this directory; they make assumptions about where they are, and about where upstream repos are. Specifically, it is assumed that GSW-Matlab, GSW-C, and GSW-Python git repos are all in the same base directory. ### Scripts - `copy_from_GSW-C.py`: copies the relevant .c and .h files from a sibling GSW-C repo, if the latter are newer. - `mat2npz.py`: generates an npz file in gsw/tests containing the test data and check values from the gsw_data_v3_0.mat file in the sibling GSW-Matlab repo. - `make_ufuncs.py`: Generates the src/_ufuncs.c file to turn the scalar C functions into numpy ufuncs. It writes ufuncs.list in the current directory as a record of the ufunc names. Functions are identified as ufunc candidates based on their signatures, parsed from src/c_gsw/gswteos-10.h. - `make_wrapped_ufuncs.py`: Generates gsw/_wrapped_ufuncs.py based on the output of make_ufuncs.py. It adds docstrings constructed from the Matlab help text. - `fix_wrapped_ufunc_typos.py`: Fixes docstring typos that have been identified, but not yet fixed, in the GSW-Matlab repo. - `codegen`: Runs the last three python scripts. ### Modules - `c_header_parser.py`: Functions for taking apart the function declarations in gswteos-10.h. - `matlab_parser.py`: Functions specifically for reading the GSW-Matlab function signatures and for splitting out the help text. - `docstring_parts.py`: Blocks of text for assembling docstrings. - `docstring_utils.py`: Functions for assembling docstrings in numpydoc format. - `categories.py`: Functions for listing gsw function names by category. This is not used by any of the other functions or scripts, but was used when initially categorizing the functions for inclusion in submodules. ### Notes - In addition to the generated src/_ufuncs.c, there are two C files that are hand-written: src/method_bodies.c and src/method_def_entries.c. These are imported by src/_ufuncs.c. They handle some C functions that are not suitable for ufuncs. - Specialized Matlab parsing is also done in gsw/tests/check_functions.py, which is used by gsw/tests/test_check_functions.py; see the docstring of the former for more info. ### Testing To test, after installation, run "pytest --pyargs gsw". gsw-3.6.21/setup.py0000644000175000017500000000340615147371315014311 0ustar alastairalastair""" Minimal setup.py for building gswc. """ import os import shutil import sys import numpy from setuptools import Extension, setup from setuptools.command.build_ext import build_ext as _build_ext rootpath = os.path.abspath(os.path.dirname(__file__)) DEFINE_MACROS = [ ("NPY_NO_DEPRECATED_API", "NPY_1_7_API_VERSION"), # 0x030B0000 -> 3.11 ("Py_LIMITED_API", "0x030B0000"), ("CYTHON_LIMITED_API", None), ] def read(*parts): return open(os.path.join(rootpath, *parts)).read() class build_ext(_build_ext): # Extension builder from pandas without the cython stuff def build_extensions(self): numpy_incl = numpy.get_include() for ext in self.extensions: if hasattr(ext, "include_dirs") and not numpy_incl in ext.include_dirs: ext.include_dirs.append(numpy_incl) _build_ext.build_extensions(self) # MSVC can't handle C complex, and distutils doesn't seem to be able to # let us force C++ compilation of .c files, so we use the following hack for # Windows. if sys.platform == "win32": cext = "cpp" shutil.copy( "src/c_gsw/gsw_oceanographic_toolbox.c", "src/c_gsw/gsw_oceanographic_toolbox.cpp", ) shutil.copy("src/c_gsw/gsw_saar.c", "src/c_gsw/gsw_saar.cpp") else: cext = "c" ufunc_src_list = [ "src/_ufuncs.c", "src/c_gsw/gsw_oceanographic_toolbox." + cext, "src/c_gsw/gsw_saar." + cext, ] config = { "ext_modules": [ Extension( "gsw._gsw_ufuncs", ufunc_src_list, define_macros=DEFINE_MACROS, py_limited_api=True)], "include_dirs": [os.path.join(rootpath, "src", "c_gsw")], "cmdclass": {"build_ext": build_ext}, "options": {"bdist_wheel": {"py_limited_api": "cp311"}}, } setup(**config) gsw-3.6.21/pyproject.toml0000644000175000017500000000472415147371315015517 0ustar alastairalastair[build-system] build-backend = "setuptools.build_meta" requires = [ "build", "numpy>=2,<3", "pip>9.0.1", "setuptools>=42", "setuptools-scm[toml]>=3.4", "wheel", ] [project] name = "gsw" description = "Gibbs Seawater Oceanographic Package of TEOS-10" license = "BSD-3-Clause" license-files = [ "LICENSE.txt" ] authors = [ { name = "Eric Firing, Filipe Fernandes", email = "efiring@hawaii.edu" }, ] requires-python = ">=3.11" classifiers = [ "Development Status :: 5 - Production/Stable", "Intended Audience :: Science/Research", "Operating System :: OS Independent", "Programming Language :: Python", "Programming Language :: Python :: 3 :: Only", "Programming Language :: Python :: 3.11", "Programming Language :: Python :: 3.12", "Programming Language :: Python :: 3.13", "Programming Language :: Python :: 3.14", "Topic :: Scientific/Engineering", ] dynamic = [ "readme", "version", ] dependencies = [ "numpy>=2", ] urls.documentation = "https://teos-10.github.io/GSW-Python/" urls.homepage = "https://www.teos-10.org/" urls.repository = "https://github.com/TEOS-10/GSW-python" [tool.setuptools] zip-safe = false include-package-data = true packages = [ "gsw", "gsw.tests" ] [tool.setuptools.dynamic] dependencies = { file = [ "requirements.txt" ] } readme = { file = "README.md", content-type = "text/markdown" } [tool.setuptools_scm] write_to = "gsw/_version.py" write_to_template = "__version__ = '{version}'" tag_regex = "^(?Pv)?(?P[^\\+]+)(?P.*)?$" [tool.ruff] target-version = "py38" line-length = 105 exclude = [ "tools", ] lint.select = [ "A", # flake8-builtins "B", # flake8-bugbear "C4", # flake8-comprehensions "F", # flakes "I", # import sorting "NPY201", # numpy 2.0 "UP", # upgrade ] lint.ignore = [ "E501", # line too long "E713", # test for membership should be 'not in' "F401", # module imported but unused ] lint.per-file-ignores."docs/conf.py" = [ "A001", # variable is shadowing a python builtin ] lint.per-file-ignores."gsw/_fixed_wrapped_ufuncs.py" = [ "F403", #'from x import *' used; unable to detect undefined names "F405", # 'import' may be undefined, or defined from star imports ] lint.per-file-ignores."gsw/_utilities.py" = [ "B904", # Within an ``except`` clause, raise exceptions with ``raise ... from err`` ] [tool.check-manifest] ignore = [ "*.yml", ".coveragerc", "docs", "docs/*", "*.enc", "tools", "tools/*", "gsw/_version.py", ] gsw-3.6.21/README.md0000644000175000017500000001351615147371315014061 0ustar alastairalastair# GSW-Python [![Tests](https://github.com/TEOS-10/GSW-Python/actions/workflows/tests.yml/badge.svg)](https://github.com/TEOS-10/GSW-Python/actions/workflows/tests.yml) [![Wheels](https://github.com/TEOS-10/GSW-Python/actions/workflows/cibuildwheel.yml/badge.svg)](https://github.com/TEOS-10/GSW-Python/actions/workflows/cibuildwheel.yml) [![DOI](https://zenodo.org/badge/86503067.svg)](https://zenodo.org/badge/latestdoi/86503067) This Python implementation of the Thermodynamic Equation of Seawater 2010 (TEOS-10) is based primarily on numpy ufunc wrappers of the GSW-C implementation. This library replaces the original [python-gsw](https://github.com/TEOS-10/python-gsw) pure-python implementation. The primary reasons for this change are that by building on the C implementation we reduce code duplication and we gain an immediate update to the 75-term equation. Additional benefits include a major increase in speed, a reduction in memory usage, and the inclusion of more functions. The penalty is that a C (or MSVC C++ for Windows) compiler is required to build the package from source. **Warning: this is for Python >=3.8 only.** Documentation is provided at https://teos-10.github.io/GSW-Python/. For the core functionality, we use an auto-generated C extension module to wrap the C functions as numpy [ufuncs](https://docs.scipy.org/doc/numpy/reference/ufuncs.html), and then use an autogenerated Python module to add docstrings and handle masked arrays. 165 scalar C functions with only double-precision arguments and return values are wrapped as ufuncs, and 158 of these are exposed in the ``gsw`` namespace with an additional wrapper in Python. A hand-written wrapper is used for one C function, and others are re-implemented directly in Python instead of being wrapped. Additional functions present in GSW-Matlab but not in GSW-C may be re-implemented in Python, but there is no expectation that all such functions will be provided. ## Installation Pip users can install the pre-built wheels with: ```shell pip install gsw ``` conda users will find binaries on conda-forge, ```shell conda install gsw --channel conda-forge ``` The development version of the package can be installed from a clone of the repo using ```shell pip install . ``` ## Citation If you use GSW-Python, please cite: McDougall, T.J. and P.M. Barker, 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox, 28pp., SCOR/IAPSO WG127, ISBN 978-0-646-55621-5 ```bibtex @book{mcdougall2011getting, author = {McDougall, T. J. and Barker, P. M.}, title = {Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox}, year = {2011}, pages = {28}, publisher = {SCOR/IAPSO WG127}, isbn = {978-0-646-55621-5} } ``` ## Note for xarray users A wrapper around gsw called [gsw-xarray](https://github.com/DocOtak/gsw-xarray) exists for xarray. It adds CF compliant attributes when possible, units, and name. ## Note on generating the docstrings The autogenerated docstrings are checked with codespell in the CIs. When autogenerating them we need to run ``pre-commit run --all-files`` and fix the documentation issues found. ## Development notes You will need a suitable compiler: gcc or clang for unix-like systems, or the MSVC compiler set used for Python itself on Windows. For Windows, some of the source code has been modified to C++ because the MSVC C compiler does not support the C99 complex data type used in original GSW-C. The subdirectory ('tools') contains modules and scripts for maintaining the code that is autogenerated from the upstream GSW-Matlab and GSW-C repos. The scripts are to be run from this directory; they make assumptions about where they are, and about where upstream repos are. Specifically, it is assumed that GSW-Matlab, GSW-C, and GSW-Python git repos are all in the same base directory. ### Scripts - `copy_from_GSW-C.py`: copies the relevant .c and .h files from a sibling GSW-C repo, if the latter are newer. - `mat2npz.py`: generates an npz file in gsw/tests containing the test data and check values from the gsw_data_v3_0.mat file in the sibling GSW-Matlab repo. - `make_ufuncs.py`: Generates the src/_ufuncs.c file to turn the scalar C functions into numpy ufuncs. It writes ufuncs.list in the current directory as a record of the ufunc names. Functions are identified as ufunc candidates based on their signatures, parsed from src/c_gsw/gswteos-10.h. - `make_wrapped_ufuncs.py`: Generates gsw/_wrapped_ufuncs.py based on the output of make_ufuncs.py. It adds docstrings constructed from the Matlab help text. - `fix_wrapped_ufunc_typos.py`: Fixes docstring typos that have been identified, but not yet fixed, in the GSW-Matlab repo. - `codegen`: Runs the last three python scripts. ### Modules - `c_header_parser.py`: Functions for taking apart the function declarations in gswteos-10.h. - `matlab_parser.py`: Functions specifically for reading the GSW-Matlab function signatures and for splitting out the help text. - `docstring_parts.py`: Blocks of text for assembling docstrings. - `docstring_utils.py`: Functions for assembling docstrings in numpydoc format. - `categories.py`: Functions for listing gsw function names by category. This is not used by any of the other functions or scripts, but was used when initially categorizing the functions for inclusion in submodules. ### Notes - In addition to the generated src/_ufuncs.c, there are two C files that are hand-written: src/method_bodies.c and src/method_def_entries.c. These are imported by src/_ufuncs.c. They handle some C functions that are not suitable for ufuncs. - Specialized Matlab parsing is also done in gsw/tests/check_functions.py, which is used by gsw/tests/test_check_functions.py; see the docstring of the former for more info. ### Testing To test, after installation, run "pytest --pyargs gsw". gsw-3.6.21/setup.cfg0000644000175000017500000000004615147371330014412 0ustar alastairalastair[egg_info] tag_build = tag_date = 0 gsw-3.6.21/src/0000755000175000017500000000000015147371330013360 5ustar alastairalastairgsw-3.6.21/src/method_bodies.c0000644000175000017500000002747515147371315016353 0ustar alastairalastair/* Custom wrappers for GSW functions that are not suitable for ufuncs. */ /* double * Returns NULL on error, dyn_height if okay gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref, int n_levels, double *dyn_height) */ static PyObject * geo_strf_dyn_height(PyObject *NPY_UNUSED(self), PyObject *args) { PyObject *sa_o, *ct_o, *p_o; double p_ref; PyArrayObject *sa_a, *ct_a, *p_a, *dh_a; int n_levels; double *ret = NULL; /* NULL on error, dyn_height if OK */ if (!PyArg_ParseTuple(args, "OOOd", &sa_o, &ct_o, &p_o, &p_ref)) return NULL; sa_a = (PyArrayObject *)PyArray_ContiguousFromAny(sa_o, NPY_DOUBLE, 1, 1); if (sa_a == NULL) return NULL; ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1); if (ct_a == NULL) { Py_XDECREF((PyObject *)sa_a); return NULL; } p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1); if (p_a == NULL) { Py_XDECREF((PyObject *)sa_a); Py_XDECREF((PyObject *)ct_a); return NULL; } n_levels = PyArray_DIM(sa_a, 0); if (PyArray_DIM(ct_a, 0) != n_levels || PyArray_DIM(p_a, 0) != n_levels) { PyErr_SetString(PyExc_ValueError, "Arguments SA, CT, and p must have the same dimensions."); Py_XDECREF((PyObject *)sa_a); Py_XDECREF((PyObject *)ct_a); Py_XDECREF((PyObject *)p_a); return NULL; } dh_a = (PyArrayObject *)PyArray_NewLikeArray(sa_a, NPY_CORDER, NULL, 0); if (dh_a == NULL) { Py_XDECREF((PyObject *)sa_a); Py_XDECREF((PyObject *)ct_a); Py_XDECREF((PyObject *)p_a); return NULL; } ret = gsw_geo_strf_dyn_height((double *)PyArray_DATA(sa_a), (double *)PyArray_DATA(ct_a), (double *)PyArray_DATA(p_a), p_ref, n_levels, (double *)PyArray_DATA(dh_a)); Py_XDECREF((PyObject *)sa_a); Py_XDECREF((PyObject *)ct_a); Py_XDECREF((PyObject *)p_a); if (ret == NULL) { PyErr_SetString(PyExc_RuntimeError, "gws_geo_strf_dyn_height failed; check input arguments"); Py_XDECREF((PyObject *)dh_a); return NULL; } return (PyObject *)dh_a; } static PyObject * geo_strf_dyn_height_1(PyObject *NPY_UNUSED(self), PyObject *args) { PyObject *sa_o, *ct_o, *p_o; double p_ref; PyArrayObject *sa_a, *ct_a, *p_a, *dh_a; int n_levels; int ret = 1; /* error (1) until set to 0 by the C function */ double max_dp_i; int interp_method; if (!PyArg_ParseTuple(args, "OOOddi", &sa_o, &ct_o, &p_o, &p_ref, &max_dp_i, &interp_method)) return NULL; sa_a = (PyArrayObject *)PyArray_ContiguousFromAny(sa_o, NPY_DOUBLE, 1, 1); if (sa_a == NULL) return NULL; ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1); if (ct_a == NULL) { Py_DECREF(sa_a); return NULL; } p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1); if (p_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); return NULL; } n_levels = PyArray_DIM(sa_a, 0); if (PyArray_DIM(ct_a, 0) != n_levels || PyArray_DIM(p_a, 0) != n_levels) { PyErr_SetString(PyExc_ValueError, "Arguments SA, CT, and p must have the same dimensions."); Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); return NULL; } dh_a = (PyArrayObject *)PyArray_NewLikeArray(sa_a, NPY_CORDER, NULL, 0); if (dh_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); return NULL; } ret = gsw_geo_strf_dyn_height_1((double *)PyArray_DATA(sa_a), (double *)PyArray_DATA(ct_a), (double *)PyArray_DATA(p_a), p_ref, n_levels, (double *)PyArray_DATA(dh_a), max_dp_i, interp_method); Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); if (ret) { PyErr_Format(PyExc_RuntimeError, "gws_geo_strf_dyn_height_1 failed with code %d; check input arguments", ret); Py_DECREF(dh_a); return NULL; } return (PyObject *)dh_a; } static PyObject * util_pchip_interp(PyObject *NPY_UNUSED(self), PyObject *args) { PyObject *x, *y, *xi; PyArrayObject *xa, *ya, *xia, *yia; int n, ni; int ret = 1; /* error (1) until set to 0 by the C function */ if (!PyArg_ParseTuple(args, "OOO", &x, &y, &xi)) return NULL; xa = (PyArrayObject *)PyArray_ContiguousFromAny(x, NPY_DOUBLE, 1, 1); if (xa == NULL) { PyErr_SetString(PyExc_RuntimeError, "failed to convert argument x"); return NULL; } ya = (PyArrayObject *)PyArray_ContiguousFromAny(y, NPY_DOUBLE, 1, 1); if (ya == NULL) { PyErr_SetString(PyExc_RuntimeError, "failed to convert argument y"); Py_DECREF(xa); return NULL; } n = PyArray_DIM(xa, 0); xia = (PyArrayObject *)PyArray_ContiguousFromAny(xi, NPY_DOUBLE, 1, 1); if (xia == NULL) { PyErr_SetString(PyExc_RuntimeError, "failed to convert argument xi"); Py_DECREF(xa); Py_DECREF(ya); return NULL; } ni = PyArray_DIM(xia, 0); yia = (PyArrayObject *)PyArray_NewLikeArray(xia, NPY_CORDER, NULL, 0); if (yia == NULL) { Py_DECREF(xa); Py_DECREF(ya); Py_DECREF(xia); return NULL; } ret = gsw_util_pchip_interp((double *)PyArray_DATA(xa), (double *)PyArray_DATA(ya), n, (double *)PyArray_DATA(xia), (double *)PyArray_DATA(yia), ni); Py_DECREF(xa); Py_DECREF(ya); Py_DECREF(xia); if (ret) { PyErr_SetString(PyExc_RuntimeError, "gsw_util_pchip_interp failed; check input arguments"); return NULL; } return (PyObject *)yia; } static PyObject * sa_ct_interp(PyObject *NPY_UNUSED(self), PyObject *args) { PyObject *sa_o, *ct_o, *p_o, *pi_o, *res; PyArrayObject *sa_a, *ct_a, *p_a, *pi_a, *sai_a, *cti_a; int np, npi; int ret = 1; /* error (1) until set to 0 by the C function */ if (!PyArg_ParseTuple(args, "OOOO", &sa_o, &ct_o, &p_o, &pi_o)) return NULL; sa_a = (PyArrayObject *)PyArray_ContiguousFromAny(sa_o, NPY_DOUBLE, 1, 1); if (sa_a == NULL) return NULL; ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1); if (ct_a == NULL) { Py_DECREF(sa_a); return NULL; } p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1); if (p_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); return NULL; } pi_a = (PyArrayObject *)PyArray_ContiguousFromAny(pi_o, NPY_DOUBLE, 1, 1); if (pi_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); return NULL; } np = PyArray_DIM(sa_a, 0); if (PyArray_DIM(ct_a, 0) != np || PyArray_DIM(p_a, 0) != np) { PyErr_SetString(PyExc_ValueError, "Arguments SA, CT, and p must have the same dimensions."); Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); return NULL; } npi = PyArray_DIM(pi_a, 0); sai_a = (PyArrayObject *)PyArray_NewLikeArray(pi_a, NPY_CORDER, NULL, 0); if (sai_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); return NULL; } cti_a = (PyArrayObject *)PyArray_NewLikeArray(pi_a, NPY_CORDER, NULL, 0); if (cti_a == NULL) { Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); Py_DECREF(sai_a); return NULL; } ret = gsw_sa_ct_interp((double *)PyArray_DATA(sa_a), (double *)PyArray_DATA(ct_a), (double *)PyArray_DATA(p_a), np, (double *)PyArray_DATA(pi_a), npi, (double *)PyArray_DATA(sai_a), (double *)PyArray_DATA(cti_a)); Py_DECREF(sa_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); if (ret) { PyErr_Format(PyExc_RuntimeError, "gsw_sa_ct_interp failed with code %d; check input arguments", ret); Py_DECREF(sai_a); Py_DECREF(cti_a); return NULL; } res = PyTuple_Pack(2, sai_a, cti_a); return res; } static PyObject * tracer_ct_interp(PyObject *NPY_UNUSED(self), PyObject *args) { PyObject *tracer_o, *ct_o, *p_o, *pi_o, *res; double factor; PyArrayObject *tracer_a, *ct_a, *p_a, *pi_a, *traceri_a, *cti_a; int np, npi; int ret = 1; /* error (1) until set to 0 by the C function */ if (!PyArg_ParseTuple(args, "OOOOd", &tracer_o, &ct_o, &p_o, &pi_o, &factor)) return NULL; tracer_a = (PyArrayObject *)PyArray_ContiguousFromAny(tracer_o, NPY_DOUBLE, 1, 1); if (tracer_a == NULL) return NULL; ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1); if (ct_a == NULL) { Py_DECREF(tracer_a); return NULL; } p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1); if (p_a == NULL) { Py_DECREF(tracer_a); Py_DECREF(ct_a); return NULL; } pi_a = (PyArrayObject *)PyArray_ContiguousFromAny(pi_o, NPY_DOUBLE, 1, 1); if (pi_a == NULL) { Py_DECREF(tracer_a); Py_DECREF(ct_a); Py_DECREF(p_a); return NULL; } np = PyArray_DIM(tracer_a, 0); if (PyArray_DIM(ct_a, 0) != np || PyArray_DIM(p_a, 0) != np) { PyErr_SetString(PyExc_ValueError, "Arguments tracer, CT, and p must have the same dimensions."); Py_DECREF(tracer_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); return NULL; } npi = PyArray_DIM(pi_a, 0); traceri_a = (PyArrayObject *)PyArray_NewLikeArray(pi_a, NPY_CORDER, NULL, 0); if (traceri_a == NULL) { Py_DECREF(tracer_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); return NULL; } cti_a = (PyArrayObject *)PyArray_NewLikeArray(pi_a, NPY_CORDER, NULL, 0); if (cti_a == NULL) { Py_DECREF(tracer_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); Py_DECREF(traceri_a); return NULL; } ret = gsw_tracer_ct_interp((double *)PyArray_DATA(tracer_a), (double *)PyArray_DATA(ct_a), (double *)PyArray_DATA(p_a), np, (double *)PyArray_DATA(pi_a), npi, factor, (double *)PyArray_DATA(traceri_a), (double *)PyArray_DATA(cti_a)); Py_DECREF(tracer_a); Py_DECREF(ct_a); Py_DECREF(p_a); Py_DECREF(pi_a); if (ret) { PyErr_Format(PyExc_RuntimeError, "gsw_tracer_ct_interp failed with code %d; check input arguments", ret); Py_DECREF(traceri_a); Py_DECREF(cti_a); return NULL; } res = PyTuple_Pack(2, traceri_a, cti_a); return res; } gsw-3.6.21/src/_ufuncs.c0000644000175000017500000036711515147371315015206 0ustar alastairalastair /* This file is auto-generated--do not edit it. */ #define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION #include "Python.h" #include "math.h" #include "numpy/ndarraytypes.h" #include "numpy/ufuncobject.h" #include "numpy/npy_3kcompat.h" #include "gswteos-10.h" /* possible hack for MSVC: */ #ifndef NAN static double NAN = 0.0/0.0; #endif #ifndef isnan # define isnan(x) ((x) != (x)) #endif #define CONVERT_INVALID(x) ((x == GSW_INVALID_VALUE)? NAN: x) /* 1 in, 1 out */ static void loop1d_d_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *out0 = args[1]; npy_intp out_step0 = steps[1]; double (*func)(double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)) { *((double *)out0) = NAN; } else { outd0 = func(*(double *)in0); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; out0 += out_step0; } } static PyUFuncGenericFunction funcs_d_d[] = {&loop1d_d_d}; static char types_d_d[] = { NPY_DOUBLE, NPY_DOUBLE, }; /* 2 in, 1 out */ static void loop1d_dd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *out0 = args[2]; npy_intp out_step0 = steps[2]; double (*func)(double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)) { *((double *)out0) = NAN; } else { outd0 = func(*(double *)in0, *(double *)in1); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; out0 += out_step0; } } static PyUFuncGenericFunction funcs_dd_d[] = {&loop1d_dd_d}; static char types_dd_d[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 2 in, 1 out */ static void loop1d_dd_i(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *out0 = args[2]; npy_intp out_step0 = steps[2]; int (*func)(double, double); int outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)) { *((int *)out0) = 0; } else { outd0 = func(*(double *)in0, *(double *)in1); *((int *)out0) = outd0; } in0 += in_step0; in1 += in_step1; out0 += out_step0; } } static PyUFuncGenericFunction funcs_dd_i[] = {&loop1d_dd_i}; static char types_dd_i[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_INT, }; /* 3 in, 1 out */ static void loop1d_ddd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *out0 = args[3]; npy_intp out_step0 = steps[3]; double (*func)(double, double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) { *((double *)out0) = NAN; } else { outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; in2 += in_step2; out0 += out_step0; } } static PyUFuncGenericFunction funcs_ddd_d[] = {&loop1d_ddd_d}; static char types_ddd_d[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 3 in, 1 out */ static void loop1d_ddd_i(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *out0 = args[3]; npy_intp out_step0 = steps[3]; int (*func)(double, double, double); int outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) { *((int *)out0) = 0; } else { outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2); *((int *)out0) = outd0; } in0 += in_step0; in1 += in_step1; in2 += in_step2; out0 += out_step0; } } static PyUFuncGenericFunction funcs_ddd_i[] = {&loop1d_ddd_i}; static char types_ddd_i[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_INT, }; /* 4 in, 1 out */ static void loop1d_dddd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *out0 = args[4]; npy_intp out_step0 = steps[4]; double (*func)(double, double, double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) { *((double *)out0) = NAN; } else { outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; out0 += out_step0; } } static PyUFuncGenericFunction funcs_dddd_d[] = {&loop1d_dddd_d}; static char types_dddd_d[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 5 in, 1 out */ static void loop1d_ddddd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *in4 = args[4]; npy_intp in_step4 = steps[4]; char *out0 = args[5]; npy_intp out_step0 = steps[5]; double (*func)(double, double, double, double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) { *((double *)out0) = NAN; } else { outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; in4 += in_step4; out0 += out_step0; } } static PyUFuncGenericFunction funcs_ddddd_d[] = {&loop1d_ddddd_d}; static char types_ddddd_d[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 2 in, 2 out */ static void loop1d_dd_dd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *out0 = args[2]; npy_intp out_step0 = steps[2]; char *out1 = args[3]; npy_intp out_step1 = steps[3]; void (*func)(double, double, double *, double *); double outd0, outd1; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)) { *((double *)out0) = NAN;*((double *)out1) = NAN; } else { func(*(double *)in0, *(double *)in1, &outd0, &outd1); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); } in0 += in_step0; in1 += in_step1; out0 += out_step0; out1 += out_step1; } } static PyUFuncGenericFunction funcs_dd_dd[] = {&loop1d_dd_dd}; static char types_dd_dd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 2 in, 3 out */ static void loop1d_dd_ddd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *out0 = args[2]; npy_intp out_step0 = steps[2]; char *out1 = args[3]; npy_intp out_step1 = steps[3]; char *out2 = args[4]; npy_intp out_step2 = steps[4]; void (*func)(double, double, double *, double *, double *); double outd0, outd1, outd2; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)) { *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN; } else { func(*(double *)in0, *(double *)in1, &outd0, &outd1, &outd2); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); *((double *)out2) = CONVERT_INVALID(outd2); } in0 += in_step0; in1 += in_step1; out0 += out_step0; out1 += out_step1; out2 += out_step2; } } static PyUFuncGenericFunction funcs_dd_ddd[] = {&loop1d_dd_ddd}; static char types_dd_ddd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 3 in, 2 out */ static void loop1d_ddd_dd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *out0 = args[3]; npy_intp out_step0 = steps[3]; char *out1 = args[4]; npy_intp out_step1 = steps[4]; void (*func)(double, double, double, double *, double *); double outd0, outd1; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) { *((double *)out0) = NAN;*((double *)out1) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); } in0 += in_step0; in1 += in_step1; in2 += in_step2; out0 += out_step0; out1 += out_step1; } } static PyUFuncGenericFunction funcs_ddd_dd[] = {&loop1d_ddd_dd}; static char types_ddd_dd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 3 in, 3 out */ static void loop1d_ddd_ddd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *out0 = args[3]; npy_intp out_step0 = steps[3]; char *out1 = args[4]; npy_intp out_step1 = steps[4]; char *out2 = args[5]; npy_intp out_step2 = steps[5]; void (*func)(double, double, double, double *, double *, double *); double outd0, outd1, outd2; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) { *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); *((double *)out2) = CONVERT_INVALID(outd2); } in0 += in_step0; in1 += in_step1; in2 += in_step2; out0 += out_step0; out1 += out_step1; out2 += out_step2; } } static PyUFuncGenericFunction funcs_ddd_ddd[] = {&loop1d_ddd_ddd}; static char types_ddd_ddd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 3 in, 5 out */ static void loop1d_ddd_ddddd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *out0 = args[3]; npy_intp out_step0 = steps[3]; char *out1 = args[4]; npy_intp out_step1 = steps[4]; char *out2 = args[5]; npy_intp out_step2 = steps[5]; char *out3 = args[6]; npy_intp out_step3 = steps[6]; char *out4 = args[7]; npy_intp out_step4 = steps[7]; void (*func)(double, double, double, double *, double *, double *, double *, double *); double outd0, outd1, outd2, outd3, outd4; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) { *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;*((double *)out3) = NAN;*((double *)out4) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2, &outd3, &outd4); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); *((double *)out2) = CONVERT_INVALID(outd2); *((double *)out3) = CONVERT_INVALID(outd3); *((double *)out4) = CONVERT_INVALID(outd4); } in0 += in_step0; in1 += in_step1; in2 += in_step2; out0 += out_step0; out1 += out_step1; out2 += out_step2; out3 += out_step3; out4 += out_step4; } } static PyUFuncGenericFunction funcs_ddd_ddddd[] = {&loop1d_ddd_ddddd}; static char types_ddd_ddddd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 4 in, 3 out */ static void loop1d_dddd_ddd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *out0 = args[4]; npy_intp out_step0 = steps[4]; char *out1 = args[5]; npy_intp out_step1 = steps[5]; char *out2 = args[6]; npy_intp out_step2 = steps[6]; void (*func)(double, double, double, double, double *, double *, double *); double outd0, outd1, outd2; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) { *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, &outd0, &outd1, &outd2); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); *((double *)out2) = CONVERT_INVALID(outd2); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; out0 += out_step0; out1 += out_step1; out2 += out_step2; } } static PyUFuncGenericFunction funcs_dddd_ddd[] = {&loop1d_dddd_ddd}; static char types_dddd_ddd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 5 in, 3 out */ static void loop1d_ddddd_ddd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *in4 = args[4]; npy_intp in_step4 = steps[4]; char *out0 = args[5]; npy_intp out_step0 = steps[5]; char *out1 = args[6]; npy_intp out_step1 = steps[6]; char *out2 = args[7]; npy_intp out_step2 = steps[7]; void (*func)(double, double, double, double, double, double *, double *, double *); double outd0, outd1, outd2; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) { *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, &outd0, &outd1, &outd2); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); *((double *)out2) = CONVERT_INVALID(outd2); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; in4 += in_step4; out0 += out_step0; out1 += out_step1; out2 += out_step2; } } static PyUFuncGenericFunction funcs_ddddd_ddd[] = {&loop1d_ddddd_ddd}; static char types_ddddd_ddd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 6 in, 2 out */ static void loop1d_dddddd_dd(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *in4 = args[4]; npy_intp in_step4 = steps[4]; char *in5 = args[5]; npy_intp in_step5 = steps[5]; char *out0 = args[6]; npy_intp out_step0 = steps[6]; char *out1 = args[7]; npy_intp out_step1 = steps[7]; void (*func)(double, double, double, double, double, double, double *, double *); double outd0, outd1; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)||isnan(*(double *)in5)) { *((double *)out0) = NAN;*((double *)out1) = NAN; } else { func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, *(double *)in5, &outd0, &outd1); *((double *)out0) = CONVERT_INVALID(outd0); *((double *)out1) = CONVERT_INVALID(outd1); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; in4 += in_step4; in5 += in_step5; out0 += out_step0; out1 += out_step1; } } static PyUFuncGenericFunction funcs_dddddd_dd[] = {&loop1d_dddddd_dd}; static char types_dddddd_dd[] = { NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 2 int in, 2 double in, 1 out */ static void loop1d_iidd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *out0 = args[4]; npy_intp out_step0 = steps[4]; double (*func)(int, int, double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in2)||isnan(*(double *)in3)) { *((double *)out0) = NAN; } else { outd0 = func((int)*(long long *)in0, (int)*(long long *)in1, *(double *)in2, *(double *)in3); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; out0 += out_step0; } } static PyUFuncGenericFunction funcs_iidd_d[] = {&loop1d_iidd_d}; static char types_iidd_d[] = { NPY_INT64, NPY_INT64, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; /* 3 int in, 3 double in, 1 out */ static void loop1d_iiiddd_d(char **args, npy_intp const *dimensions, npy_intp const* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in0 = args[0]; npy_intp in_step0 = steps[0]; char *in1 = args[1]; npy_intp in_step1 = steps[1]; char *in2 = args[2]; npy_intp in_step2 = steps[2]; char *in3 = args[3]; npy_intp in_step3 = steps[3]; char *in4 = args[4]; npy_intp in_step4 = steps[4]; char *in5 = args[5]; npy_intp in_step5 = steps[5]; char *out0 = args[6]; npy_intp out_step0 = steps[6]; double (*func)(int, int, int, double, double, double); double outd0; func = data; for (i = 0; i < n; i++) { if (isnan(*(double *)in3)||isnan(*(double *)in4)||isnan(*(double *)in5)) { *((double *)out0) = NAN; } else { outd0 = func((int)*(long long *)in0, (int)*(long long *)in1, (int)*(long long *)in2, *(double *)in3, *(double *)in4, *(double *)in5); *((double *)out0) = CONVERT_INVALID(outd0); } in0 += in_step0; in1 += in_step1; in2 += in_step2; in3 += in_step3; in4 += in_step4; in5 += in_step5; out0 += out_step0; } } static PyUFuncGenericFunction funcs_iiiddd_d[] = {&loop1d_iiiddd_d}; static char types_iiiddd_d[] = { NPY_INT64, NPY_INT64, NPY_INT64, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, }; static void *data_infunnel[] = {&gsw_infunnel}; static void *data_adiabatic_lapse_rate_from_ct[] = {&gsw_adiabatic_lapse_rate_from_ct}; static void *data_adiabatic_lapse_rate_ice[] = {&gsw_adiabatic_lapse_rate_ice}; static void *data_alpha[] = {&gsw_alpha}; static void *data_alpha_on_beta[] = {&gsw_alpha_on_beta}; static void *data_alpha_wrt_t_exact[] = {&gsw_alpha_wrt_t_exact}; static void *data_alpha_wrt_t_ice[] = {&gsw_alpha_wrt_t_ice}; static void *data_beta_const_t_exact[] = {&gsw_beta_const_t_exact}; static void *data_beta[] = {&gsw_beta}; static void *data_cabbeling[] = {&gsw_cabbeling}; static void *data_c_from_sp[] = {&gsw_c_from_sp}; static void *data_chem_potential_water_ice[] = {&gsw_chem_potential_water_ice}; static void *data_chem_potential_water_t_exact[] = {&gsw_chem_potential_water_t_exact}; static void *data_cp_ice[] = {&gsw_cp_ice}; static void *data_cp_t_exact[] = {&gsw_cp_t_exact}; static void *data_ct_freezing[] = {&gsw_ct_freezing}; static void *data_ct_freezing_poly[] = {&gsw_ct_freezing_poly}; static void *data_ct_from_enthalpy[] = {&gsw_ct_from_enthalpy}; static void *data_ct_from_enthalpy_exact[] = {&gsw_ct_from_enthalpy_exact}; static void *data_ct_from_entropy[] = {&gsw_ct_from_entropy}; static void *data_ct_from_pt[] = {&gsw_ct_from_pt}; static void *data_ct_from_t[] = {&gsw_ct_from_t}; static void *data_ct_maxdensity[] = {&gsw_ct_maxdensity}; static void *data_deltasa_atlas[] = {&gsw_deltasa_atlas}; static void *data_deltasa_from_sp[] = {&gsw_deltasa_from_sp}; static void *data_dilution_coefficient_t_exact[] = {&gsw_dilution_coefficient_t_exact}; static void *data_dynamic_enthalpy[] = {&gsw_dynamic_enthalpy}; static void *data_enthalpy_ct_exact[] = {&gsw_enthalpy_ct_exact}; static void *data_enthalpy_diff[] = {&gsw_enthalpy_diff}; static void *data_enthalpy[] = {&gsw_enthalpy}; static void *data_enthalpy_ice[] = {&gsw_enthalpy_ice}; static void *data_enthalpy_sso_0[] = {&gsw_enthalpy_sso_0}; static void *data_enthalpy_t_exact[] = {&gsw_enthalpy_t_exact}; static void *data_entropy_from_ct[] = {&gsw_entropy_from_ct}; static void *data_entropy_from_pt[] = {&gsw_entropy_from_pt}; static void *data_entropy_from_t[] = {&gsw_entropy_from_t}; static void *data_entropy_ice[] = {&gsw_entropy_ice}; static void *data_entropy_part[] = {&gsw_entropy_part}; static void *data_entropy_part_zerop[] = {&gsw_entropy_part_zerop}; static void *data_fdelta[] = {&gsw_fdelta}; static void *data_gibbs_ice_part_t[] = {&gsw_gibbs_ice_part_t}; static void *data_gibbs_ice_pt0[] = {&gsw_gibbs_ice_pt0}; static void *data_gibbs_ice_pt0_pt0[] = {&gsw_gibbs_ice_pt0_pt0}; static void *data_gibbs_pt0_pt0[] = {&gsw_gibbs_pt0_pt0}; static void *data_grav[] = {&gsw_grav}; static void *data_helmholtz_energy_ice[] = {&gsw_helmholtz_energy_ice}; static void *data_hill_ratio_at_sp2[] = {&gsw_hill_ratio_at_sp2}; static void *data_internal_energy[] = {&gsw_internal_energy}; static void *data_internal_energy_ice[] = {&gsw_internal_energy_ice}; static void *data_kappa_const_t_ice[] = {&gsw_kappa_const_t_ice}; static void *data_kappa[] = {&gsw_kappa}; static void *data_kappa_ice[] = {&gsw_kappa_ice}; static void *data_kappa_t_exact[] = {&gsw_kappa_t_exact}; static void *data_latentheat_evap_ct[] = {&gsw_latentheat_evap_ct}; static void *data_latentheat_evap_t[] = {&gsw_latentheat_evap_t}; static void *data_latentheat_melting[] = {&gsw_latentheat_melting}; static void *data_melting_ice_equilibrium_sa_ct_ratio[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio}; static void *data_melting_ice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio_poly}; static void *data_melting_ice_sa_ct_ratio[] = {&gsw_melting_ice_sa_ct_ratio}; static void *data_melting_ice_sa_ct_ratio_poly[] = {&gsw_melting_ice_sa_ct_ratio_poly}; static void *data_melting_seaice_equilibrium_sa_ct_ratio[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio}; static void *data_melting_seaice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio_poly}; static void *data_melting_seaice_sa_ct_ratio[] = {&gsw_melting_seaice_sa_ct_ratio}; static void *data_melting_seaice_sa_ct_ratio_poly[] = {&gsw_melting_seaice_sa_ct_ratio_poly}; static void *data_o2sol[] = {&gsw_o2sol}; static void *data_o2sol_sp_pt[] = {&gsw_o2sol_sp_pt}; static void *data_pot_enthalpy_from_pt_ice[] = {&gsw_pot_enthalpy_from_pt_ice}; static void *data_pot_enthalpy_from_pt_ice_poly[] = {&gsw_pot_enthalpy_from_pt_ice_poly}; static void *data_pot_enthalpy_ice_freezing[] = {&gsw_pot_enthalpy_ice_freezing}; static void *data_pot_enthalpy_ice_freezing_poly[] = {&gsw_pot_enthalpy_ice_freezing_poly}; static void *data_pot_rho_t_exact[] = {&gsw_pot_rho_t_exact}; static void *data_pressure_coefficient_ice[] = {&gsw_pressure_coefficient_ice}; static void *data_pressure_freezing_ct[] = {&gsw_pressure_freezing_ct}; static void *data_pt0_cold_ice_poly[] = {&gsw_pt0_cold_ice_poly}; static void *data_pt0_from_t[] = {&gsw_pt0_from_t}; static void *data_pt0_from_t_ice[] = {&gsw_pt0_from_t_ice}; static void *data_pt_from_ct[] = {&gsw_pt_from_ct}; static void *data_pt_from_entropy[] = {&gsw_pt_from_entropy}; static void *data_pt_from_pot_enthalpy_ice[] = {&gsw_pt_from_pot_enthalpy_ice}; static void *data_pt_from_pot_enthalpy_ice_poly_dh[] = {&gsw_pt_from_pot_enthalpy_ice_poly_dh}; static void *data_pt_from_pot_enthalpy_ice_poly[] = {&gsw_pt_from_pot_enthalpy_ice_poly}; static void *data_pt_from_t[] = {&gsw_pt_from_t}; static void *data_pt_from_t_ice[] = {&gsw_pt_from_t_ice}; static void *data_rho[] = {&gsw_rho}; static void *data_rho_ice[] = {&gsw_rho_ice}; static void *data_rho_t_exact[] = {&gsw_rho_t_exact}; static void *data_saar[] = {&gsw_saar}; static void *data_sa_freezing_from_ct[] = {&gsw_sa_freezing_from_ct}; static void *data_sa_freezing_from_ct_poly[] = {&gsw_sa_freezing_from_ct_poly}; static void *data_sa_freezing_from_t[] = {&gsw_sa_freezing_from_t}; static void *data_sa_freezing_from_t_poly[] = {&gsw_sa_freezing_from_t_poly}; static void *data_sa_from_rho[] = {&gsw_sa_from_rho}; static void *data_sa_from_sp_baltic[] = {&gsw_sa_from_sp_baltic}; static void *data_sa_from_sp[] = {&gsw_sa_from_sp}; static void *data_sa_from_sstar[] = {&gsw_sa_from_sstar}; static void *data_sa_p_inrange[] = {&gsw_sa_p_inrange}; static void *data_sigma0[] = {&gsw_sigma0}; static void *data_sigma1[] = {&gsw_sigma1}; static void *data_sigma2[] = {&gsw_sigma2}; static void *data_sigma3[] = {&gsw_sigma3}; static void *data_sigma4[] = {&gsw_sigma4}; static void *data_sound_speed[] = {&gsw_sound_speed}; static void *data_sound_speed_ice[] = {&gsw_sound_speed_ice}; static void *data_sound_speed_t_exact[] = {&gsw_sound_speed_t_exact}; static void *data_specvol_anom_standard[] = {&gsw_specvol_anom_standard}; static void *data_specvol[] = {&gsw_specvol}; static void *data_specvol_ice[] = {&gsw_specvol_ice}; static void *data_specvol_sso_0[] = {&gsw_specvol_sso_0}; static void *data_specvol_t_exact[] = {&gsw_specvol_t_exact}; static void *data_sp_from_c[] = {&gsw_sp_from_c}; static void *data_sp_from_sa_baltic[] = {&gsw_sp_from_sa_baltic}; static void *data_sp_from_sa[] = {&gsw_sp_from_sa}; static void *data_sp_from_sk[] = {&gsw_sp_from_sk}; static void *data_sp_from_sr[] = {&gsw_sp_from_sr}; static void *data_sp_from_sstar[] = {&gsw_sp_from_sstar}; static void *data_sp_salinometer[] = {&gsw_sp_salinometer}; static void *data_spiciness0[] = {&gsw_spiciness0}; static void *data_spiciness1[] = {&gsw_spiciness1}; static void *data_spiciness2[] = {&gsw_spiciness2}; static void *data_sr_from_sp[] = {&gsw_sr_from_sp}; static void *data_sstar_from_sa[] = {&gsw_sstar_from_sa}; static void *data_sstar_from_sp[] = {&gsw_sstar_from_sp}; static void *data_t_deriv_chem_potential_water_t_exact[] = {&gsw_t_deriv_chem_potential_water_t_exact}; static void *data_t_freezing[] = {&gsw_t_freezing}; static void *data_t_freezing_poly[] = {&gsw_t_freezing_poly}; static void *data_t_from_ct[] = {&gsw_t_from_ct}; static void *data_t_from_pt0_ice[] = {&gsw_t_from_pt0_ice}; static void *data_thermobaric[] = {&gsw_thermobaric}; static void *data_z_from_p[] = {&gsw_z_from_p}; static void *data_p_from_z[] = {&gsw_p_from_z}; static void *data_ct_first_derivatives[] = {&gsw_ct_first_derivatives}; static void *data_ct_first_derivatives_wrt_t_exact[] = {&gsw_ct_first_derivatives_wrt_t_exact}; static void *data_ct_freezing_first_derivatives[] = {&gsw_ct_freezing_first_derivatives}; static void *data_ct_freezing_first_derivatives_poly[] = {&gsw_ct_freezing_first_derivatives_poly}; static void *data_ct_from_rho[] = {&gsw_ct_from_rho}; static void *data_ct_second_derivatives[] = {&gsw_ct_second_derivatives}; static void *data_enthalpy_first_derivatives_ct_exact[] = {&gsw_enthalpy_first_derivatives_ct_exact}; static void *data_enthalpy_first_derivatives[] = {&gsw_enthalpy_first_derivatives}; static void *data_enthalpy_second_derivatives_ct_exact[] = {&gsw_enthalpy_second_derivatives_ct_exact}; static void *data_enthalpy_second_derivatives[] = {&gsw_enthalpy_second_derivatives}; static void *data_entropy_first_derivatives[] = {&gsw_entropy_first_derivatives}; static void *data_entropy_second_derivatives[] = {&gsw_entropy_second_derivatives}; static void *data_frazil_properties[] = {&gsw_frazil_properties}; static void *data_frazil_properties_potential[] = {&gsw_frazil_properties_potential}; static void *data_frazil_properties_potential_poly[] = {&gsw_frazil_properties_potential_poly}; static void *data_frazil_ratios_adiabatic[] = {&gsw_frazil_ratios_adiabatic}; static void *data_frazil_ratios_adiabatic_poly[] = {&gsw_frazil_ratios_adiabatic_poly}; static void *data_ice_fraction_to_freeze_seawater[] = {&gsw_ice_fraction_to_freeze_seawater}; static void *data_melting_ice_into_seawater[] = {&gsw_melting_ice_into_seawater}; static void *data_melting_seaice_into_seawater[] = {&gsw_melting_seaice_into_seawater}; static void *data_pot_enthalpy_ice_freezing_first_derivatives[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives}; static void *data_pot_enthalpy_ice_freezing_first_derivatives_poly[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives_poly}; static void *data_pt_first_derivatives[] = {&gsw_pt_first_derivatives}; static void *data_pt_second_derivatives[] = {&gsw_pt_second_derivatives}; static void *data_rho_alpha_beta[] = {&gsw_rho_alpha_beta}; static void *data_rho_first_derivatives[] = {&gsw_rho_first_derivatives}; static void *data_rho_first_derivatives_wrt_enthalpy[] = {&gsw_rho_first_derivatives_wrt_enthalpy}; static void *data_rho_second_derivatives[] = {&gsw_rho_second_derivatives}; static void *data_rho_second_derivatives_wrt_enthalpy[] = {&gsw_rho_second_derivatives_wrt_enthalpy}; static void *data_seaice_fraction_to_freeze_seawater[] = {&gsw_seaice_fraction_to_freeze_seawater}; static void *data_specvol_alpha_beta[] = {&gsw_specvol_alpha_beta}; static void *data_specvol_first_derivatives[] = {&gsw_specvol_first_derivatives}; static void *data_specvol_first_derivatives_wrt_enthalpy[] = {&gsw_specvol_first_derivatives_wrt_enthalpy}; static void *data_specvol_second_derivatives[] = {&gsw_specvol_second_derivatives}; static void *data_specvol_second_derivatives_wrt_enthalpy[] = {&gsw_specvol_second_derivatives_wrt_enthalpy}; static void *data_t_freezing_first_derivatives_poly[] = {&gsw_t_freezing_first_derivatives_poly}; static void *data_t_freezing_first_derivatives[] = {&gsw_t_freezing_first_derivatives}; static void *data_gibbs_ice[] = {&gsw_gibbs_ice}; static void *data_gibbs[] = {&gsw_gibbs}; #include "method_bodies.c" static PyMethodDef GswMethods[] = { # include "method_def_entries.c" {NULL, NULL, 0, NULL} }; static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "npufunc", NULL, -1, GswMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit__gsw_ufuncs(void) { PyObject *m, *d; PyObject *ufunc_ptr; m = PyModule_Create(&moduledef); if (!m) { return NULL; } d = PyModule_GetDict(m); import_array(); import_umath(); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_i, data_infunnel, types_ddd_i, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "infunnel", "infunnel_docstring", 0); PyDict_SetItemString(d, "infunnel", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_adiabatic_lapse_rate_from_ct, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "adiabatic_lapse_rate_from_ct", "adiabatic_lapse_rate_from_ct_docstring", 0); PyDict_SetItemString(d, "adiabatic_lapse_rate_from_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_adiabatic_lapse_rate_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "adiabatic_lapse_rate_ice", "adiabatic_lapse_rate_ice_docstring", 0); PyDict_SetItemString(d, "adiabatic_lapse_rate_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_alpha, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "alpha", "alpha_docstring", 0); PyDict_SetItemString(d, "alpha", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_alpha_on_beta, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "alpha_on_beta", "alpha_on_beta_docstring", 0); PyDict_SetItemString(d, "alpha_on_beta", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_alpha_wrt_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "alpha_wrt_t_exact", "alpha_wrt_t_exact_docstring", 0); PyDict_SetItemString(d, "alpha_wrt_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_alpha_wrt_t_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "alpha_wrt_t_ice", "alpha_wrt_t_ice_docstring", 0); PyDict_SetItemString(d, "alpha_wrt_t_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_beta_const_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "beta_const_t_exact", "beta_const_t_exact_docstring", 0); PyDict_SetItemString(d, "beta_const_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_beta, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "beta", "beta_docstring", 0); PyDict_SetItemString(d, "beta", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_cabbeling, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "cabbeling", "cabbeling_docstring", 0); PyDict_SetItemString(d, "cabbeling", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_c_from_sp, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "c_from_sp", "c_from_sp_docstring", 0); PyDict_SetItemString(d, "c_from_sp", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_chem_potential_water_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "chem_potential_water_ice", "chem_potential_water_ice_docstring", 0); PyDict_SetItemString(d, "chem_potential_water_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_chem_potential_water_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "chem_potential_water_t_exact", "chem_potential_water_t_exact_docstring", 0); PyDict_SetItemString(d, "chem_potential_water_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_cp_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "cp_ice", "cp_ice_docstring", 0); PyDict_SetItemString(d, "cp_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_cp_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "cp_t_exact", "cp_t_exact_docstring", 0); PyDict_SetItemString(d, "cp_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_ct_freezing, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_freezing", "ct_freezing_docstring", 0); PyDict_SetItemString(d, "ct_freezing", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_ct_freezing_poly, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_freezing_poly", "ct_freezing_poly_docstring", 0); PyDict_SetItemString(d, "ct_freezing_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_ct_from_enthalpy, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_from_enthalpy", "ct_from_enthalpy_docstring", 0); PyDict_SetItemString(d, "ct_from_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_ct_from_enthalpy_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_from_enthalpy_exact", "ct_from_enthalpy_exact_docstring", 0); PyDict_SetItemString(d, "ct_from_enthalpy_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_ct_from_entropy, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_from_entropy", "ct_from_entropy_docstring", 0); PyDict_SetItemString(d, "ct_from_entropy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_ct_from_pt, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_from_pt", "ct_from_pt_docstring", 0); PyDict_SetItemString(d, "ct_from_pt", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_ct_from_t, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_from_t", "ct_from_t_docstring", 0); PyDict_SetItemString(d, "ct_from_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_ct_maxdensity, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "ct_maxdensity", "ct_maxdensity_docstring", 0); PyDict_SetItemString(d, "ct_maxdensity", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_deltasa_atlas, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "deltasa_atlas", "deltasa_atlas_docstring", 0); PyDict_SetItemString(d, "deltasa_atlas", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_deltasa_from_sp, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "deltasa_from_sp", "deltasa_from_sp_docstring", 0); PyDict_SetItemString(d, "deltasa_from_sp", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_dilution_coefficient_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "dilution_coefficient_t_exact", "dilution_coefficient_t_exact_docstring", 0); PyDict_SetItemString(d, "dilution_coefficient_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_dynamic_enthalpy, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "dynamic_enthalpy", "dynamic_enthalpy_docstring", 0); PyDict_SetItemString(d, "dynamic_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_enthalpy_ct_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_ct_exact", "enthalpy_ct_exact_docstring", 0); PyDict_SetItemString(d, "enthalpy_ct_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_enthalpy_diff, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_diff", "enthalpy_diff_docstring", 0); PyDict_SetItemString(d, "enthalpy_diff", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_enthalpy, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy", "enthalpy_docstring", 0); PyDict_SetItemString(d, "enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_enthalpy_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_ice", "enthalpy_ice_docstring", 0); PyDict_SetItemString(d, "enthalpy_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_enthalpy_sso_0, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_sso_0", "enthalpy_sso_0_docstring", 0); PyDict_SetItemString(d, "enthalpy_sso_0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_enthalpy_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_t_exact", "enthalpy_t_exact_docstring", 0); PyDict_SetItemString(d, "enthalpy_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_entropy_from_ct, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_from_ct", "entropy_from_ct_docstring", 0); PyDict_SetItemString(d, "entropy_from_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_entropy_from_pt, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_from_pt", "entropy_from_pt_docstring", 0); PyDict_SetItemString(d, "entropy_from_pt", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_entropy_from_t, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_from_t", "entropy_from_t_docstring", 0); PyDict_SetItemString(d, "entropy_from_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_entropy_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_ice", "entropy_ice_docstring", 0); PyDict_SetItemString(d, "entropy_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_entropy_part, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_part", "entropy_part_docstring", 0); PyDict_SetItemString(d, "entropy_part", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_entropy_part_zerop, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "entropy_part_zerop", "entropy_part_zerop_docstring", 0); PyDict_SetItemString(d, "entropy_part_zerop", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_fdelta, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "fdelta", "fdelta_docstring", 0); PyDict_SetItemString(d, "fdelta", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_gibbs_ice_part_t, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs_ice_part_t", "gibbs_ice_part_t_docstring", 0); PyDict_SetItemString(d, "gibbs_ice_part_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_gibbs_ice_pt0, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs_ice_pt0", "gibbs_ice_pt0_docstring", 0); PyDict_SetItemString(d, "gibbs_ice_pt0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_gibbs_ice_pt0_pt0, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs_ice_pt0_pt0", "gibbs_ice_pt0_pt0_docstring", 0); PyDict_SetItemString(d, "gibbs_ice_pt0_pt0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_gibbs_pt0_pt0, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs_pt0_pt0", "gibbs_pt0_pt0_docstring", 0); PyDict_SetItemString(d, "gibbs_pt0_pt0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_grav, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "grav", "grav_docstring", 0); PyDict_SetItemString(d, "grav", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_helmholtz_energy_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "helmholtz_energy_ice", "helmholtz_energy_ice_docstring", 0); PyDict_SetItemString(d, "helmholtz_energy_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_hill_ratio_at_sp2, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "hill_ratio_at_sp2", "hill_ratio_at_sp2_docstring", 0); PyDict_SetItemString(d, "hill_ratio_at_sp2", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_internal_energy, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "internal_energy", "internal_energy_docstring", 0); PyDict_SetItemString(d, "internal_energy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_internal_energy_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "internal_energy_ice", "internal_energy_ice_docstring", 0); PyDict_SetItemString(d, "internal_energy_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_kappa_const_t_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "kappa_const_t_ice", "kappa_const_t_ice_docstring", 0); PyDict_SetItemString(d, "kappa_const_t_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_kappa, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "kappa", "kappa_docstring", 0); PyDict_SetItemString(d, "kappa", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_kappa_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "kappa_ice", "kappa_ice_docstring", 0); PyDict_SetItemString(d, "kappa_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_kappa_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "kappa_t_exact", "kappa_t_exact_docstring", 0); PyDict_SetItemString(d, "kappa_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_latentheat_evap_ct, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "latentheat_evap_ct", "latentheat_evap_ct_docstring", 0); PyDict_SetItemString(d, "latentheat_evap_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_latentheat_evap_t, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "latentheat_evap_t", "latentheat_evap_t_docstring", 0); PyDict_SetItemString(d, "latentheat_evap_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_latentheat_melting, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "latentheat_melting", "latentheat_melting_docstring", 0); PyDict_SetItemString(d, "latentheat_melting", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_melting_ice_equilibrium_sa_ct_ratio, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_ice_equilibrium_sa_ct_ratio", "melting_ice_equilibrium_sa_ct_ratio_docstring", 0); PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_melting_ice_equilibrium_sa_ct_ratio_poly, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_ice_equilibrium_sa_ct_ratio_poly", "melting_ice_equilibrium_sa_ct_ratio_poly_docstring", 0); PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_melting_ice_sa_ct_ratio, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_ice_sa_ct_ratio", "melting_ice_sa_ct_ratio_docstring", 0); PyDict_SetItemString(d, "melting_ice_sa_ct_ratio", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_melting_ice_sa_ct_ratio_poly, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_ice_sa_ct_ratio_poly", "melting_ice_sa_ct_ratio_poly_docstring", 0); PyDict_SetItemString(d, "melting_ice_sa_ct_ratio_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_melting_seaice_equilibrium_sa_ct_ratio, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_seaice_equilibrium_sa_ct_ratio", "melting_seaice_equilibrium_sa_ct_ratio_docstring", 0); PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_melting_seaice_equilibrium_sa_ct_ratio_poly, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_seaice_equilibrium_sa_ct_ratio_poly", "melting_seaice_equilibrium_sa_ct_ratio_poly_docstring", 0); PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d, data_melting_seaice_sa_ct_ratio, types_ddddd_d, 1, 5, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_seaice_sa_ct_ratio", "melting_seaice_sa_ct_ratio_docstring", 0); PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d, data_melting_seaice_sa_ct_ratio_poly, types_ddddd_d, 1, 5, 1, // ndatatypes, nin, nout PyUFunc_None, "melting_seaice_sa_ct_ratio_poly", "melting_seaice_sa_ct_ratio_poly_docstring", 0); PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d, data_o2sol, types_ddddd_d, 1, 5, 1, // ndatatypes, nin, nout PyUFunc_None, "o2sol", "o2sol_docstring", 0); PyDict_SetItemString(d, "o2sol", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_o2sol_sp_pt, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "o2sol_sp_pt", "o2sol_sp_pt_docstring", 0); PyDict_SetItemString(d, "o2sol_sp_pt", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pot_enthalpy_from_pt_ice, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_from_pt_ice", "pot_enthalpy_from_pt_ice_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pot_enthalpy_from_pt_ice_poly, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_from_pt_ice_poly", "pot_enthalpy_from_pt_ice_poly_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pot_enthalpy_ice_freezing, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_ice_freezing", "pot_enthalpy_ice_freezing_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_ice_freezing", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pot_enthalpy_ice_freezing_poly, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_ice_freezing_poly", "pot_enthalpy_ice_freezing_poly_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_pot_rho_t_exact, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "pot_rho_t_exact", "pot_rho_t_exact_docstring", 0); PyDict_SetItemString(d, "pot_rho_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pressure_coefficient_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pressure_coefficient_ice", "pressure_coefficient_ice_docstring", 0); PyDict_SetItemString(d, "pressure_coefficient_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_pressure_freezing_ct, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "pressure_freezing_ct", "pressure_freezing_ct_docstring", 0); PyDict_SetItemString(d, "pressure_freezing_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pt0_cold_ice_poly, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pt0_cold_ice_poly", "pt0_cold_ice_poly_docstring", 0); PyDict_SetItemString(d, "pt0_cold_ice_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_pt0_from_t, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "pt0_from_t", "pt0_from_t_docstring", 0); PyDict_SetItemString(d, "pt0_from_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pt0_from_t_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pt0_from_t_ice", "pt0_from_t_ice_docstring", 0); PyDict_SetItemString(d, "pt0_from_t_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pt_from_ct, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_ct", "pt_from_ct_docstring", 0); PyDict_SetItemString(d, "pt_from_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_pt_from_entropy, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_entropy", "pt_from_entropy_docstring", 0); PyDict_SetItemString(d, "pt_from_entropy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pt_from_pot_enthalpy_ice, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_pot_enthalpy_ice", "pt_from_pot_enthalpy_ice_docstring", 0); PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pt_from_pot_enthalpy_ice_poly_dh, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_pot_enthalpy_ice_poly_dh", "pt_from_pot_enthalpy_ice_poly_dh_docstring", 0); PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly_dh", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_pt_from_pot_enthalpy_ice_poly, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_pot_enthalpy_ice_poly", "pt_from_pot_enthalpy_ice_poly_docstring", 0); PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_pt_from_t, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_t", "pt_from_t_docstring", 0); PyDict_SetItemString(d, "pt_from_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_pt_from_t_ice, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "pt_from_t_ice", "pt_from_t_ice_docstring", 0); PyDict_SetItemString(d, "pt_from_t_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_rho, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "rho", "rho_docstring", 0); PyDict_SetItemString(d, "rho", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_rho_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "rho_ice", "rho_ice_docstring", 0); PyDict_SetItemString(d, "rho_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_rho_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "rho_t_exact", "rho_t_exact_docstring", 0); PyDict_SetItemString(d, "rho_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_saar, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "saar", "saar_docstring", 0); PyDict_SetItemString(d, "saar", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_freezing_from_ct, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_freezing_from_ct", "sa_freezing_from_ct_docstring", 0); PyDict_SetItemString(d, "sa_freezing_from_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_freezing_from_ct_poly, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_freezing_from_ct_poly", "sa_freezing_from_ct_poly_docstring", 0); PyDict_SetItemString(d, "sa_freezing_from_ct_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_freezing_from_t, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_freezing_from_t", "sa_freezing_from_t_docstring", 0); PyDict_SetItemString(d, "sa_freezing_from_t", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_freezing_from_t_poly, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_freezing_from_t_poly", "sa_freezing_from_t_poly_docstring", 0); PyDict_SetItemString(d, "sa_freezing_from_t_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_from_rho, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_from_rho", "sa_from_rho_docstring", 0); PyDict_SetItemString(d, "sa_from_rho", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sa_from_sp_baltic, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_from_sp_baltic", "sa_from_sp_baltic_docstring", 0); PyDict_SetItemString(d, "sa_from_sp_baltic", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sa_from_sp, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_from_sp", "sa_from_sp_docstring", 0); PyDict_SetItemString(d, "sa_from_sp", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sa_from_sstar, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_from_sstar", "sa_from_sstar_docstring", 0); PyDict_SetItemString(d, "sa_from_sstar", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_i, data_sa_p_inrange, types_dd_i, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sa_p_inrange", "sa_p_inrange_docstring", 0); PyDict_SetItemString(d, "sa_p_inrange", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sigma0, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sigma0", "sigma0_docstring", 0); PyDict_SetItemString(d, "sigma0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sigma1, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sigma1", "sigma1_docstring", 0); PyDict_SetItemString(d, "sigma1", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sigma2, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sigma2", "sigma2_docstring", 0); PyDict_SetItemString(d, "sigma2", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sigma3, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sigma3", "sigma3_docstring", 0); PyDict_SetItemString(d, "sigma3", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sigma4, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sigma4", "sigma4_docstring", 0); PyDict_SetItemString(d, "sigma4", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sound_speed, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sound_speed", "sound_speed_docstring", 0); PyDict_SetItemString(d, "sound_speed", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sound_speed_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sound_speed_ice", "sound_speed_ice_docstring", 0); PyDict_SetItemString(d, "sound_speed_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sound_speed_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sound_speed_t_exact", "sound_speed_t_exact_docstring", 0); PyDict_SetItemString(d, "sound_speed_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_specvol_anom_standard, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "specvol_anom_standard", "specvol_anom_standard_docstring", 0); PyDict_SetItemString(d, "specvol_anom_standard", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_specvol, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "specvol", "specvol_docstring", 0); PyDict_SetItemString(d, "specvol", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_specvol_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "specvol_ice", "specvol_ice_docstring", 0); PyDict_SetItemString(d, "specvol_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_specvol_sso_0, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "specvol_sso_0", "specvol_sso_0_docstring", 0); PyDict_SetItemString(d, "specvol_sso_0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_specvol_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "specvol_t_exact", "specvol_t_exact_docstring", 0); PyDict_SetItemString(d, "specvol_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sp_from_c, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_c", "sp_from_c_docstring", 0); PyDict_SetItemString(d, "sp_from_c", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_sp_from_sa_baltic, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_sa_baltic", "sp_from_sa_baltic_docstring", 0); PyDict_SetItemString(d, "sp_from_sa_baltic", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sp_from_sa, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_sa", "sp_from_sa_docstring", 0); PyDict_SetItemString(d, "sp_from_sa", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_sp_from_sk, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_sk", "sp_from_sk_docstring", 0); PyDict_SetItemString(d, "sp_from_sk", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_sp_from_sr, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_sr", "sp_from_sr_docstring", 0); PyDict_SetItemString(d, "sp_from_sr", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sp_from_sstar, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_from_sstar", "sp_from_sstar_docstring", 0); PyDict_SetItemString(d, "sp_from_sstar", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_sp_salinometer, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "sp_salinometer", "sp_salinometer_docstring", 0); PyDict_SetItemString(d, "sp_salinometer", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_spiciness0, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "spiciness0", "spiciness0_docstring", 0); PyDict_SetItemString(d, "spiciness0", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_spiciness1, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "spiciness1", "spiciness1_docstring", 0); PyDict_SetItemString(d, "spiciness1", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_spiciness2, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "spiciness2", "spiciness2_docstring", 0); PyDict_SetItemString(d, "spiciness2", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d, data_sr_from_sp, types_d_d, 1, 1, 1, // ndatatypes, nin, nout PyUFunc_None, "sr_from_sp", "sr_from_sp_docstring", 0); PyDict_SetItemString(d, "sr_from_sp", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sstar_from_sa, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sstar_from_sa", "sstar_from_sa_docstring", 0); PyDict_SetItemString(d, "sstar_from_sa", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_sstar_from_sp, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "sstar_from_sp", "sstar_from_sp_docstring", 0); PyDict_SetItemString(d, "sstar_from_sp", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_t_deriv_chem_potential_water_t_exact, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "t_deriv_chem_potential_water_t_exact", "t_deriv_chem_potential_water_t_exact_docstring", 0); PyDict_SetItemString(d, "t_deriv_chem_potential_water_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_t_freezing, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "t_freezing", "t_freezing_docstring", 0); PyDict_SetItemString(d, "t_freezing", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_t_freezing_poly, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "t_freezing_poly", "t_freezing_poly_docstring", 0); PyDict_SetItemString(d, "t_freezing_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_t_from_ct, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "t_from_ct", "t_from_ct_docstring", 0); PyDict_SetItemString(d, "t_from_ct", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d, data_t_from_pt0_ice, types_dd_d, 1, 2, 1, // ndatatypes, nin, nout PyUFunc_None, "t_from_pt0_ice", "t_from_pt0_ice_docstring", 0); PyDict_SetItemString(d, "t_from_pt0_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d, data_thermobaric, types_ddd_d, 1, 3, 1, // ndatatypes, nin, nout PyUFunc_None, "thermobaric", "thermobaric_docstring", 0); PyDict_SetItemString(d, "thermobaric", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_z_from_p, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "z_from_p", "z_from_p_docstring", 0); PyDict_SetItemString(d, "z_from_p", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d, data_p_from_z, types_dddd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "p_from_z", "p_from_z_docstring", 0); PyDict_SetItemString(d, "p_from_z", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd, data_ct_first_derivatives, types_dd_dd, 1, 2, 2, // ndatatypes, nin, nout PyUFunc_None, "ct_first_derivatives", "ct_first_derivatives_docstring", 0); PyDict_SetItemString(d, "ct_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_ct_first_derivatives_wrt_t_exact, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "ct_first_derivatives_wrt_t_exact", "ct_first_derivatives_wrt_t_exact_docstring", 0); PyDict_SetItemString(d, "ct_first_derivatives_wrt_t_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_ct_freezing_first_derivatives, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "ct_freezing_first_derivatives", "ct_freezing_first_derivatives_docstring", 0); PyDict_SetItemString(d, "ct_freezing_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_ct_freezing_first_derivatives_poly, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "ct_freezing_first_derivatives_poly", "ct_freezing_first_derivatives_poly_docstring", 0); PyDict_SetItemString(d, "ct_freezing_first_derivatives_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_ct_from_rho, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "ct_from_rho", "ct_from_rho_docstring", 0); PyDict_SetItemString(d, "ct_from_rho", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd, data_ct_second_derivatives, types_dd_ddd, 1, 2, 3, // ndatatypes, nin, nout PyUFunc_None, "ct_second_derivatives", "ct_second_derivatives_docstring", 0); PyDict_SetItemString(d, "ct_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_enthalpy_first_derivatives_ct_exact, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_first_derivatives_ct_exact", "enthalpy_first_derivatives_ct_exact_docstring", 0); PyDict_SetItemString(d, "enthalpy_first_derivatives_ct_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_enthalpy_first_derivatives, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_first_derivatives", "enthalpy_first_derivatives_docstring", 0); PyDict_SetItemString(d, "enthalpy_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_enthalpy_second_derivatives_ct_exact, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_second_derivatives_ct_exact", "enthalpy_second_derivatives_ct_exact_docstring", 0); PyDict_SetItemString(d, "enthalpy_second_derivatives_ct_exact", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_enthalpy_second_derivatives, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "enthalpy_second_derivatives", "enthalpy_second_derivatives_docstring", 0); PyDict_SetItemString(d, "enthalpy_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd, data_entropy_first_derivatives, types_dd_dd, 1, 2, 2, // ndatatypes, nin, nout PyUFunc_None, "entropy_first_derivatives", "entropy_first_derivatives_docstring", 0); PyDict_SetItemString(d, "entropy_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd, data_entropy_second_derivatives, types_dd_ddd, 1, 2, 3, // ndatatypes, nin, nout PyUFunc_None, "entropy_second_derivatives", "entropy_second_derivatives_docstring", 0); PyDict_SetItemString(d, "entropy_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_frazil_properties, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "frazil_properties", "frazil_properties_docstring", 0); PyDict_SetItemString(d, "frazil_properties", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_frazil_properties_potential, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "frazil_properties_potential", "frazil_properties_potential_docstring", 0); PyDict_SetItemString(d, "frazil_properties_potential", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_frazil_properties_potential_poly, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "frazil_properties_potential_poly", "frazil_properties_potential_poly_docstring", 0); PyDict_SetItemString(d, "frazil_properties_potential_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_frazil_ratios_adiabatic, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "frazil_ratios_adiabatic", "frazil_ratios_adiabatic_docstring", 0); PyDict_SetItemString(d, "frazil_ratios_adiabatic", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_frazil_ratios_adiabatic_poly, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "frazil_ratios_adiabatic_poly", "frazil_ratios_adiabatic_poly_docstring", 0); PyDict_SetItemString(d, "frazil_ratios_adiabatic_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_ddd, data_ice_fraction_to_freeze_seawater, types_dddd_ddd, 1, 4, 3, // ndatatypes, nin, nout PyUFunc_None, "ice_fraction_to_freeze_seawater", "ice_fraction_to_freeze_seawater_docstring", 0); PyDict_SetItemString(d, "ice_fraction_to_freeze_seawater", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd, data_melting_ice_into_seawater, types_ddddd_ddd, 1, 5, 3, // ndatatypes, nin, nout PyUFunc_None, "melting_ice_into_seawater", "melting_ice_into_seawater_docstring", 0); PyDict_SetItemString(d, "melting_ice_into_seawater", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddddd_dd, data_melting_seaice_into_seawater, types_dddddd_dd, 1, 6, 2, // ndatatypes, nin, nout PyUFunc_None, "melting_seaice_into_seawater", "melting_seaice_into_seawater_docstring", 0); PyDict_SetItemString(d, "melting_seaice_into_seawater", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd, data_pot_enthalpy_ice_freezing_first_derivatives, types_dd_dd, 1, 2, 2, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_ice_freezing_first_derivatives", "pot_enthalpy_ice_freezing_first_derivatives_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd, data_pot_enthalpy_ice_freezing_first_derivatives_poly, types_dd_dd, 1, 2, 2, // ndatatypes, nin, nout PyUFunc_None, "pot_enthalpy_ice_freezing_first_derivatives_poly", "pot_enthalpy_ice_freezing_first_derivatives_poly_docstring", 0); PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd, data_pt_first_derivatives, types_dd_dd, 1, 2, 2, // ndatatypes, nin, nout PyUFunc_None, "pt_first_derivatives", "pt_first_derivatives_docstring", 0); PyDict_SetItemString(d, "pt_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd, data_pt_second_derivatives, types_dd_ddd, 1, 2, 3, // ndatatypes, nin, nout PyUFunc_None, "pt_second_derivatives", "pt_second_derivatives_docstring", 0); PyDict_SetItemString(d, "pt_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_rho_alpha_beta, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "rho_alpha_beta", "rho_alpha_beta_docstring", 0); PyDict_SetItemString(d, "rho_alpha_beta", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_rho_first_derivatives, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "rho_first_derivatives", "rho_first_derivatives_docstring", 0); PyDict_SetItemString(d, "rho_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_rho_first_derivatives_wrt_enthalpy, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "rho_first_derivatives_wrt_enthalpy", "rho_first_derivatives_wrt_enthalpy_docstring", 0); PyDict_SetItemString(d, "rho_first_derivatives_wrt_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd, data_rho_second_derivatives, types_ddd_ddddd, 1, 3, 5, // ndatatypes, nin, nout PyUFunc_None, "rho_second_derivatives", "rho_second_derivatives_docstring", 0); PyDict_SetItemString(d, "rho_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_rho_second_derivatives_wrt_enthalpy, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "rho_second_derivatives_wrt_enthalpy", "rho_second_derivatives_wrt_enthalpy_docstring", 0); PyDict_SetItemString(d, "rho_second_derivatives_wrt_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd, data_seaice_fraction_to_freeze_seawater, types_ddddd_ddd, 1, 5, 3, // ndatatypes, nin, nout PyUFunc_None, "seaice_fraction_to_freeze_seawater", "seaice_fraction_to_freeze_seawater_docstring", 0); PyDict_SetItemString(d, "seaice_fraction_to_freeze_seawater", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_specvol_alpha_beta, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "specvol_alpha_beta", "specvol_alpha_beta_docstring", 0); PyDict_SetItemString(d, "specvol_alpha_beta", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_specvol_first_derivatives, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "specvol_first_derivatives", "specvol_first_derivatives_docstring", 0); PyDict_SetItemString(d, "specvol_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_specvol_first_derivatives_wrt_enthalpy, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "specvol_first_derivatives_wrt_enthalpy", "specvol_first_derivatives_wrt_enthalpy_docstring", 0); PyDict_SetItemString(d, "specvol_first_derivatives_wrt_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd, data_specvol_second_derivatives, types_ddd_ddddd, 1, 3, 5, // ndatatypes, nin, nout PyUFunc_None, "specvol_second_derivatives", "specvol_second_derivatives_docstring", 0); PyDict_SetItemString(d, "specvol_second_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd, data_specvol_second_derivatives_wrt_enthalpy, types_ddd_ddd, 1, 3, 3, // ndatatypes, nin, nout PyUFunc_None, "specvol_second_derivatives_wrt_enthalpy", "specvol_second_derivatives_wrt_enthalpy_docstring", 0); PyDict_SetItemString(d, "specvol_second_derivatives_wrt_enthalpy", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_t_freezing_first_derivatives_poly, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "t_freezing_first_derivatives_poly", "t_freezing_first_derivatives_poly_docstring", 0); PyDict_SetItemString(d, "t_freezing_first_derivatives_poly", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd, data_t_freezing_first_derivatives, types_ddd_dd, 1, 3, 2, // ndatatypes, nin, nout PyUFunc_None, "t_freezing_first_derivatives", "t_freezing_first_derivatives_docstring", 0); PyDict_SetItemString(d, "t_freezing_first_derivatives", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_iidd_d, data_gibbs_ice, types_iidd_d, 1, 4, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs_ice", "gibbs_ice_docstring", 0); PyDict_SetItemString(d, "gibbs_ice", ufunc_ptr); Py_DECREF(ufunc_ptr); ufunc_ptr = PyUFunc_FromFuncAndData(funcs_iiiddd_d, data_gibbs, types_iiiddd_d, 1, 6, 1, // ndatatypes, nin, nout PyUFunc_None, "gibbs", "gibbs_docstring", 0); PyDict_SetItemString(d, "gibbs", ufunc_ptr); Py_DECREF(ufunc_ptr); return m; } gsw-3.6.21/src/c_gsw/0000755000175000017500000000000015147371330014462 5ustar alastairalastairgsw-3.6.21/src/c_gsw/gsw_internal_const.h0000644000175000017500000004251515147371315020547 0ustar alastairalastair/* ** $Id: gsw_internal_const.h,v a1406e71e2a9 2016/01/08 08:01:43 fdelahoyde $ ** ** Internal constants for GSW-TEOS-10 V3.05. */ #ifndef GSW_INTERNAL_CONST_H #define GSW_INTERNAL_CONST_H /* ** The following hack is used to ensure that gcc (and gcc emulating compilers ** such as Macosx clang) do not emit unused variable warning messages. */ #ifdef __GNUC__ #define UNUSED __attribute__ ((unused)) #else #define UNUSED #endif #define GSW_TEOS10_CONSTANTS \ UNUSED double db2pa = 1.0e4, \ rec_db2pa = 1.0e-4, \ pa2db = 1.0e-4, \ rec_pa2db = 1.0e4, \ pi = 3.141592653589793, \ deg2rad = pi/180.0, \ rad2deg = 180.0/pi, \ gamma = 2.26e-7, \ /*\ ! cp0 = The "specific heat" for use [ J/(kg K) ]\ ! with Conservative Temperature \ */\ gsw_cp0 = 3991.86795711963, \ /*\ ! T0 = the Celsius zero point. [ K ]\ */\ gsw_t0 = 273.15, \ /*\ ! P0 = Absolute Pressure of one standard atmosphere. [ Pa ]\ */\ gsw_p0 = 101325.0, \ /*\ ! SSO = Standard Ocean Reference Salinity. [ g/kg ]\ */\ gsw_sso = 35.16504, \ gsw_sqrtsso = 5.930011804372737, \ /*\ ! uPS = unit conversion factor for salinities [ g/kg ]\ */\ gsw_ups = gsw_sso/35.0, \ /*\ ! sfac = 1/(40*gsw_ups)\ */\ gsw_sfac = 0.0248826675584615, \ /*\ ! deltaS = 24, offset = deltaS*gsw_sfac\ */\ offset = 5.971840214030754e-1, \ /*\ ! C3515 = Conductivity at (SP=35, t_68=15, p=0) [ mS/cm ]\ */\ gsw_c3515 = 42.9140, \ /*\ ! SonCl = SP to Chlorinity ratio [ (g/kg)^-1 ]\ */\ gsw_soncl = 1.80655, \ /*\ ! valence_factor = valence factor of sea salt of Reference Composition\ ! [ unitless ]\ */\ gsw_valence_factor = 1.2452898, \ /*\ ! atomic_weight = mole-weighted atomic weight of sea salt of Reference \ ! Composition [ g/mol ]\ */\ gsw_atomic_weight = 31.4038218 #define GSW_SPECVOL_COEFFICIENTS \ UNUSED double a000 = -1.56497346750e-5, \ a001 = 1.85057654290e-5, \ a002 = -1.17363867310e-6, \ a003 = -3.65270065530e-7, \ a004 = 3.14540999020e-7, \ a010 = 5.55242129680e-5, \ a011 = -2.34332137060e-5, \ a012 = 4.26100574800e-6, \ a013 = 5.73918103180e-7, \ a020 = -4.95634777770e-5, \ a021 = 2.37838968519e-5, \ a022 = -1.38397620111e-6, \ a030 = 2.76445290808e-5, \ a031 = -1.36408749928e-5, \ a032 = -2.53411666056e-7, \ a040 = -4.02698077700e-6, \ a041 = 2.53683834070e-6, \ a050 = 1.23258565608e-6, \ a100 = 3.50095997640e-5, \ a101 = -9.56770881560e-6, \ a102 = -5.56991545570e-6, \ a103 = -2.72956962370e-7, \ a110 = -7.48716846880e-5, \ a111 = -4.73566167220e-7, \ a112 = 7.82747741600e-7, \ a120 = 7.24244384490e-5, \ a121 = -1.03676320965e-5, \ a122 = 2.32856664276e-8, \ a130 = -3.50383492616e-5, \ a131 = 5.18268711320e-6, \ a140 = -1.65263794500e-6, \ a200 = -4.35926785610e-5, \ a201 = 1.11008347650e-5, \ a202 = 5.46207488340e-6, \ a210 = 7.18156455200e-5, \ a211 = 5.85666925900e-6, \ a212 = -1.31462208134e-6, \ a220 = -4.30608991440e-5, \ a221 = 9.49659182340e-7, \ a230 = 1.74814722392e-5, \ a300 = 3.45324618280e-5, \ a301 = -9.84471178440e-6, \ a302 = -1.35441856270e-6, \ a310 = -3.73971683740e-5, \ a311 = -9.76522784000e-7, \ a320 = 6.85899736680e-6, \ a400 = -1.19594097880e-5, \ a401 = 2.59092252600e-6, \ a410 = 7.71906784880e-6, \ a500 = 1.38645945810e-6, \ b000 = -3.10389819760e-4, \ b003 = 3.63101885150e-7, \ b004 = -1.11471254230e-7, \ b010 = 3.50095997640e-5, \ b013 = -2.72956962370e-7, \ b020 = -3.74358423440e-5, \ b030 = 2.41414794830e-5, \ b040 = -8.75958731540e-6, \ b050 = -3.30527589000e-7, \ b100 = 1.33856134076e-3, \ b103 = 3.34926075600e-8, \ b110 = -8.71853571220e-5, \ b120 = 7.18156455200e-5, \ b130 = -2.87072660960e-5, \ b140 = 8.74073611960e-6, \ b200 = -2.55143801811e-3, \ b210 = 1.03597385484e-4, \ b220 = -5.60957525610e-5, \ b230 = 6.85899736680e-6, \ b300 = 2.32344279772e-3, \ b310 = -4.78376391520e-5, \ b320 = 1.54381356976e-5, \ b400 = -1.05461852535e-3, \ b410 = 6.93229729050e-6, \ b500 = 1.91594743830e-4, \ b001 = 2.42624687470e-5, \ b011 = -9.56770881560e-6, \ b021 = -2.36783083610e-7, \ b031 = -3.45587736550e-6, \ b041 = 1.29567177830e-6, \ b101 = -6.95849219480e-5, \ b111 = 2.22016695300e-5, \ b121 = 5.85666925900e-6, \ b131 = 6.33106121560e-7, \ b201 = 1.12412331915e-4, \ b211 = -2.95341353532e-5, \ b221 = -1.46478417600e-6, \ b301 = -6.92888744480e-5, \ b311 = 1.03636901040e-5, \ b401 = 1.54637136265e-5, \ b002 = -5.84844329840e-7, \ b012 = -5.56991545570e-6, \ b022 = 3.91373870800e-7, \ b032 = 7.76188880920e-9, \ b102 = -9.62445031940e-6, \ b112 = 1.09241497668e-5, \ b122 = -1.31462208134e-6, \ b202 = 1.47789320994e-5, \ b212 = -4.06325568810e-6, \ b302 = -7.12478989080e-6, \ c000 = -6.07991438090e-5, \ c001 = 1.99712338438e-5, \ c002 = -3.39280843110e-6, \ c003 = 4.21246123200e-7, \ c004 = -6.32363064300e-8, \ c005 = 1.17681023580e-8, \ c010 = 1.85057654290e-5, \ c011 = -2.34727734620e-6, \ c012 = -1.09581019659e-6, \ c013 = 1.25816399608e-6, \ c020 = -1.17166068530e-5, \ c021 = 4.26100574800e-6, \ c022 = 8.60877154770e-7, \ c030 = 7.92796561730e-6, \ c031 = -9.22650800740e-7, \ c040 = -3.41021874820e-6, \ c041 = -1.26705833028e-7, \ c050 = 5.07367668140e-7, \ c100 = 2.42624687470e-5, \ c101 = -1.16968865968e-6, \ c102 = 1.08930565545e-6, \ c103 = -4.45885016920e-7, \ c110 = -9.56770881560e-6, \ c111 = -1.11398309114e-5, \ c112 = -8.18870887110e-7, \ c120 = -2.36783083610e-7, \ c121 = 7.82747741600e-7, \ c130 = -3.45587736550e-6, \ c131 = 1.55237776184e-8, \ c140 = 1.29567177830e-6, \ c200 = -3.47924609740e-5, \ c201 = -9.62445031940e-6, \ c202 = 5.02389113400e-8, \ c210 = 1.11008347650e-5, \ c211 = 1.09241497668e-5, \ c220 = 2.92833462950e-6, \ c221 = -1.31462208134e-6, \ c230 = 3.16553060780e-7, \ c300 = 3.74707773050e-5, \ c301 = 9.85262139960e-6, \ c310 = -9.84471178440e-6, \ c311 = -2.70883712540e-6, \ c320 = -4.88261392000e-7, \ c400 = -1.73222186120e-5, \ c401 = -3.56239494540e-6, \ c410 = 2.59092252600e-6, \ c500 = 3.09274272530e-6, \ h001 = 1.07699958620e-3, \ h002 = -3.03995719050e-5, \ h003 = 3.32853897400e-6, \ h004 = -2.82734035930e-7, \ h005 = 2.10623061600e-8, \ h006 = -2.10787688100e-9, \ h007 = 2.80192913290e-10, \ h011 = -1.56497346750e-5, \ h012 = 9.25288271450e-6, \ h013 = -3.91212891030e-7, \ h014 = -9.13175163830e-8, \ h015 = 6.29081998040e-8, \ h021 = 2.77621064840e-5, \ h022 = -5.85830342650e-6, \ h023 = 7.10167624670e-7, \ h024 = 7.17397628980e-8, \ h031 = -1.65211592590e-5, \ h032 = 3.96398280870e-6, \ h033 = -1.53775133460e-7, \ h042 = -1.70510937410e-6, \ h043 = -2.11176388380e-8, \ h041 = 6.91113227020e-6, \ h051 = -8.05396155400e-7, \ h052 = 2.53683834070e-7, \ h061 = 2.05430942680e-7, \ h101 = -3.10389819760e-4, \ h102 = 1.21312343735e-5, \ h103 = -1.94948109950e-7, \ h104 = 9.07754712880e-8, \ h105 = -2.22942508460e-8, \ h111 = 3.50095997640e-5, \ h112 = -4.78385440780e-6, \ h113 = -1.85663848520e-6, \ h114 = -6.82392405930e-8, \ h121 = -3.74358423440e-5, \ h122 = -1.18391541805e-7, \ h123 = 1.30457956930e-7, \ h131 = 2.41414794830e-5, \ h132 = -1.72793868275e-6, \ h133 = 2.58729626970e-9, \ h141 = -8.75958731540e-6, \ h142 = 6.47835889150e-7, \ h151 = -3.30527589000e-7, \ h201 = 6.69280670380e-4, \ h202 = -1.73962304870e-5, \ h203 = -1.60407505320e-6, \ h204 = 4.18657594500e-9, \ h211 = -4.35926785610e-5, \ h212 = 5.55041738250e-6, \ h213 = 1.82069162780e-6, \ h221 = 3.59078227600e-5, \ h222 = 1.46416731475e-6, \ h223 = -2.19103680220e-7, \ h231 = -1.43536330480e-5, \ h232 = 1.58276530390e-7, \ h241 = 4.37036805980e-6, \ h301 = -8.50479339370e-4, \ h302 = 1.87353886525e-5, \ h303 = 1.64210356660e-6, \ h311 = 3.45324618280e-5, \ h312 = -4.92235589220e-6, \ h313 = -4.51472854230e-7, \ h321 = -1.86985841870e-5, \ h322 = -2.44130696000e-7, \ h331 = 2.28633245560e-6, \ h401 = 5.80860699430e-4, \ h402 = -8.66110930600e-6, \ h403 = -5.93732490900e-7, \ h411 = -1.19594097880e-5, \ h421 = 3.85953392440e-6, \ h412 = 1.29546126300e-6, \ h501 = -2.10923705070e-4, \ h502 = 1.54637136265e-6, \ h511 = 1.38645945810e-6, \ h601 = 3.19324573050e-5, \ v000 = 1.0769995862e-3, \ v001 = -6.0799143809e-5, \ v002 = 9.9856169219e-6, \ v003 = -1.1309361437e-6, \ v004 = 1.0531153080e-7, \ v005 = -1.2647261286e-8, \ v006 = 1.9613503930e-9, \ v010 = -3.1038981976e-4, \ v011 = 2.4262468747e-5, \ v012 = -5.8484432984e-7, \ v013 = 3.6310188515e-7, \ v014 = -1.1147125423e-7, \ v020 = 6.6928067038e-4, \ v021 = -3.4792460974e-5, \ v022 = -4.8122251597e-6, \ v023 = 1.6746303780e-8, \ v030 = -8.5047933937e-4, \ v031 = 3.7470777305e-5, \ v032 = 4.9263106998e-6, \ v040 = 5.8086069943e-4, \ v041 = -1.7322218612e-5, \ v042 = -1.7811974727e-6, \ v050 = -2.1092370507e-4, \ v051 = 3.0927427253e-6, \ v060 = 3.1932457305e-5, \ v100 = -1.5649734675e-5, \ v101 = 1.8505765429e-5, \ v102 = -1.1736386731e-6, \ v103 = -3.6527006553e-7, \ v104 = 3.1454099902e-7, \ v110 = 3.5009599764e-5, \ v111 = -9.5677088156e-6, \ v112 = -5.5699154557e-6, \ v113 = -2.7295696237e-7, \ v120 = -4.3592678561e-5, \ v121 = 1.1100834765e-5, \ v122 = 5.4620748834e-6, \ v130 = 3.4532461828e-5, \ v131 = -9.8447117844e-6, \ v132 = -1.3544185627e-6, \ v140 = -1.1959409788e-5, \ v141 = 2.5909225260e-6, \ v150 = 1.3864594581e-6, \ v200 = 2.7762106484e-5, \ v201 = -1.1716606853e-5, \ v202 = 2.1305028740e-6, \ v203 = 2.8695905159e-7, \ v210 = -3.7435842344e-5, \ v211 = -2.3678308361e-7, \ v212 = 3.9137387080e-7, \ v220 = 3.5907822760e-5, \ v221 = 2.9283346295e-6, \ v222 = -6.5731104067e-7, \ v230 = -1.8698584187e-5, \ v231 = -4.8826139200e-7, \ v240 = 3.8595339244e-6, \ v300 = -1.6521159259e-5, \ v301 = 7.9279656173e-6, \ v302 = -4.6132540037e-7, \ v310 = 2.4141479483e-5, \ v311 = -3.4558773655e-6, \ v312 = 7.7618888092e-9, \ v320 = -1.4353633048e-5, \ v321 = 3.1655306078e-7, \ v330 = 2.2863324556e-6, \ v400 = 6.9111322702e-6, \ v401 = -3.4102187482e-6, \ v402 = -6.3352916514e-8, \ v410 = -8.7595873154e-6, \ v411 = 1.2956717783e-6, \ v420 = 4.3703680598e-6, \ v500 = -8.0539615540e-7, \ v501 = 5.0736766814e-7, \ v510 = -3.3052758900e-7, \ v600 = 2.0543094268e-7 #define GSW_SP_COEFFICIENTS \ UNUSED double a0 = 0.0080, \ a1 = -0.1692, \ a2 = 25.3851, \ a3 = 14.0941, \ a4 = -7.0261, \ a5 = 2.7081, \ b0 = 0.0005, \ b1 = -0.0056, \ b2 = -0.0066, \ b3 = -0.0375, \ b4 = 0.0636, \ b5 = -0.0144, \ c0 = 0.6766097, \ c1 = 2.00564e-2, \ c2 = 1.104259e-4, \ c3 = -6.9698e-7, \ c4 = 1.0031e-9, \ d1 = 3.426e-2, \ d2 = 4.464e-4, \ d3 = 4.215e-1, \ d4 = -3.107e-3, \ e1 = 2.070e-5, \ e2 = -6.370e-10, \ e3 = 3.989e-15, \ k = 0.0162 #define GSW_SAAR_DATA \ UNUSED int deli[4] = {0,1,1,0}, delj[4] = {0,0,1,1}, npan = 6; \ UNUSED double longs_pan[6] = {260.00, 272.59, 276.50, 278.65, 280.73, 292.0},\ lats_pan[6] = { 19.55, 13.97, 9.60, 8.10, 9.33, 3.4} #ifdef __cplusplus #define GSW_GIBBS_ICE_COEFFICIENTS \ UNUSED std::complex t1 ( 3.68017112855051e-2, 5.10878114959572e-2), \ t2 ( 3.37315741065416e-1, 3.35449415919309e-1), \ r1 ( 4.47050716285388e1, 6.56876847463481e1), \ r20 (-7.25974574329220e1, -7.81008427112870e1), \ r21 (-5.57107698030123e-5, 4.64578634580806e-5), \ r22 (2.34801409215913e-11, -2.85651142904972e-11);\ /*\ ! 1./Pt, where Pt = 611.657; Experimental triple-point pressure in Pa.\ */\ UNUSED double rec_pt = 1.634903221903779e-3, \ tt = 273.16, /*Triple-point temperature, kelvin (K).*/ \ rec_tt = 3.660858105139845e-3, /*= 1/tt */ \ g00 = -6.32020233335886e5, \ g01 = 6.55022213658955e-1, \ g02 = -1.89369929326131e-8, \ g03 = 3.3974612327105304e-15, \ g04 = -5.564648690589909e-22 #else #define GSW_GIBBS_ICE_COEFFICIENTS \ UNUSED double complex t1 =( 3.68017112855051e-2+ 5.10878114959572e-2*I), \ t2 =( 3.37315741065416e-1+ 3.35449415919309e-1*I), \ r1 =( 4.47050716285388e1+ 6.56876847463481e1*I), \ r20 =(-7.25974574329220e1+ -7.81008427112870e1*I), \ r21 =(-5.57107698030123e-5+ 4.64578634580806e-5*I), \ r22 =(2.34801409215913e-11+-2.85651142904972e-11*I); \ /*\ ! 1./Pt, where Pt = 611.657; Experimental triple-point pressure in Pa.\ */\ UNUSED double rec_pt = 1.634903221903779e-3, \ tt = 273.16, /*Triple-point temperature, kelvin (K).*/ \ rec_tt = 3.660858105139845e-3, /*= 1/tt */ \ g00 = -6.32020233335886e5, \ g01 = 6.55022213658955e-1, \ g02 = -1.89369929326131e-8, \ g03 = 3.3974612327105304e-15, \ g04 = -5.564648690589909e-22 #endif #define GSW_FREEZING_POLY_COEFFICIENTS \ UNUSED double c0 = 0.017947064327968736, \ c1 = -6.076099099929818, \ c2 = 4.883198653547851, \ c3 = -11.88081601230542, \ c4 = 13.34658511480257, \ c5 = -8.722761043208607, \ c6 = 2.082038908808201, \ c7 = -7.389420998107497, \ c8 = -2.110913185058476, \ c9 = 0.2295491578006229, \ c10 = -0.9891538123307282, \ c11 = -0.08987150128406496, \ c12 = 0.3831132432071728, \ c13 = 1.054318231187074, \ c14 = 1.065556599652796, \ c15 = -0.7997496801694032, \ c16 = 0.3850133554097069, \ c17 = -2.078616693017569, \ c18 = 0.8756340772729538, \ c19 = -2.079022768390933, \ c20 = 1.596435439942262, \ c21 = 0.1338002171109174, \ c22 = 1.242891021876471, \ /* \ ! Note that a = 0.502500117621,/gsw_sso \ */ \ a = 0.014289763856964, \ b = 0.057000649899720, \ t0 = 0.002519, \ t1 = -5.946302841607319, \ t2 = 4.136051661346983, \ t3 = -1.115150523403847e1, \ t4 = 1.476878746184548e1, \ t5 = -1.088873263630961e1, \ t6 = 2.961018839640730, \ t7 = -7.433320943962606, \ t8 = -1.561578562479883, \ t9 = 4.073774363480365e-2, \ t10 = 1.158414435887717e-2, \ t11 = -4.122639292422863e-1, \ t12 = -1.123186915628260e-1, \ t13 = 5.715012685553502e-1, \ t14 = 2.021682115652684e-1, \ t15 = 4.140574258089767e-2, \ t16 = -6.034228641903586e-1, \ t17 = -1.205825928146808e-2, \ t18 = -2.812172968619369e-1, \ t19 = 1.877244474023750e-2, \ t20 = -1.204395563789007e-1, \ t21 = 2.349147739749606e-1, \ t22 = 2.748444541144219e-3 #define GSW_BALTIC_DATA \ /*\ ! Coordinate data for the Baltic Sea\ */\ UNUSED double xb_left[3]={12.6, 7.0, 26.0},\ yb_left[3]={50.0, 59.0, 69.0},\ xb_right[2]={45.0, 26.0},\ yb_right[2]={50.0, 69.0} #ifndef max #define max(a,b) (((a)>(b))?(a):(b)) #endif #ifndef min #define min(a,b) (((a)<(b))?(a):(b)) #endif #endif /* GSW_INTERNAL_CONST_H */ gsw-3.6.21/src/c_gsw/gsw_saar_data.h0000644000175000017500004121154115147371315017446 0ustar alastairalastair/* ** $Id$ ** Extracted from ../../gsw_matlab_v3_06_16/library/gsw_data_v3_0.mat */ static int gsw_nx = 91, gsw_ny = 45, gsw_nz = 45; static char *gsw_version_date = "15th_May_2011"; static char *gsw_version_number = "3.06.16"; void gsw_get_version(char **version_date, char **version_number) { *version_date = gsw_version_date; *version_number = gsw_version_number; } static UNUSED double p_ref[45] = { 0, 10, 20, 30, 40, 50, 76, 101, 126, 151, 176, 202, 252, 303, 353, 404, 505, 606, 707, 808, 909, 1010, 1111, 1213, 1314, 1416, 1517, 1771, 2025, 2279, 2534, 2789, 3045, 3300, 3556, 3812, 4069, 4325, 4583, 4840, 5098, 5355, 5614, 5872, 6131 }; static UNUSED double lats_ref[45] = { -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26, -22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90 }; static UNUSED double longs_ref[91] = { 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332, 336, 340, 344, 348, 352, 356, 360 }; static UNUSED double saar_ref[184275] = { 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 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0.00026355026366656176, 0.00026346953253443675, 0.00026342806246564844, 0.00026393765909437636, 0.00026443504911487432, 0.00026675538985417594, 0.00026552213451088797, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 0.0001245168123560233, 0.00011683091539441242, 0.00012214419720605585, 0.00012913899258366567, 0.00013649647963518869, 0.00014557557850247525, 0.00015858008791900987, 0.00017171767037281235, 0.00018597682264790357, 0.00019725675726493729, 0.00020513836624355878, 0.00021164155783618942, 0.00021745297542256144, 0.0002218987575086376, 0.00022655436934890813, 0.00023070441191602788, 0.00023590503270678095, 0.00024081883607007652, 0.00024542593613978154, 0.0002495840095542116, 0.00025344270765089035, 0.00025626088078789809, 0.00025840907520858662, 0.0002599852898115733, 0.00026132670088173539, 0.0002621922515942538, 0.00026271533586737803, 0.00026337575481726012, 0.00026429137842908255, 0.00026476649290994376, 0.00026463501840809513, 0.00026420116830960767, 0.00026398605437415483, 0.00026381045739930404, 0.00026377574997267522, 0.00026426586516486593, 0.00026466559974567763, 0.00026489348492977563, 0.0002632863964401382, 0.00025883549864435889, 0.00025684977651215169, 0.00025307088047901201, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 9.6285713837996855e-05, 9.3321244865866851e-05, 0.00011186938621573537, 0.00012348887936858334, 0.00013340745862010334, 0.00014202965790846057, 0.00015459478091603957, 0.00016709970307330135, 0.0001842975289462646, 0.00020177339673797844, 0.00021433175946026985, 0.00022498745304770643, 0.00023507132792224857, 0.0002416274165307187, 0.00024663582229086857, 0.00025030429712627944, 0.00025411880278781057, 0.00025717183396409938, 0.00025964344384826207, 0.00026141529298538409, 0.00026282191529510408, 0.0002636595775705841, 0.00026461550280546653, 0.00026508870362654702, 0.00026554455180956304, 0.00026571836310970286, 0.00026576233541043929, 0.00026553395915892756, 0.00026530955873982413, 0.00026477798210788439, 0.00026403947472440295, 0.00026327155503737997, 0.00026242904328280643, 0.00026160824701593313, 0.0002606638210319209, 0.00025909907610304828, 0.00025683514136330845, 0.00025396318456900446, 0.00025224534772631688, 0.00025103974080080828, 0.00025024967662178716, 0.00024937561213866954, 0.0002494682414435078, 0.00024877016196887895, 8.9999999999999998e+90, 0.00010037659212991865, 9.9455383922044522e-05, 0.00011392405635250014, 0.00011712085317809109, 0.000122997687456547, 0.00012955950584123328, 0.00014327174707838981, 0.00015606217421101668, 0.0001691010685085385, 0.00018176740237849903, 0.00019202640205704085, 0.00020194539145240679, 0.00021231738630146183, 0.00021998007363782947, 0.00022600003295034972, 0.00023120265754480006, 0.0002363820771728465, 0.00024143252532884745, 0.00024533168943101298, 0.00024852060366723112, 0.00025151881045854598, 0.00025385972625508542, 0.00025631396461438846, 0.00025817041258810496, 0.00025981278001192213, 0.00026123186984708342, 0.00026223826932630711, 0.00026333628652539063, 0.00026397861400809187, 0.00026427232753497356, 0.00026412404875212372, 0.00026354516822195634, 0.00026247570856946777, 0.0002611429668544149, 0.00025959831457830193, 0.00025783794435010963, 0.00025557532827725533, 0.00025323971614703289, 0.00025101991943097336, 0.00025045022941809963, 0.00024947270457027407, 0.00024906238780945819, 0.0002487698231196571, 0.00024811322180744448, 8.9999999999999998e+90, 9.4652926064390619e-05, 9.2521810103464566e-05, 9.3461743073378292e-05, 8.7475061885582852e-05, 8.5730298710466214e-05, 8.8638019472017708e-05, 9.4605080621233098e-05, 0.0001064430995782449, 0.00011981177188349687, 0.0001325182341967883, 0.0001438346537148193, 0.0001535609727792369, 0.00016269259425088741, 0.00017101247003210439, 0.00017717084592098171, 0.000182310629845928, 0.00018767021550516964, 0.00019335198045664559, 0.00019807144154310034, 0.00020226489516162119, 0.00020728799455192398, 0.00021174058160836577, 0.00021778691175896944, 0.00022292880764021223, 0.00022779321984365116, 0.00023316388192662024, 0.00023786005045654189, 0.00024469584663528381, 8.9999999999999998e+90, 8.9999999999999998e+90, 0.00025787041927013326, 0.00026106121545500127, 0.00026298262660743579, 0.00026483496415559117, 0.00026385496579044767, 0.00026294995935852405, 0.00025962622053184669, 0.00026351270897946328, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 4.9733363688679507e-05, 4.5854879643095247e-05, 4.1130583432931125e-05, 3.3376229909607052e-05, 3.0695008812041967e-05, 2.9850247558420771e-05, 3.0073625986196586e-05, 3.410156819612446e-05, 4.3523028427044589e-05, 5.5821119715890257e-05, 6.8983805164759559e-05, 8.1276462591778074e-05, 9.3207793432047891e-05, 0.00010420177328835684, 0.00011322863919631486, 0.00012202789742119069, 0.00013259470412752125, 0.00014167410503317709, 0.00014908541316241558, 0.00015497361344847529, 0.00015838378678082507, 0.00016116251802742018, 0.00016262416179513059, 0.00016438573036468024, 0.00016587883459639709, 0.00016907337512913823, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 0.00021747032935962187, 0.00022709354925012115, 0.00023416961367320063, 0.00023975488555320385, 0.00024274335101884199, 0.00024457143479393888, 0.00024476556074827434, 0.00024554549343035512, 0.00024727103359477358, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 1.3949751603427108e-05, 1.3109872570538914e-05, 1.0583037986029512e-05, 1.0763776311901525e-05, 1.0468427609543291e-05, 1.0840941369741984e-05, 1.1079445686929199e-05, 1.2240947588812379e-05, 1.4587649791160956e-05, 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0.0042704359892561166, 0.0042504803083884017, 0.0042539414510523984, 0.0042521422752734026, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 0.0027709380436479998, 0.0034233785724586668, 0.0033516624651946663, 0.0042568698423466663, 0.0043959472028159991, 0.0044625208760319997, 0.004163703762431999, 0.0029745043067733331, 0.0024534506514773328, 0.0024749932805973335, 0.0024585930855253327, 0.0024408956998826664, 0.0023728395231573333, 0.002443397424554667, 0.0024660519313066667, 0.0025153451729919988, 0.0025020026414079989, 0.0025556507371520005, 0.0026370494454613334, 0.0027450405604693331, 0.0028730918010879997, 0.002979600412586666, 0.003127943419989333, 0.0032885170813439996, 0.0034492297274026653, 0.0035997964900693321, 0.0037835342687573322, 0.0041308107158186677, 0.0041600438318933342, 0.0041711626082133321, 0.004193678130261334, 0.0042307870462293335, 0.0042651162681173341, 0.0042712779233279995, 0.0042891142936746663, 0.0043009279935146659, 0.0043644903314773329, 0.0043699107349333332, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90 }; static UNUSED double ndepth_ref[4095] = { 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 43, 38, 37, 40, 41, 41, 41, 40, 43, 43, 43, 44, 43, 44, 41, 41, 39, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 30, 32, 28, 12, 6, 7, 10, 32, 35, 35, 35, 35, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 40, 42, 43, 38, 38, 41, 42, 42, 42, 43, 42, 42, 43, 42, 43, 44, 41, 39, 37, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 4, 32, 31, 8.9999999999999998e+90, 4, 6, 14, 28, 32, 34, 34, 35, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 41, 43, 43, 41, 38, 40, 42, 42, 42, 41, 41, 40, 42, 42, 42, 40, 39, 35, 7, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 4, 32, 32, 24, 8.9999999999999998e+90, 5, 15, 15, 30, 33, 34, 33, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 42, 43, 43, 41, 40, 41, 43, 42, 41, 40, 40, 37, 37, 37, 38, 37, 27, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 20, 32, 32, 6, 8.9999999999999998e+90, 4, 14, 11, 21, 33, 31, 30, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 41, 43, 43, 42, 41, 41, 43, 41, 40, 34, 27, 11, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 27, 36, 36, 28, 6, 8.9999999999999998e+90, 45, 45, 45, 13, 31, 28, 20, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 41, 43, 42, 40, 41, 41, 41, 41, 34, 8, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 27, 36, 36, 24, 8.9999999999999998e+90, 8.9999999999999998e+90, 45, 45, 45, 45, 15, 16, 13, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 41, 42, 42, 42, 43, 43, 42, 42, 39, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 28, 36, 33, 21, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 45, 45, 45, 15, 16, 12, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 41, 43, 43, 43, 44, 44, 43, 39, 39, 31, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 32, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 45, 45, 8.9999999999999998e+90, 15, 16, 13, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 41, 42, 43, 43, 43, 43, 43, 40, 39, 35, 27, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 22, 22, 32, 31, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 45, 45, 8.9999999999999998e+90, 15, 15, 14, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 33, 41, 42, 42, 43, 41, 40, 41, 44, 43, 41, 40, 34, 29, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 19, 28, 25, 22, 29, 21, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 13, 14, 14, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 34, 40, 42, 42, 39, 39, 38, 41, 42, 42, 41, 40, 36, 32, 33, 34, 34, 33, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 27, 28, 28, 6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 14, 14, 14, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 17, 39, 42, 42, 40, 37, 36, 38, 40, 40, 39, 38, 34, 33, 36, 37, 39, 39, 37, 8.9999999999999998e+90, 28, 26, 8, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 13, 14, 14, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 42, 42, 41, 38, 36, 38, 38, 38, 40, 41, 39, 38, 35, 40, 41, 41, 41, 36, 29, 31, 8.9999999999999998e+90, 8.9999999999999998e+90, 5, 6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 5, 11, 14, 16, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 42, 42, 41, 39, 36, 39, 38, 42, 42, 42, 42, 40, 40, 40, 42, 41, 41, 41, 41, 35, 31, 8.9999999999999998e+90, 7, 6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 5, 9, 13, 14, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 41, 41, 39, 39, 41, 41, 43, 42, 42, 41, 40, 40, 39, 37, 40, 41, 42, 41, 39, 37, 22, 31, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 14, 14, 14, 35, 39, 39, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 38, 41, 41, 40, 39, 41, 42, 43, 42, 42, 42, 41, 39, 37, 37, 39, 39, 40, 39, 39, 39, 37, 35, 34, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 13, 16, 14, 35, 39, 39, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 37, 40, 41, 39, 39, 41, 41, 42, 41, 41, 42, 38, 37, 37, 37, 37, 39, 39, 39, 39, 38, 36, 36, 34, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 10, 13, 16, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 13, 36, 39, 39, 39, 37, 38, 39, 39, 40, 40, 39, 38, 38, 37, 42, 37, 37, 37, 40, 39, 38, 36, 33, 12, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 13, 17, 34, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 20, 35, 38, 38, 37, 31, 37, 38, 39, 40, 40, 37, 40, 41, 43, 42, 41, 39, 37, 38, 39, 38, 35, 8, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 2, 12, 17, 34, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 21, 35, 37, 34, 34, 34, 35, 36, 37, 37, 39, 39, 40, 41, 42, 42, 42, 41, 39, 35, 32, 27, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 7, 16, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 16, 35, 36, 39, 39, 37, 35, 34, 35, 37, 39, 39, 42, 43, 41, 41, 42, 41, 39, 38, 35, 35, 21, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 6, 10, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 37, 39, 39, 38, 36, 34, 36, 36, 39, 40, 41, 43, 43, 43, 41, 41, 39, 37, 36, 34, 33, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 4, 15, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 38, 39, 39, 38, 36, 35, 36, 37, 38, 41, 41, 42, 43, 43, 43, 40, 39, 37, 36, 34, 32, 25, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 4, 15, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 38, 39, 39, 37, 35, 35, 37, 39, 40, 42, 42, 43, 44, 44, 42, 40, 40, 39, 35, 34, 31, 23, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 12, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 33, 38, 39, 38, 36, 34, 37, 39, 39, 39, 43, 45, 44, 45, 43, 42, 42, 42, 33, 34, 31, 20, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 29, 39, 39, 37, 35, 36, 38, 39, 45, 39, 44, 45, 45, 45, 43, 45, 43, 17, 12, 7, 6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 12, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 35, 39, 39, 37, 35, 36, 39, 44, 45, 42, 43, 45, 45, 45, 45, 45, 15, 7, 7, 7, 4, 3, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 26, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 34, 38, 39, 38, 35, 37, 39, 43, 43, 44, 44, 43, 45, 45, 45, 33, 6, 8, 27, 29, 28, 24, 6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 30, 35, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 34, 39, 39, 39, 36, 38, 39, 42, 42, 44, 44, 41, 43, 43, 45, 6, 5, 7, 32, 34, 34, 34, 13, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 33, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 33, 39, 39, 39, 36, 38, 40, 42, 42, 39, 3, 25, 44, 44, 45, 26, 23, 19, 32, 34, 34, 34, 32, 2, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 34, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 36, 39, 40, 39, 39, 39, 41, 44, 42, 8.9999999999999998e+90, 8.9999999999999998e+90, 4, 44, 44, 43, 37, 29, 42, 40, 40, 34, 34, 39, 32, 5, 5, 6, 3, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 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41, 36, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 21, 38, 38, 41, 41, 32, 29, 29, 34, 34, 33, 35, 32, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 41, 36, 37, 39, 40, 41, 40, 40, 43, 43, 42, 43, 43, 43, 41, 41, 35, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 28, 28, 36, 40, 9, 8, 21, 34, 35, 35, 35, 35, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 43, 38, 37, 40, 41, 41, 41, 40, 43, 43, 43, 44, 43, 44, 41, 41, 39, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 30, 32, 28, 12, 6, 7, 10, 32, 35, 35, 35, 35, 36, 38, 38 }; gsw-3.6.21/src/c_gsw/gsw_saar.c0000644000175000017500000002220115147371315016434 0ustar alastairalastair/* ** $Id: gsw_saar.c,v b04abca68ac0 2015/09/13 17:47:28 fdelahoyde $ ** $Version: 3.05.0-2 $ ** ** GSW TEOS-10 V3.05 */ #include "gswteos-10.h" #include "gsw_internal_const.h" #include "gsw_saar_data.h" #ifdef __cplusplus #define ISNAN(x) std::isnan(x) #else #define ISNAN(x) isnan(x) #endif static double gsw_sum(double *x, int n); static double gsw_sum(double *x, int n) { int i; double val = 0; for (i = 0; i < n; i++) val += x[i]; return (val); } #define sum(x) gsw_sum(x, sizeof(x) / sizeof(double)) /* !========================================================================== function gsw_saar(p,long,lat) !========================================================================== ! Calculates the Absolute Salinity Anomaly Ratio, SAAR at a geographic point. ! ! p : sea pressure [dbar] ! long : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_saar : Absolute Salinity Anomaly Ratio [unitless] */ double gsw_saar(double p, double lon, double lat) { GSW_SAAR_DATA; int nx = gsw_nx, ny = gsw_ny, nz = gsw_nz; int indx0, indy0, indz0, k, ndepth_index; double saar[4], saar_old[4]; double sa_upper, sa_lower, dlong, dlat; double r1, s1, t1, ndepth_max, return_value; return_value = GSW_INVALID_VALUE; if (ISNAN(lat) || ISNAN(lon) || ISNAN(p)) return (return_value); if (lat < -86.0 || lat > 90.0) return (return_value); lon = fmod(lon, 360.0); if (lon < 0.0) lon += 360.0; dlong = longs_ref[1] - longs_ref[0]; dlat = lats_ref[1] - lats_ref[0]; indx0 = floor(0 + (nx - 1) * (lon - longs_ref[0]) / (longs_ref[nx - 1] - longs_ref[0])); if (indx0 == nx - 1) indx0 = nx - 2; indy0 = floor(0 + (ny - 1) * (lat - lats_ref[0]) / (lats_ref[ny - 1] - lats_ref[0])); if (indy0 == ny - 1) indy0 = ny - 2; /* ! Look for the maximum valid "ndepth_ref" value around our point. ! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes ! Matlab origins), but we have replaced the NaNs with a value of "9e90", ! hence we need an additional upper-limit check in the code below so they ! will not be recognised as valid values. */ ndepth_max = -1.0; for (k = 0; k < 4; k++) { ndepth_index = indy0 + delj[k] + (indx0 + deli[k]) * ny; if (ndepth_ref[ndepth_index] > 0.0 && ndepth_ref[ndepth_index] < 1e90) ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]); } /* ! If we are a long way from the ocean then there will be no valid "ndepth_ref" ! values near the point (ie. surrounded by NaNs) - so just return SAAR = 0.0 */ if (ndepth_max == -1.0) return (0.0); if (p > p_ref[(int)(ndepth_max)-1]) p = p_ref[(int)(ndepth_max)-1]; indz0 = gsw_util_indx(p_ref, nz, p); r1 = (lon - longs_ref[indx0]) / (longs_ref[indx0 + 1] - longs_ref[indx0]); s1 = (lat - lats_ref[indy0]) / (lats_ref[indy0 + 1] - lats_ref[indy0]); t1 = (p - p_ref[indz0]) / (p_ref[indz0 + 1] - p_ref[indz0]); for (k = 0; k < 4; k++) saar[k] = saar_ref[indz0 + nz * (indy0 + delj[k] + (indx0 + deli[k]) * ny)]; if (longs_pan[0] <= lon && lon <= longs_pan[npan - 1] - 0.001 && lats_pan[npan - 1] <= lat && lat <= lats_pan[0]) { memmove(saar_old, saar, 4 * sizeof(double)); gsw_add_barrier(saar_old, lon, lat, longs_ref[indx0], lats_ref[indy0], dlong, dlat, saar); } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) { memmove(saar_old, saar, 4 * sizeof(double)); gsw_add_mean(saar_old, saar); } sa_upper = (1.0 - s1) * (saar[0] + r1 * (saar[1] - saar[0])) + s1 * (saar[3] + r1 * (saar[2] - saar[3])); for (k = 0; k < 4; k++) saar[k] = saar_ref[indz0 + 1 + nz * (indy0 + delj[k] + (indx0 + deli[k]) * ny)]; if (longs_pan[0] <= lon && lon <= longs_pan[npan - 1] - 0.001 && lats_pan[npan - 1] <= lat && lat <= lats_pan[0]) { memmove(saar_old, saar, 4 * sizeof(double)); gsw_add_barrier(saar_old, lon, lat, longs_ref[indx0], lats_ref[indy0], dlong, dlat, saar); } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) { memmove(saar_old, saar, 4 * sizeof(double)); gsw_add_mean(saar_old, saar); } sa_lower = (1.0 - s1) * (saar[0] + r1 * (saar[1] - saar[0])) + s1 * (saar[3] + r1 * (saar[2] - saar[3])); if (fabs(sa_lower) >= GSW_ERROR_LIMIT) sa_lower = sa_upper; return_value = sa_upper + t1 * (sa_lower - sa_upper); if (fabs(return_value) >= GSW_ERROR_LIMIT) return_value = GSW_INVALID_VALUE; return (return_value); } /* !========================================================================== function gsw_deltasa_atlas(p,lon,lat) !========================================================================== ! Calculates the Absolute Salinity Anomaly atlas value, delta_SA_atlas. ! ! p : sea pressure [dbar] ! lon : longiture [deg E] ! lat : latitude [deg N] ! ! deltasa_atlas : Absolute Salinity Anomaly atlas value [g/kg] */ double gsw_deltasa_atlas(double p, double lon, double lat) { GSW_SAAR_DATA; int nx = gsw_nx, ny = gsw_ny, nz = gsw_nz; int indx0, indy0, indz0, k, ndepth_index; double dsar[4], dsar_old[4]; double dlong, dlat; double return_value, sa_upper, sa_lower; double r1, s1, t1, ndepth_max; return_value = GSW_INVALID_VALUE; if (ISNAN(lat) || ISNAN(lon) || ISNAN(p)) return (return_value); if (lat < -86.0 || lat > 90.0) return (return_value); lon = fmod(lon, 360.0); if (lon < 0.0) lon += 360.0; dlong = longs_ref[1] - longs_ref[0]; dlat = lats_ref[1] - lats_ref[0]; indx0 = floor(0 + (nx - 1) * (lon - longs_ref[0]) / (longs_ref[nx - 1] - longs_ref[0])); if (indx0 == nx - 1) indx0 = nx - 2; indy0 = floor(0 + (ny - 1) * (lat - lats_ref[0]) / (lats_ref[ny - 1] - lats_ref[0])); if (indy0 == ny - 1) indy0 = ny - 2; /* ! Look for the maximum valid "ndepth_ref" value around our point. ! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes ! Matlab origins), but we have replaced the NaNs with a value of "9e90", ! hence we need an additional upper-limit check in the code below so they ! will not be recognised as valid values. */ ndepth_max = -1; for (k = 0; k < 4; k++) { ndepth_index = indy0 + delj[k] + (indx0 + deli[k]) * ny; if (ndepth_ref[ndepth_index] > 0.0 && ndepth_ref[ndepth_index] < 1e90) ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]); } /* ! If we are a long way from the ocean then there will be no valid "ndepth_ref" ! values near the point (ie. surrounded by NaNs) - so deltasa_atlas = 0.0 */ if (ndepth_max == -1.0) return (0.0); if (p > p_ref[(int)(ndepth_max)-1]) p = p_ref[(int)(ndepth_max)-1]; indz0 = gsw_util_indx(p_ref, nz, p); r1 = (lon - longs_ref[indx0]) / (longs_ref[indx0 + 1] - longs_ref[indx0]); s1 = (lat - lats_ref[indy0]) / (lats_ref[indy0 + 1] - lats_ref[indy0]); t1 = (p - p_ref[indz0]) / (p_ref[indz0 + 1] - p_ref[indz0]); for (k = 0; k < 4; k++) dsar[k] = delta_sa_ref[indz0 + nz * (indy0 + delj[k] + (indx0 + deli[k]) * ny)]; if (longs_pan[0] <= lon && lon <= longs_pan[npan - 1] - 0.001 && lats_pan[npan - 1] <= lat && lat <= lats_pan[0]) { memmove(dsar_old, dsar, 4 * sizeof(double)); gsw_add_barrier(dsar_old, lon, lat, longs_ref[indx0], lats_ref[indy0], dlong, dlat, dsar); } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) { memmove(dsar_old, dsar, 4 * sizeof(double)); gsw_add_mean(dsar_old, dsar); } sa_upper = (1.0 - s1) * (dsar[0] + r1 * (dsar[1] - dsar[0])) + s1 * (dsar[3] + r1 * (dsar[2] - dsar[3])); for (k = 0; k < 4; k++) dsar[k] = delta_sa_ref[indz0 + 1 + nz * (indy0 + delj[k] + (indx0 + deli[k]) * ny)]; if (longs_pan[0] <= lon && lon <= longs_pan[npan - 1] && lats_pan[npan - 1] <= lat && lat <= lats_pan[0]) { memmove(dsar_old, dsar, 4 * sizeof(double)); gsw_add_barrier(dsar_old, lon, lat, longs_ref[indx0], lats_ref[indy0], dlong, dlat, dsar); } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) { memmove(dsar_old, dsar, 4 * sizeof(double)); gsw_add_mean(dsar_old, dsar); } sa_lower = (1.0 - s1) * (dsar[0] + r1 * (dsar[1] - dsar[0])) + s1 * (dsar[3] + r1 * (dsar[2] - dsar[3])); if (fabs(sa_lower) >= GSW_ERROR_LIMIT) sa_lower = sa_upper; return_value = sa_upper + t1 * (sa_lower - sa_upper); if (fabs(return_value) >= GSW_ERROR_LIMIT) return (GSW_INVALID_VALUE); return (return_value); } gsw-3.6.21/src/c_gsw/gsw_oceanographic_toolbox.c0000644000175000017500000175421415147371315022077 0ustar alastairalastair/* ** $Id: gsw_oceanographic_toolbox-head,v c61271a7810d 2016/08/19 20:04:03 fdelahoyde $ ** Version: 3.05.0-3 ** ** This is a translation of the original f90 source code into C ** by the Shipboard Technical Support Computing Resources group ** at Scripps Institution of Oceanography -- sts-cr@sio.ucsd.edu. ** The original notices follow. ** ========================================================================== Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10 (Fortran) ========================================================================== This is a subset of functions contained in the Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10. Version 1.0 written by David Jackett Modified by Paul Barker (version 3.02) Modified by Glenn Hyland (version 3.04+) For help with this Oceanographic Toolbox email: help@teos-10.org This software is available from http://www.teos-10.org ========================================================================== gsw_data_v3_0.nc NetCDF file that contains the global data set of Absolute Salinity Anomaly Ratio, the global data set of Absolute Salinity Anomaly atlas, and check values and computation accuracy values for use in gsw_check_function. The data set gsw_data_v3_0.nc must not be tampered with. gsw_check_function.f90 Contains the check functions. We suggest that after downloading, unzipping and installing the toolbox the user runs this program to ensure that the toolbox is installed correctly and there are no conflicts. This toolbox has been tested to compile and run with gfortran. cd test make ./gsw_check Note that gfortran is the name of the GNU Fortran project, developing a free Fortran 95/2003/2008 compiler for GCC, the GNU Compiler Collection. It is available from http://gcc.gnu.org/fortran/ ========================================================================== */ #include "gswteos-10.h" #ifdef __cplusplus # define DCOMPLEX std::complex #else # define DCOMPLEX double complex # define real(x) creal(x) # define log(x) clog(x) #endif #include "gsw_internal_const.h" /* !========================================================================== subroutine gsw_add_barrier(input_data,lon,lat,long_grid,lat_grid,dlong_grid,dlat_grid,output_data) !========================================================================== ! Adds a barrier through Central America (Panama) and then averages ! over the appropriate side of the barrier ! ! data_in : data [unitless] ! lon : Longitudes of data degrees east [0 ... +360] ! lat : Latitudes of data degrees north [-90 ... +90] ! longs_grid : Longitudes of regular grid degrees east [0 ... +360] ! lats_grid : Latitudes of regular grid degrees north [-90 ... +90] ! dlongs_grid : Longitude difference of regular grid degrees [deg longitude] ! dlats_grid : Latitude difference of regular grid degrees [deg latitude] ! ! output_data : average of data depending on which side of the ! Panama canal it is on [unitless] */ void gsw_add_barrier(double *input_data, double lon, double lat, double long_grid, double lat_grid, double dlong_grid, double dlat_grid, double *output_data) { GSW_SAAR_DATA; int above_line[4]; int k, nmean, above_line0, kk; double r, lats_line, data_mean; k = gsw_util_indx(longs_pan,npan,lon); /* the lon/lat point */ r = (lon-longs_pan[k])/(longs_pan[k+1]-longs_pan[k]); lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]); above_line0 = (lats_line <= lat); k = gsw_util_indx(longs_pan,npan,long_grid); /*the 1 & 4 lon/lat points*/ r = (long_grid-longs_pan[k])/ (longs_pan[k+1]-longs_pan[k]); lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]); above_line[0] = (lats_line <= lat_grid); above_line[3] = (lats_line <= lat_grid+dlat_grid); k = gsw_util_indx(longs_pan,6,long_grid+dlong_grid); /*the 2 & 3 lon/lat points */ r = (long_grid+dlong_grid-longs_pan[k])/ (longs_pan[k+1]-longs_pan[k]); lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]); above_line[1] = (lats_line <= lat_grid); above_line[2] = (lats_line <= lat_grid+dlat_grid); nmean = 0; data_mean = 0.0; for (kk=0; kk<4; kk++) { if ((fabs(input_data[kk]) <= 100.0) && above_line0 == above_line[kk]) { nmean = nmean+1; data_mean = data_mean+input_data[kk]; } } if (nmean == 0) data_mean = 0.0; /*errorreturn*/ else data_mean = data_mean/nmean; for (kk=0; kk<4; kk++) { if ((fabs(input_data[kk]) >= 1.0e10) || above_line0 != above_line[kk]) output_data[kk] = data_mean; else output_data[kk] = input_data[kk]; } return; } /* !========================================================================== subroutine gsw_add_mean(data_in,data_out) !========================================================================== ! Replaces NaN's with non-nan mean of the 4 adjacent neighbours ! ! data_in : data set of the 4 adjacent neighbours ! ! data_out : non-nan mean of the 4 adjacent neighbours [unitless] */ void gsw_add_mean(double *data_in, double *data_out) { int k, nmean; double data_mean; nmean = 0; data_mean = 0.0; for (k=0; k<4; k++) { if (fabs(data_in[k]) <= 100.0) { nmean++; data_mean = data_mean+data_in[k]; } } if (nmean == 0.0) data_mean = 0.0; /*errorreturn*/ else data_mean = data_mean/nmean; for (k=0; k<4; k++) { if (fabs(data_in[k]) >= 100.0) data_out[k] = data_mean; else data_out[k] = data_in[k]; } return; } /* !========================================================================== function gsw_infunnel(sa,ct,p) !========================================================================== ! "oceanographic funnel" check for the 75-term equation ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_infunnel : 0, if SA, CT and p are outside the "funnel" ! 1, if SA, CT and p are inside the "funnel" ! ! Note. The term "funnel" (McDougall et al., 2003) describes the range of ! SA, CT and p over which the error in the fit of the computationally ! efficient 75-term expression for specific volume in terms of SA, CT ! and p was calculated (Roquet et al., 2015). */ int gsw_infunnel(double sa, double ct, double p) { return !(p > 8000 || sa < 0 || sa > 42 || (p < 500 && ct < gsw_ct_freezing(sa, p, 0)) || (p >= 500 && p < 6500 && sa < p * 5e-3 - 2.5) || (p >= 500 && p < 6500 && ct > (31.66666666666667 - p * 3.333333333333334e-3)) || (p >= 500 && ct < gsw_ct_freezing(sa, 500, 0)) || (p >= 6500 && sa < 30) || (p >= 6500 && ct > 10.0) ); } /* !========================================================================== function gsw_adiabatic_lapse_rate_from_ct(sa,ct,p) !========================================================================== ! Calculates the adiabatic lapse rate from Conservative Temperature ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_adiabatic_lapse_rate_from_ct : adiabatic lapse rate [K/Pa] */ double gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p) { int n0=0, n1=1, n2=2; double pt0, pr0=0.0, t; pt0 = gsw_pt_from_ct(sa,ct); t = gsw_pt_from_t(sa,pt0,pr0,p); return (-gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n2,n0,sa,t,p)); } /* !========================================================================== elemental function gsw_adiabatic_lapse_rate_ice (t, p) !========================================================================== ! ! Calculates the adiabatic lapse rate of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! Note. The output is in unit of degrees Celsius per Pa, ! (or equivalently K/Pa) not in units of K/dbar. !-------------------------------------------------------------------------- */ double gsw_adiabatic_lapse_rate_ice(double t, double p) { return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(2,0,t,p)); } /* !========================================================================== function gsw_alpha(sa,ct,p) !========================================================================== ! Calculates the thermal expansion coefficient of seawater with respect to ! Conservative Temperature using the computationally-efficient 48-term ! expression for density in terms of SA, CT and p (IOC et al., 2010) ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_alpha : thermal expansion coefficient of seawater (48 term equation) */ double gsw_alpha(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double xs, ys, z, v_ct_part; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))); return (0.025*v_ct_part/gsw_specvol(sa,ct,p)); } /* !========================================================================== function gsw_alpha_on_beta(sa,ct,p) !========================================================================== ! Calculates alpha divided by beta, where alpha is the thermal expansion ! coefficient and beta is the saline contraction coefficient of seawater ! from Absolute Salinity and Conservative Temperature. This function uses ! the computationally-efficient expression for specific volume in terms of ! SA, CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! ! alpha_on_beta ! : thermal expansion coefficient with respect to [kg g^-1 K^-1] ! Conservative Temperature divided by the saline ! contraction coefficient at constant Conservative ! Temperature */ double gsw_alpha_on_beta(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double xs, ys, z, v_ct_part, v_sa_part; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))); v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); return (-(v_ct_part*xs)/(20.0*gsw_sfac*v_sa_part)); } /* !========================================================================== function gsw_alpha_wrt_t_exact(sa,t,p) !========================================================================== ! Calculates thermal expansion coefficient of seawater with respect to ! in-situ temperature ! ! sa : Absolute Salinity [g/kg] ! t : insitu temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_alpha_wrt_t_exact : thermal expansion coefficient [1/K] ! wrt (in-situ) temperature */ double gsw_alpha_wrt_t_exact(double sa, double t, double p) { int n0=0, n1=1; return (gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p)); } /* !========================================================================== elemental function gsw_alpha_wrt_t_ice (t, p) !========================================================================== ! ! Calculates the thermal expansion coefficient of ice with respect to ! in-situ temperature. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! alpha_wrt_t_ice = thermal expansion coefficient of ice with respect ! to in-situ temperature [ 1/K ] !-------------------------------------------------------------------------- */ double gsw_alpha_wrt_t_ice(double t, double p) { return (gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== function gsw_beta(sa,ct,p) !========================================================================== ! Calculates the saline (i.e. haline) contraction coefficient of seawater ! at constant Conservative Temperature using the computationally-efficient ! expression for specific volume in terms of SA, CT and p ! (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! beta : saline contraction coefficient of seawater [kg/g] ! at constant Conservative Temperature */ double gsw_beta(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double xs, ys, z, v_sa_part; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); return (-v_sa_part*0.5*gsw_sfac/(gsw_specvol(sa,ct,p)*xs)); } /* !========================================================================== function gsw_beta_const_t_exact(sa,t,p) !========================================================================== ! Calculates saline (haline) contraction coefficient of seawater at ! constant in-situ temperature. ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! beta_const_t_exact : haline contraction coefficient [kg/g] */ double gsw_beta_const_t_exact(double sa, double t, double p) { int n0=0, n1=1; return (-gsw_gibbs(n1,n0,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p)); } /* !========================================================================== function gsw_c_from_sp(sp,t,p) !========================================================================== ! Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range ! 2 < SP < 42. If the input Practical Salinity is less than 2 then a ! modified form of the Hill et al. (1986) formula is used for Practical ! Salinity. The modification of the Hill et al. (1986) expression is to ! ensure that it is exactly consistent with PSS-78 at SP = 2. ! ! The conductivity ratio returned by this function is consistent with the ! input value of Practical Salinity, SP, to 2x10^-14 psu over the full ! range of input parameters (from pure fresh water up to SP = 42 psu). ! This error of 2x10^-14 psu is machine precision at typical seawater ! salinities. This accuracy is achieved by having four different ! polynomials for the starting value of Rtx (the square root of Rt) in ! four different ranges of SP, and by using one and a half iterations of ! a computationally efficient modified Newton-Raphson technique (McDougall ! and Wotherspoon, 2012) to find the root of the equation. ! ! Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical ! Salinity in terms of the conductivity ratio, R, without actually ! specifying the value of C(35,15,0) (which we currently take to be ! 42.9140 mS/cm). ! ! sp : Practical Salinity [unitless] ! t : in-situ temperature [ITS-90] [deg C] ! p : sea pressure [dbar] ! ! c : conductivity [ mS/cm ] */ double gsw_c_from_sp(double sp, double t, double p) { GSW_TEOS10_CONSTANTS; GSW_SP_COEFFICIENTS; double p0 = 4.577801212923119e-3, p1 = 1.924049429136640e-1, p2 = 2.183871685127932e-5, p3 = -7.292156330457999e-3, p4 = 1.568129536470258e-4, p5 = -1.478995271680869e-6, p6 = 9.086442524716395e-4, p7 = -1.949560839540487e-5, p8 = -3.223058111118377e-6, p9 = 1.175871639741131e-7, p10 = -7.522895856600089e-5, p11 = -2.254458513439107e-6, p12 = 6.179992190192848e-7, p13 = 1.005054226996868e-8, p14 = -1.923745566122602e-9, p15 = 2.259550611212616e-6, p16 = 1.631749165091437e-7, p17 = -5.931857989915256e-9, p18 = -4.693392029005252e-9, p19 = 2.571854839274148e-10, p20 = 4.198786822861038e-12, q0 = 5.540896868127855e-5, q1 = 2.015419291097848e-1, q2 = -1.445310045430192e-5, q3 = -1.567047628411722e-2, q4 = 2.464756294660119e-4, q5 = -2.575458304732166e-7, q6 = 5.071449842454419e-3, q7 = -9.081985795339206e-5, q8 = -3.635420818812898e-6, q9 = 2.249490528450555e-8, q10 = -1.143810377431888e-3, q11 = 2.066112484281530e-5, q12 = 7.482907137737503e-7, q13 = 4.019321577844724e-8, q14 = -5.755568141370501e-10, q15 = 1.120748754429459e-4, q16 = -2.420274029674485e-6, q17 = -4.774829347564670e-8, q18 = -4.279037686797859e-9, q19 = -2.045829202713288e-10, q20 = 5.025109163112005e-12, s0 = 3.432285006604888e-3, s1 = 1.672940491817403e-1, s2 = 2.640304401023995e-5, s3 = 1.082267090441036e-1, s4 = -6.296778883666940e-5, s5 = -4.542775152303671e-7, s6 = -1.859711038699727e-1, s7 = 7.659006320303959e-4, s8 = -4.794661268817618e-7, s9 = 8.093368602891911e-9, s10 = 1.001140606840692e-1, s11 = -1.038712945546608e-3, s12 = -6.227915160991074e-6, s13 = 2.798564479737090e-8, s14 = -1.343623657549961e-10, s15 = 1.024345179842964e-2, s16 = 4.981135430579384e-4, s17 = 4.466087528793912e-6, s18 = 1.960872795577774e-8, s19 = -2.723159418888634e-10, s20 = 1.122200786423241e-12, u0 = 5.180529787390576e-3, u1 = 1.052097167201052e-3, u2 = 3.666193708310848e-5, u3 = 7.112223828976632e0, u4 = -3.631366777096209e-4, u5 = -7.336295318742821e-7, u6 = -1.576886793288888e+2, u7 = -1.840239113483083e-3, u8 = 8.624279120240952e-6, u9 = 1.233529799729501e-8, u10 = 1.826482800939545e+3, u11 = 1.633903983457674e-1, u12 = -9.201096427222349e-5, u13 = -9.187900959754842e-8, u14 = -1.442010369809705e-10, u15 = -8.542357182595853e+3, u16 = -1.408635241899082e0, u17 = 1.660164829963661e-4, u18 = 6.797409608973845e-7, u19 = 3.345074990451475e-10, u20 = 8.285687652694768e-13; double t68, ft68, x, rtx=0.0, dsp_drtx, sqrty, part1, part2, hill_ratio, sp_est, rtx_old, rt, aa, bb, cc, dd, ee, ra,r, rt_lc, rtxm, sp_hill_raw; t68 = t*1.00024e0; ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0)); x = sqrt(sp); /* |-------------------------------------------------------------------------- ! Finding the starting value of Rtx, the square root of Rt, using four ! different polynomials of SP and t68. !-------------------------------------------------------------------------- */ if (sp >= 9.0) { rtx = p0 + x*(p1 + p4*t68 + x*(p3 + p7*t68 + x*(p6 + p11*t68 + x*(p10 + p16*t68 + x*p15)))) + t68*(p2+ t68*(p5 + x*x*(p12 + x*p17) + p8*x + t68*(p9 + x*(p13 + x*p18)+ t68*(p14 + p19*x + p20*t68)))); } else if (sp >= 0.25 && sp < 9.0) { rtx = q0 + x*(q1 + q4*t68 + x*(q3 + q7*t68 + x*(q6 + q11*t68 + x*(q10 + q16*t68 + x*q15)))) + t68*(q2+ t68*(q5 + x*x*(q12 + x*q17) + q8*x + t68*(q9 + x*(q13 + x*q18)+ t68*(q14 + q19*x + q20*t68)))); } else if (sp >= 0.003 && sp < 0.25) { rtx = s0 + x*(s1 + s4*t68 + x*(s3 + s7*t68 + x*(s6 + s11*t68 + x*(s10 + s16*t68 + x*s15)))) + t68*(s2+ t68*(s5 + x*x*(s12 + x*s17) + s8*x + t68*(s9 + x*(s13 + x*s18)+ t68*(s14 + s19*x + s20*t68)))); } else if (sp < 0.003) { rtx = u0 + x*(u1 + u4*t68 + x*(u3 + u7*t68 + x*(u6 + u11*t68 + x*(u10 + u16*t68 + x*u15)))) + t68*(u2+ t68*(u5 + x*x*(u12 + x*u17) + u8*x + t68*(u9 + x*(u13 + x*u18)+ t68*(u14 + u19*x + u20*t68)))); } /* !-------------------------------------------------------------------------- ! Finding the starting value of dSP_dRtx, the derivative of SP with respect ! to Rtx. !-------------------------------------------------------------------------- */ dsp_drtx = a1 + (2e0*a2 + (3e0*a3 + (4e0*a4 + 5e0*a5*rtx)*rtx)*rtx)*rtx + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 + 5e0*b5*rtx)*rtx)*rtx)*rtx); if (sp < 2.0) { x = 400e0*(rtx*rtx); sqrty = 10.0*rtx; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); hill_ratio = gsw_hill_ratio_at_sp2(t); dsp_drtx = dsp_drtx + a0*800e0*rtx*(1.5e0 + 2e0*x)/(part1*part1) + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/ (part2*part2); dsp_drtx = hill_ratio*dsp_drtx; } /* !-------------------------------------------------------------------------- ! One iteration through the modified Newton-Raphson method (McDougall and ! Wotherspoon, 2012) achieves an error in Practical Salinity of about ! 10^-12 for all combinations of the inputs. One and a half iterations of ! the modified Newton-Raphson method achevies a maximum error in terms of ! Practical Salinity of better than 2x10^-14 everywhere. ! ! We recommend one and a half iterations of the modified Newton-Raphson ! method. ! ! Begin the modified Newton-Raphson method. !-------------------------------------------------------------------------- */ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx); if (sp_est < 2.0) { x = 400e0*(rtx*rtx); sqrty = 10e0*rtx; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2; hill_ratio = gsw_hill_ratio_at_sp2(t); sp_est = hill_ratio*sp_hill_raw; } rtx_old = rtx; rtx = rtx_old - (sp_est - sp)/dsp_drtx; rtxm = 0.5e0*(rtx + rtx_old); /*This mean value of Rtx, Rtxm, is the value of Rtx at which the derivative dSP_dRtx is evaluated.*/ dsp_drtx= a1 + (2e0*a2 + (3e0*a3 + (4e0*a4 + 5e0*a5*rtxm)*rtxm)*rtxm)*rtxm + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 + 5e0*b5*rtxm)*rtxm)*rtxm)*rtxm); if (sp_est < 2.0) { x = 400e0*(rtxm*rtxm); sqrty = 10e0*rtxm; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); dsp_drtx = dsp_drtx + a0*800e0*rtxm*(1.5e0 + 2e0*x)/(part1*part1) + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/ (part2*part2); hill_ratio = gsw_hill_ratio_at_sp2(t); dsp_drtx = hill_ratio*dsp_drtx; } /* !-------------------------------------------------------------------------- ! The line below is where Rtx is updated at the end of the one full ! iteration of the modified Newton-Raphson technique. !-------------------------------------------------------------------------- */ rtx = rtx_old - (sp_est - sp)/dsp_drtx; /* !-------------------------------------------------------------------------- ! Now we do another half iteration of the modified Newton-Raphson ! technique, making a total of one and a half modified N-R iterations. !-------------------------------------------------------------------------- */ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx); if (sp_est < 2.0) { x = 400e0*(rtx*rtx); sqrty = 10e0*rtx; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2; hill_ratio = gsw_hill_ratio_at_sp2(t); sp_est = hill_ratio*sp_hill_raw; } rtx = rtx - (sp_est - sp)/dsp_drtx; /* !-------------------------------------------------------------------------- ! Now go from Rtx to Rt and then to the conductivity ratio R at pressure p. !-------------------------------------------------------------------------- */ rt = rtx*rtx; aa = d3 + d4*t68; bb = 1e0 + t68*(d1 + d2*t68); cc = p*(e1 + p*(e2 + e3*p)); /* rt_lc (i.e. rt_lower_case) corresponds to rt as defined in the UNESCO 44 (1983) routines. */ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68; dd = bb - aa*rt_lc*rt; ee = rt_lc*rt*aa*(bb + cc); ra = sqrt(dd*dd + 4e0*ee) - dd; r = 0.5e0*ra/aa; /* ! The dimensionless conductivity ratio, R, is the conductivity input, C, ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is ! 42.9140 mS/cm (=4.29140 S/m^). */ return (gsw_c3515*r); } /* !========================================================================== function gsw_cabbeling(sa,ct,p) !========================================================================== ! Calculates the cabbeling coefficient of seawater with respect to ! Conservative Temperature. This function uses the computationally- ! efficient expression for specific volume in terms of SA, CT and p ! (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! cabbeling : cabbeling coefficient with respect to [1/K^2] ! Conservative Temperature. */ double gsw_cabbeling(double sa, double ct, double p) { double alpha_ct, alpha_on_beta, alpha_sa, beta_sa, rho, v_sa, v_ct, v_sa_sa, v_sa_ct, v_ct_ct; gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct, NULL); gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct, NULL, NULL); rho = gsw_rho(sa,ct,p); alpha_ct = rho*(v_ct_ct - rho*v_ct*v_ct); alpha_sa = rho*(v_sa_ct - rho*v_sa*v_ct); beta_sa = -rho*(v_sa_sa - rho*v_sa*v_sa); alpha_on_beta = gsw_alpha_on_beta(sa,ct,p); return (alpha_ct + alpha_on_beta*(2.0*alpha_sa - alpha_on_beta*beta_sa)); } /* !========================================================================== elemental function gsw_chem_potential_water_ice (t, p) !========================================================================== ! ! Calculates the chemical potential of water in ice from in-situ ! temperature and pressure. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! chem_potential_water_ice = chemical potential of ice [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_chem_potential_water_ice(double t, double p) { return (gsw_gibbs_ice(0,0,t,p)); } /* !========================================================================== elemental function gsw_chem_potential_water_t_exact (sa, t, p) !========================================================================== ! ! Calculates the chemical potential of water in seawater. ! ! SA = Absolute Salinity [ g/kg ] ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! chem_potential_water_t_exact = chemical potential of water in seawater ! [ J/g ] !-------------------------------------------------------------------------- */ double gsw_chem_potential_water_t_exact(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; double g03_g, g08_g, g_sa_part, x, x2, y, z, kg2g = 1e-3; x2 = gsw_sfac*sa; x = sqrt(x2); y = t*0.025; z = p*1e-4; g03_g = 101.342743139674 + z*(100015.695367145 + z*(-2544.5765420363 + z*(284.517778446287 + z*(-33.3146754253611 + (4.20263108803084 - 0.546428511471039*z)*z)))) + y*(5.90578347909402 + z*(-270.983805184062 + z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 - 2.13290083518327*z)*z))) + y*(-12357.785933039 + z*(1455.0364540468 + z*(-756.558385769359 + z*(273.479662323528 + z*(-55.5604063817218 + 4.34420671917197*z)))) + y*(736.741204151612 + z*(-672.50778314507 + z*(499.360390819152 + z*(-239.545330654412 + (48.8012518593872 - 1.66307106208905*z)*z))) + y*(-148.185936433658 + z*(397.968445406972 + z*(-301.815380621876 + (152.196371733841 - 26.3748377232802*z)*z)) + y*(58.0259125842571 + z*(-194.618310617595 + z*(120.520654902025 + z*(-55.2723052340152 + 6.48190668077221*z))) + y*(-18.9843846514172 + y*(3.05081646487967 - 9.63108119393062*z) + z*(63.5113936641785 + z*(-22.2897317140459 + 8.17060541818112*z)))))))); g08_g = x2*(1416.27648484197 + x*(-2432.14662381794 + x*(2025.80115603697 + y*(543.835333000098 + y*(-68.5572509204491 + y*(49.3667694856254 + y*(-17.1397577419788 + 2.49697009569508*y))) - 22.6683558512829*z) + x*(-1091.66841042967 - 196.028306689776*y + x*(374.60123787784 - 48.5891069025409*x + 36.7571622995805*y) + 36.0284195611086*z) + z*(-54.7919133532887 + (-4.08193978912261 - 30.1755111971161*z)*z)) + z*(199.459603073901 + z*(-52.2940909281335 + (68.0444942726459 - 3.41251932441282*z)*z)) + y*(-493.407510141682 + z*(-175.292041186547 + (83.1923927801819 - 29.483064349429*z)*z) + y*(-43.0664675978042 + z*(383.058066002476 + z*(-54.1917262517112 + 25.6398487389914*z)) + y*(-10.0227370861875 - 460.319931801257*z + y*(0.875600661808945 + 234.565187611355*z))))) + y*(168.072408311545)); g_sa_part = 8645.36753595126 + x*(-7296.43987145382 + x*(8103.20462414788 + y*(2175.341332000392 + y*(-274.2290036817964 + y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y))) - 90.6734234051316*z) + x*(-5458.34205214835 - 980.14153344888*y + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y) + 180.142097805543*z) + z*(-219.1676534131548 + (-16.32775915649044 - 120.7020447884644*z)*z)) + z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377 - 10.23755797323846*z)*z)) + y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-129.1994027934126 + z*(1149.174198007428 + z*(-162.5751787551336 + 76.9195462169742*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835 + 703.695562834065*z))))) + y*(1187.3715515697959); return (kg2g*(g03_g + g08_g - 0.5*x2*g_sa_part)); } /* !========================================================================== elemental function gsw_cp_ice (t, p) !========================================================================== ! ! Calculates the isobaric heat capacity of seawater. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! gsw_cp_ice = heat capacity of ice [J kg^-1 K^-1] !-------------------------------------------------------------------------- */ double gsw_cp_ice(double t, double p) { GSW_TEOS10_CONSTANTS; return (-(t + gsw_t0)*gsw_gibbs_ice(2,0,t,p)); } /* !========================================================================== function gsw_cp_t_exact(sa,t,p) !========================================================================== ! Calculates isobaric heat capacity of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_cp_t_exact : heat capacity [J/(kg K)] */ double gsw_cp_t_exact(double sa, double t, double p) { int n0, n2; n0 = 0; n2 = 2; return (-(t+273.15e0)*gsw_gibbs(n0,n2,n0,sa,t,p)); } /* !========================================================================== elemental subroutine gsw_ct_first_derivatives (sa, pt, ct_sa, ct_pt) !========================================================================== ! ! Calculates the following two derivatives of Conservative Temperature ! (1) CT_SA, the derivative with respect to Absolute Salinity at ! constant potential temperature (with pr = 0 dbar), and ! 2) CT_pt, the derivative with respect to potential temperature ! (the regular potential temperature which is referenced to 0 dbar) ! at constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! pt = potential temperature (ITS-90) [ deg C ] ! (whose reference pressure is 0 dbar) ! ! CT_SA = The derivative of Conservative Temperature with respect to ! Absolute Salinity at constant potential temperature ! (the regular potential temperature which has reference ! sea pressure of 0 dbar). ! The CT_SA output has units of: [ K/(g/kg)] ! CT_pt = The derivative of Conservative Temperature with respect to ! potential temperature (the regular one with pr = 0 dbar) ! at constant SA. CT_pt is dimensionless. [ unitless ] !-------------------------------------------------------------------------- */ void gsw_ct_first_derivatives(double sa, double pt, double *ct_sa, double *ct_pt) { GSW_TEOS10_CONSTANTS; double abs_pt, g_sa_mod, g_sa_t_mod, x, y_pt; abs_pt = gsw_t0 + pt ; if (ct_pt != NULL) *ct_pt = -(abs_pt*gsw_gibbs_pt0_pt0(sa,pt))/gsw_cp0; if (ct_sa == NULL) return; x = sqrt(gsw_sfac*sa); y_pt = 0.025*pt; g_sa_t_mod = 1187.3715515697959 + x*(-1480.222530425046 + x*(2175.341332000392 + x*(-980.14153344888 + 220.542973797483*x) + y_pt*(-548.4580073635929 + y_pt*(592.4012338275047 + y_pt*(-274.2361238716608 + 49.9394019139016*y_pt)))) + y_pt*(-258.3988055868252 + y_pt*(-90.2046337756875 + y_pt*10.50720794170734))) + y_pt*(3520.125411988816 + y_pt*(-1351.605895580406 + y_pt*(731.4083582010072 + y_pt*(-216.60324087531103 + 25.56203650166196*y_pt)))); g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod; g_sa_mod = 8645.36753595126 + x*(-7296.43987145382 + x*(8103.20462414788 + y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 + y_pt*(197.4670779425016 + y_pt*(-68.5590309679152 + 9.98788038278032*y_pt)))) + x*(-5458.34205214835 - 980.14153344888*y_pt + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y_pt))) + y_pt*(-1480.222530425046 + y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625 + y_pt*(2.626801985426835 ))))) + y_pt*(1187.3715515697959 + y_pt*(1760.062705994408 + y_pt*(-450.535298526802 + y_pt*(182.8520895502518 + y_pt*(-43.3206481750622 + 4.26033941694366*y_pt))))); g_sa_mod = 0.5*gsw_sfac*g_sa_mod; *ct_sa = (g_sa_mod - abs_pt*g_sa_t_mod)/gsw_cp0; } /* !========================================================================== elemental subroutine gsw_ct_first_derivatives_wrt_t_exact (sa, t, p, & ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t) !========================================================================== ! ! Calculates the following three derivatives of Conservative Temperature. ! These derivatives are done with respect to in-situ temperature t (in the ! case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of ! CT_SA_wrt_t and CT_P_wrt_t). ! (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity ! at constant t and p, and ! (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t ! at constant SA and p. ! (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at ! constant SA and t. ! ! This function uses the full Gibbs function. Note that this function ! avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were ! evaluated in the straightforward way from the derivatives of the Gibbs ! function function. ! ! SA = Absolute Salinity [ g/kg ] ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar) ! ! CT_SA_wrt_t = The first derivative of Conservative Temperature with ! respect to Absolute Salinity at constant t and p. ! [ K/(g/kg)] i.e. [ K kg/g ] ! CT_T_wrt_t = The first derivative of Conservative Temperature with ! respect to in-situ temperature, t, at constant SA and p. ! [ unitless ] ! CT_P_wrt_t = The first derivative of Conservative Temperature with ! respect to pressure P (in Pa) at constant SA and t. ! [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_ct_first_derivatives_wrt_t_exact(double sa, double t, double p, double *ct_sa_wrt_t, double *ct_t_wrt_t, double *ct_p_wrt_t) { GSW_TEOS10_CONSTANTS; double g_sa_mod, g_sa_t_mod, pt0, x, y, y_pt, z; pt0 = gsw_pt0_from_t(sa,t,p); if (ct_sa_wrt_t != NULL) { x = sqrt(gsw_sfac*sa); y = 0.025*t; y_pt = 0.025*pt0; z = rec_db2pa*p; /* the input pressure (p) is sea pressure in units of dbar */ g_sa_t_mod = 1187.3715515697959 + z*(1458.233059470092 + z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146 + 14.09317606630898*z)))) + x*(-1480.222530425046 + x*(2175.341332000392 + x*(-980.14153344888 + 220.542973797483*x) + y*(-548.4580073635929 + y*(592.4012338275047 + y*(-274.2361238716608 + 49.9394019139016*y))) - 90.6734234051316*z) + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-258.3988055868252 + z*(2298.348396014856 + z*(-325.1503575102672 + 153.8390924339484*z)) + y*(-90.2046337756875 - 4142.8793862113125*z + y*(10.50720794170734 + 2814.78225133626*z)))) + y*(3520.125411988816 + y*(-1351.605895580406 + y*(731.4083582010072 + y*(-216.60324087531103 + 25.56203650166196*y) + z*(-2381.829935897496 + (597.809129110048 - 291.8983352012704*z)*z)) + z*(4165.4688847996085 + z*(-1229.337851789418 + (681.370187043564 - 66.7696405958478*z)*z))) + z*(-3443.057215135908 + z*(1349.638121077468 + z*(-713.258224830552 + (176.8161433232 - 31.68006188846728*z)*z)))); g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod; g_sa_mod = 8645.36753595126 + x*(-7296.43987145382 + x*(8103.20462414788 + y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 + y_pt*(197.4670779425016 + y_pt*(-68.5590309679152 + 9.98788038278032*y_pt)))) + x*(-5458.34205214835 - 980.14153344888*y_pt + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y_pt))) + y_pt*(-1480.222530425046 + y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625 + y_pt*(2.626801985426835 ))))) + y_pt*(1187.3715515697959 + y_pt*(1760.062705994408 + y_pt*(-450.535298526802 + y_pt*(182.8520895502518 + y_pt*(-43.3206481750622 + 4.26033941694366*y_pt))))); g_sa_mod = 0.5*gsw_sfac*g_sa_mod; *ct_sa_wrt_t = (g_sa_mod - (gsw_t0+pt0)*g_sa_t_mod)/gsw_cp0; } if (ct_t_wrt_t != NULL) *ct_t_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,2,0,sa,t,p)/gsw_cp0; if (ct_p_wrt_t != NULL) *ct_p_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,1,1,sa,t,p)/gsw_cp0; } /* !========================================================================== elemental function gsw_ct_freezing (sa, p, saturation_fraction) !========================================================================== ! ! Calculates the Conservative Temperature at which seawater freezes. The ! Conservative Temperature freezing point is calculated from the exact ! in-situ freezing temperature which is found by a modified Newton-Raphson ! iteration (McDougall and Wotherspoon, 2013) of the equality of the ! chemical potentials of water in seawater and in ice. ! ! An alternative GSW function, gsw_CT_freezing_poly, it is based on a ! computationally-efficient polynomial, and is accurate to within -5e-4 K ! and 6e-4 K, when compared with this function. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ] !-------------------------------------------------------------------------- */ double gsw_ct_freezing(double sa, double p, double saturation_fraction) { double t_freezing; t_freezing = gsw_t_freezing(sa,p,saturation_fraction); return (gsw_ct_from_t(sa,t_freezing,p)); } /* !========================================================================== elemental subroutine gsw_ct_freezing_first_derivatives (sa, p, & saturation_fraction, ctfreezing_sa, ctfreezing_p) !========================================================================== ! ! Calculates the first derivatives of the Conservative Temperature at ! which seawater freezes, with respect to Absolute Salinity SA and ! pressure P (in Pa). ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! CTfreezing_SA = the derivative of the Conservative Temperature at ! freezing (ITS-90) with respect to Absolute Salinity at ! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ] ! ! CTfreezing_P = the derivative of the Conservative Temperature at ! freezing (ITS-90) with respect to pressure (in Pa) at ! fixed Absolute Salinity [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_ct_freezing_first_derivatives(double sa, double p, double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p) { double tf_sa, tf_p, ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t, tf; tf = gsw_t_freezing(sa,p,saturation_fraction); if (ctfreezing_sa != NULL && ctfreezing_p != NULL) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, &tf_sa,&tf_p); gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p, &ct_sa_wrt_t,&ct_t_wrt_t,&ct_p_wrt_t); *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa; *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p; } else if (ctfreezing_sa != NULL && ctfreezing_p == NULL) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, &tf_sa, NULL); gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p, &ct_sa_wrt_t,&ct_t_wrt_t,NULL); *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa; } else if (ctfreezing_sa == NULL && ctfreezing_p != NULL) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, NULL, &tf_p); gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p, NULL,&ct_t_wrt_t,&ct_p_wrt_t); *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p; } } /* !========================================================================== elemental subroutine gsw_ct_freezing_first_derivatives_poly (sa, p, & saturation_fraction, ctfreezing_sa, ctfreezing_p) !========================================================================== ! ! Calculates the first derivatives of the Conservative Temperature at ! which seawater freezes, with respect to Absolute Salinity SA and ! pressure P (in Pa) of the comptationally efficient polynomial fit of the ! freezing temperature (McDougall et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! CTfreezing_SA = the derivative of the Conservative Temperature at ! freezing (ITS-90) with respect to Absolute Salinity at ! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ] ! ! CTfreezing_P = the derivative of the Conservative Temperature at ! freezing (ITS-90) with respect to pressure (in Pa) at ! fixed Absolute Salinity [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_ct_freezing_first_derivatives_poly(double sa, double p, double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p) { GSW_TEOS10_CONSTANTS; GSW_FREEZING_POLY_COEFFICIENTS; double p_r, sa_r, x, d = -a - a*b - 2.4*b/gsw_sso, e = 2.0*a*b/gsw_sso; sa_r = sa*1e-2; x = sqrt(sa_r); p_r = p*1e-4; if (ctfreezing_sa != NULL) *ctfreezing_sa = (c1 + x*(1.5*c2 + x*(2.0*c3 + x*(2.5*c4 + x*(3.0*c5 + 3.5*c6*x)))) + p_r*(c10 + x*(1.5*c11 + x*(2.0*c13 + x*(2.5*c16 + x*(3.0*c19 + 3.5*c22*x)))) + p_r*(c12 + x*(1.5*c14 + x*(2.0*c17 + 2.5*c20*x)) + p_r*(c15 + x*(1.5*c18 + 2.0*c21*x)))))*1e-2 - saturation_fraction*1e-3*(d - sa*e); if (ctfreezing_p != NULL) *ctfreezing_p = (c7 + sa_r*(c10 + x*(c11 + x*(c13 + x*(c16 + x*(c19 + c22*x))))) + p_r*(2.0*c8 + sa_r*(2.0*c12 + x*(2.0*c14 + x*(2.0*c17 + 2.0*c20*x))) + p_r*(3.0*c9 + sa_r*(3.0*c15 + x*(3.0*c18 + 3.0*c21*x)))))*1e-8; } /* !========================================================================== elemental function gsw_ct_freezing_poly (sa, p, saturation_fraction) !========================================================================== ! ! Calculates the Conservative Temperature at which seawater freezes. ! The error of this fit ranges between -5e-4 K and 6e-4 K when compared ! with the Conservative Temperature calculated from the exact in-situ ! freezing temperature which is found by a Newton-Raphson iteration of the ! equality of the chemical potentials of water in seawater and in ice. ! Note that the Conservative temperature freezing temperature can be found ! by this exact method using the function gsw_CT_freezing. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ] ! That is, the freezing temperature expressed in ! terms of Conservative Temperature (ITS-90). !-------------------------------------------------------------------------- */ double gsw_ct_freezing_poly(double sa, double p, double saturation_fraction) { GSW_TEOS10_CONSTANTS; GSW_FREEZING_POLY_COEFFICIENTS; double p_r, sa_r, x, return_value; sa_r = sa*1.0e-2; x = sqrt(sa_r); p_r = p*1.0e-4; return_value = c0 + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x))))) + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12 + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r) + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r))); /* Adjust for the effects of dissolved air */ return_value = return_value - saturation_fraction* (1e-3)*(2.4 - a*sa)*(1.0 + b*(1.0 - sa/gsw_sso)); return (return_value); } /* !========================================================================== elemental function gsw_ct_from_enthalpy (sa, h, p) !========================================================================== ! ! Calculates the Conservative Temperature of seawater, given the Absolute ! Salinity, specific enthalpy, h, and pressure p. ! ! SA = Absolute Salinity [ g/kg ] ! h = specific enthalpy [ J/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! ! CT = Conservative Temperature ( ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_ct_from_enthalpy(double sa, double h, double p) { GSW_TEOS10_CONSTANTS; double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40, ct_40 = 40.0; ct_freezing = gsw_ct_freezing(sa,p,0.0); h_freezing = gsw_enthalpy(sa,ct_freezing,p); if (h < (h_freezing - gsw_cp0)) { /* ! The input, seawater enthalpy h, is less than the enthalpy at the ! freezing temperature, i.e. the water is frozen. */ return (GSW_INVALID_VALUE); } h_40 = gsw_enthalpy(sa,ct_40,p); if (h > h_40) { /* ! The input seawater enthalpy is greater than the enthalpy ! when CT is 40C */ return (GSW_INVALID_VALUE); } /* first guess of ct */ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/ (h_40 - h_freezing); gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct); /* !------------------------------------------------------ ! Begin the modified Newton-Raphson iterative procedure !------------------------------------------------------ */ ct_old = ct; f = gsw_enthalpy(sa,ct_old,p) - h; ct = ct_old - f/h_ct; ct_mean = 0.5*(ct + ct_old); gsw_enthalpy_first_derivatives(sa,ct_mean,p,NULL,&h_ct); ct = ct_old - f/h_ct; ct_old = ct; f = gsw_enthalpy(sa,ct_old,p) - h; ct = ct_old - f/h_ct; /* ! After 1.5d0 iterations of this modified Newton-Raphson iteration, ! the error in CT is no larger than 4x10^-13 degrees C, which ! is machine precision for this calculation. */ return (ct); } /* !========================================================================== elemental function gsw_ct_from_enthalpy_exact (sa, h, p) !========================================================================== ! ! Calculates the Conservative Temperature of seawater, given the Absolute ! Salinity, specific enthalpy, h, and pressure p. ! ! SA = Absolute Salinity [ g/kg ] ! h = specific enthalpy [ J/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! ! CT = Conservative Temperature ( ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_ct_from_enthalpy_exact(double sa, double h, double p) { GSW_TEOS10_CONSTANTS; double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40, ct_40 = 40.0; ct_freezing = gsw_ct_freezing(sa,p,0.0); h_freezing = gsw_enthalpy_ct_exact(sa,ct_freezing,p); if (h < (h_freezing - gsw_cp0)) { /* ! The input, seawater enthalpy h, is less than the enthalpy at the ! freezing temperature, i.e. the water is frozen. */ return (GSW_INVALID_VALUE); } h_40 = gsw_enthalpy_ct_exact(sa,ct_40,p); if (h > h_40) { /* ! The input seawater enthalpy is greater than the enthalpy ! when CT is 40C */ return (GSW_INVALID_VALUE); } /* First guess of ct */ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/ (h_40 - h_freezing); gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,NULL,&h_ct); /* !------------------------------------------------------ ! Begin the modified Newton-Raphson iterative procedure !------------------------------------------------------ */ ct_old = ct; f = gsw_enthalpy_ct_exact(sa,ct_old,p) - h; ct = ct_old - f/h_ct; ct_mean = 0.5*(ct + ct_old); gsw_enthalpy_first_derivatives_ct_exact(sa,ct_mean,p,NULL,&h_ct); ct = ct_old - f/h_ct; /* ! After 1 iteration of this modified Newton-Raphson iteration, ! the error in CT is no larger than 5x10^-14 degrees C, which ! is machine precision for this calculation. */ return (ct); } /* !========================================================================= elemental function gsw_ct_from_entropy (sa, entropy) !========================================================================= ! ! Calculates Conservative Temperature with entropy as an input variable. ! ! SA = Absolute Salinity [ g/kg ] ! entropy = specific entropy [ deg C ] ! ! CT = Conservative Temperature (ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_ct_from_entropy(double sa, double entropy) { double pt; pt = gsw_pt_from_entropy(sa,entropy); return (gsw_ct_from_pt(sa,pt)); } /* !========================================================================== function gsw_ct_from_pt(sa,pt) !========================================================================== ! Calculates Conservative Temperature from potential temperature of seawater ! ! sa : Absolute Salinity [g/kg] ! pt : potential temperature with [deg C] ! reference pressure of 0 dbar ! ! gsw_ct_from_pt : Conservative Temperature [deg C] */ double gsw_ct_from_pt(double sa, double pt) { GSW_TEOS10_CONSTANTS; double x2, x, y, pot_enthalpy; x2 = gsw_sfac*sa; x = sqrt(x2); y = pt*0.025e0; /*! normalize for F03 and F08 */ pot_enthalpy = 61.01362420681071e0 + y*(168776.46138048015e0 + y*(-2735.2785605119625e0 + y*(2574.2164453821433e0 + y*(-1536.6644434977543e0 + y*(545.7340497931629e0 + (-50.91091728474331e0 - 18.30489878927802e0*y)*y))))) + x2*(268.5520265845071e0 + y*(-12019.028203559312e0 + y*(3734.858026725145e0 + y*(-2046.7671145057618e0 + y*(465.28655623826234e0 + (-0.6370820302376359e0 - 10.650848542359153e0*y)*y)))) + x*(937.2099110620707e0 + y*(588.1802812170108e0+ y*(248.39476522971285e0 + (-3.871557904936333e0- 2.6268019854268356e0*y)*y)) + x*(-1687.914374187449e0 + x*(246.9598888781377e0 + x*(123.59576582457964e0 - 48.5891069025409e0*x)) + y*(936.3206544460336e0 + y*(-942.7827304544439e0 + y*(369.4389437509002e0 + (-33.83664947895248e0 - 9.987880382780322e0*y)*y)))))); return (pot_enthalpy/gsw_cp0); } /* !========================================================================== elemental subroutine gsw_ct_from_rho (rho, sa, p, ct, ct_multiple) ! ========================================================================= ! ! Calculates the Conservative Temperature of a seawater sample, for given ! values of its density, Absolute Salinity and sea pressure (in dbar). ! ! rho = density of a seawater sample (e.g. 1026 kg/m^3) [ kg/m^3 ] ! Note. This input has not had 1000 kg/m^3 subtracted from it. ! That is, it is 'density', not 'density anomaly'. ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! CT = Conservative Temperature (ITS-90) [ deg C ] ! CT_multiple = Conservative Temperature (ITS-90) [ deg C ] ! Note that at low salinities, in brackish water, there are two possible ! Conservative Temperatures for a single density. This programme will ! output both valid solutions. To see this second solution the user ! must call the programme with two outputs (i.e. [CT,CT_multiple]), if ! there is only one possible solution and the programme has been ! called with two outputs the second variable will be set to NaN. !-------------------------------------------------------------------------- */ void gsw_ct_from_rho(double rho, double sa, double p, double *ct, double *ct_multiple) { int number_of_iterations; double a, alpha_freezing, alpha_mean, b, c, ct_a, ct_b, ct_diff, ct_freezing, ct_max_rho, ct_mean, ct_old, delta_ct, delta_v, factor, factorqa, factorqb, rho_40, rho_extreme, rho_freezing, rho_max, rho_mean, rho_old, sqrt_disc, top, v_ct, v_lab; /*alpha_limit is the positive value of the thermal expansion coefficient ! which is used at the freezing temperature to distinguish between ! salty and fresh water.*/ double alpha_limit = 1e-5; /*rec_half_rho_TT is a constant representing the reciprocal of half the ! second derivative of density with respect to temperature near the ! temperature of maximum density.*/ double rec_half_rho_tt = -110.0; rho_40 = gsw_rho(sa,40.0,p); if (rho < rho_40) { *ct = GSW_INVALID_VALUE; if (ct_multiple != NULL) *ct_multiple = *ct; return; } ct_max_rho = gsw_ct_maxdensity(sa,p); rho_max = gsw_rho(sa,ct_max_rho,p); rho_extreme = rho_max; /*Assumes that the seawater is always unsaturated with air*/ ct_freezing = gsw_ct_freezing_poly(sa,p,0.0); gsw_rho_alpha_beta(sa,ct_freezing,p,&rho_freezing,&alpha_freezing,NULL); /*reset the extreme values*/ if (ct_freezing > ct_max_rho) rho_extreme = rho_freezing; if (rho > rho_extreme) { *ct = GSW_INVALID_VALUE; if (ct_multiple != NULL) *ct_multiple = *ct; return; } if (alpha_freezing > alpha_limit) { ct_diff = 40.0 - ct_freezing; top = rho_40 - rho_freezing + rho_freezing*alpha_freezing*ct_diff; a = top/(ct_diff*ct_diff); b = -rho_freezing*alpha_freezing; c = rho_freezing - rho; sqrt_disc = sqrt(b*b - 4*a*c); *ct = ct_freezing + 0.5*(-b - sqrt_disc)/a; } else { ct_diff = 40.0 - ct_max_rho; factor = (rho_max - rho)/(rho_max - rho_40); delta_ct = ct_diff*sqrt(factor); if (delta_ct > 5.0) *ct = ct_max_rho + delta_ct; else { /*Set the initial value of the quadratic solution roots.*/ ct_a = ct_max_rho + sqrt(rec_half_rho_tt*(rho - rho_max)); for (number_of_iterations = 1; number_of_iterations <= 7; number_of_iterations++) { ct_old = ct_a; rho_old = gsw_rho(sa,ct_old,p); factorqa = (rho_max - rho)/(rho_max - rho_old); ct_a = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqa); } if ((ct_freezing - ct_a) < 0.0) { *ct = GSW_INVALID_VALUE; if (ct_multiple != NULL) *ct_multiple = *ct; return; } *ct = ct_a; if (ct_multiple == NULL) return; /*Set the initial value of the quadratic solution roots.*/ ct_b = ct_max_rho - sqrt(rec_half_rho_tt*(rho - rho_max)); for (number_of_iterations = 1; number_of_iterations <= 7; number_of_iterations++) { ct_old = ct_b; rho_old = gsw_rho(sa,ct_old,p); factorqb = (rho_max - rho)/(rho_max - rho_old); ct_b = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqb); } /* ! After seven iterations of this quadratic iterative procedure, ! the error in rho is no larger than 4.6x10^-13 kg/m^3. */ if ((ct_freezing - ct_b) < 0.0) { *ct = GSW_INVALID_VALUE; *ct_multiple = *ct; return; } *ct_multiple = ct_b; return; } } /*Begin the modified Newton-Raphson iterative method*/ v_lab = 1.0/rho; gsw_rho_alpha_beta(sa,*ct,p,&rho_mean,&alpha_mean,NULL); v_ct = alpha_mean/rho_mean; for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { ct_old = *ct; delta_v = gsw_specvol(sa,ct_old,p) - v_lab; *ct = ct_old - delta_v/v_ct; ct_mean = 0.5*(*ct + ct_old); gsw_rho_alpha_beta(sa,ct_mean,p,&rho_mean,&alpha_mean,NULL); v_ct = alpha_mean/rho_mean; *ct = ct_old - delta_v/v_ct ; } /* ! After three iterations of this modified Newton-Raphson iteration, ! the error in rho is no larger than 1.6x10^-12 kg/m^3. */ if (ct_multiple != NULL) *ct_multiple = GSW_INVALID_VALUE; return; } /* !========================================================================== function gsw_ct_from_t(sa,t,p) !========================================================================== ! Calculates Conservative Temperature from in-situ temperature ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_ct_from_t : Conservative Temperature [deg C] */ double gsw_ct_from_t(double sa, double t, double p) { double pt0; pt0 = gsw_pt0_from_t(sa,t,p); return (gsw_ct_from_pt(sa,pt0)); } /* !========================================================================== elemental function gsw_ct_maxdensity (sa, p) !========================================================================== ! ! Calculates the Conservative Temperature of maximum density of seawater. ! This function returns the Conservative temperature at which the density ! of seawater is a maximum, at given Absolute Salinity, SA, and sea ! pressure, p (in dbar). ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! CT_maxdensity = Conservative Temperature at which [ deg C ] ! the density of seawater is a maximum for ! given Absolute Salinity and pressure. !-------------------------------------------------------------------------- */ double gsw_ct_maxdensity(double sa, double p) { int number_of_iterations; double alpha, ct, ct_mean, ct_old, dalpha_dct, dct = 0.001; ct = 3.978 - 0.22072*sa; /*the initial guess of ct.*/ dalpha_dct = 1.1e-5; /*the initial guess for dalpha_dct.*/ for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { ct_old = ct; alpha = gsw_alpha(sa,ct_old,p); ct = ct_old - alpha/dalpha_dct; ct_mean = 0.5*(ct + ct_old); dalpha_dct = (gsw_alpha(sa,ct_mean+dct,p) - gsw_alpha(sa,ct_mean-dct,p))/(dct + dct); ct = ct_old - alpha/dalpha_dct; } /* ! After three iterations of this modified Newton-Raphson (McDougall and ! Wotherspoon, 2012) iteration, the error in CT_maxdensity is typically ! no larger than 1x10^-15 degrees C. */ return (ct); } /* !========================================================================== elemental subroutine gsw_ct_second_derivatives (sa, pt, ct_sa_sa, ct_sa_pt, & ct_pt_pt) !========================================================================== ! ! Calculates the following three, second-order derivatives of Conservative ! Temperature ! (1) CT_SA_SA, the second derivative with respect to Absolute Salinity ! at constant potential temperature (with p_ref = 0 dbar), ! (2) CT_SA_pt, the derivative with respect to potential temperature ! (the regular potential temperature which is referenced to 0 dbar) ! and Absolute Salinity, and ! (3) CT_pt_pt, the second derivative with respect to potential ! temperature (the regular potential temperature which is referenced ! to 0 dbar) at constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! pt = potential temperature (ITS-90) [ deg C ] ! (whose reference pressure is 0 dbar) ! ! CT_SA_SA = The second derivative of Conservative Temperature with ! respect to Absolute Salinity at constant potential ! temperature (the regular potential temperature which ! has reference sea pressure of 0 dbar). ! CT_SA_SA has units of: [ K/((g/kg)^2) ] ! CT_SA_pt = The derivative of Conservative Temperature with ! respect to potential temperature (the regular one with ! p_ref = 0 dbar) and Absolute Salinity. ! CT_SA_pt has units of: [ 1/(g/kg) ] ! CT_pt_pt = The second derivative of Conservative Temperature with ! respect to potential temperature (the regular one with ! p_ref = 0 dbar) at constant SA. ! CT_pt_pt has units of: [ 1/K ] !-------------------------------------------------------------------------- */ void gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa, double *ct_sa_pt, double *ct_pt_pt) { double ct_pt_l, ct_pt_u, ct_sa_l, ct_sa_u, pt_l, pt_u, sa_l, sa_u, delta, dsa = 1e-3, dpt = 1e-2; if ((ct_sa_sa != NULL)) { sa_u = sa + dsa; sa_l = sa - dsa; if (sa_l < 0.0) { sa_l = 0.0; delta = sa_u; } else { delta = 2 * dsa; } gsw_ct_first_derivatives(sa_l,pt,&ct_sa_l,NULL); gsw_ct_first_derivatives(sa_u,pt,&ct_sa_u,NULL); *ct_sa_sa = (ct_sa_u - ct_sa_l)/delta; } if ((ct_sa_pt != NULL) || (ct_pt_pt != NULL)) { pt_l = pt - dpt; pt_u = pt + dpt; delta = 2 * dpt; if ((ct_sa_pt != NULL) && (ct_pt_pt != NULL)) { gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,&ct_pt_l); gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,&ct_pt_u); *ct_sa_pt = (ct_sa_u - ct_sa_l)/delta; *ct_pt_pt = (ct_pt_u - ct_pt_l)/delta; } else if ((ct_sa_pt != NULL) && (ct_pt_pt == NULL)) { gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,NULL); gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,NULL); *ct_sa_pt = (ct_sa_u - ct_sa_l)/delta; } else if ((ct_sa_pt == NULL) && (ct_pt_pt != NULL)) { gsw_ct_first_derivatives(sa,pt_l,NULL,&ct_pt_l); gsw_ct_first_derivatives(sa,pt_u,NULL,&ct_pt_u); *ct_pt_pt = (ct_pt_u - ct_pt_l)/delta; } } } /* !========================================================================== function gsw_deltasa_from_sp(sp,p,lon,lat) !========================================================================== ! Calculates Absolute Salinity Anomaly, deltaSA, from Practical Salinity, SP. ! ! sp : Practical Salinity [unitless] ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_deltasa_from_sp : Absolute Salinty Anomaly [g/kg] */ double gsw_deltasa_from_sp(double sp, double p, double lon, double lat) { double res; res = gsw_sa_from_sp(sp,p,lon,lat) - gsw_sr_from_sp(sp); if (res > GSW_ERROR_LIMIT) res = GSW_INVALID_VALUE; return (res); } /* !========================================================================== elemental function gsw_dilution_coefficient_t_exact (sa, t, p) !========================================================================== ! ! Calculates the dilution coefficient of seawater. The dilution ! coefficient of seawater is defined as the Absolute Salinity times the ! second derivative of the Gibbs function with respect to Absolute ! Salinity, that is, SA.*g_SA_SA. ! ! SA = Absolute Salinity [ g/kg ] ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! dilution_coefficient_t_exact = dilution coefficient [ (J/kg)(kg/g) ] !-------------------------------------------------------------------------- */ double gsw_dilution_coefficient_t_exact(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; double g08, x, x2, y, z; x2 = gsw_sfac*sa; x = sqrt(x2); y = t*0.025; z = p*1e-4; /*note.the input pressure (p) is sea pressure in units of dbar.*/ g08 = 2.0*(8103.20462414788 + y*(2175.341332000392 + y*(-274.2290036817964 + y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y))) - 90.6734234051316*z) + 1.5*x*(-5458.34205214835 - 980.14153344888*y + (4.0/3.0)*x*(2247.60742726704 - 340.1237483177863*1.25*x + 220.542973797483*y) + 180.142097805543*z) + z*(-219.1676534131548 + (-16.32775915649044 - 120.7020447884644*z)*z)); g08 = x2*g08 + x*(-7296.43987145382 + z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377 - 10.23755797323846*z)*z)) + y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-129.1994027934126 + z*(1149.174198007428 + z*(-162.5751787551336 + 76.9195462169742*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835 + 703.695562834065*z))))) + 11625.62913253464 + 1702.453469893412*y; return (0.25*gsw_sfac*g08); /* ! Note that this function avoids the singularity that occurs at SA = 0 if ! the straightforward expression for the dilution coefficient of seawater, ! SA*g_SA_SA is simply evaluated as SA.*gsw_gibbs(2,0,0,SA,t,p). */ } /* !========================================================================== function gsw_dynamic_enthalpy(sa,ct,p) !========================================================================== ! Calculates dynamic enthalpy of seawater using the computationally- ! efficient expression for specific volume in terms of SA, CT and p ! (Roquet et al., 2014). Dynamic enthalpy is defined as enthalpy minus | potential enthalpy (Young, 2010). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! dynamic_enthalpy : dynamic enthalpy [J/kg] */ double gsw_dynamic_enthalpy(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double dynamic_enthalpy_part, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; dynamic_enthalpy_part = z*(h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401 + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211 + xs*(h311 + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321 + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041 + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys))))) + z*(h002 + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs)))) + ys*(h012 + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022 + xs*(h122 + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs) + ys*(h042 + h142*xs + h052*ys)))) + z*(h003 + xs*(h103 + xs*(h203 + xs*(h303 + h403*xs))) + ys*(h013 + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023 + xs*(h123 + h223*xs) + ys*(h033 + h133*xs + h043*ys))) + z*(h004 + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys) + z*(h005 + h105*xs + h015*ys + z*(h006 + h007*z)))))); return (dynamic_enthalpy_part*db2pa*1e4); } /* !========================================================================== function gsw_enthalpy(sa,ct,p) !========================================================================== ! Calculates specific enthalpy of seawater using the computationally- ! efficient expression for specific volume in terms of SA, CT and p ! (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! enthalpy : specific enthalpy of seawater [J/kg] */ double gsw_enthalpy(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; return (gsw_cp0*ct + gsw_dynamic_enthalpy(sa,ct,p)); } /* !========================================================================== elemental function gsw_enthalpy_ct_exact (sa, ct, p) !========================================================================== ! ! Calculates specific enthalpy of seawater from Absolute Salinity and ! Conservative Temperature and pressure. ! ! Note that this function uses the full Gibbs function. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! enthalpy_CT_exact = specific enthalpy [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_enthalpy_ct_exact(double sa, double ct, double p) { double t; t = gsw_t_from_ct(sa,ct,p); return (gsw_enthalpy_t_exact(sa,t,p)); } /* !========================================================================== elemental function gsw_enthalpy_diff (sa, ct, p_shallow, p_deep) !========================================================================== ! ! Calculates the difference of the specific enthalpy of seawater between ! two different pressures, p_deep (the deeper pressure) and p_shallow ! (the shallower pressure), at the same values of SA and CT. This ! function uses the computationally-efficient expression for specific ! volume in terms of SA, CT and p (Roquet et al., 2014). The output ! (enthalpy_diff_CT) is the specific enthalpy evaluated at (SA,CT,p_deep) ! minus the specific enthalpy at (SA,CT,p_shallow). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p_shallow = upper sea pressure [ dbar ] ! ( i.e. shallower absolute pressure - 10.1325 dbar ) ! p_deep = lower sea pressure [ dbar ] ! ( i.e. deeper absolute pressure - 10.1325 dbar ) ! ! enthalpy_diff_CT = difference of specific enthalpy [ J/kg ] ! (deep minus shallow) !-------------------------------------------------------------------------- */ double gsw_enthalpy_diff(double sa, double ct, double p_shallow, double p_deep) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double dynamic_enthalpy_shallow, dynamic_enthalpy_deep, part_1, part_2, part_3, part_4, part_5, xs, ys, z_deep, z_shallow; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z_shallow = p_shallow*1e-4; z_deep = p_deep*1e-4; part_1 = h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401 + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211+ xs*(h311 + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321 + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041 + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys))))); part_2 = h002 + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs)))) + ys*(h012 + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022 + xs*(h122 + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs) + ys*(h042 + h142*xs + h052*ys)))); part_3 = h003 + xs*(h103 + xs*(h203 + xs*(h303 + h403*xs))) + ys*(h013 + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023 + xs*(h123 + h223*xs) + ys*(h033 + h133*xs + h043*ys))); part_4 = h004 + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys); part_5 = h005 + h105*xs + h015*ys; dynamic_enthalpy_shallow = z_shallow*(part_1 + z_shallow*(part_2 + z_shallow*(part_3 + z_shallow*(part_4 + z_shallow*(part_5 + z_shallow*(h006 + h007*z_shallow)))))); dynamic_enthalpy_deep = z_deep*(part_1 + z_deep*(part_2 + z_deep*(part_3 + z_deep*(part_4+z_deep*(part_5 + z_deep*(h006 + h007*z_deep)))))); return ((dynamic_enthalpy_deep - dynamic_enthalpy_shallow)*db2pa*1e4); } /* !========================================================================== elemental subroutine gsw_enthalpy_first_derivatives (sa, ct, p, h_sa, h_ct) !========================================================================== ! ! Calculates the following two derivatives of specific enthalpy (h) of ! seawater using the computationally-efficient expression for ! specific volume in terms of SA, CT and p (Roquet et al., 2014). ! (1) h_SA, the derivative with respect to Absolute Salinity at ! constant CT and p, and ! (2) h_CT, derivative with respect to CT at constant SA and p. ! Note that h_P is specific volume (1/rho) it can be calculated by calling ! gsw_specvol(SA,CT,p). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! h_SA = The first derivative of specific enthalpy with respect to ! Absolute Salinity at constant CT and p. ! [ J/(kg (g/kg))] i.e. [ J/g ] ! h_CT = The first derivative of specific enthalpy with respect to ! CT at constant SA and p. [ J/(kg K) ] !-------------------------------------------------------------------------- */ void gsw_enthalpy_first_derivatives(double sa, double ct, double p, double *h_sa, double *h_ct) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double dynamic_h_ct_part, dynamic_h_sa_part, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; if (h_sa != NULL) { dynamic_h_sa_part = z*(h101 + xs*(2.0*h201 + xs*(3.0*h301 + xs*(4.0*h401 + xs*(5.0*h501 + 6.0*h601*xs)))) + ys*(h111 + xs*(2.0*h211 + xs*(3.0*h311 + xs*(4.0*h411 + 5.0*h511*xs))) + ys*(h121 + xs*(2.0*h221 + xs*(3.0*h321 + 4.0*h421*xs)) + ys*(h131 + xs*(2.0*h231 + 3.0*h331*xs) + ys*(h141 + 2.0*h241*xs + h151*ys)))) + z*(h102 + xs*(2.0*h202 + xs*(3.0*h302 + xs*(4.0*h402 + 5.0*h502*xs))) + ys*(h112 + xs*(2.0*h212 + xs*(3.0*h312 + 4.0*h412*xs)) + ys*(h122 + xs*(2.0*h222 + 3.0*h322*xs) + ys*(h132 + 2.0*h232*xs + h142*ys ))) + z*(h103 + xs*(2.0*h203 + xs*(3.0*h303 + 4.0*h403*xs)) + ys*(h113 + xs*(2.0*h213 + 3.0*h313*xs) + ys*(h123 + 2.0*h223*xs + h133*ys)) + z*(h104 + 2.0*h204*xs + h114*ys + h105*z)))); *h_sa = 1e8*0.5*gsw_sfac*dynamic_h_sa_part/xs; } if (h_ct != NULL) { dynamic_h_ct_part = z*(h011 + xs*(h111 + xs*(h211 + xs*(h311 + xs*(h411 + h511*xs)))) + ys*(2.0*(h021 + xs*(h121 + xs*(h221 + xs*(h321 + h421*xs)))) + ys*(3.0*(h031 + xs*(h131 + xs*(h231 + h331*xs))) + ys*(4.0*(h041 + xs*(h141 + h241*xs)) + ys*(5.0*(h051 + h151*xs) + 6.0*h061*ys)))) + z*(h012 + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(2.0*(h022 + xs*(h122 + xs*(h222 + h322*xs))) + ys*(3.0*(h032 + xs*(h132 + h232*xs)) + ys*(4.0*(h042 + h142*xs) + 5.0*h052*ys))) + z*(h013 + xs*(h113 + xs*(h213 + h313*xs)) + ys*(2.0*(h023 + xs*(h123 + h223*xs)) + ys*(3.0*(h033 + h133*xs) + 4.0*h043*ys)) + z*(h014 + h114*xs + 2.0*h024*ys + h015*z )))); *h_ct = gsw_cp0 + 1e8*0.025*dynamic_h_ct_part; } } /* !========================================================================== elemental subroutine gsw_enthalpy_first_derivatives_ct_exact (sa, ct, p, & h_sa, h_ct) !========================================================================== ! ! Calculates the following two derivatives of specific enthalpy (h) ! (1) h_SA, the derivative with respect to Absolute Salinity at ! constant CT and p, and ! (2) h_CT, derivative with respect to CT at constant SA and p. ! Note that h_P is specific volume (1/rho) it can be calculated by calling ! gsw_specvol_CT_exact(SA,CT,p). This function uses the full Gibbs function. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! h_SA = The first derivative of specific enthalpy with respect to ! Absolute Salinity at constant CT and p. ! [ J/(kg (g/kg))] i.e. [ J/g ] ! h_CT = The first derivative of specific enthalpy with respect to ! CT at constant SA and p. [ J/(kg K) ] !-------------------------------------------------------------------------- */ void gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct, double p, double *h_sa, double *h_ct) { GSW_TEOS10_CONSTANTS; double g_sa_mod_pt, g_sa_mod_t, pt0, t, temp_ratio, x, y, y_pt, z; t = gsw_t_from_ct(sa,ct,p); pt0 = gsw_pt_from_ct(sa,ct); temp_ratio = (gsw_t0 + t)/(gsw_t0 + pt0); if (h_ct != NULL) *h_ct = gsw_cp0*temp_ratio; if (h_sa == NULL) return; x = sqrt(gsw_sfac*sa); y = 0.025*t; z = rec_db2pa*p; /*note.the input pressure (p) is sea pressure in units of dbar.*/ g_sa_mod_t = 8645.36753595126 + z*(-6620.98308089678 + z*(769.588305957198 + z*(-193.0648640214916 + (31.6816345533648 - 5.24960313181984*z)*z))) + x*(-7296.43987145382 + x*(8103.20462414788 + y*(2175.341332000392 + y*(-274.2290036817964 + y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y))) - 90.6734234051316*z) + x*(-5458.34205214835 - 980.14153344888*y + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y) + 180.142097805543*z) + z*(-219.1676534131548 + (-16.32775915649044 - 120.7020447884644*z)*z)) + z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377 - 10.23755797323846*z)*z)) + y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-129.1994027934126 + z*(1149.174198007428 + z*(-162.5751787551336 + 76.9195462169742*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835 + 703.695562834065*z))))) + y*(1187.3715515697959 + z*(1458.233059470092 + z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146 + 14.09317606630898*z)))) + y*(1760.062705994408 + y*(-450.535298526802 + y*(182.8520895502518 + y*(-43.3206481750622 + 4.26033941694366*y) + z*(-595.457483974374 + (149.452282277512 - 72.9745838003176*z)*z)) + z*(1388.489628266536 + z*(-409.779283929806 + (227.123395681188 - 22.2565468652826*z)*z))) + z*(-1721.528607567954 + z*(674.819060538734 + z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z))))); g_sa_mod_t = 0.5*gsw_sfac*g_sa_mod_t; y_pt = 0.025*pt0; g_sa_mod_pt = 8645.36753595126 + x*(-7296.43987145382 + x*(8103.20462414788 + y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 + y_pt*(197.4670779425016 + y_pt*(-68.5590309679152 + 9.98788038278032*y_pt)))) + x*(-5458.34205214835 - 980.14153344888*y_pt + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y_pt))) + y_pt*(-1480.222530425046 + y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625 + y_pt*2.626801985426835)))) + y_pt*(1187.3715515697959 + y_pt*(1760.062705994408 + y_pt*(-450.535298526802 + y_pt*(182.8520895502518 + y_pt*(-43.3206481750622 + 4.26033941694366*y_pt))))); g_sa_mod_pt = 0.5*gsw_sfac*g_sa_mod_pt; *h_sa = g_sa_mod_t - temp_ratio*g_sa_mod_pt; } /* !========================================================================== elemental function gsw_enthalpy_ice (t, p) !========================================================================== ! ! Calculates the specific enthalpy of ice (h_Ih). ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! gsw_enthalpy_ice : specific enthalpy of ice [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_enthalpy_ice(double t, double p) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double tau, dzi, g0; DCOMPLEX r2, sqtau_t1, sqtau_t2, g; tau = (t + gsw_t0)*rec_tt; dzi = db2pa*p*rec_pt; g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi))); r2 = r20 + dzi*(r21 + r22*dzi); sqtau_t1 = (tau*tau)/(t1*t1); sqtau_t2 = (tau*tau)/(t2*t2); g = r1*t1*(log(1.0 - sqtau_t1) + sqtau_t1) + r2*t2*(log(1.0 - sqtau_t2) + sqtau_t2); return (g0 + tt*real(g)); } /* !========================================================================== elemental subroutine gsw_enthalpy_second_derivatives (sa, ct, p, h_sa_sa, & h_sa_ct, h_ct_ct) ! ========================================================================= ! ! Calculates the following three second-order derivatives of specific ! enthalpy (h),using the computationally-efficient expression for ! specific volume in terms of SA, CT and p (Roquet et al., 2014). ! (1) h_SA_SA, second-order derivative with respect to Absolute Salinity ! at constant CT & p. ! (2) h_SA_CT, second-order derivative with respect to SA & CT at ! constant p. ! (3) h_CT_CT, second-order derivative with respect to CT at constant SA ! and p. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! h_SA_SA = The second derivative of specific enthalpy with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! h_SA_CT = The second derivative of specific enthalpy with respect to ! SA and CT at constant p. [ J/(kg K(g/kg)) ] ! h_CT_CT = The second derivative of specific enthalpy with respect to ! CT at constant SA and p. [ J/(kg K^2) ] !-------------------------------------------------------------------------- */ void gsw_enthalpy_second_derivatives(double sa, double ct, double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double dynamic_h_ct_ct_part, dynamic_h_sa_ct_part, dynamic_h_sa_sa_part, xs, xs2, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; if (h_sa_sa != NULL) { xs2 = pow(xs,2); dynamic_h_sa_sa_part = z*(-h101 + xs2*(3.0*h301 + xs*(8.0*h401 + xs*(15.0*h501 + 24.0*h601*xs))) + ys*(- h111 + xs2*(3.0*h311 + xs*(8.0*h411 + 15.0*h511*xs)) + ys*(-h121 + xs2*(3.0*h321 + 8.0*h421*xs) + ys*(-h131 + 3.0*h331*xs2 + ys*(-h141 - h151*ys)))) + z*(-h102 + xs2*(3.0*h302 + xs*(8.0*h402 + 15.0*h502*xs)) + ys*(-h112 + xs2*(3.0*h312 + 8.0*h412*xs) + ys*(-h122 + 3.0*h322*xs2 + ys*(-h132 - h142*ys ))) + z*(xs2*(8.0*h403*xs + 3.0*h313*ys) + z*(-h103 + 3.0*h303*xs2 + ys*(-h113 + ys*(-h123 - h133*ys)) + z*(-h104 - h114*ys - h105*z))))); *h_sa_sa = 1e8*0.25*gsw_sfac*gsw_sfac*dynamic_h_sa_sa_part/ pow(xs,3); } if (h_sa_ct != NULL) { dynamic_h_sa_ct_part = z*(h111 + xs*(2.0*h211 + xs*(3.0*h311 + xs*(4.0*h411 + 5.0*h511*xs))) + ys*(2.0*h121 + xs*(4.0*h221 + xs*(6.0*h321 + 8.0*h421*xs)) + ys*(3.0*h131 + xs*(6.0*h231 + 9.0*h331*xs) + ys*(4.0*h141 + 8.0*h241*xs + 5.0*h151*ys ))) + z*(h112 + xs*(2.0*h212 + xs*(3.0*h312 + 4.0*h412*xs)) + ys*(2.0*h122 + xs*(4.0*h222 + 6.0*h322*xs) + ys*(3.0*h132 + 6.0*h232*xs + 4.0*h142*ys)) + z*(h113 + xs*(2.0*h213 + 3.0*h313*xs) + ys*(2.0*h123 + 4.0*h223*xs + 3.0*h133*ys) + h114*z))); *h_sa_ct = 1e8*0.025*0.5*gsw_sfac*dynamic_h_sa_ct_part/xs; } if (h_ct_ct != NULL) { dynamic_h_ct_ct_part = z*(2.0*h021 + xs*(2.0*h121 + xs*(2.0*h221 + xs*(2.0*h321 + 2.0*h421*xs))) + ys*(6.0*h031 + xs*(6.0*h131 + xs*(6.0*h231 + 6.0*h331*xs)) + ys*(12.0*h041 + xs*(12.0*h141 + 12.0*h241*xs) + ys*(20.0*h051 + 20.0*h151*xs + 30.0*h061*ys))) + z*(2.0*h022 + xs*(2.0*h122 + xs*(2.0*h222 + 2.0*h322*xs)) + ys*(6.0*h032 + xs*(6.0*h132 + 6.0*h232*xs) + ys*(12.0*h042 + 12.0*h142*xs + 20.0*h052*ys)) + z*(2.0*h023 + xs*(2.0*h123 + 2.0*h223*xs) + ys*(6.0*h133*xs + 6.0*h033 + 12.0*h043*ys) + 2.0*h024*z))); *h_ct_ct = 1e8*6.25e-4*dynamic_h_ct_ct_part; } } /* !========================================================================== elemental subroutine gsw_enthalpy_second_derivatives_ct_exact (sa, ct, p, & h_sa_sa, h_sa_ct, h_ct_ct) !========================================================================== ! ! Calculates three second-order derivatives of specific enthalpy (h). ! Note that this function uses the full Gibbs function. ! ! sa = Absolute Salinity [ g/kg ] ! ct = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! h_sa_sa = The second derivative of specific enthalpy with respect to ! Absolute Salinity at constant ct & p. [ J/(kg (g/kg)^2) ] ! h_sa_ct = The second derivative of specific enthalpy with respect to ! sa and ct at constant p. [ J/(kg K(g/kg)) ] ! h_ct_ct = The second derivative of specific enthalpy with respect to ! ct at constant sa and p. [ J/(kg K^2) ] !-------------------------------------------------------------------------- */ void gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct, double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct) { GSW_TEOS10_CONSTANTS; double factor, gsa_pt0, gsat_pt0, gsat, part_b, pt0, h_ct_ct_val, rec_abs_pt0, rec_gtt_pt0, rec_gtt, t, temp_ratio, gsasa, gsasa_pt0, pr0 = 0.0, sa_small = 1e-100; int n0=0, n1=1, n2=2; pt0 = gsw_pt_from_ct(sa,ct); rec_abs_pt0 = 1.0/(gsw_t0 + pt0); t = gsw_pt_from_t(sa,pt0,pr0,p); temp_ratio = (gsw_t0 + t)*rec_abs_pt0; rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa,pt0,pr0); rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa,t,p); /*h_ct_ct is naturally well-behaved as sa approaches zero.*/ h_ct_ct_val = gsw_cp0*gsw_cp0* (temp_ratio*rec_gtt_pt0 - rec_gtt)*(rec_abs_pt0*rec_abs_pt0); if (h_ct_ct != NULL) *h_ct_ct = h_ct_ct_val; if ((h_sa_sa == NULL) && (h_sa_ct == NULL)) return; gsat_pt0 = gsw_gibbs(n1,n1,n0,sa,pt0,pr0); gsat = gsw_gibbs(n1,n1,n0,sa,t,p); gsa_pt0 = gsw_gibbs(n1,n0,n0,sa,pt0,pr0); part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0 - gsat*rec_gtt)*rec_abs_pt0; factor = gsa_pt0/gsw_cp0; if (h_sa_sa != NULL) { gsasa = gsw_gibbs(n2,n0,n0,sa,t,p); gsasa_pt0 = gsw_gibbs(n2,n0,n0,sa,pt0,pr0); /* ! h_sa_sa has a singularity at sa = 0, and blows up as sa ! approaches zero. */ *h_sa_sa = gsasa - temp_ratio*gsasa_pt0 + temp_ratio*gsat_pt0*gsat_pt0*rec_gtt_pt0 - gsat*gsat*rec_gtt - 2.0*gsa_pt0*part_b + (factor*factor)*h_ct_ct_val; } if (h_sa_ct == NULL) return; /* ! h_sa_ct should not blow up as sa approaches zero. ! The following lines of code ensure that the h_sa_ct output ! of this function does not blow up in this limit. ! That is, when sa < 1e-100 g/kg, we force the h_sa_ct ! output to be the same as if sa = 1e-100 g/kg. */ if (sa < sa_small) { rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa_small,pt0,pr0); rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa_small,t,p); gsat_pt0 = gsw_gibbs(n1,n1,n0,sa_small,pt0,pr0); gsat = gsw_gibbs(n1,n1,n0,sa_small,t,p); gsa_pt0 = gsw_gibbs(n1,n0,n0,sa_small,pt0,pr0); part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0 - gsat*rec_gtt)*rec_abs_pt0; factor = gsa_pt0/gsw_cp0; } *h_sa_ct = gsw_cp0*part_b - factor*h_ct_ct_val; } /* !========================================================================== function gsw_enthalpy_sso_0(p) !========================================================================== ! This function calculates enthalpy at the Standard Ocean Salinity, SSO, ! and at a Conservative Temperature of zero degrees C, as a function of ! pressure, p, in dbar, using a streamlined version of the ! computationally-efficient expression for specific volume, that is, a ! streamlined version of the code "gsw_enthalpy(SA,CT,p)". ! ! p : sea pressure [dbar] ! ! enthalpy_sso_0 : enthalpy(sso,0,p) */ double gsw_enthalpy_sso_0(double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double dynamic_enthalpy_sso_0_p, z; z = p*1.0e-4; dynamic_enthalpy_sso_0_p = z*( 9.726613854843870e-4 + z*(-2.252956605630465e-5 + z*( 2.376909655387404e-6 + z*(-1.664294869986011e-7 + z*(-5.988108894465758e-9 + z*(h006 + h007*z)))))); return (dynamic_enthalpy_sso_0_p*db2pa*1.0e4); } /* !========================================================================== function gsw_enthalpy_t_exact(sa,t,p) !========================================================================== ! Calculates the specific enthalpy of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_enthalpy_t_exact : specific enthalpy [J/kg] */ double gsw_enthalpy_t_exact(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; int n0=0, n1=1; return (gsw_gibbs(n0,n0,n0,sa,t,p) - (t+gsw_t0)*gsw_gibbs(n0,n1,n0,sa,t,p)); } /* !========================================================================== elemental subroutine gsw_entropy_first_derivatives (sa, ct, eta_sa, eta_ct) ! ========================================================================= ! ! Calculates the following two partial derivatives of specific entropy ! (eta) ! (1) eta_SA, the derivative with respect to Absolute Salinity at ! constant Conservative Temperature, and ! (2) eta_CT, the derivative with respect to Conservative Temperature at ! constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! eta_SA = The derivative of specific entropy with respect to ! Absolute Salinity (in units of g kg^-1) at constant ! Conservative Temperature. ! eta_SA has units of: [ J/(kg K(g/kg))] or [ J/(g K) ] ! eta_CT = The derivative of specific entropy with respect to ! Conservative Temperature at constant Absolute Salinity. ! eta_CT has units of: [ J/(kg K^2) ] !-------------------------------------------------------------------------- */ void gsw_entropy_first_derivatives(double sa, double ct, double *eta_sa, double *eta_ct) { GSW_TEOS10_CONSTANTS; double pt, pr0 = 0.0; int n0=0, n1=1; pt = gsw_pt_from_ct(sa,ct); if (eta_sa != NULL) *eta_sa = -(gsw_gibbs(n1,n0,n0,sa,pt,pr0))/(gsw_t0 + pt); if (eta_ct != NULL) *eta_ct = gsw_cp0/(gsw_t0 + pt); } /* !========================================================================= elemental function gsw_entropy_from_ct (sa, ct) !========================================================================= ! ! Calculates specific entropy of seawater from Conservative Temperature. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! entropy = specific entropy [ deg C ] !-------------------------------------------------------------------------- */ double gsw_entropy_from_ct(double sa, double ct) { double pt0; pt0 = gsw_pt_from_ct(sa, ct); return (-gsw_gibbs(0,1,0,sa,pt0,0)); } /* !========================================================================== elemental function gsw_entropy_from_pt (sa, pt) !========================================================================== ! ! Calculates specific entropy of seawater. ! ! SA = Absolute Salinity [ g/kg ] ! pt = potential temperature (ITS-90) [ deg C ] ! ! entropy = specific entropy [ J/(kg*K) ] !-------------------------------------------------------------------------- */ double gsw_entropy_from_pt(double sa, double pt) { int n0 = 0, n1 = 1; double pr0 = 0.0; return (-gsw_gibbs(n0,n1,n0,sa,pt,pr0)); } /* !========================================================================== function gsw_entropy_from_t(sa,t,p) !========================================================================== ! Calculates the specific entropy of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_entropy_from_t : specific entropy [J/(kg K)] */ double gsw_entropy_from_t(double sa, double t, double p) { int n0=0, n1=1; return (-gsw_gibbs(n0,n1,n0,sa,t,p)); } /* !========================================================================== elemental function gsw_entropy_ice (t, p) !========================================================================== ! ! Calculates specific entropy of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! ice_entropy = specific entropy of ice [ J kg^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_entropy_ice(double t, double p) { return (-gsw_gibbs_ice(1,0,t,p)); } /* !========================================================================== function gsw_entropy_part(sa,t,p) !========================================================================== ! entropy minus the terms that are a function of only SA ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! entropy_part : entropy part */ double gsw_entropy_part(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; double x2, x, y, z, g03, g08; x2 = gsw_sfac*sa; x = sqrt(x2); y = t*0.025; z = p*1e-4; g03 = z*(-270.983805184062 + z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 - 2.13290083518327*z)*z))) + y*(-24715.571866078 + z*(2910.0729080936 + z*(-1513.116771538718 + z*(546.959324647056 + z*(-111.1208127634436 + 8.68841343834394*z)))) + y*(2210.2236124548363 + z*(-2017.52334943521 + z*(1498.081172457456 + z*(-718.6359919632359 + (146.4037555781616 - 4.9892131862671505*z)*z))) + y*(-592.743745734632 + z*(1591.873781627888 + z*(-1207.261522487504 + (608.785486935364 - 105.4993508931208*z)*z)) + y*(290.12956292128547 + z*(-973.091553087975 + z*(602.603274510125 + z*(-276.361526170076 + 32.40953340386105*z))) + y*(-113.90630790850321 + y*(21.35571525415769 - 67.41756835751434*z) + z*(381.06836198507096 + z*(-133.7383902842754 + 49.023632509086724*z))))))); g08 = x2*(z*(729.116529735046 + z*(-343.956902961561 + z*(124.687671116248 + z*(-31.656964386073 + 7.04658803315449*z)))) + x*( x*(y*(-137.1145018408982 + y*(148.10030845687618 + y*(-68.5590309679152 + 12.4848504784754*y))) - 22.6683558512829*z) + z*(-175.292041186547 + (83.1923927801819 - 29.483064349429*z)*z) + y*(-86.1329351956084 + z*(766.116132004952 + z*(-108.3834525034224 + 51.2796974779828*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(3.50240264723578 + 938.26075044542*z)))) + y*(1760.062705994408 + y*(-675.802947790203 + y*(365.7041791005036 + y*(-108.30162043765552 + 12.78101825083098*y) + z*(-1190.914967948748 + (298.904564555024 - 145.9491676006352*z)*z)) + z*(2082.7344423998043 + z*(-614.668925894709 + (340.685093521782 - 33.3848202979239*z)*z))) + z*(-1721.528607567954 + z*(674.819060538734 + z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z))))); return (-(g03 + g08)*0.025); } /* !========================================================================== function gsw_entropy_part_zerop(sa,pt0) !========================================================================== ! entropy part evaluated at the sea surface ! ! sa : Absolute Salinity [g/kg] ! pt0 : insitu temperature [deg C] ! ! entropy_part_zerop : entropy part at the sea surface */ double gsw_entropy_part_zerop(double sa, double pt0) { GSW_TEOS10_CONSTANTS; double x2, x, y, g03, g08; x2 = gsw_sfac*sa; x = sqrt(x2); y = pt0*0.025; g03 = y*(-24715.571866078 + y*(2210.2236124548363 + y*(-592.743745734632 + y*(290.12956292128547 + y*(-113.90630790850321 + y*21.35571525415769))))); g08 = x2*(x*(x*(y*(-137.1145018408982 + y*(148.10030845687618 + y*(-68.5590309679152 + 12.4848504784754*y)))) + y*(-86.1329351956084 + y*(-30.0682112585625 + y*3.50240264723578))) + y*(1760.062705994408 + y*(-675.802947790203 + y*(365.7041791005036 + y*(-108.30162043765552 + 12.78101825083098*y))))); return (-(g03 + g08)*0.025); } /* !========================================================================== elemental subroutine gsw_entropy_second_derivatives (sa, ct, eta_sa_sa, & eta_sa_ct, eta_ct_ct) ! ========================================================================= ! ! Calculates the following three second-order partial derivatives of ! specific entropy (eta) ! (1) eta_SA_SA, the second derivative with respect to Absolute ! Salinity at constant Conservative Temperature, and ! (2) eta_SA_CT, the derivative with respect to Absolute Salinity and ! Conservative Temperature. ! (3) eta_CT_CT, the second derivative with respect to Conservative ! Temperature at constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! eta_SA_SA = The second derivative of specific entropy with respect ! to Absolute Salinity (in units of g kg^-1) at constant ! Conservative Temperature. ! eta_SA_SA has units of: [ J/(kg K(g/kg)^2)] ! eta_SA_CT = The second derivative of specific entropy with respect ! to Conservative Temperature at constant Absolute ! Salinity. eta_SA_CT has units of: [ J/(kg (g/kg) K^2) ] ! eta_CT_CT = The second derivative of specific entropy with respect ! to Conservative Temperature at constant Absolute ! Salinity. eta_CT_CT has units of: [ J/(kg K^3) ] !-------------------------------------------------------------------------- */ void gsw_entropy_second_derivatives(double sa, double ct, double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct) { GSW_TEOS10_CONSTANTS; double abs_pt, ct_pt, ct_sa, pt, ct_ct, pr0 = 0.0; int n0=0, n1=1, n2=2; pt = gsw_pt_from_ct(sa,ct); abs_pt = gsw_t0 + pt; ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0; ct_ct = -gsw_cp0/(ct_pt*abs_pt*abs_pt); if ((eta_sa_ct != NULL) || (eta_sa_sa != NULL)) { ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) - (abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0)))/gsw_cp0; if (eta_sa_ct != NULL) *eta_sa_ct = -ct_sa*ct_ct; if (eta_sa_sa != NULL) *eta_sa_sa = -gsw_gibbs(n2,n0,n0,sa,pt,pr0)/abs_pt + ct_sa*ct_sa*ct_ct; } if (eta_ct_ct != NULL) *eta_ct_ct = ct_ct; } /* !========================================================================== function gsw_fdelta(p,lon,lat) !========================================================================== ! Calculates fdelta. ! ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_fdelta : Absolute Salinty Anomaly [unitless] */ double gsw_fdelta(double p, double lon, double lat) { double sa, saar; saar = gsw_saar(p,lon,lat); if (saar >= GSW_ERROR_LIMIT) sa = GSW_INVALID_VALUE; else sa = ((1.0 + 0.35)*saar)/(1.0 - 0.35*saar); return (sa); } /* !========================================================================== elemental subroutine gsw_frazil_properties (sa_bulk, h_bulk, p, & sa_final, ct_final, w_ih_final) !========================================================================== ! ! Calculates the mass fraction of ice (mass of ice divided by mass of ice ! plus seawater), w_Ih_final, which results from given values of the bulk ! Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occurring at pressure ! p. The final values of Absolute Salinity, SA_final, and Conservative ! Temperature, CT_final, of the interstitial seawater phase are also ! returned. This code assumes that there is no dissolved air in the ! seawater (that is, saturation_fraction is assumed to be zero ! throughout the code). ! ! When the mass fraction w_Ih_final is calculated as being a positive ! value, the seawater-ice mixture is at thermodynamic equilibrium. ! ! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, ! is sufficiently large (i.e. sufficiently "warm") so that there is no ice ! present in the final state. In this case the final state consists of ! only seawater rather than being an equilibrium mixture of seawater and ! ice which occurs when w_Ih_final is positive. Note that when ! w_Ih_final = 0, the final seawater is not at the freezing temperature. ! ! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture ! [ g/kg ] ! h_bulk = bulk enthalpy of the seawater and ice mixture [ J/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! SA_final = Absolute Salinity of the seawater in the final state, ! whether or not any ice is present. [ g/kg ] ! CT_final = Conservative Temperature of the seawater in the the final ! state, whether or not any ice is present. [ deg C ] ! w_Ih_final = mass fraction of ice in the final seawater-ice mixture. ! If this ice mass fraction is positive, the system is at ! thermodynamic equilibrium. If this ice mass fraction is ! zero there is no ice in the final state which consists ! only of seawater which is warmer than the freezing ! temperature. [unitless] !-------------------------------------------------------------------------- */ void gsw_frazil_properties(double sa_bulk, double h_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final) { int number_of_iterations; double cp_ih, ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly, func, func0, hf, h_hat_ct, h_hat_sa, h_ihf, sa, tf_sa, tf, w_ih_mean, w_ih_old, w_ih, /* ! Throughout this code seawater is taken to contain ! no dissolved air. */ saturation_fraction = 0.0, num_f = 5.0e-2, num_f2 = 6.9e-7, num_p = 2.21; /* !--------------- ! Finding func0 !-------------- */ ctf = gsw_ct_freezing(sa_bulk,p,saturation_fraction); func0 = h_bulk - gsw_enthalpy_ct_exact(sa_bulk,ctf,p); /* !----------------------------------------------------------------------- ! When func0 is zero or positive we can immediately calculate the three ! outputs, as the bulk enthalpy, h_bulk, is too large to allow any ice ! at thermodynamic equilibrium. The result will be (warm) seawater with ! no frazil ice being present. The three outputs can be set and the rest ! of this code does not need to be performed. !----------------------------------------------------------------------- */ if (func0 >= 0.0) { *sa_final = sa_bulk; *ct_final = gsw_ct_from_enthalpy_exact(sa_bulk,h_bulk,p); *w_ih_final = 0.0; return; } /* !----------------------------------------------------------------------- ! Begin to find the solution for those data points that have func0 < 0, ! implying that the output will be a positive ice mass fraction ! w_Ih_final. ! ! Do a quasi-Newton step with a separate polynomial estimate of the ! derivative of func with respect to the ice mass fraction. This ! section of the code delivers initial values of both w_Ih and SA to ! the rest of the more formal modified Newtons Method approach of ! McDougall and Wotherspoon (2014). !----------------------------------------------------------------------- */ dfunc_dw_ih_mean_poly = 3.347814e+05 - num_f*func0*(1.0 + num_f2*func0) - num_p*p; w_ih = min(-func0/dfunc_dw_ih_mean_poly, 0.95); sa = sa_bulk/(1.0 - w_ih); if (sa < 0.0 || sa > 120.0) { *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } /* !----------------------------------------------------------------------- ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be ! fed into the iterative Newton's Method. !----------------------------------------------------------------------- */ ctf = gsw_ct_freezing(sa,p,saturation_fraction); hf = gsw_enthalpy_ct_exact(sa,ctf,p); tf = gsw_t_freezing(sa,p,saturation_fraction); h_ihf = gsw_enthalpy_ice(tf,p); cp_ih = gsw_cp_ice(tf,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p, &h_hat_sa,&h_hat_ct); gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa, NULL); gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,NULL); dfunc_dw_ih = hf - h_ihf - sa*(h_hat_sa + h_hat_ct*ctf_sa + w_ih*cp_ih*tf_sa/ (1.0 - w_ih)); /* !----------------------------------------------------------------------- ! Enter the main McDougall-Wotherspoon (2014) modified Newton-Raphson | loop !----------------------------------------------------------------------- */ for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { if (number_of_iterations > 1) { /* on the first iteration these values are already known */ ctf = gsw_ct_freezing(sa,p,saturation_fraction); hf = gsw_enthalpy_ct_exact(sa,ctf,p); tf = gsw_t_freezing(sa,p,saturation_fraction); h_ihf = gsw_enthalpy_ice(tf,p); } func = h_bulk - (1.0 - w_ih)*hf - w_ih*h_ihf; w_ih_old = w_ih; w_ih = w_ih_old - func/dfunc_dw_ih; w_ih_mean = 0.5*(w_ih + w_ih_old); if (w_ih_mean > 0.9) { /*This ensures that the mass fraction of ice never exceeds 0.9*/ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } sa = sa_bulk/(1.0 - w_ih_mean); ctf = gsw_ct_freezing(sa,p,saturation_fraction); hf = gsw_enthalpy_ct_exact(sa,ctf,p); tf = gsw_t_freezing(sa,p,saturation_fraction); h_ihf = gsw_enthalpy_ice(tf,p); cp_ih = gsw_cp_ice(tf,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p, &h_hat_sa,&h_hat_ct); gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa, NULL); gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa, NULL); dfunc_dw_ih = hf - h_ihf - sa*(h_hat_sa + h_hat_ct*ctf_sa + w_ih_mean*cp_ih*tf_sa/ (1.0 - w_ih_mean)); w_ih = w_ih_old - func/dfunc_dw_ih; if (w_ih > 0.9) { /*This ensures that the mass fraction of ice never exceeds 0.9*/ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } sa = sa_bulk/(1.0 - w_ih); } *sa_final = sa; *ct_final = gsw_ct_freezing(sa,p,saturation_fraction); *w_ih_final = w_ih; if (*w_ih_final < 0.0) { /* ! This will only trap cases that are smaller than zero by just ! machine precision */ *sa_final = sa_bulk; *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_bulk,p); *w_ih_final = 0.0; } } /* !========================================================================== elemental subroutine gsw_frazil_properties_potential (sa_bulk, h_pot_bulk,& p, sa_final, ct_final, w_ih_final) !========================================================================== ! ! Calculates the mass fraction of ice (mass of ice divided by mass of ice ! plus seawater), w_Ih_final, which results from given values of the bulk ! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, ! occurring at pressure p. The final equilibrium values of Absolute ! Salinity, SA_final, and Conservative Temperature, CT_final, of the ! interstitial seawater phase are also returned. This code assumes that ! there is no dissolved air in the seawater (that is, saturation_fraction ! is assumed to be zero throughout the code). ! ! When the mass fraction w_Ih_final is calculated as being a positive ! value, the seawater-ice mixture is at thermodynamic equilibrium. ! ! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, ! is sufficiently large (i.e. sufficiently "warm") so that there is no ice ! present in the final state. In this case the final state consists of ! only seawater rather than being an equilibrium mixture of seawater and ! ice which occurs when w_Ih_final is positive. Note that when ! w_Ih_final = 0, the final seawater is not at the freezing temperature. ! ! Note that this code uses the exact forms of CT_freezing and ! pot_enthalpy_ice_freezing. ! ! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture ! [ g/kg ] ! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture ! [ J/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! SA_final = Absolute Salinity of the seawater in the final state, ! whether or not any ice is present. [ g/kg ] ! CT_final = Conservative Temperature of the seawater in the the final ! state, whether or not any ice is present. [ deg C ] ! w_Ih_final = mass fraction of ice in the final seawater-ice mixture. ! If this ice mass fraction is positive, the system is at ! thermodynamic equilibrium. If this ice mass fraction is ! zero there is no ice in the final state which consists ! only of seawater which is warmer than the freezing ! temperature. [unitless] !-------------------------------------------------------------------------- */ void gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final) { GSW_TEOS10_CONSTANTS; int iterations, max_iterations; double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly, dpot_h_ihf_dsa, func, func0, h_pot_ihf, sa, w_ih_old, w_ih, x, xa, y, z; double f01 = -9.041191886754806e-1, f02 = 4.169608567309818e-2, f03 = -9.325971761333677e-3, f04 = 4.699055851002199e-2, f05 = -3.086923404061666e-2, f06 = 1.057761186019000e-2, f07 = -7.349302346007727e-2, f08 = 1.444842576424337e-1, f09 = -1.408425967872030e-1, f10 = 1.070981398567760e-1, f11 = -1.768451760854797e-2, f12 = -4.013688314067293e-1, f13 = 7.209753205388577e-1, f14 = -1.807444462285120e-1, f15 = 1.362305015808993e-1, f16 = -9.500974920072897e-1, f17 = 1.192134856624248, f18 = -9.191161283559850e-2, f19 = -1.008594411490973, f20 = 8.020279271484482e-1, f21 = -3.930534388853466e-1, f22 = -2.026853316399942e-2, f23 = -2.722731069001690e-2, f24 = 5.032098120548072e-2, f25 = -2.354888890484222e-2, f26 = -2.454090179215001e-2, f27 = 4.125987229048937e-2, f28 = -3.533404753585094e-2, f29 = 3.766063025852511e-2, f30 = -3.358409746243470e-2, f31 = -2.242158862056258e-2, f32 = 2.102254738058931e-2, f33 = -3.048635435546108e-2, f34 = -1.996293091714222e-2, f35 = 2.577703068234217e-2, f36 = -1.292053030649309e-2, g01 = 3.332286683867741e5, g02 = 1.416532517833479e4, g03 = -1.021129089258645e4, g04 = 2.356370992641009e4, g05 = -8.483432350173174e3, g06 = 2.279927781684362e4, g07 = 1.506238790315354e4, g08 = 4.194030718568807e3, g09 = -3.146939594885272e5, g10 = -7.549939721380912e4, g11 = 2.790535212869292e6, g12 = 1.078851928118102e5, g13 = -1.062493860205067e7, g14 = 2.082909703458225e7, g15 = -2.046810820868635e7, g16 = 8.039606992745191e6, g17 = -2.023984705844567e4, g18 = 2.871769638352535e4, g19 = -1.444841553038544e4, g20 = 2.261532522236573e4, g21 = -2.090579366221046e4, g22 = -1.128417003723530e4, g23 = 3.222965226084112e3, g24 = -1.226388046175992e4, g25 = 1.506847628109789e4, g26 = -4.584670946447444e4, g27 = 1.596119496322347e4, g28 = -6.338852410446789e4, g29 = 8.951570926106525e4, saturation_fraction = 0.0; /* !----------------------------------------------------------------------- ! Finding func0. This is the value of the function, func, that would ! result in the output w_Ih_final being exactly zero. !----------------------------------------------------------------------- */ func0 = h_pot_bulk - gsw_cp0 *gsw_ct_freezing(sa_bulk,p,saturation_fraction); /* !----------------------------------------------------------------------- ! Setting the three outputs for data points that have func0 non-negative !----------------------------------------------------------------------- */ if (func0 >= 0.0) { /* ! When func0 is zero or positive then the final answer will contain ! no frazil ice; that is, it will be pure seawater that is warmer ! than the freezing temperature. If func0 >= 0 we do not need to go ! through the modified Newton-Raphson procedure and we can simply ! write down the answer, as in the following 4 lines of code. */ *sa_final = sa_bulk; *ct_final = h_pot_bulk/gsw_cp0; *w_ih_final = 0.0; return; } /* !----------------------------------------------------------------------- !Begin finding the solution for data points that have func0 < 0, so that !the output will have a positive ice mass fraction w_Ih_final. !----------------------------------------------------------------------- */ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/ x = sa_bulk*1e-2; y = func0/3e5; z = p*1e-4; w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x)))) + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13 + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26 + f27*x) + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34 + f35*x + f36*y)))); if (w_ih > 0.9) { /* ! The ice mass fraction out of this code is restricted to be !less than 0.9. */ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } /* !The initial guess at the absolute salinity of the interstitial seawater */ sa = sa_bulk/(1.0 - w_ih); /* !----------------------------------------------------------------------- ! Doing a Newton step with a separate polynomial estimate of the mean ! derivative dfunc_dw_Ih_mean_poly. !-----------------------------------------------------------------------' */ ctf = gsw_ct_freezing(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p); func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf; xa = sa*1e-2; dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa))) + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa) + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15 + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20 + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih)) + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih))); w_ih_old = w_ih; w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly; sa = sa_bulk/(1.0 - w_ih); /* !----------------------------------------------------------------------- ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be ! fed into Newton's Method. !----------------------------------------------------------------------- */ ctf = gsw_ct_freezing(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p); gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa, NULL); gsw_pot_enthalpy_ice_freezing_first_derivatives(sa,p,&dpot_h_ihf_dsa, NULL); dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf - sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih)); if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0 && sa < 60.0 && p <= 3000.0) { max_iterations = 1; } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0 && sa < 120.0 && p <= 3500.0) { max_iterations = 2; } else { max_iterations = 3; } for (iterations = 1; iterations <= max_iterations; iterations++) { if (iterations > 1) { /*On the first iteration ctf and h_pot_ihf are both known*/ ctf = gsw_ct_freezing(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p); } /*This is the function, func, whose zero we seek ...*/ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf; w_ih_old = w_ih; w_ih = w_ih_old - func/dfunc_dw_ih; if (w_ih > 0.9) { *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } sa = sa_bulk/(1.0 - w_ih); } if (w_ih < 0.0) { *sa_final = sa_bulk; *ct_final = h_pot_bulk/gsw_cp0; *w_ih_final = 0.0; } else { *sa_final = sa; *ct_final = gsw_ct_freezing(sa,p,saturation_fraction); *w_ih_final = w_ih; } } /* !========================================================================== elemental subroutine gsw_frazil_properties_potential_poly (sa_bulk, & h_pot_bulk, p, sa_final, ct_final, w_ih_final) !========================================================================== ! ! Calculates the mass fraction of ice (mass of ice divided by mass of ice ! plus seawater), w_Ih_final, which results from given values of the bulk ! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, ! occurring at pressure p. The final equilibrium values of Absolute ! Salinity, SA_final, and Conservative Temperature, CT_final, of the ! interstitial seawater phase are also returned. This code assumes that ! there is no dissolved air in the seawater (that is, saturation_fraction ! is assumed to be zero throughout the code). ! ! When the mass fraction w_Ih_final is calculated as being a positive ! value, the seawater-ice mixture is at thermodynamic equilibrium. ! ! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, ! is sufficiently large (i.e. sufficiently "warm") so that there is no ice ! present in the final state. In this case the final state consists of ! only seawater rather than being an equilibrium mixture of seawater and ! ice which occurs when w_Ih_final is positive. Note that when ! w_Ih_final = 0, the final seawater is not at the freezing temperature. ! ! Note that this code uses the polynomial forms of CT_freezing and ! pot_enthalpy_ice_freezing. This code is intended to be used in ocean ! models where the model prognostic variables are SA_bulk and h_pot_bulk. ! ! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture ! [ g/kg ] ! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture ! [ J/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! SA_final = Absolute Salinity of the seawater in the final state, ! whether or not any ice is present. [ g/kg ] ! CT_final = Conservative Temperature of the seawater in the the final ! state, whether or not any ice is present. [ deg C ] ! w_Ih_final = mass fraction of ice in the final seawater-ice mixture. ! If this ice mass fraction is positive, the system is at ! thermodynamic equilibrium. If this ice mass fraction is ! zero there is no ice in the final state which consists ! only of seawater which is warmer than the freezing ! temperature. [unitless] !-------------------------------------------------------------------------- */ void gsw_frazil_properties_potential_poly(double sa_bulk, double h_pot_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final) { GSW_TEOS10_CONSTANTS; int iterations, max_iterations; double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly, dpot_h_ihf_dsa, func, func0, h_pot_ihf, sa, w_ih_old, w_ih, x, xa, y, z; double f01 = -9.041191886754806e-1, f02 = 4.169608567309818e-2, f03 = -9.325971761333677e-3, f04 = 4.699055851002199e-2, f05 = -3.086923404061666e-2, f06 = 1.057761186019000e-2, f07 = -7.349302346007727e-2, f08 = 1.444842576424337e-1, f09 = -1.408425967872030e-1, f10 = 1.070981398567760e-1, f11 = -1.768451760854797e-2, f12 = -4.013688314067293e-1, f13 = 7.209753205388577e-1, f14 = -1.807444462285120e-1, f15 = 1.362305015808993e-1, f16 = -9.500974920072897e-1, f17 = 1.192134856624248, f18 = -9.191161283559850e-2, f19 = -1.008594411490973, f20 = 8.020279271484482e-1, f21 = -3.930534388853466e-1, f22 = -2.026853316399942e-2, f23 = -2.722731069001690e-2, f24 = 5.032098120548072e-2, f25 = -2.354888890484222e-2, f26 = -2.454090179215001e-2, f27 = 4.125987229048937e-2, f28 = -3.533404753585094e-2, f29 = 3.766063025852511e-2, f30 = -3.358409746243470e-2, f31 = -2.242158862056258e-2, f32 = 2.102254738058931e-2, f33 = -3.048635435546108e-2, f34 = -1.996293091714222e-2, f35 = 2.577703068234217e-2, f36 = -1.292053030649309e-2, g01 = 3.332286683867741e5, g02 = 1.416532517833479e4, g03 = -1.021129089258645e4, g04 = 2.356370992641009e4, g05 = -8.483432350173174e3, g06 = 2.279927781684362e4, g07 = 1.506238790315354e4, g08 = 4.194030718568807e3, g09 = -3.146939594885272e5, g10 = -7.549939721380912e4, g11 = 2.790535212869292e6, g12 = 1.078851928118102e5, g13 = -1.062493860205067e7, g14 = 2.082909703458225e7, g15 = -2.046810820868635e7, g16 = 8.039606992745191e6, g17 = -2.023984705844567e4, g18 = 2.871769638352535e4, g19 = -1.444841553038544e4, g20 = 2.261532522236573e4, g21 = -2.090579366221046e4, g22 = -1.128417003723530e4, g23 = 3.222965226084112e3, g24 = -1.226388046175992e4, g25 = 1.506847628109789e4, g26 = -4.584670946447444e4, g27 = 1.596119496322347e4, g28 = -6.338852410446789e4, g29 = 8.951570926106525e4, saturation_fraction = 0.0; /* !----------------------------------------------------------------------- ! Finding func0. This is the value of the function, func, that would ! result in the output w_Ih_final being exactly zero. !----------------------------------------------------------------------- */ func0 = h_pot_bulk - gsw_cp0 *gsw_ct_freezing_poly(sa_bulk,p,saturation_fraction); /* !----------------------------------------------------------------------- ! Setting the three outputs for data points that have func0 non-negative !----------------------------------------------------------------------- */ if (func0 >= 0.0) { /* ! When func0 is zero or positive then the final answer will contain ! no frazil ice; that is, it will be pure seawater that is warmer ! han the freezing temperature. If func0 >= 0 we do not need to go ! through the modified Newton-Raphson procedure and we can simply ! write down the answer, as in the following 4 lines of code. */ *sa_final = sa_bulk; *ct_final = h_pot_bulk/gsw_cp0; *w_ih_final = 0.0; return; } /* !----------------------------------------------------------------------- !Begin finding the solution for data points that have func0 < 0, so that !the output will have a positive ice mass fraction w_Ih_final. !----------------------------------------------------------------------- */ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/ x = sa_bulk*1e-2; y = func0/3e5; z = p*1e-4; w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x)))) + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13 + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26 + f27*x) + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34 + f35*x + f36*y)))); if (w_ih > 0.9) { /* ! The ice mass fraction out of this code is restricted to be ! less than 0.9. */ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } /* ! The initial guess at the absolute salinity of the interstitial ! seawater */ sa = sa_bulk/(1.0 - w_ih); /* !----------------------------------------------------------------------- ! Doing a Newton step with a separate polynomial estimate of the mean ! derivative dfunc_dw_Ih_mean_poly. !----------------------------------------------------------------------- */ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p); func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf; xa = sa*1e-2; dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa))) + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa) + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15 + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20 + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih)) + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih))); w_ih_old = w_ih; w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly; sa = sa_bulk/(1.0 - w_ih); /* !----------------------------------------------------------------------- ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be ! fed into Newton's Method. !----------------------------------------------------------------------- */ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p); gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,&ctf_sa, NULL); gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(sa,p, &dpot_h_ihf_dsa, NULL); dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf - sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih)); if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0 && sa < 60.0 && p <= 3000.0) { max_iterations = 1; } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0 && sa < 120.0 && p <= 3500.0) { max_iterations = 2; } else { max_iterations = 3; } for (iterations = 1; iterations <= max_iterations; iterations++) { if (iterations > 1) { /*On the first iteration ctf and h_pot_ihf are both known*/ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p); } /*This is the function, func, whose zero we seek ...*/ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf; w_ih_old = w_ih; w_ih = w_ih_old - func/dfunc_dw_ih; if (w_ih > 0.9) { *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } sa = sa_bulk/(1.0 - w_ih); } if (w_ih < 0.0) { *sa_final = sa_bulk; *ct_final = h_pot_bulk/gsw_cp0; *w_ih_final = 0.0; } else { *sa_final = sa; *ct_final = gsw_ct_freezing_poly(sa,p,saturation_fraction); *w_ih_final = w_ih; } } /* !========================================================================== elemental subroutine gsw_frazil_ratios_adiabatic (sa, p, w_ih, & dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil) !========================================================================== ! ! Calculates the ratios of SA, CT and P changes when frazil ice forms or ! melts in response to an adiabatic change in pressure of a mixture of ! seawater and frazil ice crystals. ! ! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than ! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero ! whereas dCT/dSA would then be infinite. ! ! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure ! derivatives with the pressure measured in Pa not dbar. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! p = sea pressure of seawater at which melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! w_Ih = mass fraction of ice, that is the mass of ice divided by the ! sum of the masses of ice and seawater. That is, the mass of ! ice divided by the mass of the final mixed fluid. ! w_Ih must be between 0 and 1. [ unitless ] ! ! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity ! to that of Conservative Temperature [ g/(kg K) ] ! dSA_dP_frazil = the ratio of the changes in Absolute Salinity ! to that of pressure (in Pa) [ g/(kg Pa) ] ! dCT_dP_frazil = the ratio of the changes in Conservative Temperature ! to that of pressure (in Pa) [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_frazil_ratios_adiabatic (double sa, double p, double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil) { double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part, rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p, ctf, ctf_sa, ctf_p; double saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); tf = gsw_t_freezing(sa,p,saturation_fraction); h = gsw_enthalpy_ct_exact(sa,ctf,p); h_ih = gsw_enthalpy_ice(tf,p); cp_ih = gsw_cp_ice(tf,p); gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct); gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,&tf_p); gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction, &ctf_sa,&ctf_p); wcp = cp_ih*w_ih/(1.0 - w_ih); part = (tf_p - gamma_ih)/ctf_p; bracket1 = h_hat_ct + wcp*part; bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa)); rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa + wcp*tf_sa)); *dsa_dct_frazil = sa*(bracket1/bracket2); *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3; *dct_dp_frazil = ctf_p*bracket2*rec_bracket3; } /* !========================================================================== elemental subroutine gsw_frazil_ratios_adiabatic_poly (sa, p, w_ih, & dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil) !========================================================================== ! ! Calculates the ratios of SA, CT and P changes when frazil ice forms or ! melts in response to an adiabatic change in pressure of a mixture of ! seawater and frazil ice crystals. ! ! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than ! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero ! whereas dCT/dSA would then be infinite. ! ! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure ! derivatives with the pressure measured in Pa not dbar. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! p = sea pressure of seawater at which melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! w_Ih = mass fraction of ice, that is the mass of ice divided by the ! sum of the masses of ice and seawater. That is, the mass of ! ice divided by the mass of the final mixed fluid. ! w_Ih must be between 0 and 1. [ unitless ] ! ! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity ! to that of Conservative Temperature [ g/(kg K) ] ! dSA_dP_frazil = the ratio of the changes in Absolute Salinity ! to that of pressure (in Pa) [ g/(kg Pa) ] ! dCT_dP_frazil = the ratio of the changes in Conservative Temperature ! to that of pressure (in Pa) [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_frazil_ratios_adiabatic_poly(double sa, double p, double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil) { double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part, rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p, ctf, ctf_sa, ctf_p; double saturation_fraction = 0.0; tf = gsw_t_freezing_poly(sa,p,saturation_fraction); ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); h = gsw_enthalpy(sa,ctf,p); h_ih = gsw_enthalpy_ice(tf,p); cp_ih = gsw_cp_ice(tf,p); gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p); gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct); gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction, &tf_sa,&tf_p); gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction, &ctf_sa,&ctf_p); wcp = cp_ih*w_ih/(1.0 - w_ih); part = (tf_p - gamma_ih)/ctf_p; bracket1 = h_hat_ct + wcp*part; bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa)); rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa + wcp*tf_sa)); *dsa_dct_frazil = sa*(bracket1/bracket2); *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3; *dct_dp_frazil = ctf_p*bracket2*rec_bracket3; } /* ** The following function is buggy; users are advised to use ** gsw_geo_strf_dyn_height_1 instead. !========================================================================== pure function gsw_geo_strf_dyn_height (sa, ct, p, p_ref) !========================================================================== ! ! Calculates dynamic height anomaly as the integral of specific volume ! anomaly from the pressure p of the bottle to the reference pressure ! p_ref. ! ! Hence, geo_strf_dyn_height is the dynamic height anomaly with respect ! to a given reference pressure. This is the geostrophic streamfunction ! for the difference between the horizontal velocity at the pressure ! concerned, p, and the horizontal velocity at p_ref. Dynamic height ! anomaly is the geostrophic streamfunction in an isobaric surface. The ! reference values used for the specific volume anomaly are ! SSO = 35.16504 g/kg and CT = 0 deg C. This function calculates ! specific volume anomaly using the computationally efficient ! expression for specific volume of Roquet et al. (2015). ! ! This function evaluates the pressure integral of specific volume using ! SA and CT interpolated with respect to pressure using the method of ! Reiniger and Ross (1968). It uses a weighted mean of (i) values ! obtained from linear interpolation of the two nearest data points, and ! (ii) a linear extrapolation of the pairs of data above and below. This ! "curve fitting" method resembles the use of cubic splines. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! p_ref = reference pressure [ dbar ] ! ( i.e. reference absolute pressure - 10.1325 dbar ) ! ! geo_strf_dyn_height = dynamic height anomaly [ m^2/s^2 ] ! Note. If p_ref exceeds the pressure of the deepest bottle on a ! vertical profile, the dynamic height anomaly for each bottle ! on the whole vertical profile is returned as NaN. !-------------------------------------------------------------------------- */ static void p_sequence(double p1,double p2,double max_dp_i,double *pseq, int *nps); /* forward reference */ double * /* Returns NULL on error, dyn_height if okay */ gsw_geo_strf_dyn_heightRR(double *sa, double *ct, double *p, double p_ref, int n_levels, double *dyn_height) { GSW_TEOS10_CONSTANTS; int m_levels = (n_levels <= 0) ? 1 : n_levels, p_cnt, top_pad, i, nz, ibottle, ipref, np_max, np, ibpr=0, *iidata; double dp_min, dp_max, p_min, p_max, max_dp_i, *b, *b_av, *dp, *dp_i, *sa_i=NULL, *ct_i, *p_i=NULL, *geo_strf_dyn_height0; /* !-------------------------------------------------------------------------- ! This max_dp_i is the limit we choose for the evaluation of specific ! volume in the pressure integration. That is, the vertical integration ! of specific volume with respect to pressure is performed with the pressure ! increment being no more than max_dp_i (the default value being 1 dbar). !-------------------------------------------------------------------------- */ max_dp_i = 1.0; if ((nz = m_levels) <= 1) return (NULL); dp = (double *) malloc(nz*sizeof (double)); dp_min = 11000.0; dp_max = -11000.0; for (i=0; i dp_max) dp_max = dp[i]; } if (dp_min <= 0.0) { /* pressure must be monotonic */ free(dp); return (NULL); } p_min = p[0]; p_max = p[nz-1]; if (p_ref > p_max) { /*the reference pressure p_ref is deeper than all bottles*/ free(dp); return (NULL); } /* Determine if there is a "bottle" at exactly p_ref */ ipref = -1; for (ibottle = 0; ibottle < nz; ibottle++) { if (p[ibottle] == p_ref) { ipref = ibottle; break; } } if ((dp_max <= max_dp_i) && (p[0] == 0.0) && (ipref >= 0)) { /* !vertical resolution is good (bottle gap is no larger than max_dp_i) ! & the vertical profile begins at the surface (i.e. at p = 0 dbar) ! & the profile contains a "bottle" at exactly p_ref. */ b = (double *) malloc(3*nz*sizeof (double)); b_av = b+nz; geo_strf_dyn_height0 = b_av+nz; for (i=0; i 0) b_av[i-1] = 0.5*(b[i] + b[i-1]); } /* ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect ! to p_ref = 0 (the surface). */ geo_strf_dyn_height0[0] = 0.0; for (i=1; i= 0)) { /* ! Vertical resolution is already good (no larger than max_dp_i), and ! there is a "bottle" at exactly p_ref. */ sa_i = (double *) malloc(2*(nz+1)*sizeof (double)); ct_i = sa_i+nz+1; p_i = (double *) malloc((nz+1)*sizeof (double));; if (p_min > 0.0) { /* ! resolution is fine and there is a bottle at p_ref, but ! there is not a bottle at p = 0. So add an extra bottle. */ for (i=0; i 0.0) { /* ! there is not a bottle at p = 0. */ if (p_ref < p_min) { /* ! p_ref is shallower than the minimum bottle pressure. */ p_i[0] = 0.0; p_sequence(p_i[0],p_ref,max_dp_i, p_i+1,&np); ibpr = p_cnt = np; p_cnt++; p_sequence(p_ref,p_min,max_dp_i, p_i+p_cnt,&np); p_cnt += np; top_pad = p_cnt; } else { /* ! p_ref is deeper than the minimum bottle pressure. */ p_i[0] = 0.0; p_i[1] = p_min; top_pad = 2; p_cnt = 2; } } else { /* ! there is a bottle at p = 0. */ p_i[0] = p_min; top_pad = 1; p_cnt = 1; } for (ibottle=0; ibottle < nz-1; ibottle++) { iidata[ibottle] = p_cnt-1; if (p[ibottle] == p_ref) ibpr = p_cnt-1; if (p[ibottle] < p_ref && p[ibottle+1] > p_ref) { /* ! ... reference pressure is spanned by bottle pairs - ! need to include p_ref as an interpolated pressure. */ p_sequence(p[ibottle],p_ref,max_dp_i, p_i+p_cnt,&np); p_cnt += np; ibpr = p_cnt-1; p_sequence(p_ref,p[ibottle+1],max_dp_i,p_i+p_cnt,&np); p_cnt += np; } else { /* ! ... reference pressure is not spanned by bottle pairs. */ p_sequence(p[ibottle],p[ibottle+1],max_dp_i, p_i+p_cnt,&np); p_cnt += np; } } iidata[nz-1] = p_cnt-1; if (p[nz-1] == p_ref) ibpr = p_cnt-1; sa_i = (double *) malloc(2*p_cnt*sizeof (double)); ct_i = sa_i+p_cnt; if (top_pad > 1) { gsw_linear_interp_sa_ct(sa,ct,p,nz, p_i,top_pad-1,sa_i,ct_i); } gsw_rr68_interp_sa_ct(sa,ct,p,nz,p_i+top_pad-1,p_cnt-top_pad+1, sa_i+top_pad-1,ct_i+top_pad-1); } b = (double *) malloc(4*p_cnt*sizeof (double)); b_av = b+p_cnt; dp_i = b_av+p_cnt; geo_strf_dyn_height0 = dp_i+p_cnt; for (i=0; i 0) { dp_i[i-1] = p_i[i]-p_i[i-1]; b_av[i-1] = 0.5*(b[i] + b[i-1]); } } /* ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect ! to p_ref = 0 (the surface). */ geo_strf_dyn_height0[0] = 0.0; for (i=1; i p_next - p_tol) { iuniform++; } continue; } /* We did not insert p_ref, so insert either p_next or p[iorig]. */ if (p_next < p[iorig] - p_tol) { p_i[i] = p_next; if (p_ref == p_next) { *p_ref_ind_ptr = i; } iuniform++; } else { p_i[i] = p[iorig]; if (p_ref == p[iorig]) { *p_ref_ind_ptr = i; } p_indices[iorig] = i; /* Skip this p_next if it is close to the point we just added. */ if (p_next < p[iorig] + p_tol) { iuniform++; } iorig++; } } if (i == ni_max) { return (-1); /* error! */ } return (i); /* number of elements in p_i */ } /* Linearly interpolate to the grid made by define_grid_for_dh. We take advantage of what we know about the grids: they match at the end points, and both are monotonic. */ static int linear_interp_SA_CT_for_dh(double *sa, double *ct, double *p, int nz, double *p_i, int n_i, double *sa_i, double *ct_i) { int i, ii; double pfac; sa_i[0] = sa[0]; sa_i[n_i-1] = sa[nz-1]; ct_i[0] = ct[0]; ct_i[n_i-1] = ct[nz-1]; i = 1; for (ii=1; ii dp_max) { dp_max = dp[i]; } } if (dp_min <= 0.0) { /* pressure must be monotonic */ free(dp); return (2); } p_min = p[0]; p_max = p[nz-1]; if (p_ref > p_max || p_ref < p_min) { /* Reference pressure must be within the data range. */ free(dp); return (3); } /* Determine if there is a sample at exactly p_ref */ ipref = -1; for (i = 0; i < nz; i++) { if (p[i] == p_ref) { ipref = i; break; } } if ((dp_max <= max_dp_i) && (ipref >= 0)) { /* !vertical resolution is good (bottle gap is no larger than max_dp_i) ! & the profile contains a "bottle" at exactly p_ref. */ b = (double *)malloc(nz*sizeof (double)); b_av = (double *)malloc((nz-1) * sizeof(double)); for (i=0; i 0.0) g08 = g08 + x2*(5812.81456626732 + 851.226734946706*y)*log(x); return_value = g03 + g08; } else if (ns == 1 && nt == 0 && np == 0) { g08 = 8645.36753595126 + z*(-6620.98308089678 + z*(769.588305957198 + z*(-193.0648640214916 + (31.6816345533648 - 5.24960313181984*z)*z))) + x*(-7296.43987145382 + x*(8103.20462414788 + y*(2175.341332000392 + y*(-274.2290036817964 + y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y))) - 90.6734234051316*z) + x*(-5458.34205214835 - 980.14153344888*y + x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y) + 180.142097805543*z) + z*(-219.1676534131548 + (-16.32775915649044 - 120.7020447884644*z)*z)) + z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377 - 10.23755797323846*z)*z)) + y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-129.1994027934126 + z*(1149.174198007428 + z*(-162.5751787551336 + 76.9195462169742*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835 + 703.695562834065*z))))) + y*(1187.3715515697959 + z*(1458.233059470092 + z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146 + 14.09317606630898*z)))) + y*(1760.062705994408 + y*(-450.535298526802 + y*(182.8520895502518 + y*(-43.3206481750622 + 4.26033941694366*y) + z*(-595.457483974374 + (149.452282277512 - 72.9745838003176*z)*z)) + z*(1388.489628266536 + z*(-409.779283929806 + (227.123395681188 - 22.2565468652826*z)*z))) + z*(-1721.528607567954 + z*(674.819060538734 + z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z))))); if (sa > 0.0) g08 = g08 + (11625.62913253464 + 1702.453469893412*y)* log(x); else g08 = 0.0; return_value = 0.5*gsw_sfac*g08; } else if (ns == 0 && nt == 1 && np == 0) { g03 = 5.90578347909402 + z*(-270.983805184062 + z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 - 2.13290083518327*z)*z))) + y*(-24715.571866078 + z*(2910.0729080936 + z*(-1513.116771538718 + z*(546.959324647056 + z*(-111.1208127634436 + 8.68841343834394*z)))) + y*(2210.2236124548363 + z*(-2017.52334943521 + z*(1498.081172457456 + z*(-718.6359919632359 + (146.4037555781616 - 4.9892131862671505*z)*z))) + y*(-592.743745734632 + z*(1591.873781627888 + z*(-1207.261522487504 + (608.785486935364 - 105.4993508931208*z)*z)) + y*(290.12956292128547 + z*(-973.091553087975 + z*(602.603274510125 + z*(-276.361526170076 + 32.40953340386105*z))) + y*(-113.90630790850321 + y*(21.35571525415769 - 67.41756835751434*z) + z*(381.06836198507096 + z*(-133.7383902842754 + 49.023632509086724*z))))))); g08 = x2*(168.072408311545 + z*(729.116529735046 + z*(-343.956902961561 + z*(124.687671116248 + z*(-31.656964386073 + 7.04658803315449*z)))) + x*(-493.407510141682 + x*(543.835333000098 + x*(-196.028306689776 + 36.7571622995805*x) + y*(-137.1145018408982 + y*(148.10030845687618 + y*(-68.5590309679152 + 12.4848504784754*y))) - 22.6683558512829*z) + z*(-175.292041186547 + (83.1923927801819 - 29.483064349429*z)*z) + y*(-86.1329351956084 + z*(766.116132004952 + z*(-108.3834525034224 + 51.2796974779828*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(3.50240264723578 + 938.26075044542*z)))) + y*(1760.062705994408 + y*(-675.802947790203 + y*(365.7041791005036 + y*(-108.30162043765552 + 12.78101825083098*y) + z*(-1190.914967948748 + (298.904564555024 - 145.9491676006352*z)*z)) + z*(2082.7344423998043 + z*(-614.668925894709 + (340.685093521782 - 33.3848202979239*z)*z))) + z*(-1721.528607567954 + z*(674.819060538734 + z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z))))); if (sa > 0.0) g08 = g08 + 851.226734946706*x2*log(x); return_value = (g03 + g08)*0.025; } else if (ns == 0 && nt == 0 && np == 1) { g03 = 100015.695367145 + z*(-5089.1530840726 + z*(853.5533353388611 + z*(-133.2587017014444 + (21.0131554401542 - 3.278571068826234*z)*z))) + y*(-270.983805184062 + z*(1552.307223226202 + z*(-589.53765264366 + (115.91861051767 - 10.664504175916349*z)*z)) + y*(1455.0364540468 + z*(-1513.116771538718 + z*(820.438986970584 + z*(-222.2416255268872 + 21.72103359585985*z))) + y*(-672.50778314507 + z*(998.720781638304 + z*(-718.6359919632359 + (195.2050074375488 - 8.31535531044525*z)*z)) + y*(397.968445406972 + z*(-603.630761243752 + (456.589115201523 - 105.4993508931208*z)*z) + y*(-194.618310617595 + y*(63.5113936641785 - 9.63108119393062*y + z*(-44.5794634280918 + 24.511816254543362*z)) + z*(241.04130980405 + z*(-165.8169157020456 + 25.92762672308884*z))))))); g08 = x2*(-3310.49154044839 + z*(769.588305957198 + z*(-289.5972960322374 + (63.3632691067296 - 13.1240078295496*z)*z)) + x*(199.459603073901 + x*(-54.7919133532887 + 36.0284195611086*x - 22.6683558512829*y + (-8.16387957824522 - 90.52653359134831*z)*z) + z*(-104.588181856267 + (204.1334828179377 - 13.65007729765128*z)*z) + y*(-175.292041186547 + (166.3847855603638 - 88.449193048287*z)*z + y*(383.058066002476 + y*(-460.319931801257 + 234.565187611355*y) + z*(-108.3834525034224 + 76.9195462169742*z)))) + y*(729.116529735046 + z*(-687.913805923122 + z*(374.063013348744 + z*(-126.627857544292 + 35.23294016577245*z))) + y*(-860.764303783977 + y*(694.244814133268 + y*(-297.728741987187 + (149.452282277512 - 109.46187570047641*z)*z) + z*(-409.779283929806 + (340.685093521782 - 44.5130937305652*z)*z)) + z*(674.819060538734 + z*(-534.943668622914 + (176.8161433232 - 39.600077360584095*z)*z))))); return_value = (g03 + g08)*1.0e-8; } else if (ns == 0 && nt == 2 && np == 0) { g03 = -24715.571866078 + z*(2910.0729080936 + z* (-1513.116771538718 + z*(546.959324647056 + z*(-111.1208127634436 + 8.68841343834394*z)))) + y*(4420.4472249096725 + z*(-4035.04669887042 + z*(2996.162344914912 + z*(-1437.2719839264719 + (292.8075111563232 - 9.978426372534301*z)*z))) + y*(-1778.231237203896 + z*(4775.621344883664 + z*(-3621.784567462512 + (1826.356460806092 - 316.49805267936244*z)*z)) + y*(1160.5182516851419 + z*(-3892.3662123519 + z*(2410.4130980405 + z*(-1105.446104680304 + 129.6381336154442*z))) + y*(-569.531539542516 + y*(128.13429152494615 - 404.50541014508605*z) + z*(1905.341809925355 + z*(-668.691951421377 + 245.11816254543362*z)))))); g08 = x2*(1760.062705994408 + x*(-86.1329351956084 + x*(-137.1145018408982 + y*(296.20061691375236 + y*(-205.67709290374563 + 49.9394019139016*y))) + z*(766.116132004952 + z*(-108.3834525034224 + 51.2796974779828*z)) + y*(-60.136422517125 - 2761.9195908075417*z + y*(10.50720794170734 + 2814.78225133626*z))) + y*(-1351.605895580406 + y*(1097.1125373015109 + y*(-433.20648175062206 + 63.905091254154904*y) + z*(-3572.7449038462437 + (896.713693665072 - 437.84750280190565*z)*z)) + z*(4165.4688847996085 + z*(-1229.337851789418 + (681.370187043564 - 66.7696405958478*z)*z))) + z*(-1721.528607567954 + z*(674.819060538734 + z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z)))); return_value = (g03 + g08)*0.000625; } else if (ns == 1 && nt == 0 && np == 1) { g08 = -6620.98308089678 + z*(1539.176611914396 + z*(-579.1945920644748 + (126.7265382134592 - 26.2480156590992*z)*z)) + x*(598.378809221703 + x*(-219.1676534131548 + 180.142097805543*x - 90.6734234051316*y + (-32.65551831298088 - 362.10613436539325*z)*z) + z*(-313.764545568801 + (612.4004484538132 - 40.95023189295384*z)*z) + y*(-525.876123559641 + (499.15435668109143 - 265.347579144861*z)*z + y*(1149.174198007428 + y*(-1380.9597954037708 + 703.695562834065*y) + z*(-325.1503575102672 + 230.7586386509226*z)))) + y*(1458.233059470092 + z*(-1375.827611846244 + z*(748.126026697488 + z*(-253.255715088584 + 70.4658803315449*z))) + y*(-1721.528607567954 + y*(1388.489628266536 + y*(-595.457483974374 + (298.904564555024 - 218.92375140095282*z)*z) + z*(-819.558567859612 + (681.370187043564 - 89.0261874611304*z)*z)) + z*(1349.638121077468 + z*(-1069.887337245828 + (353.6322866464 - 79.20015472116819*z)*z)))); return_value = g08*gsw_sfac*0.5e-8; } else if (ns == 0 && nt == 1 && np == 1) { g03 = -270.983805184062 + z*(1552.307223226202 + z*(-589.53765264366 + (115.91861051767 - 10.664504175916349*z)*z)) + y*(2910.0729080936 + z*(-3026.233543077436 + z*(1640.877973941168 + z*(-444.4832510537744 + 43.4420671917197*z))) + y*(-2017.52334943521 + z*(2996.162344914912 + z*(-2155.907975889708 + (585.6150223126464 - 24.946065931335752*z)*z)) + y*(1591.873781627888 + z*(-2414.523044975008 + (1826.356460806092 - 421.9974035724832*z)*z) + y*(-973.091553087975 + z*(1205.20654902025 + z*(-829.084578510228 + 129.6381336154442*z)) + y*(381.06836198507096 - 67.41756835751434*y + z*(-267.4767805685508 + 147.07089752726017*z)))))); g08 = x2*(729.116529735046 + z*(-687.913805923122 + z*(374.063013348744 + z*(-126.627857544292 + 35.23294016577245*z))) + x*(-175.292041186547 - 22.6683558512829*x + (166.3847855603638 - 88.449193048287*z)*z + y*(766.116132004952 + y*(-1380.9597954037708 + 938.26075044542*y) + z*(-216.7669050068448 + 153.8390924339484*z))) + y*(-1721.528607567954 + y*(2082.7344423998043 + y*(-1190.914967948748 + (597.809129110048 - 437.84750280190565*z)*z) + z*(-1229.337851789418 + (1022.055280565346 - 133.5392811916956*z)*z)) + z*(1349.638121077468 + z*(-1069.887337245828 + (353.6322866464 - 79.20015472116819*z)*z)))); return_value = (g03 + g08)*2.5e-10; } else if (ns == 1 && nt == 1 && np == 0) { g08 = 1187.3715515697959 + z*(1458.233059470092 + z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146 + 14.09317606630898*z)))) + x*(-1480.222530425046 + x*(2175.341332000392 + x*(-980.14153344888 + 220.542973797483*x) + y*(-548.4580073635929 + y*(592.4012338275047 + y*(-274.2361238716608 + 49.9394019139016*y))) - 90.6734234051316*z) + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-258.3988055868252 + z*(2298.348396014856 + z*(-325.1503575102672 + 153.8390924339484*z)) + y*(-90.2046337756875 - 4142.8793862113125*z + y*(10.50720794170734 + 2814.78225133626*z)))) + y*(3520.125411988816 + y*(-1351.605895580406 + y*(731.4083582010072 + y*(-216.60324087531103 + 25.56203650166196*y) + z*(-2381.829935897496 + (597.809129110048 - 291.8983352012704*z)*z)) + z*(4165.4688847996085 + z*(-1229.337851789418 + (681.370187043564 - 66.7696405958478*z)*z))) + z*(-3443.057215135908 + z*(1349.638121077468 + z*(-713.258224830552 + (176.8161433232 - 31.68006188846728*z)*z)))); if (sa > 0.0) g08 = g08 + 1702.453469893412*log(x); return_value = 0.5*gsw_sfac*0.025*g08; } else if (ns == 2 && nt == 0 && np == 0) { g08 = 2.0*(8103.20462414788 + y*(2175.341332000392 + y*(-274.2290036817964 + y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y))) - 90.6734234051316*z) + 1.5*x*(-5458.34205214835 - 980.14153344888*y + (4.0/3.0)*x*(2247.60742726704 - 340.1237483177863*1.25*x + 220.542973797483*y) + 180.142097805543*z) + z*(-219.1676534131548 + (-16.32775915649044 - 120.7020447884644*z)*z)); if (x > 0.0) { g08 += (-7296.43987145382 + z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377 - 10.23755797323846*z)*z)) + y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-129.1994027934126 + z*(1149.174198007428 + z*(-162.5751787551336 + 76.9195462169742*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835 + 703.695562834065*z)))))/x + (11625.62913253464 + 1702.453469893412*y)/x2; } else g08 = 0.0; return_value = 0.25*gsw_sfac*gsw_sfac*g08; } else if (ns == 0 && nt == 0 && np == 2) { g03 = -5089.1530840726 + z*(1707.1066706777221 + z*(-399.7761051043332 + (84.0526217606168 - 16.39285534413117*z)*z)) + y*(1552.307223226202 + z*(-1179.07530528732 + (347.75583155301 - 42.658016703665396*z)*z) + y*(-1513.116771538718 + z*(1640.877973941168 + z*(-666.7248765806615 + 86.8841343834394*z)) + y*(998.720781638304 + z*(-1437.2719839264719 + (585.6150223126464 - 33.261421241781*z)*z) + y*(-603.630761243752 + (913.178230403046 - 316.49805267936244*z)*z + y*(241.04130980405 + y*(-44.5794634280918 + 49.023632509086724*z) + z*(-331.6338314040912 + 77.78288016926652*z)))))); g08 = x2*(769.588305957198 + z*(-579.1945920644748 + (190.08980732018878 - 52.4960313181984*z)*z) + x*(-104.588181856267 + x*(-8.16387957824522 - 181.05306718269662*z) + (408.2669656358754 - 40.95023189295384*z)*z + y*(166.3847855603638 - 176.898386096574*z + y*(-108.3834525034224 + 153.8390924339484*z))) + y*(-687.913805923122 + z*(748.126026697488 + z*(-379.883572632876 + 140.9317606630898*z)) + y*(674.819060538734 + z*(-1069.887337245828 + (530.4484299696 - 158.40030944233638*z)*z) + y*(-409.779283929806 + y*(149.452282277512 - 218.92375140095282*z) + (681.370187043564 - 133.5392811916956*z)*z)))); return_value = (g03 + g08)*1e-16 ; } else return_value = GSW_INVALID_VALUE; return (return_value); } /* ! ========================================================================= elemental function gsw_gibbs_ice (nt, np, t, p) ! ========================================================================= ! ! Ice specific Gibbs energy and derivatives up to order 2. ! ! nt = order of t derivative [ integers 0, 1 or 2 ] ! np = order of p derivative [ integers 0, 1 or 2 ] ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ! gibbs_ice = Specific Gibbs energy of ice or its derivatives. ! The Gibbs energy (when nt = np = 0) has units of: [ J/kg ] ! The temperature derivatives are output in units of: ! [ (J/kg) (K)^(-nt) ] ! The pressure derivatives are output in units of: ! [ (J/kg) (Pa)^(-np) ] ! The mixed derivatives are output in units of: ! [ (J/kg) (K)^(-nt) (Pa)^(-np) ] ! Note. The derivatives are taken with respect to pressure in Pa, not ! withstanding that the pressure input into this routine is in dbar. !-------------------------------------------------------------------------- */ double gsw_gibbs_ice (int nt, int np, double t, double p) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double dzi, g0, g0p, g0pp, sqrec_pt; DCOMPLEX r2, r2p, r2pp, g, sqtau_t1, sqtau_t2, tau, tau_t1, tau_t2; double s0 = -3.32733756492168e3; tau = (t + gsw_t0)*rec_tt; dzi = db2pa*p*rec_pt; if (nt == 0 && np == 0) { tau_t1 = tau/t1; sqtau_t1 = tau_t1*tau_t1; tau_t2 = tau/t2; sqtau_t2 = tau_t2*tau_t2; g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi))); r2 = r20 + dzi*(r21 + r22*dzi); g = r1*(tau*log((1.0 + tau_t1)/(1.0 - tau_t1)) + t1*(log(1.0 - sqtau_t1) - sqtau_t1)) + r2*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2)) + t2*(log(1.0 - sqtau_t2) - sqtau_t2)); return real(g0 - tt*(s0*tau - real(g))); // EF: bug in original. } else if (nt == 1 && np == 0) { tau_t1 = tau/t1; tau_t2 = tau/t2; r2 = r20 + dzi*(r21 + r22*dzi); g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1) + r2*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2); return (-s0 + real(g)); } else if (nt == 0 && np == 1) { tau_t2 = tau/t2; sqtau_t2 = tau_t2*tau_t2; g0p = rec_pt*(g01 + dzi*(2.0*g02 + dzi*(3.0*g03 + 4.0*g04*dzi))); r2p = rec_pt*(r21 + 2.0*r22*dzi); g = r2p*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2)) + t2*(log(1.0 - sqtau_t2) - sqtau_t2)); return (g0p + tt*real(g)); } else if (nt == 1 && np == 1) { tau_t2 = tau/t2; r2p = rec_pt*(r21 + 2.0*r22*dzi) ; g = r2p*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2); return (real(g)); } else if (nt == 2 && np == 0) { r2 = r20 + dzi*(r21 + r22*dzi); g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1) + r2*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2); return (rec_tt*real(g)); } else if (nt == 0 && np == 2) { sqrec_pt = rec_pt*rec_pt; tau_t2 = tau/t2; sqtau_t2 = tau_t2*tau_t2; g0pp = sqrec_pt*(2.0*g02 + dzi*(6.0*g03 + 12.0*g04*dzi)); r2pp = 2.0*r22*sqrec_pt; g = r2pp*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2)) + t2*(log(1.0 - sqtau_t2) - sqtau_t2)); return (g0pp + tt*real(g)); } else return (GSW_INVALID_VALUE); } /* ! ========================================================================= elemental function gsw_gibbs_ice_part_t (t, p) ! ========================================================================= ! ! part of the the first temperature derivative of Gibbs energy of ice ! that is the output is gibbs_ice(1,0,t,p) + S0 ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ! gibbs_ice_part_t = part of temperature derivative [ J kg^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_gibbs_ice_part_t(double t, double p) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double dzi, tau; DCOMPLEX g, tau_t1, tau_t2, r2; tau = (t + gsw_t0)*rec_tt; dzi = db2pa*p*rec_pt; tau_t1 = tau/t1; tau_t2 = tau/t2; r2 = r20 + dzi*(r21 + r22*dzi); g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1) + r2*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2); return (real(g)); } /* ! ========================================================================= elemental function gsw_gibbs_ice_pt0 (pt0) ! ========================================================================= ! ! Part of the the first temperature derivative of Gibbs energy of ice ! that is the output is "gibbs_ice(1,0,pt0,0) + s0" ! ! pt0 = potential temperature with reference sea pressure of zero dbar ! [ deg C ] ! ! gsw_gibbs_ice_pt0 = part of temperature derivative [ J kg^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_gibbs_ice_pt0(double pt0) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double tau; DCOMPLEX g, tau_t1, tau_t2; tau = (pt0 + gsw_t0)*rec_tt; tau_t1 = tau/t1; tau_t2 = tau/t2; g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1) + r20*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2); return (real(g)); } /* ! ========================================================================= elemental function gsw_gibbs_ice_pt0_pt0 (pt0) ! ========================================================================= ! ! The second temperature derivative of Gibbs energy of ice at the ! potential temperature with reference sea pressure of zero dbar. That is ! the output is gibbs_ice(2,0,pt0,0). ! ! pt0 = potential temperature with reference sea pressure of zero dbar ! [ deg C ] ! ! gsw_gibbs_ice_pt0_pt0 = temperature second derivative at pt0 !-------------------------------------------------------------------------- */ double gsw_gibbs_ice_pt0_pt0(double pt0) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double tau; DCOMPLEX g; tau = (pt0 + gsw_t0)*rec_tt; g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1) + r20*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2); return (rec_tt*real(g)); } /* !========================================================================== function gsw_gibbs_pt0_pt0(sa,pt0) !========================================================================== ! gibbs_tt at (sa,pt,0) ! ! sa : Absolute Salinity [g/kg] ! pt0 : potential temperature [deg C] ! ! gibbs_pt0_pt0 : gibbs_tt at (sa,pt,0) */ double gsw_gibbs_pt0_pt0(double sa, double pt0) { GSW_TEOS10_CONSTANTS; double x2, x, y, g03, g08; x2 = gsw_sfac*sa; x = sqrt(x2); y = pt0*0.025; g03 = -24715.571866078 + y*(4420.4472249096725 + y*(-1778.231237203896 + y*(1160.5182516851419 + y*(-569.531539542516 + y*128.13429152494615)))); g08 = x2*(1760.062705994408 + x*(-86.1329351956084 + x*(-137.1145018408982 + y*(296.20061691375236 + y*(-205.67709290374563 + 49.9394019139016*y))) + y*(-60.136422517125 + y*10.50720794170734)) + y*(-1351.605895580406 + y*(1097.1125373015109 + y*(-433.20648175062206 + 63.905091254154904*y)))); return ((g03 + g08)*0.000625); } /* !========================================================================== function gsw_grav(lat,p) !========================================================================== ! Calculates acceleration due to gravity as a function of latitude and as ! a function of pressure in the ocean. ! ! lat = latitude in decimal degrees north [ -90 ... +90 ] ! p = sea pressure [ dbar ] ! ! grav : grav = gravitational acceleration [ m s^-2 ] */ double gsw_grav(double lat, double p) { GSW_TEOS10_CONSTANTS; double x, sin2, gs, z; x = sin(lat*deg2rad); /* convert to radians */ sin2 = x*x; gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2); z = gsw_z_from_p(p,lat, 0, 0); return (gs*(1.0 - gamma*z)); /* z is the height corresponding to p. Note. In the ocean z is negative. */ } /* !========================================================================== elemental function gsw_helmholtz_energy_ice (t, p) !========================================================================== ! ! Calculates the Helmholtz energy of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! Helmholtz_energy_ice = Helmholtz energy of ice [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_helmholtz_energy_ice(double t, double p) { GSW_TEOS10_CONSTANTS; return (gsw_gibbs_ice(0,0,t,p) - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== function gsw_hill_ratio_at_sp2(t) !========================================================================== ! Calculates the Hill ratio, which is the adjustment needed to apply for ! Practical Salinities smaller than 2. This ratio is defined at a ! Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill ! ratio is the ratio of 2 to the output of the Hill et al. (1986) formula ! for Practical Salinity at the conductivity ratio, Rt, at which Practical ! Salinity on the PSS-78 scale is exactly 2. ! ! t : in-situ temperature (ITS-90) [deg C] ! hill_ratio_at_sp2 : Hill ratio [dimensionless] */ double gsw_hill_ratio_at_sp2(double t) { GSW_SP_COEFFICIENTS; double g0 = 2.641463563366498e-1, g1 = 2.007883247811176e-4, g2 = -4.107694432853053e-6, g3 = 8.401670882091225e-8, g4 = -1.711392021989210e-9, g5 = 3.374193893377380e-11, g6 = -5.923731174730784e-13, g7 = 8.057771569962299e-15, g8 = -7.054313817447962e-17, g9 = 2.859992717347235e-19, sp2 = 2.0; double t68, ft68, rtx0, dsp_drtx, sp_est, rtx, rtxm, x, part1, part2; double sqrty, sp_hill_raw_at_sp2; t68 = t*1.00024; ft68 = (t68 - 15.0)/(1.0 + k*(t68 - 15.0)); /*!------------------------------------------------------------------------ **! Find the initial estimates of Rtx (Rtx0) and of the derivative dSP_dRtx **! at SP = 2. **!------------------------------------------------------------------------ */ rtx0 = g0 + t68*(g1 + t68*(g2 + t68*(g3 + t68*(g4 + t68*(g5 + t68*(g6 + t68*(g7 + t68*(g8 + t68*g9)))))))); dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtx0)*rtx0)*rtx0)*rtx0 + ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtx0)*rtx0)*rtx0)*rtx0); /*!------------------------------------------------------------------------- **! Begin a single modified Newton-Raphson iteration to find Rt at SP = 2. **!------------------------------------------------------------------------- */ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx0)*rtx0)*rtx0)*rtx0)*rtx0 + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx0)*rtx0)*rtx0)* rtx0)*rtx0); rtx = rtx0 - (sp_est - sp2)/dsp_drtx; rtxm = 0.5*(rtx + rtx0); dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtxm)*rtxm)*rtxm)*rtxm + ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtxm)* rtxm)*rtxm)*rtxm); rtx = rtx0 - (sp_est - sp2)/dsp_drtx; /* **! This is the end of one full iteration of the modified Newton-Raphson **! iterative equation solver. The error in Rtx at this point is equivalent **! to an error in SP of 9e-16 psu. */ x = 400.0*rtx*rtx; sqrty = 10.0*rtx; part1 = 1.0 + x*(1.5 + x); part2 = 1.0 + sqrty*(1.0 + sqrty*(1.0 + sqrty)); sp_hill_raw_at_sp2 = sp2 - a0/part1 - b0*ft68/part2; return (2.0/sp_hill_raw_at_sp2); } /* !========================================================================== elemental subroutine gsw_ice_fraction_to_freeze_seawater (sa, ct, p, & t_ih, sa_freeze, ct_freeze, w_ih) !========================================================================== ! ! Calculates the mass fraction of ice (mass of ice divided by mass of ice ! plus seawater), which, when melted into seawater having (SA,CT,p) causes ! the final dilute seawater to be at the freezing temperature. The other ! outputs are the Absolute Salinity and Conservative Temperature of the ! final diluted seawater. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! t_Ih = in-situ temperature of the ice at pressure p (ITS-90) [ deg C ] ! ! SA_freeze = Absolute Salinity of seawater after the mass fraction of ! ice, ice_fraction, at temperature t_Ih has melted into the ! original seawater, and the final mixture is at the freezing ! temperature of seawater. [ g/kg ] ! ! CT_freeze = Conservative Temperature of seawater after the mass ! fraction, w_Ih, of ice at temperature t_Ih has melted into ! the original seawater, and the final mixture is at the ! freezing temperature of seawater. [ deg C ] ! ! w_Ih = mass fraction of ice, having in-situ temperature t_Ih, ! which, when melted into seawater at (SA,CT,p) leads to the ! final diluted seawater being at the freezing temperature. ! This output must be between 0 and 1. [unitless] !-------------------------------------------------------------------------- */ void gsw_ice_fraction_to_freeze_seawater(double sa, double ct, double p, double t_ih, double *sa_freeze, double *ct_freeze, double *w_ih) { int no_iter; double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero, dfunc_dsaf, func, func_plus1, func_zero, h, h_ih, saf, saf_mean, saf_old, tf, h_hat_sa, h_hat_ct, ctf_sa; double sa0 = 0.0, saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); if (ct < ctf) { /*The seawater ct input is below the freezing temp*/ *sa_freeze = GSW_INVALID_VALUE; *ct_freeze = *sa_freeze; *w_ih = *sa_freeze; return; } tf = gsw_t_freezing(sa0,p,saturation_fraction); if (t_ih > tf) { /*The input, t_Ih, exceeds the freezing temperature at sa = 0*/ *sa_freeze = GSW_INVALID_VALUE; *ct_freeze = *sa_freeze; *w_ih = *sa_freeze; return; } h = gsw_enthalpy_ct_exact(sa,ct,p); h_ih = gsw_enthalpy_ice(t_ih,p); ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction); func_zero = sa*(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h_ih); ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction); func_plus1 = sa*(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p) - h) - (h - h_ih); saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero); /*initial guess*/ ctf = gsw_ct_freezing(saf,p,saturation_fraction); gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct); gsw_ct_freezing_first_derivatives(saf,p,1.0,&ctf_sa,NULL); dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih); for (no_iter = 1; no_iter <= 2; no_iter++) { saf_old = saf; ctf_old = ctf; func = sa*(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h) - (saf_old - sa)*(h - h_ih); saf = saf_old - func/dfunc_dsaf; saf_mean = 0.5*(saf + saf_old); ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction); gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p, &h_hat_sa, &h_hat_ct); gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction, &ctf_sa, NULL); dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih); saf = saf_old - func/dfunc_dsaf; ctf = gsw_ct_freezing(saf,p,saturation_fraction); } /* ! After these 2 iterations of this modified Newton-Raphson method, the ! error in SA_freeze is less than 1.3d0x10^-13 g/kg, in CT_freeze is ! less than ! 4x10^-13 deg C and in w_Ih is less than 3.8d0x10^-15 ! which represent machine precision for these calculations. */ *sa_freeze = saf; *ct_freeze = ctf; *w_ih = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p))/(h - h_ih); } /* !========================================================================== function gsw_internal_energy(sa,ct,p) !========================================================================== ! Calculates internal energy of seawater. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! internal_energy : internal_energy of seawater [J/kg] */ double gsw_internal_energy(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; return (gsw_enthalpy(sa,ct,p) - (gsw_p0 + db2pa*p) *gsw_specvol(sa,ct,p)); } /* !========================================================================== elemental function gsw_internal_energy_ice (t, p) !========================================================================== ! ! Calculates the specific internal energy of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! internal_energy_ice = specific internal energy (u) [J/kg] !-------------------------------------------------------------------------- */ double gsw_internal_energy_ice(double t, double p) { GSW_TEOS10_CONSTANTS; return (gsw_gibbs_ice(0,0,t,p) - (gsw_t0 + t)*gsw_gibbs_ice(1,0,t,p) - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== subroutine gsw_ipv_vs_fnsquared_ratio(sa,ct,p,pref,nz,ipv_vs_fnsquared_ratio,p_mid) !========================================================================== ! Calculates the ratio of the vertical gradient of potential density to ! the vertical gradient of locally-referenced potential density. This ! ratio is also the ratio of the planetary Isopycnal Potential Vorticity ! (IPV) to f times N^2, hence the name for this variable, ! IPV_vs_fNsquared_ratio (see Eqn. (3.20.5) of IOC et al. (2010)). ! The reference sea pressure, p_ref, of the potential density surface must ! have a constant value. ! ! IPV_vs_fNsquared_ratio is evaluated at the mid pressure between the ! individual data points in the vertical. ! sa : Absolute Salinity (a profile (length nz)) [g/kg] ! ct : Conservative Temperature (a profile (length nz)) [deg C] ! p : sea pressure (a profile (length nz)) [dbar] ! p_ref : reference sea pressure of the potential density surface ! ( i.e. absolute reference pressure - 10.1325 dbar ) [dbar] ! nz : number of bottles ! IPV_vs_fNsquared_ratio ! : The ratio of the vertical gradient of potential density ! referenced to p_ref, to the vertical gradient of locally- ! referenced potential density. It is output on the same ! vertical (M-1)xN grid as p_mid. ! IPV_vs_fNsquared_ratio is dimensionless. [ unitless ] ! p_mid : Mid pressure between p grid (length nz-1) [dbar] */ void gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p, double p_ref, int nz, double *ipv_vs_fnsquared_ratio, double *p_mid) { int k; double dsa, sa_mid, dct, ct_mid; double alpha_mid, beta_mid; double alpha_pref, beta_pref, numerator, denominator; if (nz < 2) { *p_mid = *ipv_vs_fnsquared_ratio = GSW_INVALID_VALUE; return; } for (k = 0; k < nz-1; k++) { dsa = (sa[k] - sa[k+1]); dct = (ct[k] - ct[k+1]); sa_mid = 0.5*(sa[k] + sa[k+1]); ct_mid = 0.5*(ct[k] + ct[k+1]); p_mid[k] = 0.5*(p[k] + p[k+1]); alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]); beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]); alpha_pref = gsw_alpha(sa_mid,ct_mid,p_ref); beta_pref = gsw_beta(sa_mid,ct_mid,p_ref); numerator = dct*alpha_pref - dsa*beta_pref; denominator = dct*alpha_mid - dsa*beta_mid; if (denominator == 0.0) ipv_vs_fnsquared_ratio[k] = GSW_INVALID_VALUE; else ipv_vs_fnsquared_ratio[k] = numerator/denominator; } } /* !========================================================================== function gsw_kappa(sa,ct,p) !========================================================================== ! Calculates isentropic compressibility of seawater. This function ! has inputs of Absolute Salinity and Conservative Temperature. This ! function uses the computationally-efficient expression for ! specific volume in terms of SA, CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! kappa : isentropic compressibility [1.0/Pa] */ double gsw_kappa(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v, v_p, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); v_p = c000 + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs)))) + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020 + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs) + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201 + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs)) + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys))) + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys) + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z)))); return (-1e-8*v_p/v); } /* !========================================================================== elemental function gsw_kappa_const_t_ice (t, p) !========================================================================== ! ! Calculates isothermal compressibility of ice. ! Note. This is the compressibility of ice AT CONSTANT IN-SITU ! TEMPERATURE ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! kappa_const_t_ice = isothermal compressibility [ 1/Pa ] ! Note. The output units are 1/Pa not 1/dbar. !-------------------------------------------------------------------------- */ double gsw_kappa_const_t_ice(double t, double p) { return (-gsw_gibbs_ice(0,2,t,p)/gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== elemental function gsw_kappa_ice (t, p) !========================================================================== ! ! Calculates the isentropic compressibility of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! kappa_ice = isentropic compressibility [ 1/Pa ] ! Note. The output units are 1/Pa not 1/dbar. !-------------------------------------------------------------------------- */ double gsw_kappa_ice(double t, double p) { double gi_tp, gi_tt; gi_tt = gsw_gibbs_ice(2,0,t,p); gi_tp = gsw_gibbs_ice(1,1,t,p); return ((gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p))/ (gsw_gibbs_ice(0,1,t,p)*gi_tt)); } /* !========================================================================== function gsw_kappa_t_exact(sa,t,p) !========================================================================== ! isentropic compressibility of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_kappa_t_exact : isentropic compressibility [1/Pa] */ double gsw_kappa_t_exact(double sa, double t, double p) { int n0=0, n1=1, n2=2; double g_tt, g_tp; g_tt = gsw_gibbs(n0,n2,n0,sa,t,p); g_tp = gsw_gibbs(n0,n1,n1,sa,t,p); return ((g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p)) / (gsw_gibbs(n0,n0,n1,sa,t,p)*g_tt)); } /* !========================================================================== function gsw_latentheat_evap_ct(sa,ct) !========================================================================== ! Calculates latent heat, or enthalpy, of evaporation. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! latentheat_evaporation : latent heat of evaporation [J/kg] */ double gsw_latentheat_evap_ct(double sa, double ct) { GSW_TEOS10_CONSTANTS; double c0 = 2.499065844825125e6, c1 = -1.544590633515099e-1, c2 = -9.096800915831875e4, c3 = 1.665513670736000e2, c4 = 4.589984751248335e1, c5 = 1.894281502222415e1, c6 = 1.192559661490269e3, c7 = -6.631757848479068e3, c8 = -1.104989199195898e2, c9 = -1.207006482532330e3, c10 = -3.148710097513822e3, c11 = 7.437431482069087e2, c12 = 2.519335841663499e3, c13 = 1.186568375570869e1, c14 = 5.731307337366114e2, c15 = 1.213387273240204e3, c16 = 1.062383995581363e3, c17 = -6.399956483223386e2, c18 = -1.541083032068263e3, c19 = 8.460780175632090e1, c20 = -3.233571307223379e2, c21 = -2.031538422351553e2, c22 = 4.351585544019463e1, c23 = -8.062279018001309e2, c24 = 7.510134932437941e2, c25 = 1.797443329095446e2, c26 = -2.389853928747630e1, c27 = 1.021046205356775e2; double x, y; x = sqrt(gsw_sfac*sa); y = ct/40.0; return (c0 + x*(c1 + c4*y + x*(c3 + y*(c7 + c12*y) + x*(c6 + y*(c11 + y*(c17 + c24*y)) + x*(c10 + y*(c16 + c23*y) + x*(c15 + c22*y + c21*x))))) + y*(c2 + y*(c5 + c8*x + y*(c9 + x*(c13 + c18*x) + y*(c14 + x*(c19 + c25*x) + y*(c20 + c26*x + c27*y)))))); } /* !========================================================================== function gsw_latentheat_evap_t(sa,t) !========================================================================== ! ! Calculates latent heat, or enthalpy, of evaporation. ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! ! gsw_latentheat_evap_t : latent heat of evaporation [J/kg] */ double gsw_latentheat_evap_t(double sa, double t) { double ct = gsw_ct_from_pt(sa,t); return (gsw_latentheat_evap_ct(sa,ct)); } /* !-------------------------------------------------------------------------- ! isobaric melting enthalpy and isobaric evaporation enthalpy !-------------------------------------------------------------------------- !========================================================================== function gsw_latentheat_melting(sa,p) !========================================================================== ! Calculates latent heat, or enthalpy, of melting. ! ! sa : Absolute Salinity [g/kg] ! p : sea pressure [dbar] ! ! latentheat_melting : latent heat of melting [kg/m^3] */ double gsw_latentheat_melting(double sa, double p) { GSW_TEOS10_CONSTANTS; double tf = gsw_t_freezing(sa,p,0.0); return (1000.0*(gsw_chem_potential_water_t_exact(sa,tf,p) - (gsw_t0 + tf)*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p)) - gsw_enthalpy_ice(tf,p)); } /* !========================================================================== pure subroutine gsw_linear_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i) !========================================================================== ! This function interpolates the cast with respect to the interpolating ! variable p. This function finds the values of SA, CT at p_i on this cast. ! ! VERSION NUMBER: 3.05 (27th January 2015) ! ! This function was adapted from Matlab's interp1q. !========================================================================== */ void gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np, double *p_i, int npi, double *sa_i, double *ct_i) { char *in_rng; int *j, *k, *r, *jrev, *ki, imax_p, imin_p, i, n, m, ii; double *xi, *xxi, u, max_p, min_p; min_p = max_p = p[0]; imin_p = imax_p = 0; for (i=1; i max_p) { max_p = p[i]; imax_p = i; } } in_rng = (char *) malloc(npi*sizeof (char)); memset(in_rng, 0, npi*sizeof (char)); for (i=n=0; i= max_p) { sa_i[i] = sa[imax_p]; ct_i[i] = ct[imax_p]; } else { in_rng[i] = 1; n++; } } if (n==0) return; xi =(double *) malloc(n*sizeof (double)); k = (int *) malloc(3*n*sizeof (int)); ki = k+n; r = ki+n; m = np + n; xxi = (double *) malloc(m*sizeof (double)); j = (int *) malloc(2*m*sizeof (int)); jrev = j+m; ii = 0; for (i = 0; i tf_ih) { /* ! t_ih input exceeds the freezing temp. ! The 1e-6 C buffer in the allowable ! t_Ih is to ensure that there is some ice Ih in the sea ice. */ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } sa_bulk = (1.0 - w_ih)*sa; h_bulk = (1.0 - w_ih)*gsw_enthalpy_ct_exact(sa,ct,p) + w_ih*gsw_enthalpy_ice(t_ih,p); gsw_frazil_properties(sa_bulk,h_bulk,p,sa_final,ct_final,w_ih_final); if (*sa_final > GSW_ERROR_LIMIT) { *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; *w_ih_final = *sa_final; return; } } /* !========================================================================== elemental function gsw_melting_ice_sa_ct_ratio (sa, ct, p, t_ih) !========================================================================== ! ! Calculates the ratio of SA to CT changes when ice melts into seawater. ! It is assumed that a small mass of ice melts into an infinite mass of ! seawater. Because of the infinite mass of seawater, the ice will always ! melt. ! ! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. ! This is done so that when SA = 0, the output, dSA/dCT is zero whereas ! dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ] ! ! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts ! into a large mass of seawater ! [ g kg^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p, double t_ih) { double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); if (ct < ctf) { /*the seawater ct input is below the freezing temperature*/ return (GSW_INVALID_VALUE); } tf = gsw_t_freezing(0.0,p,saturation_fraction); if (t_ih > tf) { /*t_ih exceeds the freezing temperature at sa = 0*/ return (GSW_INVALID_VALUE); } h = gsw_enthalpy_ct_exact(sa,ct,p); h_ih = gsw_enthalpy_ice(t_ih,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct); /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa)); } /* !========================================================================== elemental function gsw_melting_ice_sa_ct_ratio_poly (sa, ct, p, t_ih) !========================================================================== ! ! Calculates the ratio of SA to CT changes when ice melts into seawater. ! It is assumed that a small mass of ice melts into an infinite mass of ! seawater. Because of the infinite mass of seawater, the ice will always ! melt. ! ! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. ! This is done so that when SA = 0, the output, dSA/dCT is zero whereas ! dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325d0 dbar ) ! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ] ! ! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts ! into a large mass of seawater ! [ g kg^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p, double t_ih) { double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); if (ct < ctf) { /*the seawater ct input is below the freezing temperature*/ return (GSW_INVALID_VALUE); } tf = gsw_t_freezing_poly(0.0,p,saturation_fraction); if (t_ih > tf) { /*t_ih exceeds the freezing temperature at sa = 0*/ return (GSW_INVALID_VALUE); } h = gsw_enthalpy(sa,ct,p); h_ih = gsw_enthalpy_ice(t_ih,p); gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct); /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa)); } /* !========================================================================== elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio (sa, p) !========================================================================== ! ! Calculates the ratio of SA to CT changes when sea ice melts into ! seawater with both the seawater and the sea ice temperatures being ! almost equal to the equilibrium freezing temperature. It is assumed ! that a small mass of seaice melts into an infinite mass of seawater. If ! indeed the temperature of the seawater and the sea ice were both equal ! to the freezing temperature, then no melting or freezing would occur; an ! imbalance between these three temperatures is needed for freezing or ! melting to occur (the three temperatures being (1) the seawater ! temperature, (2) the sea ice temperature, and (3) the freezing ! temperature. ! ! Note that the output of this function, dSA/dCT is independent of the ! sea ice salinity, SA_seaice. That is, the output applies equally to ! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result ! is proven in the manuscript, McDougall et al. (2013). ! ! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather ! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is ! zero whereas dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT ! changes when sea ice melts into seawater, with ! the seawater and sea ice being close to the ! freezing temperature. [ g/(kg K) ] !-------------------------------------------------------------------------- */ double gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p) { double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); t_seaice = gsw_t_freezing(sa,p,saturation_fraction); h = gsw_enthalpy_ct_exact(sa,ctf,p); h_ih = gsw_enthalpy_ice(t_seaice,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct); return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa)); } /* !========================================================================== elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio_poly (sa, p) !========================================================================== ! ! Calculates the ratio of SA to CT changes when sea ice melts into ! seawater with both the seawater and the sea ice temperatures being ! almost equal to the equilibrium freezing temperature. It is assumed ! that a small mass of seaice melts into an infinite mass of seawater. If ! indeed the temperature of the seawater and the sea ice were both equal ! to the freezing temperature, then no melting or freezing would occur; an ! imbalance between these three temperatures is needed for freezing or ! melting to occur (the three temperatures being (1) the seawater ! temperature, (2) the sea ice temperature, and (3) the freezing ! temperature. ! ! Note that the output of this function, dSA/dCT is independent of the ! sea ice salinity, SA_seaice. That is, the output applies equally to ! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result ! is proven in the manuscript, McDougall et al. (2013). ! ! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather ! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is ! zero whereas dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT ! changes when sea ice melts into seawater, with ! the seawater and sea ice being close to the ! freezing temperature. [ g/(kg K) ] !-------------------------------------------------------------------------- */ double gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa, double p) { double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); t_seaice = gsw_t_freezing_poly(sa,p,saturation_fraction); h = gsw_enthalpy(sa,ctf,p); h_ih = gsw_enthalpy_ice(t_seaice,p); gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct); return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa)); } /* !========================================================================== elemental subroutine gsw_melting_seaice_into_seawater (sa, ct, p, & w_seaice, sa_seaice, t_seaice, sa_final, ct_final) !========================================================================== ! ! Calculates the Absolute Salinity and Conservative Temperature that ! results when a given mass of sea ice (or ice) melts and is mixed into a ! known mass of seawater (whose properties are (SA,CT,p)). ! ! If the ice contains no salt (e.g. if it is of glacial origin), then the ! input 'SA_seaice' should be set to zero. ! ! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg ! and 12 g/kg of salt (defined as the mass of salt divided by the mass of ! ice Ih plus brine) and this programme returns NaN's if the input ! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, ! usually this would imply that the pressure p should be zero, as sea ice ! only occurs near the sea surface. The code does not impose that p = 0 ! if SA_seaice is non-zero. Rather, this is left to the user. ! ! The Absolute Salinity, SA_brine, of the brine trapped in little pockets ! in the sea ice, is in thermodynamic equilibrium with the ice Ih that ! surrounds these pockets. As the sea ice temperature, t_seaice, may be ! less than the freezing temperature, SA_brine is usually greater than the ! Absolute Salinity of the seawater at the time and place when and where ! the sea ice was formed. So usually SA_brine will be larger than SA. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! w_seaice = mass fraction of sea ice, that is the mass of sea ice ! divided by the sum of the masses of sea ice and seawater. ! That is, the mass of sea ice divided by the mass of the ! final mixed fluid. w_seaice must be between 0 and 1. ! [ unitless ] ! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of ! salt in sea ice, expressed in g of salt per kg of sea ice. ! [ g/kg ] ! t_seaice = the in-situ temperature of the sea ice (or ice) (ITS-90) ! [ deg C ] ! ! SA_final = Absolute Salinity of the mixture of the melted sea ice ! (or ice) and the original seawater [ g/kg ] ! CT_final = Conservative Temperature of the mixture of the melted ! sea ice (or ice) and the original seawater [ deg C ] !-------------------------------------------------------------------------- */ void gsw_melting_seaice_into_seawater(double sa, double ct, double p, double w_seaice, double sa_seaice, double t_seaice, double *sa_final, double *ct_final) { double ctf, h, h_brine, h_final, h_ih, sa_brine, tf_sa_seaice; double saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); if (ct < ctf) { /*The seawater ct input is below the freezing temp*/ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; return; } tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction) - 1e-6; if (t_seaice > tf_sa_seaice) { /* ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice ! is allowed to be exactly equal to tf_sa_seaice, the seaice is ! actually 100% brine at Absolute Salinity of SA_seaice. */ *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; return; } sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction); if (sa_brine >= GSW_ERROR_LIMIT) { *sa_final = GSW_INVALID_VALUE; *ct_final = *sa_final; return; } h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p); h = gsw_enthalpy_ct_exact(sa,ct,p); h_ih = gsw_enthalpy_ice(t_seaice,p); h_final = h - w_seaice*(h - h_ih - (h_brine - h_ih)*sa_seaice/sa_brine); *sa_final = sa - w_seaice*(sa - sa_seaice); /* !ctf = gsw_ct_freezing(sa_final,p,saturation_fraction) ! !if (h_final .lt. gsw_enthalpy_ct_exact(sa_final,ctf,p)) then ! ! Melting this much seaice is not possible as it would result in ! ! frozen seawater ! sa_final = gsw_error_code(4,func_name) ! ct_final = sa_final ! return !end if */ *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_final,p); if (*ct_final > GSW_ERROR_LIMIT) { *sa_final = *ct_final; return; } } /* !========================================================================== elemental function gsw_melting_seaice_sa_ct_ratio (sa, ct, p, sa_seaice, & t_seaice) !========================================================================== ! ! Calculates the ratio of SA to CT changes when sea ice melts into seawater. ! It is assumed that a small mass of sea ice melts into an infinite mass of ! seawater. Because of the infinite mass of seawater, the sea ice will ! always melt. ! ! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg ! and 12 g/kg of salt (defined as the mass of salt divided by the mass of ! ice Ih plus brine) and this programme returns NaN's if the input ! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, ! usually this would imply that the pressure p should be zero, as sea ice ! only occurs near the sea surface. The code does not impose that p = 0 if ! SA_seaice is non-zero. Rather, this is left to the user. ! ! The Absolute Salinity, SA_brine, of the brine trapped in little pockets ! in the sea ice, is in thermodynamic equilibrium with the ice Ih that ! surrounds these pockets. As the seaice temperature, t_seaice, may be ! less than the freezing temperature, SA_brine is usually greater than the ! Absolute Salinity of the seawater at the time and place when and where ! the sea ice was formed. So usually SA_brine will be larger than SA. ! ! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. ! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is ! zero whereas dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction ! of salt in sea ice expressed in g of salt per kg of ! sea ice [ g/kg ] ! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ] ! ! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when ! sea ice melts into a large mass of seawater [ g/(kg K) ] !-------------------------------------------------------------------------- */ double gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p, double sa_seaice, double t_seaice) { double ctf, delsa, h, h_brine, h_ih, sa_brine, tf_sa_seaice, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; if (sa_seaice < 0.0 || sa_seaice > 15.0) { return (GSW_INVALID_VALUE); } ctf = gsw_ct_freezing(sa,p,saturation_fraction); if (ct < ctf) { /*the seawater ct input is below the freezing temp*/ return (GSW_INVALID_VALUE); } tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction) - 1e-6; if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/ return (GSW_INVALID_VALUE); } /* !----------------------------------------------------------------------- !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is !some ice Ih in the sea ice. Without this buffer, that is if t_seaice !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually !100% brine at Absolute Salinity of SA_seaice. !----------------------------------------------------------------------- */ h = gsw_enthalpy_ct_exact(sa,ct,p); h_ih = gsw_enthalpy_ice(t_seaice,p); gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct); sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction); if (sa_brine > GSW_ERROR_LIMIT) { return (GSW_INVALID_VALUE); } h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p); delsa = sa - sa_seaice; return (h_hat_ct*delsa / (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine)); } /* !========================================================================== elemental function gsw_melting_seaice_sa_ct_ratio_poly (sa, ct, p, & sa_seaice, t_seaice) !========================================================================== ! ! Calculates the ratio of SA to CT changes when sea ice melts into seawater. ! It is assumed that a small mass of sea ice melts into an infinite mass of ! seawater. Because of the infinite mass of seawater, the sea ice will ! always melt. ! ! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg ! and 12 g/kg of salt (defined as the mass of salt divided by the mass of ! ice Ih plus brine) and this programme returns NaN's if the input ! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, ! usually this would imply that the pressure p should be zero, as sea ice ! only occurs near the sea surface. The code does not impose that p = 0 if ! SA_seaice is non-zero. Rather, this is left to the user. ! ! The Absolute Salinity, SA_brine, of the brine trapped in little pockets ! in the sea ice, is in thermodynamic equilibrium with the ice Ih that ! surrounds these pockets. As the seaice temperature, t_seaice, may be ! less than the freezing temperature, SA_brine is usually greater than the ! Absolute Salinity of the seawater at the time and place when and where ! the sea ice was formed. So usually SA_brine will be larger than SA. ! ! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. ! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is ! zero whereas dCT/dSA would be infinite. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction ! of salt in sea ice expressed in g of salt per kg of ! sea ice [ g/kg ] ! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ] ! ! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when ! sea ice melts into a large mass of seawater [ g/(kg K) ] !-------------------------------------------------------------------------- */ double gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct, double p, double sa_seaice, double t_seaice) { double ctf, delsa, h, h_brine, h_ih, sa_brine, ct_brine, tf_sa_seaice, h_hat_sa, h_hat_ct; double saturation_fraction = 0.0; if (sa_seaice < 0.0 || sa_seaice > 15.0) { return (GSW_INVALID_VALUE); } ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); if (ct < ctf) { /*the seawater ct input is below the freezing temp*/ return (GSW_INVALID_VALUE); } tf_sa_seaice = gsw_t_freezing_poly(sa_seaice,p,saturation_fraction) - 1e-6; if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/ return (GSW_INVALID_VALUE); } /* !----------------------------------------------------------------------- !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is !some ice Ih in the sea ice. Without this buffer, that is if t_seaice !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually !100% brine at Absolute Salinity of SA_seaice. !----------------------------------------------------------------------- */ h = gsw_enthalpy(sa,ct,p); h_ih = gsw_enthalpy_ice(t_seaice,p); gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct); sa_brine = gsw_sa_freezing_from_t_poly(t_seaice,p,saturation_fraction); if (sa_brine > GSW_ERROR_LIMIT) { return (GSW_INVALID_VALUE); } ct_brine = gsw_ct_from_t(sa_brine,t_seaice,p); h_brine = gsw_enthalpy(sa_brine,ct_brine,p); delsa = sa - sa_seaice; return (h_hat_ct*delsa / (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine)); } /* !-------------------------------------------------------------------------- ! water column properties, based on the 48-term expression for density !-------------------------------------------------------------------------- !========================================================================== subroutine gsw_nsquared(sa,ct,p,lat,nz,n2,p_mid) !========================================================================== ! Calculates the buoyancy frequency squared (N^2)(i.e. the Brunt-Vaisala ! frequency squared) at the mid pressure from the equation, ! ! ! 2 2 beta.d(SA) - alpha.d(CT) ! N = g .rho_local. ------------------------- ! dP ! ! The pressure increment, dP, in the above formula is in Pa, so that it is ! 10^4 times the pressure increment dp in dbar. ! ! sa : Absolute Salinity (a profile (length nz)) [g/kg] ! ct : Conservative Temperature (a profile (length nz)) [deg C] ! p : sea pressure (a profile (length nz)) [dbar] ! lat : latitude (a profile (length nz)) [deg N] ! nz : number of levels in the profile ! n2 : Brunt-Vaisala Frequency squared (length nz-1) [s^-2] ! p_mid : Mid pressure between p grid (length nz-1) [dbar] */ void gsw_nsquared(double *sa, double *ct, double *p, double *lat, int nz, double *n2, double *p_mid) { GSW_TEOS10_CONSTANTS; int k; double p_grav, n_grav, grav_local, dsa, sa_mid, dct, ct_mid, dp, rho_mid, alpha_mid, beta_mid; if (nz < 2) return; p_grav = gsw_grav(lat[0],p[0]); for (k = 0; k < nz-1; k++) { n_grav = gsw_grav(lat[k+1],p[k+1]); grav_local = 0.5*(p_grav + n_grav); dsa = (sa[k+1] - sa[k]); sa_mid = 0.5*(sa[k] + sa[k+1]); dct = (ct[k+1] - ct[k]); ct_mid = 0.5*(ct[k] + ct[k+1]); dp = (p[k+1] - p[k]); p_mid[k] = 0.5*(p[k] + p[k+1]); rho_mid = gsw_rho(sa_mid,ct_mid,p_mid[k]); alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]); beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]); n2[k] = (grav_local*grav_local)*(rho_mid/(db2pa*dp))* (beta_mid*dsa - alpha_mid*dct); p_grav = n_grav; } } /* !========================================================================== function gsw_o2sol(sa, ct, p, lon, lat) !========================================================================== ! ! Calculates the oxygen concentration expected at equilibrium with air at ! an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including ! saturated water vapor. This function uses the solubility coefficients ! derived from the data of Benson and Krause (1984), as fitted by Garcia ! and Gordon (1992, 1993). ! ! Note that this algorithm has not been approved by IOC and is not work ! from SCOR/IAPSO Working Group 127. It is included in the GSW ! Oceanographic Toolbox as it seems to be oceanographic best practice. ! ! SA : Absolute Salinity of seawater [ g/kg ] ! CT : Conservative Temperature of seawater (ITS-90) [ deg C ] ! p : sea pressure at which the melting occurs [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! lat : latitude [deg] ! lon : longitude [deg] ! ! gsw_o2sol : olubility of oxygen in micro-moles per kg [umol/kg] */ double gsw_o2sol(double sa, double ct, double p, double lon, double lat) { GSW_TEOS10_CONSTANTS; double sp, pt, pt68, x, y, o2sol, a0, a1, a2, a3, a4, a5, b0, b1, b2, b3, c0; sp = gsw_sp_from_sa(sa, p, lon, lat); x = sp; pt = gsw_pt_from_ct(sa, ct); pt68 = pt*1.00024; y = log((298.15 - pt68)/(gsw_t0 + pt68)); a0 = 5.80871; a1 = 3.20291; a2 = 4.17887; a3 = 5.10006; a4 = -9.86643e-2; a5 = 3.80369; b0 = -7.01577e-3; b1 = -7.70028e-3; b2 = -1.13864e-2; b3 = -9.51519e-3; c0 = -2.75915e-7; o2sol = exp(a0 + y*(a1 + y*(a2 + y*(a3 + y*(a4 + a5*y)))) + x*(b0 + y*(b1 + y*(b2 + b3*y)) + c0*x)); return o2sol; } /* !========================================================================== function gsw_o2sol_sp_pt(sp, pt) !========================================================================== ! ! Calculates the oxygen concentration expected at equilibrium with air at ! an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including ! saturated water vapor. This function uses the solubility coefficients ! derived from the data of Benson and Krause (1984), as fitted by Garcia ! and Gordon (1992, 1993). ! ! Note that this algorithm has not been approved by IOC and is not work ! from SCOR/IAPSO Working Group 127. It is included in the GSW ! Oceanographic Toolbox as it seems to be oceanographic best practice. ! ! SP : Practical Salinity (PSS-78) [ unitless ] ! pt : potential temperature (ITS-90) referenced [ dbar ] ! to one standard atmosphere (0 dbar). ! ! gsw_o2sol_sp_pt : olubility of oxygen in micro-moles per kg [umol/kg] */ double gsw_o2sol_sp_pt(double sp, double pt) { GSW_TEOS10_CONSTANTS; double pt68, x, y, o2sol, a0, a1, a2, a3, a4, a5, b0, b1, b2, b3, c0; x = sp; pt68 = pt*1.00024; y = log((298.15 - pt68)/(gsw_t0 + pt68)); a0 = 5.80871; a1 = 3.20291; a2 = 4.17887; a3 = 5.10006; a4 = -9.86643e-2; a5 = 3.80369; b0 = -7.01577e-3; b1 = -7.70028e-3; b2 = -1.13864e-2; b3 = -9.51519e-3; c0 = -2.75915e-7; o2sol = exp(a0 + y*(a1 + y*(a2 + y*(a3 + y*(a4 + a5*y)))) + x*(b0 + y*(b1 + y*(b2 + b3*y)) + c0*x)); return o2sol; } /* !========================================================================== function gsw_p_from_z(z,lat, geo_strf_dyn_height, sea_surface_geopotential) !========================================================================== ! Calculates the pressure p from height z ! ! z : height [m] ! lat : latitude [deg] ! geo_strf_dyn_height : dynamic height anomaly [m^2/s^2] ! Note that the reference pressure, p_ref, of geo_strf_dyn_height must ! be zero (0) dbar. ! sea_surface_geopotential : geopotential at zero sea pressure [m^2/s^2] ! ! gsw_p_from_z : pressure [dbar] */ double gsw_p_from_z(double z, double lat, double geo_strf_dyn_height, double sea_surface_geopotential) { GSW_TEOS10_CONSTANTS; double sinlat, sin2, gs, c1, p, df_dp, f, p_old, p_mid; if (z > 5) return GSW_INVALID_VALUE; sinlat = sin(lat*deg2rad); sin2 = sinlat*sinlat; gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2); /* get the first estimate of p from Saunders (1981) */ c1 = 5.25e-3*sin2 + 5.92e-3; p = -2.0*z/((1-c1) + sqrt((1-c1)*(1-c1) + 8.84e-6*z)) ; /* end of the first estimate from Saunders (1981) */ df_dp = db2pa*gsw_specvol_sso_0(p); /* initial value of the derivative of f */ f = gsw_enthalpy_sso_0(p) + gs*(z - 0.5*gamma*(z*z)) - (geo_strf_dyn_height + sea_surface_geopotential); p_old = p; p = p_old - f/df_dp; p_mid = 0.5*(p + p_old); df_dp = db2pa*gsw_specvol_sso_0(p_mid); p = p_old - f/df_dp; return p; } /* !========================================================================== elemental function gsw_pot_enthalpy_from_pt_ice (pt0_ice) !========================================================================== ! ! Calculates the potential enthalpy of ice from potential temperature of ! ice (whose reference sea pressure is zero dbar). ! ! pt0_ice = potential temperature of ice (ITS-90) [ deg C ] ! ! gsw_pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_pot_enthalpy_from_pt_ice(double pt0_ice) { GSW_TEOS10_CONSTANTS; GSW_GIBBS_ICE_COEFFICIENTS; double tau; DCOMPLEX h0_part, sqtau_t1, sqtau_t2; tau = (pt0_ice + gsw_t0)*rec_tt; sqtau_t1 = (tau/t1)*(tau/t1); sqtau_t2 = (tau/t2)*(tau/t2); h0_part = r1*t1*(log(1.0 - sqtau_t1) + sqtau_t1) + r20*t2*(log(1.0 - sqtau_t2) + sqtau_t2); return (g00 + tt*real(h0_part)); } /* !========================================================================== elemental function gsw_pot_enthalpy_from_pt_ice_poly (pt0_ice) !========================================================================== ! ! Calculates the potential enthalpy of ice from potential temperature of ! ice (whose reference sea pressure is zero dbar). This is a ! compuationally efficient polynomial fit to the potential enthalpy of ! ice. ! ! pt0_ice = potential temperature of ice (ITS-90) [ deg C ] ! ! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice) { int iteration; double df_dt, f, pot_enthalpy_ice, pot_enthalpy_ice_mid, pot_enthalpy_ice_old, p0 = -3.333601570157700e5, p1 = 2.096693916810367e3, p2 = 3.687110754043292, p3 = 4.559401565980682e-4, p4 = -2.516011957758120e-6, p5 = -1.040364574632784e-8, p6 = -1.701786588412454e-10, p7 = -7.667191301635057e-13; /*initial estimate of the potential enthalpy.*/ pot_enthalpy_ice = p0 + pt0_ice*(p1 + pt0_ice*(p2 + pt0_ice*(p3 + pt0_ice*(p4 + pt0_ice*(p5 + pt0_ice*(p6 + pt0_ice*p7)))))); df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice); for (iteration = 1; iteration <= 5; iteration++) { pot_enthalpy_ice_old = pot_enthalpy_ice; f = gsw_pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice_old) - pt0_ice; pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt; pot_enthalpy_ice_mid = 0.5*(pot_enthalpy_ice+pot_enthalpy_ice_old); df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice_mid); pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt; } /* ! The error of this fit ranges between -6e-3 and 6e-3 J/kg over the | potential temperature range of -100 to 2 deg C, or the potential | enthalpy range of -5.7 x 10^5 to -3.3 x 10^5 J/kg. */ return (pot_enthalpy_ice); } /* !========================================================================== elemental function gsw_pot_enthalpy_ice_freezing (sa, p) !========================================================================== ! ! Calculates the potential enthalpy of ice at which seawater freezes. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing ! of seawater [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pot_enthalpy_ice_freezing(double sa, double p) { double pt0_ice, t_freezing; t_freezing = gsw_t_freezing(sa,p,0.0) ; pt0_ice = gsw_pt0_from_t_ice(t_freezing,p); return (gsw_pot_enthalpy_from_pt_ice(pt0_ice)); } /* !========================================================================== elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives (sa, & p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p) !========================================================================== ! ! Calculates the first derivatives of the potential enthalpy of ice at ! which seawater freezes, with respect to Absolute Salinity SA and ! pressure P (in Pa). ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy ! of ice at freezing (ITS-90) with respect to Absolute ! salinity at fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ] ! ! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy ! of ice at freezing (ITS-90) with respect to pressure ! (in Pa) at fixed Absolute Salinity [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa, double p, double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p) { GSW_TEOS10_CONSTANTS; double cp_ihf, pt_icef, ratio_temp, tf, tf_p, tf_sa; double saturation_fraction = 0.0; tf = gsw_t_freezing(sa,p,saturation_fraction); pt_icef = gsw_pt0_from_t_ice(tf,p); ratio_temp = (gsw_t0 + pt_icef)/(gsw_t0 + tf); cp_ihf = gsw_cp_ice(tf,p); if ((pot_enthalpy_ice_freezing_sa != NULL) && (pot_enthalpy_ice_freezing_p != NULL)) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, &tf_sa,&tf_p); } else if (pot_enthalpy_ice_freezing_sa != NULL) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, &tf_sa, NULL); } else if (pot_enthalpy_ice_freezing_p != NULL) { gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, NULL,&tf_p); } if (pot_enthalpy_ice_freezing_sa != NULL) *pot_enthalpy_ice_freezing_sa = ratio_temp*cp_ihf*tf_sa; if (pot_enthalpy_ice_freezing_p != NULL) *pot_enthalpy_ice_freezing_p = ratio_temp*cp_ihf*tf_p - (gsw_t0 + pt_icef)*gsw_gibbs_ice(1,1,tf,p); } /* !========================================================================== elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(& sa, p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p) !========================================================================== ! ! Calculates the first derivatives of the potential enthalpy of ice Ih at ! which ice melts into seawater with Absolute Salinity SA and at pressure ! p. This code uses the comptationally efficient polynomial fit of the ! freezing potential enthalpy of ice Ih (McDougall et al., 2015). ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy ! of ice at freezing (ITS-90) with respect to Absolute ! salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e. [ J/g ] ! ! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy ! of ice at freezing (ITS-90) with respect to pressure ! (in Pa) at fixed Absolute Salinity [ (J/kg)/Pa ] !-------------------------------------------------------------------------- */ void gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa, double p, double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p) { double p_r, sa_r, x, d1 = -1.249490228128056e4, d2 = 1.336783910789822e4, d3 = -4.811989517774642e4, d4 = 8.044864276240987e4, d5 = -7.124452125071862e4, d6 = 2.280706828014839e4, d7 = 0.315423710959628e3, d8 = -3.592775732074710e2, d9 = 1.644828513129230e3, d10 = -4.809640968940840e3, d11 = 2.901071777977272e3, d12 = -9.218459682855746e2, d13 = 0.379377450285737e3, d14 = -2.672164989849465e3, d15 = 5.044317489422632e3, d16 = -2.631711865886377e3, d17 = -0.160245473297112e3, d18 = 4.029061696035465e2, d19 = -3.682950019675760e2, f1 = -2.034535061416256e4, f2 = 0.315423710959628e3, f3 = -0.239518382138314e3, f4 = 0.822414256564615e3, f5 = -1.923856387576336e3, f6 = 0.967023925992424e3, f7 = -0.263384562367307e3, f8 = -5.051613740291480e3, f9 = 7.587549005714740e2, f10 = -3.562886653132620e3, f11 = 5.044317489422632e3, f12 = -2.105369492709102e3, f13 = 6.387082316647800e2, f14 = -4.807364198913360e2, f15 = 8.058123392070929e2, f16 = -5.524425029513641e2; sa_r = sa*1e-2; x = sqrt(sa_r); p_r = p*1e-4; if (pot_enthalpy_ice_freezing_sa != NULL) *pot_enthalpy_ice_freezing_sa = (d1 + x*(d2 + x*(d3 + x*(d4 + x*(d5 + d6*x)))) + p_r*(d7 + x*(d8 + x*(d9 + x*(d10 + x*(d11 + d12*x)))) + p_r*(d13 + x*(d14 + x*(d15 + d16*x)) + p_r*(d17 + x*(d18 + d19*x)))))*1e-2; if (pot_enthalpy_ice_freezing_p != NULL) *pot_enthalpy_ice_freezing_p = (f1 + sa_r*(f2 + x*(f3 + x*(f4 + x*(f5 + x*(f6 + f7*x))))) + p_r*(f8 + sa_r*(f9 + x*(f10 + x*(f11 + f12*x))) + p_r*(f13 + sa_r*(f14 + x*(f15 + f16*x)))))*1e-8; } /* !========================================================================== elemental function gsw_pot_enthalpy_ice_freezing_poly (sa, p) !========================================================================== ! ! Calculates the potential enthalpy of ice at which seawater freezes. ! The error of this fit ranges between -2.5 and 1 J/kg with an rms of ! 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the ! error in the fit is between -0.7 and 0.7 with an rms of ! 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when ! compared with the potential enthalpy calculated from the exact in-situ ! freezing temperature which is found by a Newton-Raphson iteration of the ! equality of the chemical potentials of water in seawater and in ice. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing ! of seawater [ J/kg ] !-------------------------------------------------------------------------- */ double gsw_pot_enthalpy_ice_freezing_poly(double sa, double p) { double p_r, sa_r, x, c0 = -3.333548730778702e5, c1 = -1.249490228128056e4, c2 = 0.891189273859881e4, c3 = -2.405994758887321e4, c4 = 3.217945710496395e4, c5 = -2.374817375023954e4, c6 = 0.651630522289954e4, c7 = -2.034535061416256e4, c8 = -0.252580687014574e4, c9 = 0.021290274388826e4, c10 = 0.315423710959628e3, c11 = -0.239518382138314e3, c12 = 0.379377450285737e3, c13 = 0.822414256564615e3, c14 = -1.781443326566310e3, c15 = -0.160245473297112e3, c16 = -1.923856387576336e3, c17 = 2.522158744711316e3, c18 = 0.268604113069031e3, c19 = 0.967023925992424e3, c20 = -1.052684746354551e3, c21 = -0.184147500983788e3, c22 = -0.263384562367307e3; sa_r = sa*1e-2; x = sqrt(sa_r); p_r = p*1e-4; return (c0 + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x))))) + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12 + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r) + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r)))); } /* !========================================================================== function gsw_pot_rho_t_exact(sa,t,p,p_ref) !========================================================================== ! Calculates the potential density of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! p_ref : reference sea pressure [dbar] ! ! gsw_pot_rho_t_exact : potential density [kg/m^3] */ double gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref) { double pt = gsw_pt_from_t(sa,t,p,p_ref); return (gsw_rho_t_exact(sa,pt,p_ref)); } /* !========================================================================== elemental function gsw_pressure_coefficient_ice (t, p) !========================================================================== ! ! Calculates pressure coefficient of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pressure_coefficient_ice = pressure coefficient of ice [Pa/K] ! Note. The output units are Pa/K NOT dbar/K. !-------------------------------------------------------------------------- */ double gsw_pressure_coefficient_ice(double t, double p) { return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,2,t,p)); } /* !========================================================================== elemental function gsw_pressure_freezing_ct (sa, ct, saturation_fraction) !========================================================================== ! ! Calculates the pressure (in dbar) of seawater at the freezing ! temperature. That is, the output is the pressure at which seawater, ! with Absolute Salinity SA, Conservative Temperature CT, and with ! saturation_fraction of dissolved air, freezes. If the input values are ! such that there is no value of pressure in the range between 0 dbar and ! 10,000 dbar for which seawater is at the freezing temperature, the ! output, pressure_freezing, is put equal to NaN. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! pressure_freezing = sea pressure at which the seawater freezes [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) !-------------------------------------------------------------------------- */ double gsw_pressure_freezing_ct(double sa, double ct, double saturation_fraction) { GSW_TEOS10_CONSTANTS; int i_iter, number_of_iterations = 3; double ct_freezing_p0, ct_freezing_p10000, dctf_dp, f, pf, pfm, pf_old, ctfreezing_p; /* ! rec_Pa2dbar is to have dCTf_dp in units of K/dbar rather than K/Pa ! Find CT > CT_freezing_p0. If this is the case, the input CT value ! represent seawater that will not be frozen at any positive p. */ ct_freezing_p0 = gsw_ct_freezing(sa,0.0,saturation_fraction); if (ct > ct_freezing_p0) { return (GSW_INVALID_VALUE); } /* ! Find CT < CT_freezing_p10000. If this is the case, the input CT value ! represent seawater that is frozen even at p = 10,000 dbar. */ ct_freezing_p10000 = gsw_ct_freezing(sa,1e4,saturation_fraction); if (ct < ct_freezing_p10000) { return (GSW_INVALID_VALUE); } /* ! This is the initial (linear) guess of the freezing pressure, in dbar. */ pf = rec_pa2db*(ct_freezing_p0 - ct)/ (ct_freezing_p0 - ct_freezing_p10000); gsw_ct_freezing_first_derivatives(sa,pf,saturation_fraction, NULL,&ctfreezing_p); dctf_dp = rec_pa2db*ctfreezing_p; /* ! this dctf_dp is the initial value of the partial derivative of ! ct_freezing with respect to pressure (in dbar) at fixed sa, ! assuming that the saturation_fraction is zero. */ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) { pf_old = pf; f = gsw_ct_freezing(sa,pf_old,saturation_fraction) - ct; pf = pf_old - f/dctf_dp; pfm = 0.5*(pf + pf_old); gsw_ct_freezing_first_derivatives(sa,pfm,saturation_fraction, NULL,&ctfreezing_p); dctf_dp = rec_pa2db*ctfreezing_p; pf = pf_old - f/dctf_dp; } if (gsw_sa_p_inrange(sa,pf)) return (pf); return (GSW_INVALID_VALUE); } /* !========================================================================== elemental function gsw_pt0_cold_ice_poly (pot_enthalpy_ice) !========================================================================== ! ! Calculates an initial estimate of pt0_ice when it is less than about ! -100 deg C. ! ! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] ! ! pt0_cold_ice_poly = initial estimate of potential temperature ! of very cold ice in dgress C (not K) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pt0_cold_ice_poly(double pot_enthalpy_ice) { GSW_TEOS10_CONSTANTS; double log_abs_theta0, log_h_diff, /*h00 = gsw_enthalpy_ice(-gsw_t0,0)*/ h00 = -6.320202333358860e5, s0 = 1.493103204647916, s1 = 2.372788609320607e-1, s2 = -2.014996002119374e-3, s3 = 2.640600197732682e-6, s4 = 3.134706016844293e-5, s5 = 2.733592344937913e-6, s6 = 4.726828010223258e-8, s7 = -2.735193883189589e-9, s8 = -8.547714991377670e-11; log_h_diff = log(pot_enthalpy_ice - h00); log_abs_theta0 = s0 + log_h_diff*(s1 + log_h_diff*(s2 + log_h_diff*(s3 + log_h_diff*(s4 + log_h_diff*(s5 + log_h_diff*(s6 + log_h_diff*(s7 + log_h_diff*s8))))))); return (exp(log_abs_theta0) - gsw_t0); } /* !========================================================================== function gsw_pt0_from_t(sa,t,p) !========================================================================== ! Calculates potential temperature with reference pressure, p_ref = 0 dbar. ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_pt0_from_t : potential temperature, p_ref = 0 [deg C] */ double gsw_pt0_from_t(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; int no_iter; double pt0, pt0_old, dentropy, dentropy_dt; double s1, true_entropy_part, pt0m; s1 = sa/gsw_ups; pt0 = t+p*( 8.65483913395442e-6 - s1 * 1.41636299744881e-6 - p * 7.38286467135737e-9 + t *(-8.38241357039698e-6 + s1 * 2.83933368585534e-8 + t * 1.77803965218656e-8 + p * 1.71155619208233e-10)); dentropy_dt = gsw_cp0/((gsw_t0+pt0)*(1.0-0.05*(1.0-sa/gsw_sso))); true_entropy_part = gsw_entropy_part(sa,t,p); for (no_iter=1; no_iter <= 2; no_iter++) { pt0_old = pt0; dentropy = gsw_entropy_part_zerop(sa,pt0_old) - true_entropy_part; pt0 = pt0_old - dentropy/dentropy_dt; pt0m = 0.5*(pt0 + pt0_old); dentropy_dt = -gsw_gibbs_pt0_pt0(sa,pt0m); pt0 = pt0_old - dentropy/dentropy_dt; } return (pt0); } /* ! ========================================================================= elemental function gsw_pt0_from_t_ice (t, p) ! ========================================================================= ! ! Calculates potential temperature of ice Ih with a reference pressure of ! 0 dbar, from in-situ temperature, t. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! pt0_ice = potential temperature of ice Ih with reference pressure of ! zero dbar (ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pt0_from_t_ice(double t, double p) { GSW_TEOS10_CONSTANTS; int number_of_iterations; double dentropy, dentropy_dt, pt0_ice, pt0_ice_old, ptm_ice, true_entropy, /*This is the starting polynomial for pt0 of ice Ih.*/ s1 = -2.256611570832386e-4, s2 = -6.045305921314694e-7, s3 = 5.546699019612661e-9, s4 = 1.795030639186685e-11, s5 = 1.292346094030742e-9, p1 = -2.259745637898635e-4, p2 = 1.486236778150360e-9, p3 = 6.257869607978536e-12, p4 = -5.253795281359302e-7, p5 = 6.752596995671330e-9, p6 = 2.082992190070936e-11, q1 = -5.849191185294459e-15, q2 = 9.330347971181604e-11, q3 = 3.415888886921213e-13, q4 = 1.064901553161811e-12, q5 = -1.454060359158787e-10, q6 = -5.323461372791532e-13; true_entropy = -gsw_gibbs_ice_part_t(t,p); if (t < -45.0 && t > -273.0) { pt0_ice = t + p*(p1 + p*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t))); if (pt0_ice < -gsw_t0) pt0_ice = -gsw_t0; /* ! we add 0.05d0 to the initial estimate of pt0_ice at ! temps less than -273 to ensure that it is never less than -273.15. */ if (pt0_ice < -273.0) pt0_ice = pt0_ice + 0.05; dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice); for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { pt0_ice_old = pt0_ice; dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy; pt0_ice = pt0_ice_old - dentropy/dentropy_dt; ptm_ice = 0.5*(pt0_ice + pt0_ice_old); dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice); pt0_ice = pt0_ice_old - dentropy/dentropy_dt; } } else { pt0_ice = t + p*(s1 + t*(s2 + t*(s3 + t*s4)) + s5*p); dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice); pt0_ice_old = pt0_ice; dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy; pt0_ice = pt0_ice_old - dentropy/dentropy_dt; ptm_ice = 0.5*(pt0_ice + pt0_ice_old); dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice); pt0_ice = pt0_ice_old - dentropy/dentropy_dt; } if (pt0_ice < -273.0) { pt0_ice = t + p*(q1 + p*(q2 + q3*t) + t*(q4 + t*(q5 + q6*t))); /* ! add 0.01d0 to the initial estimate of pt_ice used in the ! derivative to ensure that it is never less than -273.15d0 ! because the derivative approaches zero at absolute zero. */ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice+0.01); for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { pt0_ice_old = pt0_ice; dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy; pt0_ice = pt0_ice_old - dentropy/dentropy_dt; ptm_ice = 0.5*(pt0_ice + pt0_ice_old); /* ! add 0.01d0 to the estimate of ptm_ice for temperatures less | than -273 to ensure that they are never less than -273.15d0 ! because the derivative approaches zero at absolute zero and ! the addition of 0.01d0 degrees c ensures that when we divide ! by the derivatve in the modified newton routine the function ! does not blow up. */ ptm_ice = ptm_ice + 0.01; dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice); pt0_ice = pt0_ice_old - dentropy/dentropy_dt; } } /* ! For temperatures less than -273.1 degsC the maximum error is less ! than 2x10^-7 degsC. For temperatures between -273.1 and 273 the ! maximum error is less than 8x10^-8 degsC, and for temperatures ! greater than -273 degsC the ! maximum error is 1.5x10^-12 degsC. ! These errors are over the whole ocean depths with p varying between ! 0 and 10,000 dbar, while the in-situ temperature varied independently ! between -273.15 and +2 degsC. */ return (pt0_ice); } /* !========================================================================== elemental subroutine gsw_pt_first_derivatives (sa, ct, pt_sa, pt_ct) ! ========================================================================= ! ! Calculates the following two partial derivatives of potential temperature ! (the regular potential temperature whose reference sea pressure is 0 dbar) ! (1) pt_SA, the derivative with respect to Absolute Salinity at ! constant Conservative Temperature, and ! (2) pt_CT, the derivative with respect to Conservative Temperature at ! constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! pt_SA = The derivative of potential temperature with respect to ! Absolute Salinity at constant Conservative Temperature. ! [ K/(g/kg)] ! pt_CT = The derivative of potential temperature with respect to ! Conservative Temperature at constant Absolute Salinity. ! pt_CT is dimensionless. [ unitless ] !-------------------------------------------------------------------------- */ void gsw_pt_first_derivatives (double sa, double ct, double *pt_sa, double *pt_ct) { GSW_TEOS10_CONSTANTS; double abs_pt, ct_pt, ct_sa, pt, pr0 = 0.0; int n0=0, n1=1, n2=2; pt = gsw_pt_from_ct(sa,ct); abs_pt = (gsw_t0 + pt); ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0; if (pt_sa != NULL) { ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) - abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0))/gsw_cp0; *pt_sa = -ct_sa/ct_pt; } if (pt_ct != NULL) *pt_ct = 1.0/ct_pt; } /* !========================================================================== function gsw_pt_from_ct(sa,ct) !========================================================================== ! potential temperature of seawater from conservative temperature ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_pt_from_ct : potential temperature with [deg C] ! reference pressure of 0 dbar */ double gsw_pt_from_ct(double sa, double ct) { GSW_TEOS10_CONSTANTS; double a5ct, b3ct, ct_factor, pt_num, pt_recden, ct_diff; double pt, pt_old, ptm, dpt_dct, s1; double a0 = -1.446013646344788e-2, a1 = -3.305308995852924e-3, a2 = 1.062415929128982e-4, a3 = 9.477566673794488e-1, a4 = 2.166591947736613e-3, a5 = 3.828842955039902e-3, b0 = 1.000000000000000e0, b1 = 6.506097115635800e-4, b2 = 3.830289486850898e-3, b3 = 1.247811760368034e-6; s1 = sa/gsw_ups; a5ct = a5*ct; b3ct = b3*ct; ct_factor = (a3 + a4*s1 + a5ct); pt_num = a0 + s1*(a1 + a2*s1) + ct*ct_factor; pt_recden = 1.0/(b0 + b1*s1 + ct*(b2 + b3ct)); pt = pt_num*pt_recden; dpt_dct = pt_recden*(ct_factor + a5ct - (b2 + b3ct + b3ct)*pt); /* ** Start the 1.5 iterations through the modified Newton-Raphson ** iterative method. */ ct_diff = gsw_ct_from_pt(sa,pt) - ct; pt_old = pt; pt = pt_old - ct_diff*dpt_dct; ptm = 0.5*(pt + pt_old); dpt_dct = -gsw_cp0/((ptm + gsw_t0)*gsw_gibbs_pt0_pt0(sa,ptm)); pt = pt_old - ct_diff*dpt_dct; ct_diff = gsw_ct_from_pt(sa,pt) - ct; pt_old = pt; return (pt_old - ct_diff*dpt_dct); } /* ! ========================================================================= elemental function gsw_pt_from_entropy (sa, entropy) ! ========================================================================= ! ! Calculates potential temperature with reference pressure p_ref = 0 dbar ! and with entropy as an input variable. ! ! SA = Absolute Salinity [ g/kg ] ! entropy = specific entropy [ deg C ] ! ! pt = potential temperature [ deg C ] ! with reference sea pressure (p_ref) = 0 dbar. ! Note. The reference sea pressure of the output, pt, is zero dbar. !-------------------------------------------------------------------------- */ double gsw_pt_from_entropy(double sa, double entropy) { GSW_TEOS10_CONSTANTS; int number_of_iterations; double c, dentropy, dentropy_dt, ent_sa, part1, part2, pt, ptm, pt_old; /*Find the initial value of pt*/ part1 = 1.0 - sa/gsw_sso; part2 = 1.0 - 0.05*part1; ent_sa = (gsw_cp0/gsw_t0)*part1*(1.0 - 1.01*part1); c = (entropy - ent_sa)*(part2/gsw_cp0); pt = gsw_t0*(exp(c) - 1.0); dentropy_dt = gsw_cp0/((gsw_t0 + pt)*part2); for (number_of_iterations = 1; number_of_iterations <= 2; number_of_iterations++) { pt_old = pt; dentropy = gsw_entropy_from_pt(sa,pt_old) - entropy; pt = pt_old - dentropy/dentropy_dt; ptm = 0.5*(pt + pt_old); dentropy_dt = -gsw_gibbs_pt0_pt0(sa,ptm); pt = pt_old - dentropy/dentropy_dt; } /* ! Maximum error of 2.2x10^-6 degrees C for one iteration. ! Maximum error is 1.4x10^-14 degrees C for two iterations ! (two iterations is the default, "for Number_of_iterations = 1:2"). */ return (pt); } /* !========================================================================== elemental function gsw_pt_from_pot_enthalpy_ice (pot_enthalpy_ice) !========================================================================== ! ! Calculates the potential temperature of ice from the potential enthalpy ! of ice. The reference sea pressure of both the potential temperature ! and the potential enthalpy is zero dbar. ! ! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] ! ! pt0_ice = potential temperature of ice (ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice) { int iteration; double df_dt, f, mod_pot_enthalpy_ice, pt0_cold_ice, recip_df_dt, pt0_cold_ice_old, pt0_ice, pt0_ice_old, ptm_cold_ice, ptm_ice; double h00 = -6.320202333358860e5, /*gsw_enthalpy_ice(-gsw_t0,0)*/ p0 = 0.0; mod_pot_enthalpy_ice = max(pot_enthalpy_ice,h00); if (mod_pot_enthalpy_ice >= -5.1e5) { /* ! For input potential enthalpies greater than -5.1e-5, the above part of ! the code gives the output potential temperature of ice accurate to | 1e-13 degrees C. */ pt0_ice = gsw_pt_from_pot_enthalpy_ice_poly(mod_pot_enthalpy_ice); /* ! The variable "df_dt" below is the derivative of the above polynomial ! with respect to pot_enthalpy_ice. This is the initial value of the ! derivative of the function f. */ recip_df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(mod_pot_enthalpy_ice); pt0_ice_old = pt0_ice; f = gsw_pot_enthalpy_from_pt_ice(pt0_ice_old) - mod_pot_enthalpy_ice; pt0_ice = pt0_ice_old - f*recip_df_dt; ptm_ice = 0.5*(pt0_ice + pt0_ice_old); recip_df_dt = 1.0/gsw_cp_ice(ptm_ice,p0); pt0_ice = pt0_ice_old - f*recip_df_dt; } else { /* ! For pot_enthalpy_ice < -5.1e5 (or pt0_ice less than about -100 deg c) ! these temperatures are less than those found in nature on planet earth */ pt0_cold_ice = gsw_pt0_cold_ice_poly(mod_pot_enthalpy_ice); df_dt = gsw_cp_ice(pt0_cold_ice+0.02,p0); /* ! the heat capacity, cp, is ! evaluated at 0.02 c greater than usual in order to avoid stability ! issues and to ensure convergence near zero absolute temperature. */ for (iteration = 1; iteration <= 6; iteration++) { pt0_cold_ice_old = pt0_cold_ice; f = gsw_pot_enthalpy_from_pt_ice(pt0_cold_ice_old) - mod_pot_enthalpy_ice; pt0_cold_ice = pt0_cold_ice_old - f/df_dt; ptm_cold_ice = 0.5*(pt0_cold_ice + pt0_cold_ice_old); df_dt = gsw_cp_ice(ptm_cold_ice+0.02,p0); /*note the extra 0.02 c here as well*/ pt0_cold_ice = pt0_cold_ice_old - f/df_dt; } pt0_ice = pt0_cold_ice; } /* !The potential temperature has a maximum error as listed in the table below. ! ! potential temperature error (deg C) | @ potential temperature (deg C) !--------------------------------------|-------------------------------- ! 0.012 | -273.15 to -273.12 ! 4 x 10^-4 | -232.12 to -273.0 ! 2.5 x 10^-6 | -273 ! 7 x 10^-9 | -272 ! 3.7 x 10^-10 | -270 ! 6 x 10^-11 | -268 ! 2.5 x 10^11 | -266 ! 3 x 10^-12 | -260 ! 7 x 10^-13 | -250 ! 2.2 x 10^-13 | -220 ! 1.7 x 10^-13 | >= -160 ! ! Note. The above errors in each temperature range are machine precissions ! for this calculation. */ return (pt0_ice); } /* !========================================================================== elemental function gsw_pt_from_pot_enthalpy_ice_poly (pot_enthalpy_ice) !========================================================================== ! ! Calculates the potential temperature of ice (whose reference sea ! pressure is zero dbar) from the potential enthalpy of ice. This is a ! compuationally efficient polynomial fit to the potential enthalpy of ! ice. ! ! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] ! ! pt0_ice = potential temperature of ice (ITS-90) [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice) { double q0 = 2.533588268773218e2, q1 = 2.594351081876611e-3, q2 = 1.765077810213815e-8, q3 = 7.768070564290540e-14, q4 = 2.034842254277530e-19, q5 = 3.220014531712841e-25, q6 = 2.845172809636068e-31, q7 = 1.094005878892950e-37; /* ! The error of this fit ranges between -5e-5 and 2e-4 deg C over the potential ! temperature range of -100 to 2 deg C, or the potential enthalpy range of ! -5.7 x 10^5 to -3.3 x 10^5 J/kg. */ return (q0 + pot_enthalpy_ice*(q1 + pot_enthalpy_ice*(q2 + pot_enthalpy_ice*(q3 + pot_enthalpy_ice*(q4 + pot_enthalpy_ice*(q5 + pot_enthalpy_ice*(q6 + pot_enthalpy_ice*q7))))))); } /* !========================================================================== elemental function gsw_pt_from_pot_enthalpy_ice_poly_dh (pot_enthalpy_ice) !========================================================================== ! ! Calculates the derivative of potential temperature of ice with respect ! to potential enthalpy. This is based on the compuationally-efficient ! polynomial fit to the potential enthalpy of ice. ! ! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ] ! ! dpt0_ice_dh = derivative of potential temperature of ice ! with respect to potential enthalpy [ deg C ] !-------------------------------------------------------------------------- */ double gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice) { double q1 = 2.594351081876611e-3, p2 = 3.530155620427630e-8, p3 = 2.330421169287162e-13, p4 = 8.139369017110120e-19, p5 = 1.610007265856420e-24, p6 = 1.707103685781641e-30, p7 = 7.658041152250651e-37; return (q1 + pot_enthalpy_ice*(p2 + pot_enthalpy_ice*(p3 + pot_enthalpy_ice*(p4 + pot_enthalpy_ice*(p5 + pot_enthalpy_ice*(p6 + pot_enthalpy_ice*p7)))))); } /* !========================================================================== function gsw_pt_from_t(sa,t,p,p_ref) !========================================================================== ! Calculates potential temperature of seawater from in-situ temperature ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! p_ref : reference sea pressure [dbar] ! ! gsw_pt_from_t : potential temperature [deg C] */ double gsw_pt_from_t(double sa, double t, double p, double p_ref) { GSW_TEOS10_CONSTANTS; int n0=0, n2=2, no_iter; double s1, pt, ptm, pt_old, dentropy, dentropy_dt, true_entropy_part; s1 = sa/gsw_ups; pt = t+(p-p_ref)*( 8.65483913395442e-6 - s1 * 1.41636299744881e-6 - (p+p_ref) * 7.38286467135737e-9 + t *(-8.38241357039698e-6 + s1 * 2.83933368585534e-8 + t * 1.77803965218656e-8 + (p+p_ref) * 1.71155619208233e-10)); dentropy_dt = gsw_cp0/((gsw_t0 + pt)*(1.0-0.05*(1.0 - sa/gsw_sso))); true_entropy_part = gsw_entropy_part(sa,t,p); for (no_iter=1; no_iter <= 2; no_iter++) { pt_old = pt; dentropy = gsw_entropy_part(sa,pt_old,p_ref) - true_entropy_part; pt = pt_old - dentropy/dentropy_dt; ptm = 0.5*(pt + pt_old); dentropy_dt = -gsw_gibbs(n0,n2,n0,sa,ptm,p_ref); pt = pt_old - dentropy/dentropy_dt; } return (pt); } /* ! ========================================================================= elemental function gsw_pt_from_t_ice (t, p, p_ref) ! ========================================================================= ! ! Calculates potential temperature of ice Ih with the general reference ! pressure, p_ref, from in-situ temperature, t. ! ! A faster gsw routine exists if p_ref is indeed zero dbar. This routine ! is "gsw_pt0_from_t_ice(t,p)". ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! p_ref = reference pressure [ dbar ] !-------------------------------------------------------------------------- */ double gsw_pt_from_t_ice(double t, double p, double p_ref) { GSW_TEOS10_CONSTANTS; int number_of_iterations; double dentropy, dentropy_dt, dp, pt_ice, pt_ice_old, ptm_ice, true_entropy, p1 = -2.259745637898635e-4, p2 = 1.486236778150360e-9, p3 = 6.257869607978536e-12, p4 = -5.253795281359302e-7, p5 = 6.752596995671330e-9, p6 = 2.082992190070936e-11, q1 = -5.849191185294459e-15, q2 = 9.330347971181604e-11, q3 = 3.415888886921213e-13, q4 = 1.064901553161811e-12, q5 = -1.454060359158787e-10, q6 = -5.323461372791532e-13; /*This is the starting polynomial for pt of ice Ih.*/ dp = p - p_ref; pt_ice = t + dp*(p1 + (p + p_ref)*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t))); if (pt_ice < -gsw_t0) pt_ice = -gsw_t0; if (pt_ice < -273.0) pt_ice = pt_ice + 0.05; /* ! we add 0.05 to the initial estimate of pt_ice at temps less than ! -273 to ensure that it is never less than -273.15. */ dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice,p_ref); true_entropy = -gsw_gibbs_ice_part_t(t,p); for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { pt_ice_old = pt_ice; dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref) - true_entropy; pt_ice = pt_ice_old - dentropy/dentropy_dt; ptm_ice = 0.5*(pt_ice + pt_ice_old); dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref); pt_ice = pt_ice_old - dentropy/dentropy_dt; } if (pt_ice < -273.0) { pt_ice = t + (p - p_ref)*(q1 + (p + p_ref)*(q2 + q3*t) + t*(q4 + t*(q5 + q6*t))); dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice+0.01,p_ref); /* ! we add 0.01 to the initial estimate of pt_ice used in the derivative ! to ensure that it is never less than -273.15 because the derivative ! approaches zero at absolute zero. */ for (number_of_iterations = 1; number_of_iterations <= 3; number_of_iterations++) { pt_ice_old = pt_ice; dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref) - true_entropy; pt_ice = pt_ice_old - dentropy/dentropy_dt; ptm_ice = 0.5*(pt_ice + pt_ice_old); ptm_ice = ptm_ice + 0.01; dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref); pt_ice = pt_ice_old - dentropy/dentropy_dt; } } /* ! For temperatures less than -273.1 degsC the maximum error is less than ! 2x10^-7 degsC. For temperatures between -273.1 and 273 the maximum error ! is less than 8x10^-8 degsC, and for temperatures greater than -273 degsC the ! maximum error is 1.5x10^-12 degsC. These errors are over the whole ! ocean depths with both p and pref varying independently between 0 and ! 10,000 dbar, while the in-situ temperature varied independently between ! -273.15 and +2 degsC. */ return (pt_ice); } /* !========================================================================== elemental subroutine gsw_pt_second_derivatives (sa, ct, pt_sa_sa, & pt_sa_ct, pt_ct_ct) ! ========================================================================= ! ! Calculates the following three second-order derivatives of potential ! temperature (the regular potential temperature which has a reference ! sea pressure of 0 dbar), ! (1) pt_SA_SA, the second derivative with respect to Absolute Salinity ! at constant Conservative Temperature, ! (2) pt_SA_CT, the derivative with respect to Conservative Temperature ! and Absolute Salinity, and ! (3) pt_CT_CT, the second derivative with respect to Conservative ! Temperature at constant Absolute Salinity. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! pt_SA_SA = The second derivative of potential temperature (the ! regular potential temperature which has reference sea ! pressure of 0 dbar) with respect to Absolute Salinity ! at constant Conservative Temperature. ! pt_SA_SA has units of: [ K/((g/kg)^2) ] ! pt_SA_CT = The derivative of potential temperature with respect ! to Absolute Salinity and Conservative Temperature. ! pt_SA_CT has units of: [ 1/(g/kg) ] ! pt_CT_CT = The second derivative of potential temperature (the ! regular one with p_ref = 0 dbar) with respect to ! Conservative Temperature at constant SA. ! pt_CT_CT has units of: [ 1/K ] !-------------------------------------------------------------------------- */ void gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa, double *pt_sa_ct, double *pt_ct_ct) { double ct_l, ct_u, pt_ct_l, pt_ct_u, pt_sa_l, pt_sa_u, sa_l, sa_u, delta, dct = 1e-2, dsa = 1e-3; if (pt_sa_sa != NULL) { sa_u = sa + dsa; sa_l = sa - dsa; if (sa_l < 0.0) { sa_l = 0.0; delta = sa_u; } else { delta = 2 * dsa; } gsw_pt_first_derivatives(sa_l,ct,&pt_sa_l,NULL); gsw_pt_first_derivatives(sa_u,ct,&pt_sa_u,NULL); *pt_sa_sa = (pt_sa_u - pt_sa_l)/delta; } if (pt_sa_ct != NULL || pt_ct_ct != NULL) { ct_l = ct - dct; ct_u = ct + dct; delta = 2 * dct; if ((pt_sa_ct != NULL) && (pt_ct_ct != NULL)) { gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,&pt_ct_l); gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,&pt_ct_u); *pt_sa_ct = (pt_sa_u - pt_sa_l)/delta; *pt_ct_ct = (pt_ct_u - pt_ct_l)/delta; } else if ((pt_sa_ct != NULL) && (pt_ct_ct == NULL)) { gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,NULL); gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,NULL); *pt_sa_ct = (pt_sa_u - pt_sa_l)/delta; } else if ((pt_sa_ct == NULL) && (pt_ct_ct != NULL)) { gsw_pt_first_derivatives(sa,ct_l,NULL,&pt_ct_l); gsw_pt_first_derivatives(sa,ct_u,NULL,&pt_ct_u); *pt_ct_ct = (pt_ct_u - pt_ct_l)/delta; } } } /* !-------------------------------------------------------------------------- ! density and enthalpy, based on the 48-term expression for density !-------------------------------------------------------------------------- !========================================================================== function gsw_rho(sa,ct,p) !========================================================================== ! Calculates in-situ density from Absolute Salinity and Conservative ! Temperature, using the computationally-efficient expression for ! specific volume in terms of SA, CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho : in-situ density [kg/m] */ double gsw_rho(double sa, double ct, double p) { return (1.0/gsw_specvol(sa,ct,p)); } /* !========================================================================== elemental subroutine gsw_rho_alpha_beta (sa, ct, p, rho, alpha, beta) !========================================================================== ! ! Calculates in-situ density, the appropriate thermal expansion coefficient ! and the appropriate saline contraction coefficient of seawater from ! Absolute Salinity and Conservative Temperature. This function uses the ! computationally-efficient expression for specific volume in terms of ! SA, CT and p (Roquet et al., 2014). ! ! Note that potential density (pot_rho) with respect to reference pressure ! p_ref is obtained by calling this function with the pressure argument ! being p_ref as in [pot_rho, ~, ~] = gsw_rho_alpha_beta(SA,CT,p_ref). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho = in-situ density [ kg/m ] ! alpha = thermal expansion coefficient [ 1/K ] ! with respect to Conservative Temperature ! beta = saline (i.e. haline) contraction [ kg/g ] ! coefficient at constant Conservative Temperature !-------------------------------------------------------------------------- */ void gsw_rho_alpha_beta (double sa, double ct, double p, double *rho, double *alpha, double *beta) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v, v_ct_part, v_sa_part, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); if (rho != NULL) *rho = 1.0/v; if (alpha != NULL) { v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))); *alpha = 0.025*v_ct_part/v; } if (beta != NULL) { v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); *beta = -v_sa_part*0.5*gsw_sfac/(v*xs); } } /* !========================================================================== subroutine gsw_rho_first_derivatives(sa, ct, p, drho_dsa, drho_dct, drho_dp) !========================================================================== ! Calculates the three (3) partial derivatives of in situ density with ! respect to Absolute Salinity, Conservative Temperature and pressure. ! Note that the pressure derivative is done with respect to pressure in ! Pa, not dbar. This function uses the computationally-efficient expression ! for specific volume in terms of SA, CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! p : sea pressure [dbar] ! drho_dsa : partial derivatives of density [kg^2/(g m^3)] ! with respect to Absolute Salinity ! drho_dct : partial derivatives of density [kg/(K m^3)] ! with respect to Conservative Temperature ! drho_dp : partial derivatives of density [kg/(Pa m^3)] ! with respect to pressure in Pa */ void gsw_rho_first_derivatives(double sa, double ct, double p, double *drho_dsa, double *drho_dct, double *drho_dp) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double rho2, v_ct, v_p, v_sa, xs, ys, z, v; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); rho2 = pow(1.0/v, 2.0); if (drho_dsa != NULL) { v_sa = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); *drho_dsa = -rho2*0.5*gsw_sfac*v_sa/xs; } if (drho_dct != NULL) { v_ct = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))); *drho_dct = -rho2*0.025*v_ct; } if (drho_dp != NULL) { v_p = c000 + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs)))) + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020 + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs) + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201 + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs)) + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys))) + z*(c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys) + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z)))); *drho_dp = 1e-4*pa2db*-rho2*v_p; } return; } /* !========================================================================== elemental subroutine gsw_rho_first_derivatives_wrt_enthalpy (sa, ct, p, & rho_sa, rho_h) ! ========================================================================= ! ! Calculates two first-order derivatives of specific volume (v). ! Note that this function uses the using the computationally-efficient ! expression for specific volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho_SA = The first derivative of rho with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! rho_h = The first derivative of rho with respect to ! SA and CT at constant p. [ J/(kg K(g/kg)) ] !-------------------------------------------------------------------------- */ void gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct, double p, double *rho_sa, double *rho_h) { double rec_v2, v_h=0.0, v_sa; if ((rho_sa != NULL) && (rho_h != NULL)) { gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,&v_h); } else if (rho_sa != NULL) { gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,NULL); } else if (rho_h != NULL) { gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,NULL,&v_h); } rec_v2 = pow(1.0/gsw_specvol(sa,ct,p), 2); if (rho_sa != NULL) *rho_sa = -v_sa*rec_v2; if (rho_h != NULL) *rho_h = -v_h*rec_v2; } /* !========================================================================== elemental function gsw_rho_ice (t, p) !========================================================================== ! ! Calculates in-situ density of ice from in-situ temperature and pressure. ! Note that the output, rho_ice, is density, not density anomaly; that ! is, 1000 kg/m^3 is not subtracted from it. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho_ice = in-situ density of ice (not density anomaly) [ kg/m^3 ] !-------------------------------------------------------------------------- */ double gsw_rho_ice(double t, double p) { return (1.0/gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== elemental subroutine gsw_rho_second_derivatives (sa, ct, p, rho_sa_sa, & rho_sa_ct, rho_ct_ct, rho_sa_p, rho_ct_p) !========================================================================== ! ! Calculates five second-order derivatives of rho. Note that this function ! uses the computationally-efficient expression for specific ! volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho_SA_SA = The second-order derivative of rho with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! rho_SA_CT = The second-order derivative of rho with respect to ! SA and CT at constant p. [ J/(kg K(g/kg)) ] ! rho_CT_CT = The second-order derivative of rho with respect to CT at ! constant SA & p ! rho_SA_P = The second-order derivative with respect to SA & P at ! constant CT. ! rho_CT_P = The second-order derivative with respect to CT & P at ! constant SA. !-------------------------------------------------------------------------- */ void gsw_rho_second_derivatives(double sa, double ct, double p, double *rho_sa_sa, double *rho_sa_ct, double *rho_ct_ct, double *rho_sa_p, double *rho_ct_p) { double rec_v, rec_v2, rec_v3, v_ct, v_ct_ct, v_ct_p, v_p, v_sa, v_sa_ct, v_sa_p, v_sa_sa; gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,&v_p); gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct, &v_sa_p,&v_ct_p); rec_v = 1.0/gsw_specvol(sa,ct,p); rec_v2 = pow(rec_v, 2); rec_v3 = rec_v2*rec_v; if (rho_sa_sa != NULL) *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3; if (rho_sa_ct != NULL) *rho_sa_ct = -v_sa_ct*rec_v2 + 2.0*v_sa*v_ct*rec_v3; if (rho_ct_ct != NULL) *rho_ct_ct = -v_ct_ct*rec_v2 + 2.0*v_ct*v_ct*rec_v3; if (rho_sa_p != NULL) *rho_sa_p = -v_sa_p*rec_v2 + 2.0*v_sa*v_p*rec_v3; if (rho_ct_p != NULL) *rho_ct_p = -v_ct_p*rec_v2 + 2.0*v_ct*v_p*rec_v3; } /* !========================================================================== elemental subroutine gsw_rho_second_derivatives_wrt_enthalpy (sa, ct, p, & rho_sa_sa, rho_sa_h, rho_h_h) ! ========================================================================= ! ! Calculates three second-order derivatives of rho with respect to enthalpy. ! Note that this function uses the using the computationally-efficient ! expression for specific volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! rho_SA_SA = The second-order derivative of rho with respect to ! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ] ! rho_SA_h = The second-order derivative of rho with respect to ! SA and h at constant p. [ J/(kg K(g/kg)) ] ! rho_h_h = The second-order derivative of rho with respect to h at ! constant SA & p !-------------------------------------------------------------------------- */ void gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct, double p, double *rho_sa_sa, double *rho_sa_h, double *rho_h_h) { double rec_v, rec_v2, rec_v3, v_h, v_h_h, v_sa, v_sa_h, v_sa_sa, *pv_sa, *pv_h, *pv_sa_sa, *pv_sa_h, *pv_h_h; pv_sa = ((rho_sa_sa != NULL) || (rho_sa_h != NULL)) ? &v_sa : NULL; pv_h = ((rho_sa_h != NULL) || (rho_h_h != NULL)) ? &v_h : NULL; gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,pv_sa,pv_h); pv_sa_sa = ((rho_sa_sa != NULL)) ? &v_sa_sa : NULL; pv_sa_h = ((rho_sa_h != NULL)) ? &v_sa_h : NULL; pv_h_h = ((rho_h_h != NULL)) ? &v_h_h : NULL; gsw_specvol_second_derivatives_wrt_enthalpy(sa,ct,p, pv_sa_sa,pv_sa_h,pv_h_h); rec_v = 1.0/gsw_specvol(sa,ct,p); rec_v2 = rec_v*rec_v; rec_v3 = rec_v2*rec_v; if (rho_sa_sa != NULL) *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3; if (rho_sa_h != NULL) *rho_sa_h = -v_sa_h*rec_v2 + 2.0*v_sa*v_h*rec_v3; if (rho_h_h != NULL) *rho_h_h = -v_h_h*rec_v2 + 2.0*v_h*v_h*rec_v3; } /* !========================================================================== function gsw_rho_t_exact(sa,t,p) !========================================================================== ! Calculates in-situ density of seawater from Absolute Salinity and ! in-situ temperature. ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_rho_t_exact : in-situ density [kg/m^3] */ double gsw_rho_t_exact(double sa, double t, double p) { int n0=0, n1=1; return (1.0/gsw_gibbs(n0,n0,n1,sa,t,p)); } /* !========================================================================== pure subroutine gsw_rr68_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i) !========================================================================== ! ! Interpolate Absolute Salinity and Conservative Temperature values to ! arbitrary pressures using the Reiniger and Ross (1968) interpolation ! scheme. ! Note that this interpolation scheme requires at least four observed ! bottles on the cast. ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! p_i = pressures to interpolate to. ! ! SA_i = interpolated SA values at pressures p_i. ! CT_i = interpolated CT values at pressures p_i. !-------------------------------------------------------------------------- */ static void rr68_interp_section(int sectnum, double *sa, double *ct, double *p, int mp, int nsect, double *ip_sect, int *ip_isect, double *p_i, double *sa_i, double *ct_i); /* forward reference */ void gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp, double *p_i, int mp_i, double *sa_i, double *ct_i) { int i, j, nshallow, ncentral, ndeep, *ip, *ip_i, *ip_ishallow, *ip_icentral, *ip_ideep; char *shallow, *central, *deep; double *ip_shallow, *ip_central, *ip_deep, *dp, *p_ii; if (mp < 4) { /* need at least four bottles to perform this interpolation */ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE; return; } dp = (double *) malloc(mp*sizeof (double)); for (i=1; i= p[0] && p_i[i] <= p[1]) { nshallow++; shallow[i] = 1; } if (p_i[i] >= p[1] && p_i[i] <= p[mp-2]) { ncentral++; central[i] = 1; } if (p_i[i] >= p[mp-2] && p_i[i] <= p[mp-1]) { ndeep++; deep[i] = 1; } } if ((nshallow == 0) || (ncentral == 0) || (ndeep == 0)) { free(shallow); free(dp); ct_i[0] = sa_i[0] = GSW_INVALID_VALUE; return; } ip = (int *) malloc((mp+mp_i)*sizeof (int)); ip_i = ip+mp; for (i=0; i 0) { /* deep */ for (i=0; i 0) { gsw_util_sort_real(p_obs, prof_len, p_idx); for (i=0; i= min_p_obs && p_all[i] <= max_p_obs) { i_obs_plus_interp[i_obs_plus_interp_len] = i; p_obs_plus_interp[i_obs_plus_interp_len] = p_all[i]; i_obs_plus_interp_len++; } if (p_all[i] <= max_p_obs) { i_surf_and_obs_plus_interp[i_surf_and_obs_plus_interp_len] = i; p_surf_and_obs_plus_interp[i_surf_and_obs_plus_interp_len] = p_all[i]; i_surf_and_obs_plus_interp_len++; } } i_out_len = gsw_util_intersect(p_i_tmp, m_i, p_surf_and_obs_plus_interp, i_surf_and_obs_plus_interp_len, i_out, i_1); i_2_len = gsw_util_intersect(p_obs, prof_len, p_obs_plus_interp, i_obs_plus_interp_len, i_2, i_3); independent_variable = (double *) malloc(prof_len*sizeof (double)); independent_variable_obs_plus_interp = (double *) malloc(i_obs_plus_interp_len*sizeof (double)); for(i=0; i=0; --i_shallower) { if ((i_3[i_shallower] - i_frozen) <= 0) { break; } } i_above = i_2[i_shallower]; i_above_i = i_3[i_shallower]; if ((i_above + 1) > i_3[i_2_len - 1]) { i_below_i = i_3[i_2_len - 1]; } else { i_below_i = i_3[i_above + 1]; } for (i=i_above_i; i<=i_below_i; ++i) { sa_i_obs_plus_interp[i] = sa_i_limiting_obs_plus_interp[i]; ct_i_obs_plus_interp[i] = ct_i_limiting_obs_plus_interp[i]; ctf_i_tointerp[i] = gsw_ct_freezing_poly(sa_i_obs_plus_interp[i], p_all[i], 0.); } } sa_i_tooutput = (double *)malloc(i_surf_and_obs_plus_interp_len*sizeof (double)); ct_i_tooutput = (double *)malloc(i_surf_and_obs_plus_interp_len*sizeof (double)); if (min_p_obs != 0.) { for (i=0; i CT_freezing_zero_SA. If this is the case, the input values ! represent seawater that is not frozen (for any positive SA). */ ct_freezing_zero_sa = gsw_ct_freezing(0.0,p,saturation_fraction); if (ct > ct_freezing_zero_sa) return (GSW_INVALID_VALUE); /*Form the first estimate of SA from a polynomial in CT and p*/ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL); if (sa < -sa_cut_off) return (GSW_INVALID_VALUE); /* ! Form the first estimate of CTfreezing_SA, ! the derivative of CT_freezing with respect to SA at fixed p. */ sa = max(sa,0.0); gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction, &ctfreezing_sa, NULL); /* ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA ! with one based on (CT_freezing_zero_SA - CT). */ if (fabs(sa) < sa_cut_off) sa = (ct - ct_freezing_zero_sa)/ctfreezing_sa; /* !----------------------------------------------------------------------- ! Begin the modified Newton-Raphson method to solve ! f = (CT_freezing - CT) = 0 for SA. !----------------------------------------------------------------------- */ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) { sa_old = sa; f = gsw_ct_freezing(sa,p,saturation_fraction) - ct; sa = sa_old - f/ctfreezing_sa; sa_mean = 0.5*(sa + sa_old); gsw_ct_freezing_first_derivatives(sa_mean,p,saturation_fraction, &ctfreezing_sa, NULL); sa = sa_old - f/ctfreezing_sa; } if (gsw_sa_p_inrange(sa,p)) return (sa); return (GSW_INVALID_VALUE); } /* !========================================================================== elemental function gsw_sa_freezing_from_ct_poly (ct, p, saturation_fraction) !========================================================================== ! ! Calculates the Absolute Salinity of seawater at the freezing temperature. ! That is, the output is the Absolute Salinity of seawater, with the ! fraction saturation_fraction of dissolved air, that is in equilibrium ! with ice at Conservative Temperature CT and pressure p. If the input ! values are such that there is no positive value of Absolute Salinity for ! which seawater is frozen, the output is put equal to Nan. ! ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! sa_freezing_from_ct = Absolute Salinity of seawater when it freezes, ! for given input values of Conservative Temperature ! pressure and air saturation fraction. [ g/kg ] !-------------------------------------------------------------------------- */ double gsw_sa_freezing_from_ct_poly(double ct, double p, double saturation_fraction) { int i_iter, number_of_iterations = 2; double ct_freezing, ct_freezing_zero_sa, dct_dsa, sa, sa_old, sa_mean; /* ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat ! differently in calculating the initial values of both SA and dCT_dSA. */ double sa_cut_off = 2.5; /* ! Find CT > CT_freezing_zero_SA. If this is the case, the input values ! represent seawater that is not frozen (at any positive SA). */ ct_freezing_zero_sa = gsw_ct_freezing_poly(0.0,p,saturation_fraction); if (ct > ct_freezing_zero_sa) return (GSW_INVALID_VALUE); /*Form the first estimate of SA from a polynomial in CT and p */ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL); if (sa < -sa_cut_off) return (GSW_INVALID_VALUE); /* ! Form the first estimate of dCT_dSA, the derivative of CT with respect ! to SA at fixed p. */ sa = max(sa,0.0); gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction, &dct_dsa, NULL); /* ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA ! with one based on (CT_freezing_zero_SA - CT). */ if (fabs(sa) < sa_cut_off) sa = (ct - ct_freezing_zero_sa)/dct_dsa; /* !----------------------------------------------------------------------- ! Begin the modified Newton-Raphson method to solve the root of ! CT_freezing = CT for SA. !----------------------------------------------------------------------- */ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) { sa_old = sa; ct_freezing = gsw_ct_freezing_poly(sa_old,p,saturation_fraction); sa = sa_old - (ct_freezing - ct)/dct_dsa; sa_mean = 0.5*(sa + sa_old); gsw_ct_freezing_first_derivatives_poly(sa_mean,p, saturation_fraction, &dct_dsa, NULL); sa = sa_old - (ct_freezing - ct)/dct_dsa; } if (gsw_sa_p_inrange(sa,p)) return (sa); return (GSW_INVALID_VALUE); } /* !========================================================================== elemental function gsw_sa_freezing_from_t (t, p, saturation_fraction) !========================================================================== ! ! Calculates the Absolute Salinity of seawater at the freezing temperature. ! That is, the output is the Absolute Salinity of seawater, with the ! fraction saturation_fraction of dissolved air, that is in equilibrium ! with ice at in-situ temperature t and pressure p. If the input values ! are such that there is no positive value of Absolute Salinity for which ! seawater is frozen, the output is set to NaN. ! ! t = in-situ Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! (i.e., saturation_fraction must be between 0 and 1, and the default ! is 1, completely saturated) ! ! sa_freezing_from_t = Absolute Salinity of seawater when it freezes, for ! given input values of in situ temperature, pressure and ! air saturation fraction. [ g/kg ] !--------------------------------------------------------------------------- */ double gsw_sa_freezing_from_t(double t, double p, double saturation_fraction) { int i_iter, number_of_iterations = 2; double f, sa, sa_mean, sa_old, t_freezing_zero_sa, tfreezing_sa; /* ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat ! differently in calculating the initial values of both SA and dCT_dSA. */ double sa_cut_off = 2.5; /* ! Find t > t_freezing_zero_SA. If this is the case, the input values ! represent seawater that is not frozen (at any positive SA). */ t_freezing_zero_sa = gsw_t_freezing(0.0,p,saturation_fraction); if (t > t_freezing_zero_sa) return (GSW_INVALID_VALUE); /* ! This is the initial guess of SA using a purpose-built ! polynomial in CT and p */ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t); if (sa < -sa_cut_off) return (GSW_INVALID_VALUE); /* ! Form the first estimate of tfreezing_SA, the derivative of ! CT_freezing with respect to SA at fixed p. */ sa = max(sa,0.0); gsw_t_freezing_first_derivatives(sa,p,saturation_fraction, &tfreezing_sa,NULL); /* ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA ! with one based on (t_freezing_zero_SA - t). */ if (fabs(sa) < sa_cut_off) sa = (t - t_freezing_zero_sa)/tfreezing_sa; /* !----------------------------------------------------------------------- ! Begin the modified Newton-Raphson method to find the root of ! f = (t_freezing - t) = 0 for SA. !----------------------------------------------------------------------- */ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) { sa_old = sa; f = gsw_t_freezing(sa_old,p,saturation_fraction) - t; sa = sa_old - f/tfreezing_sa; sa_mean = 0.5*(sa + sa_old); gsw_t_freezing_first_derivatives(sa_mean,p,saturation_fraction, &tfreezing_sa, NULL); sa = sa_old - f/tfreezing_sa; } if (gsw_sa_p_inrange(sa,p)) return (sa); return (GSW_INVALID_VALUE); } /* !========================================================================== elemental function gsw_sa_freezing_from_t_poly (t, p, saturation_fraction) !========================================================================== ! ! Calculates the Absolute Salinity of seawater at the freezing temperature. ! That is, the output is the Absolute Salinity of seawater, with the ! fraction saturation_fraction of dissolved air, that is in equilibrium ! with ice at in-situ temperature t and pressure p. If the input values ! are such that there is no positive value of Absolute Salinity for which ! seawater is frozen, the output is put equal to Nan. ! ! t = in-situ Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! sa_freezing_from_t_poly = Absolute Salinity of seawater when it freezes, ! for given input values of in situ temperature, pressure and ! air saturation fraction. [ g/kg ] !-------------------------------------------------------------------------- */ double gsw_sa_freezing_from_t_poly(double t, double p, double saturation_fraction) { int i_iter, number_of_iterations = 5; double dt_dsa, sa, sa_old, sa_mean, t_freezing, t_freezing_zero_sa; /* ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat ! differently in calculating the initial values of both SA and dCT_dSA. */ double sa_cut_off = 2.5; /* ! Find t > t_freezing_zero_SA. If this is the case, the input values ! represent seawater that is not frozen (at any positive SA). */ t_freezing_zero_sa = gsw_t_freezing_poly(0.0,p,saturation_fraction); if (t > t_freezing_zero_sa) return (GSW_INVALID_VALUE); /* ! This is the initial guess of SA using a purpose-built ! polynomial in CT and p */ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t); if (sa < -sa_cut_off) return (GSW_INVALID_VALUE); /* ! Form the first estimate of dt_dSA, the derivative of t with respect ! to SA at fixed p. */ sa = max(sa,0.0); gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction, &dt_dsa, NULL); /* ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA ! with one based on (t_freezing_zero_SA - t). */ if (fabs(sa) < sa_cut_off) sa = (t - t_freezing_zero_sa)/dt_dsa; /* !----------------------------------------------------------------------- ! Begin the modified Newton-Raphson method to find the root of ! t_freezing = t for SA. !----------------------------------------------------------------------- */ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) { sa_old = sa; t_freezing = gsw_t_freezing_poly(sa_old,p,saturation_fraction); sa = sa_old - (t_freezing - t)/dt_dsa; sa_mean = 0.5*(sa + sa_old); gsw_t_freezing_first_derivatives_poly(sa_mean,p,saturation_fraction, &dt_dsa, NULL); sa = sa_old - (t_freezing - t)/dt_dsa; } if (gsw_sa_p_inrange(sa,p)) return (sa); return (GSW_INVALID_VALUE); } /* !========================================================================== function gsw_sa_from_rho(rho,ct,p) !========================================================================== ! Calculates the Absolute Salinity of a seawater sample, for given values ! of its density, Conservative Temperature and sea pressure (in dbar). ! ! rho = density of a seawater sample (e.g. 1026 kg/m^3). [ kg/m^3 ] ! Note. This input has not had 1000 kg/m^3 subtracted from it. ! That is, it is 'density', not 'density anomaly'. ! ct = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ! sa = Absolute Salinity [g/kg] */ double gsw_sa_from_rho(double rho, double ct, double p) { int no_iter; double sa, v_lab, v_0, v_50, v_sa, sa_old, delta_v, sa_mean; v_lab = 1.0/rho; v_0 = gsw_specvol(0.0,ct,p); v_50 = gsw_specvol(50.0,ct,p); sa = 50.0*(v_lab - v_0)/(v_50 - v_0); if (sa < 0.0 || sa > 50.0) return (GSW_INVALID_VALUE); v_sa = (v_50 - v_0)/50.0; for (no_iter=1; no_iter <= 2; no_iter++) { sa_old = sa; delta_v = gsw_specvol(sa_old,ct,p) - v_lab; sa = sa_old - delta_v/v_sa; sa_mean = 0.5*(sa + sa_old); gsw_specvol_first_derivatives(sa_mean,ct,p,&v_sa,NULL,NULL); sa = sa_old - delta_v/v_sa; if (sa < 0.0 || sa > 50.0) return (GSW_INVALID_VALUE); } return (sa); } /* !========================================================================== function gsw_sa_from_sp(sp,p,lon,lat) !========================================================================== ! Calculates Absolute Salinity, SA, from Practical Salinity, SP ! ! sp : Practical Salinity [unitless] ! p : sea pressure [dbar] ! lon : longitude [DEG E] ! lat : latitude [DEG N] ! ! gsw_sa_from_sp : Absolute Salinity [g/kg] */ double gsw_sa_from_sp(double sp, double p, double lon, double lat) { GSW_TEOS10_CONSTANTS; double saar, gsw_sa_baltic; gsw_sa_baltic = gsw_sa_from_sp_baltic(sp,lon,lat); if (gsw_sa_baltic < GSW_ERROR_LIMIT) return (gsw_sa_baltic); saar = gsw_saar(p,lon,lat); if (saar == GSW_INVALID_VALUE) return (saar); return (gsw_ups*sp*(1.e0 + saar)); } /* !========================================================================== function gsw_sa_from_sp_baltic(sp,lon,lat) !========================================================================== ! For the Baltic Sea, calculates Absolute Salinity with a value ! computed analytically from Practical Salinity ! ! sp : Practical Salinity [unitless] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! sa_from_sp_baltic : Absolute Salinity [g/kg] */ double gsw_sa_from_sp_baltic(double sp, double lon, double lat) { GSW_TEOS10_CONSTANTS; GSW_BALTIC_DATA; double xx_left, xx_right, return_value; lon = fmod(lon, 360.0); if (lon < 0.0) lon += 360.0; if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat && lat < yb_left[2]) { xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat); xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat); if (xx_left <= lon && lon <= xx_right) return_value =((gsw_sso - 0.087)/35.0)*sp + 0.087; else return_value = GSW_INVALID_VALUE; } else return_value = GSW_INVALID_VALUE; return (return_value); } /* !========================================================================== function gsw_sa_from_sstar(sstar,p,lon,lat) !========================================================================== ! Calculates Absolute Salinity, SA, from Preformed Salinity, Sstar. ! ! Sstar : Preformed Salinity [g/kg] ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_sa_from_sstar : Absolute Salinity [g/kg] */ double gsw_sa_from_sstar(double sstar, double p, double lon, double lat) { double saar; saar = gsw_saar(p,lon,lat); if (saar == GSW_INVALID_VALUE) return (saar); /* **! In the Baltic Sea, Sstar = SA, and note that gsw_saar returns zero **! for SAAR in the Baltic. */ return (sstar*(1e0 + saar)/(1e0 - 0.35e0*saar)); } /* !========================================================================== elemental function gsw_sa_p_inrange (sa, p) !========================================================================== ! ! Check for any values that are out of the TEOS-10 range ... ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) !--------------------------------------------------------------------------- */ int gsw_sa_p_inrange(double sa, double p) { if (p > 10000.0 || sa > 120.0 || (p + sa*71.428571428571402) > 13571.42857142857) return (0); return (1); } /* !========================================================================== elemental subroutine gsw_seaice_fraction_to_freeze_seawater (sa, ct, p, & sa_seaice, t_seaice, sa_freeze, ct_freeze, w_seaice) !========================================================================== ! ! Calculates the mass fraction of sea ice (mass of sea ice divided by mass ! of sea ice plus seawater), which, when melted into seawater having the ! properties (SA,CT,p) causes the final seawater to be at the freezing ! temperature. The other outputs are the Absolute Salinity and ! Conservative Temperature of the final seawater. ! ! SA = Absolute Salinity of seawater [ g/kg ] ! CT = Conservative Temperature of seawater (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of ! salt in sea ice, expressed in g of salt per kg of sea ice. ! [ g/kg ] ! t_seaice = in-situ temperature of the sea ice at pressure p (ITS-90) ! [ deg C ] ! ! SA_freeze = Absolute Salinity of seawater after the mass fraction of ! sea ice, w_seaice, at temperature t_seaice has melted into ! the original seawater, and the final mixture is at the ! freezing temperature of seawater. [ g/kg ] ! ! CT_freeze = Conservative Temperature of seawater after the mass ! fraction, w_seaice, of sea ice at temperature t_seaice has ! melted into the original seawater, and the final mixture ! is at the freezing temperature of seawater. [ deg C ] ! ! w_seaice = mass fraction of sea ice, at SA_seaice and t_seaice, ! which, when melted into seawater at (SA,CT,p) leads to the ! final mixed seawater being at the freezing temperature. ! This output is between 0 and 1. [unitless] !-------------------------------------------------------------------------- */ void gsw_seaice_fraction_to_freeze_seawater(double sa, double ct, double p, double sa_seaice, double t_seaice, double *sa_freeze, double *ct_freeze, double *w_seaice) { int number_of_iterations; double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero, dfunc_dsaf, func, func_plus1, func_zero, h, h_brine, h_ih, sa_freezing, saf, saf_mean, saf_old, salt_ratio, tf_sa_seaice, h_hat_sa, h_hat_ct, ctf_sa, sa0 = 0.0, saturation_fraction = 0.0; ctf = gsw_ct_freezing(sa,p,saturation_fraction); if (ct < ctf) { /*The seawater ct input is below the freezing temp*/ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE; return; } tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction) - 1e-6; if (t_seaice > tf_sa_seaice) { /* ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice ! is allowed to be exactly equal to tf_sa_seaice, the sea ice is ! actually 100% brine at Absolute Salinity of SA_seaice. */ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE; return; } sa_freezing = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction); if (sa_freezing > GSW_ERROR_LIMIT) { *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE; return; } h_brine = gsw_enthalpy_t_exact(sa_freezing,t_seaice,p); salt_ratio = sa_seaice/sa_freezing; h = gsw_enthalpy_ct_exact(sa,ct,p); h_ih = gsw_enthalpy_ice(t_seaice,p); ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction); func_plus1 = (sa - sa_seaice) *(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p) - h) - (h - h_ih) + salt_ratio*(h_brine - h_ih); ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction); func_zero = (sa - sa_seaice) *(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h) + sa*((h - h_ih) - salt_ratio*(h_brine - h_ih)); saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero); /*initial guess of saf*/ ctf = gsw_ct_freezing(saf,p,saturation_fraction); gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct); gsw_ct_freezing_first_derivatives(saf,p,saturation_fraction, &ctf_sa, NULL); dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih) + salt_ratio*(h_brine - h_ih); for (number_of_iterations = 1; number_of_iterations <= 4; number_of_iterations++) { saf_old = saf; ctf_old = ctf; func = (sa - sa_seaice) *(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h) - (saf_old - sa)*((h - h_ih) - salt_ratio*(h_brine - h_ih)); saf = saf_old - func/dfunc_dsaf; saf_mean = 0.5*(saf + saf_old); ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction); gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p, &h_hat_sa,&h_hat_ct); gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction, &ctf_sa, NULL); dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih) + salt_ratio*(h_brine - h_ih); saf = saf_old - func/dfunc_dsaf; ctf = gsw_ct_freezing(saf,p,saturation_fraction); } /* ! After these 4 iterations of this modified Newton-Raphson method, the ! errors in SA_freeze is less than 1.5x10^-12 g/kg, in CT_freeze is less than ! 2x10^-13 deg C and in w_seaice is less than 2.8x10^-13 which represent machine ! precision for these calculations. */ *sa_freeze = saf; *ct_freeze = ctf; *w_seaice = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p)) / (h - h_ih - salt_ratio*(h_brine - h_ih)); return; } /* !========================================================================== function gsw_sigma0(sa,ct) !========================================================================== ! Calculates potential density anomaly with reference pressure of 0 dbar, ! this being this particular potential density minus 1000 kg/m^3. This ! function has inputs of Absolute Salinity and Conservative Temperature. ! This function uses the computationally-efficient 48-term expression for ! density in terms of SA, CT and p (IOC et al., 2010). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! gsw_sigma0 : potential density anomaly with reference pressure of 0 ! (48 term equation) */ double gsw_sigma0(double sa, double ct) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double vp0, xs, ys; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; vp0 = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))); return (1.0/vp0 - 1000.0); } /* !========================================================================== function gsw_sigma1(sa,ct) !========================================================================== ! Calculates potential density anomaly with reference pressure of 1000 dbar, ! this being this particular potential density minus 1000 kg/m^3. This ! function has inputs of Absolute Salinity and Conservative Temperature. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! sigma1 : potential density anomaly with reference pressure of 1000 */ double gsw_sigma1(double sa, double ct) { return (gsw_rho(sa,ct,1000.0) - 1000.0); } /* !========================================================================== function gsw_sigma2(sa,ct) !========================================================================== ! Calculates potential density anomaly with reference pressure of 2000 dbar, ! this being this particular potential density minus 1000 kg/m^3. This ! function has inputs of Absolute Salinity and Conservative Temperature. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! sigma2 : potential density anomaly with reference pressure of 2000 */ double gsw_sigma2(double sa, double ct) { return (gsw_rho(sa,ct,2000.0) - 1000.0); } /* !========================================================================== function gsw_sigma3(sa,ct) !========================================================================== ! Calculates potential density anomaly with reference pressure of 3000 dbar, ! this being this particular potential density minus 1000 kg/m^3. This ! function has inputs of Absolute Salinity and Conservative Temperature. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! sigma3 : potential density anomaly with reference pressure of 3000 */ double gsw_sigma3(double sa, double ct) { return (gsw_rho(sa,ct,3000.0) - 1000.0); } /* !========================================================================== function gsw_sigma4(sa,ct) !========================================================================== ! Calculates potential density anomaly with reference pressure of 4000 dbar, ! this being this particular potential density minus 1000 kg/m^3. This ! function has inputs of Absolute Salinity and Conservative Temperature. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! sigma4 : potential density anomaly with reference pressure of 4000 */ double gsw_sigma4(double sa, double ct) { return (gsw_rho(sa,ct,4000.0) - 1000.0); } /* !========================================================================== function gsw_sound_speed(sa,ct,p) !========================================================================== ! Calculates the speed of sound in seawater. This function has inputs of ! Absolute Salinity and Conservative Temperature. This function uses the ! computationally-efficient expression for specific volume in terms of SA, ! CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! sound_speed : speed of sound in seawater [m/s] */ double gsw_sound_speed(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v, v_p, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); v_p = c000 + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs)))) + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020 + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs) + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201 + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs)) + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys))) + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys) + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z)))); return (10000.0*sqrt(-v*v/v_p)); } /* !========================================================================== elemental function gsw_sound_speed_ice (t, p) !========================================================================== ! ! Calculates the compression speed of sound in ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! sound_speed_ice = compression speed of sound in ice [ m/s ] !-------------------------------------------------------------------------- */ double gsw_sound_speed_ice(double t, double p) { double gi_tp, gi_tt; gi_tt = gsw_gibbs_ice(2,0,t,p); gi_tp = gsw_gibbs_ice(1,1,t,p); return (gsw_gibbs_ice(0,1,t,p) * sqrt(gi_tt/(gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p)))); } /* !========================================================================== function gsw_sound_speed_t_exact(sa,t,p) !========================================================================== ! Calculates the speed of sound in seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! gsw_sound_speed_t_exact : sound speed [m/s] */ double gsw_sound_speed_t_exact(double sa, double t, double p) { int n0=0, n1=1, n2=2; double g_tt, g_tp; g_tt = gsw_gibbs(n0,n2,n0,sa,t,p); g_tp = gsw_gibbs(n0,n1,n1,sa,t,p); return (gsw_gibbs(n0,n0,n1,sa,t,p) * sqrt(g_tt/(g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p)))); } /* !-------------------------------------------------------------------------- ! Practical Salinity (SP), PSS-78 !-------------------------------------------------------------------------- !========================================================================== function gsw_sp_from_c(c,t,p) !========================================================================== ! Calculates Practical Salinity, SP, from conductivity, C, primarily using ! the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical ! Salinity is only valid in the range 2 < SP < 42. If the PSS-78 ! algorithm produces a Practical Salinity that is less than 2 then the ! Practical Salinity is recalculated with a modified form of the Hill et ! al. (1986) formula. The modification of the Hill et al. (1986) ! expression is to ensure that it is exactly consistent with PSS-78 ! at SP = 2. Note that the input values of conductivity need to be in ! units of mS/cm (not S/m). ! ! c : conductivity [ mS/cm ] ! t : in-situ temperature [ITS-90] [deg C] ! p : sea pressure [dbar] ! ! sp : Practical Salinity [unitless] */ double gsw_sp_from_c(double c, double t, double p) { GSW_TEOS10_CONSTANTS; GSW_SP_COEFFICIENTS; double sp, t68, ft68, r, rt_lc, rp, rt, rtx, hill_ratio, x, sqrty, part1, part2, sp_hill_raw; t68 = t*1.00024e0; ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0)); /* ! The dimensionless conductivity ratio, R, is the conductivity input, C, ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is ! 42.9140 mS/cm (=4.29140 S/m), (Culkin and Smith, 1980). */ r = c/gsw_c3515; /* 0.023302418791070513 = 1./42.9140 */ /*rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.*/ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68; rp = 1e0 + (p*(e1 + e2*p + e3*p*p))/(1e0 + d1*t68 + d2*t68*t68 + (d3 + d4*t68)*r); rt = r/(rp*rt_lc); if (rt < 0.0) { return (GSW_INVALID_VALUE); } rtx = sqrt(rt); sp = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx + ft68*(b0 + (b1 + (b2 + (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx); /* ! The following section of the code is designed for SP < 2 based on the ! Hill et al. (1986) algorithm. This algorithm is adjusted so that it is ! exactly equal to the PSS-78 algorithm at SP = 2. */ if (sp < 2) { hill_ratio = gsw_hill_ratio_at_sp2(t); x = 400e0*rt; sqrty = 10e0*rtx; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); sp_hill_raw = sp - a0/part1 - b0*ft68/part2; sp = hill_ratio*sp_hill_raw; } /* This line ensures that SP is non-negative. */ if (sp < 0.0) { sp = GSW_INVALID_VALUE; } return (sp); } /* !========================================================================== function gsw_sp_from_sa(sa,p,lon,lat) !========================================================================== ! Calculates Practical salinity, sp, from Absolute salinity, sa ! ! sa : Absolute Salinity [g/kg] ! p : sea pressure [dbar] ! lon : longitude [DEG E] ! lat : latitude [DEG N] ! ! gsw_sp_from_sa : Practical Salinity [unitless] */ double gsw_sp_from_sa(double sa, double p, double lon, double lat) { GSW_TEOS10_CONSTANTS; double saar, gsw_sp_baltic; gsw_sp_baltic = gsw_sp_from_sa_baltic(sa,lon,lat); if (gsw_sp_baltic < GSW_ERROR_LIMIT) return (gsw_sp_baltic); saar = gsw_saar(p,lon,lat); if (saar == GSW_INVALID_VALUE) return (saar); return ((sa/gsw_ups)/(1e0 + saar)); } /* !========================================================================== function gsw_sp_from_sa_baltic(sa,lon,lat) !========================================================================== ! For the Baltic Sea, calculates Practical Salinity with a value ! computed analytically from Absolute Salinity ! ! sa : Absolute Salinity [g/kg] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_sp_from_sa_baltic : Practical Salinity [unitless] */ double gsw_sp_from_sa_baltic(double sa, double lon, double lat) { GSW_TEOS10_CONSTANTS; GSW_BALTIC_DATA; double xx_left, xx_right, return_value; lon = fmod(lon, 360.0); if (lon < 0.0) lon += 360.0; if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat && lat < yb_left[2]) { xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat); xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat); if (xx_left <= lon && lon <= xx_right) return_value = (35.0/(gsw_sso - 0.087))*(sa - 0.087); else return_value = GSW_INVALID_VALUE; } else return_value = GSW_INVALID_VALUE; return (return_value); } /* !========================================================================== function gsw_sp_from_sk(sk) !========================================================================== ! Calculates Practical Salinity, SP, from SK ! ! SK : Knudsen Salinity [parts per thousand, ppt] ! ! gsw_sp_from_sk : Practical Salinity [unitless] */ double gsw_sp_from_sk(double sk) { GSW_TEOS10_CONSTANTS; double gsw_sp_from_sk_value; gsw_sp_from_sk_value = (sk - 0.03e0)*(gsw_soncl/1.805e0); if (gsw_sp_from_sk_value < 0e0) gsw_sp_from_sk_value = GSW_INVALID_VALUE; return (gsw_sp_from_sk_value); } /* !========================================================================== function gsw_sp_from_sr(sr) !========================================================================== ! Calculates Practical Salinity, sp, from Reference Salinity, sr. ! ! sr : Reference Salinity [g/kg] ! ! gsw_sp_from_sr : Practical Salinity [unitless] */ double gsw_sp_from_sr(double sr) { GSW_TEOS10_CONSTANTS; return(sr/gsw_ups); } /* !========================================================================== function gsw_sp_from_sstar(sstar,p,lon,lat) !========================================================================== ! Calculates Practical Salinity, SP, from Preformed Salinity, Sstar. ! ! sstar : Preformed Salinity [g/kg] ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_sp_from_Sstar : Preformed Salinity [g/kg] */ double gsw_sp_from_sstar(double sstar, double p, double lon, double lat) { GSW_TEOS10_CONSTANTS; double saar, sp_baltic; /* **! In the Baltic Sea, SA = Sstar. */ sp_baltic = gsw_sp_from_sa_baltic(sstar,lon,lat); if (sp_baltic < GSW_ERROR_LIMIT) return (sp_baltic); saar = gsw_saar(p,lon,lat); if (saar == GSW_INVALID_VALUE) return (saar); return ((sstar/gsw_ups)/(1.0 - 0.35e0*saar)); } /* !========================================================================== function gsw_sp_salinometer(rt,t) !========================================================================== ! Calculates Practical Salinity SP from a salinometer, primarily using the ! PSS-78 algorithm. Note that the PSS-78 algorithm for Practical Salinity ! is only valid in the range 2 < SP < 42. If the PSS-78 algorithm ! produces a Practical Salinity that is less than 2 then the Practical ! Salinity is recalculated with a modified form of the Hill et al. (1986) ! formula. The modification of the Hill et al. (1986) expression is to ! ensure that it is exactly consistent with PSS-78 at SP = 2. ! ! A laboratory salinometer has the ratio of conductivities, Rt, as an ! output, and the present function uses this conductivity ratio and the ! temperature t of the salinometer bath as the two input variables. ! ! rt = C(SP,t_68,0)/C(SP=35,t_68,0) [ unitless ] ! t = temperature of the bath of the salinometer, ! measured on the ITS-90 scale (ITS-90) [ deg C ] ! ! gsw_sp_salinometer = Practical Salinity on the PSS-78 scale [ unitless ] */ double gsw_sp_salinometer(double rt, double t) { GSW_SP_COEFFICIENTS; double t68, ft68, rtx, sp, hill_ratio, x, sqrty, part1, part2, sp_hill_raw; if (rt < 0){ return NAN; } t68 = t*1.00024; ft68 = (t68 - 15)/(1 + k*(t68 - 15)); rtx = sqrt(rt); sp = a0 + (a1 + (a2 + (a3 + (a4 + a5 * rtx) * rtx) * rtx) * rtx) * rtx + ft68 * (b0 + (b1 + (b2+ (b3 + (b4 + b5 * rtx) * rtx) * rtx) * rtx) * rtx); /* ! The following section of the code is designed for SP < 2 based on the ! Hill et al. (1986) algorithm. This algorithm is adjusted so that it is ! exactly equal to the PSS-78 algorithm at SP = 2. */ if (sp < 2) { hill_ratio = gsw_hill_ratio_at_sp2(t); x = 400e0*rt; sqrty = 10e0*rtx; part1 = 1e0 + x*(1.5e0 + x); part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty)); sp_hill_raw = sp - a0/part1 - b0*ft68/part2; sp = hill_ratio*sp_hill_raw; } return sp; } /* !========================================================================== function gsw_specvol(sa,ct,p) !========================================================================== ! ! Calculates specific volume from Absolute Salinity, Conservative ! Temperature and pressure, using the computationally-efficient ! polynomial expression for specific volume (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! specvol: specific volume [m^3/kg] */ double gsw_specvol(double sa, double ct, double p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double xs, ys, z, value; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; value = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); return (value); } /* !========================================================================== elemental subroutine gsw_specvol_alpha_beta (sa, ct, p, specvol, alpha, & beta) !========================================================================== ! ! Calculates specific volume, the appropriate thermal expansion coefficient ! and the appropriate saline contraction coefficient of seawater from ! Absolute Salinity and Conservative Temperature. This function uses the ! computationally-efficient expression for specific volume in terms of ! SA, CT and p (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! specvol = specific volume [ m/kg ] ! alpha = thermal expansion coefficient [ 1/K ] ! with respect to Conservative Temperature ! beta = saline (i.e. haline) contraction [ kg/g ] ! coefficient at constant Conservative Temperature !-------------------------------------------------------------------------- */ void gsw_specvol_alpha_beta(double sa, double ct, double p, double *specvol, double *alpha, double *beta) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v, v_ct, v_sa_part, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050 + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140 + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs))) + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410 + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011 + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111 + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221 + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs))) + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212 + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013 + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys + z*(v005 + v006*z))))); if (specvol != NULL) *specvol = v; if (alpha != NULL) { v_ct = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))); *alpha = 0.025*v_ct/v; } if (beta != NULL) { v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); *beta = -v_sa_part*0.5*gsw_sfac/(v*xs); } } /* !========================================================================== function gsw_specvol_anom_standard(sa,ct,p) !========================================================================== ! ! Calculates specific volume anomaly of seawater. ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! specvol_anom : specific volume anomaly of seawater */ double gsw_specvol_anom_standard(double sa, double ct, double p) { return (gsw_specvol(sa,ct,p) - gsw_specvol_sso_0(p)); } /* !========================================================================== elemental subroutine gsw_specvol_first_derivatives (sa, ct, p, v_sa, v_ct, & v_p, iflag) ! ========================================================================= ! ! Calculates three first-order derivatives of specific volume (v). ! Note that this function uses the computationally-efficient ! expression for specific volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! v_SA = The first derivative of specific volume with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! v_CT = The first derivative of specific volume with respect to ! CT at constant SA and p. [ J/(kg K(g/kg)) ] ! v_P = The first derivative of specific volume with respect to ! P at constant SA and CT. [ J/(kg K^2) ] !-------------------------------------------------------------------------- */ void gsw_specvol_first_derivatives (double sa, double ct, double p, double *v_sa, double *v_ct, double *v_p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v_ct_part, v_p_part, v_sa_part, xs, ys, z; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; z = p*1e-4; if (v_sa != NULL) { v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs)))) + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030 + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys)))) + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys)) + z*(b003 + b103*xs + b013*ys + b004*z))); *v_sa = 0.5*gsw_sfac*v_sa_part/xs; } if (v_ct != NULL) { v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs)))) + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030 + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys )))) + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys)) + z*(a003 + a103*xs + a013*ys + a004*z))) ; *v_ct = 0.025*v_ct_part; } if (v_p != NULL) { v_p_part = c000 + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs)))) + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020 + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs) + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201 + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs)) + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys))) + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys) + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z)))); *v_p = 1e-8*v_p_part; } } /* !========================================================================== elemental subroutine gsw_specvol_first_derivatives_wrt_enthalpy (sa, ct, & p, v_sa, v_h, iflag) ! ========================================================================= ! ! Calculates two first-order derivatives of specific volume (v). ! Note that this function uses the using the computationally-efficient ! expression for specific volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! v_SA = The first derivative of specific volume with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! v_h = The first derivative of specific volume with respect to ! SA and CT at constant p. [ J/(kg K(g/kg)) ] !-------------------------------------------------------------------------- */ void gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct, double p, double *v_sa, double *v_h) { double h_ct=1.0, h_sa, rec_h_ct, vct_ct, vct_sa; if (v_sa != NULL) { gsw_specvol_first_derivatives(sa,ct,p,&vct_sa,&vct_ct,NULL); gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct); } else if (v_h != NULL) { gsw_specvol_first_derivatives(sa,ct,p,NULL,&vct_ct,NULL); gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct); } rec_h_ct = 1.0/h_ct; if (v_sa != NULL) *v_sa = vct_sa - (vct_ct*h_sa)*rec_h_ct; if (v_h != NULL) *v_h = vct_ct*rec_h_ct; return; } /* !========================================================================== elemental function gsw_specvol_ice (t, p) !========================================================================== ! ! Calculates the specific volume of ice. ! ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! specvol_ice = specific volume [ m^3/kg ] !-------------------------------------------------------------------------- */ double gsw_specvol_ice(double t, double p) { return (gsw_gibbs_ice(0,1,t,p)); } /* !========================================================================== elemental subroutine gsw_specvol_second_derivatives (sa, ct, p, v_sa_sa, & v_sa_ct, v_ct_ct, v_sa_p, v_ct_p, iflag) ! ========================================================================= ! ! Calculates five second-order derivatives of specific volume (v). ! Note that this function uses the computationally-efficient ! expression for specific volume (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! v_SA_SA = The second derivative of specific volume with respect to ! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ] ! v_SA_CT = The second derivative of specific volume with respect to ! SA and CT at constant p. [ J/(kg K(g/kg)) ] ! v_CT_CT = The second derivative of specific volume with respect to ! CT at constant SA and p. [ J/(kg K^2) ] ! v_SA_P = The second derivative of specific volume with respect to ! SA and P at constant CT. [ J/(kg K(g/kg)) ] ! v_CT_P = The second derivative of specific volume with respect to ! CT and P at constant SA. [ J/(kg K(g/kg)) ] !-------------------------------------------------------------------------- */ void gsw_specvol_second_derivatives (double sa, double ct, double p, double *v_sa_sa, double *v_sa_ct, double *v_ct_ct, double *v_sa_p, double *v_ct_p) { GSW_TEOS10_CONSTANTS; GSW_SPECVOL_COEFFICIENTS; double v_ct_ct_part, v_ct_p_part, v_sa_ct_part, v_sa_p_part, v_sa_sa_part, xs, xs2, ys, z; xs2 = gsw_sfac*sa + offset; xs = sqrt(xs2); ys = ct*0.025; z = p*1e-4; if (v_sa_sa != NULL) { v_sa_sa_part = (-b000 + xs2*(b200 + xs*(2.0*b300 + xs*(3.0*b400 + 4.0*b500*xs))) + ys*(-b010 + xs2*(b210 + xs*(2.0*b310 + 3.0*b410*xs)) + ys*(-b020 + xs2*(b220 + 2.0*b320*xs) + ys*(-b030 + b230*xs2 + ys*(-b040 - b050*ys)))) + z*(-b001 + xs2*(b201 + xs*(2.0*b301 + 3.0*b401*xs)) + ys*(-b011 + xs2*(b211 + 2.0*b311*xs) + ys*(-b021 + b221*xs2 + ys*(-b031 - b041*ys))) + z*(-b002 + xs2*(b202 + 2.0*b302*xs) + ys*(-b012 + b212*xs2 + ys*(-b022 - b032*ys)) + z*(-b003 - b013*ys - b004*z))))/xs2; *v_sa_sa = 0.25*gsw_sfac*gsw_sfac*v_sa_sa_part/xs; } if (v_sa_ct != NULL) { v_sa_ct_part = (b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs))) + ys*(2.0*(b020 + xs*(b120 + xs*(b220 + b320*xs))) + ys*(3.0*(b030 + xs*(b130 + b230*xs)) + ys*(4.0*(b040 + b140*xs) + 5.0*b050*ys))) + z*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(2.0*(b021 + xs*(b121 + b221*xs)) + ys*(3.0*(b031 + b131*xs) + 4.0*b041*ys)) + z*(b012 + xs*(b112 + b212*xs) + ys*(2.0*(b022 + b122*xs) + 3.0*b032*ys) + b013*z)))/xs; *v_sa_ct = 0.025*0.5*gsw_sfac*v_sa_ct_part; } if (v_ct_ct != NULL) { v_ct_ct_part = a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs))) + ys*(2.0*(a020 + xs*(a120 + xs*(a220 + a320*xs))) + ys*(3.0*(a030 + xs*(a130 + a230*xs)) + ys*(4.0*(a040 + a140*xs) + 5.0*a050*ys))) + z*( a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(2.0*(a021 + xs*(a121 + a221*xs)) + ys*(3.0*(a031 + a131*xs) + 4.0*a041*ys)) + z*(a012 + xs*(a112 + a212*xs) + ys*(2.0*(a022 + a122*xs) + 3.0*a032*ys) + a013*z)); *v_ct_ct = 0.025*0.025*v_ct_ct_part; } if (v_sa_p != NULL) { v_sa_p_part = b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys))) + z*(2.0*(b002 + xs*(b102 + xs*(b202 + b302*xs)) + ys*(b012 + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))) + z*(3.0*(b003 + b103*xs + b013*ys) + 4.0*b004*z)); *v_sa_p = 1e-8*0.5*gsw_sfac*v_sa_p_part/xs; } if (v_ct_p != NULL) { v_ct_p_part = a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs))) + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021 + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys))) + z*(2.0*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))) + z*(3.0*(a003 + a103*xs + a013*ys) + 4.0*a004*z)); *v_ct_p = 1e-8*0.025*v_ct_p_part; } } /* !========================================================================== elemental subroutine gsw_specvol_second_derivatives_wrt_enthalpy (sa, ct, & p, v_sa_sa, v_sa_h, v_h_h, iflag) ! ========================================================================= ! ! Calculates three first-order derivatives of specific volume (v) with ! respect to enthalpy. Note that this function uses the using the ! computationally-efficient expression for specific volume ! (Roquet et al., 2014). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! v_SA_SA = The second-order derivative of specific volume with respect to ! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ] ! v_SA_h = The second-order derivative of specific volume with respect to ! SA and h at constant p. [ J/(kg K(g/kg)) ] ! v_h_h = The second-order derivative with respect to h at ! constant SA & p. !-------------------------------------------------------------------------- */ void gsw_specvol_second_derivatives_wrt_enthalpy (double sa, double ct, double p, double *v_sa_sa, double *v_sa_h, double *v_h_h) { double h_ct, h_ct_ct, h_sa, h_sa_ct, h_sa_sa, rec_h_ct, v_h_h_part, rec_h_ct2, v_ct, vct_ct_ct, vct_sa_ct, vct_sa_sa, v_sa_h_part; gsw_specvol_first_derivatives(sa,ct,p,NULL, &v_ct, NULL); if ((v_sa_sa != NULL) || (v_sa_h != NULL)) gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct); else gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct); if (v_sa_sa != NULL) gsw_specvol_second_derivatives(sa,ct,p,&vct_sa_sa,&vct_sa_ct, &vct_ct_ct, NULL, NULL); else if (v_sa_h != NULL) gsw_specvol_second_derivatives(sa,ct,p,NULL,&vct_sa_ct,&vct_ct_ct, NULL, NULL); else gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,&vct_ct_ct, NULL, NULL); if (v_sa_sa != NULL) gsw_enthalpy_second_derivatives(sa,ct,p,&h_sa_sa,&h_sa_ct,&h_ct_ct); else if (v_sa_h != NULL) gsw_enthalpy_second_derivatives(sa,ct,p,NULL,&h_sa_ct,&h_ct_ct); else gsw_enthalpy_second_derivatives(sa,ct,p,NULL,NULL,&h_ct_ct); rec_h_ct = 1.0/h_ct; rec_h_ct2 = rec_h_ct*rec_h_ct; v_h_h_part = (vct_ct_ct*h_ct - h_ct_ct*v_ct)*(rec_h_ct2*rec_h_ct); if (v_h_h != NULL) *v_h_h = v_h_h_part; if ((v_sa_sa != NULL) || (v_sa_h != NULL)) { v_sa_h_part = (vct_sa_ct*h_ct - v_ct*h_sa_ct)*rec_h_ct2 - h_sa*v_h_h_part; if (v_sa_h != NULL) *v_sa_h = v_sa_h_part; if (v_sa_sa != NULL) *v_sa_sa = vct_sa_sa - (h_ct*(vct_sa_ct*h_sa + v_ct*h_sa_sa) - v_ct*h_sa*h_sa_ct)*rec_h_ct2 - h_sa*v_sa_h_part; } } /* !========================================================================== function gsw_specvol_sso_0(p) !========================================================================== ! This function calculates specific volume at the Standard Ocean Salinty, ! SSO, and at a Conservative Temperature of zero degrees C, as a function ! of pressure, p, in dbar, using a streamlined version of the CT version ! of specific volume, that is, a streamlined version of the code ! "gsw_specvol(SA,CT,p)". ! ! p : sea pressure [dbar] ! 3 -1 ! specvol_sso_0 : specvol(sso,0,p) [m kg ] */ double gsw_specvol_sso_0(double p) { GSW_SPECVOL_COEFFICIENTS; double z, return_value; z = p*1.0e-4; return_value = 9.726613854843870e-04 + z*(-4.505913211160929e-05 + z*(7.130728965927127e-06 + z*(-6.657179479768312e-07 + z*(-2.994054447232880e-08 + z*(v005 + v006*z))))); return (return_value); } /* !========================================================================== function gsw_specvol_t_exact(sa,t,p) !========================================================================== ! Calculates the specific volume of seawater ! ! sa : Absolute Salinity [g/kg] ! t : in-situ temperature [deg C] ! p : sea pressure [dbar] ! ! specvol_t_exact : specific volume [kg/m^3] */ double gsw_specvol_t_exact(double sa, double t, double p) { int n0=0, n1=1; return (gsw_gibbs(n0,n0,n1,sa,t,p)); } /* !========================================================================== function gsw_spiciness0(sa,ct) !========================================================================== ! ! Calculates spiciness from Absolute Salinity and Conservative ! Temperature at a pressure of 0 dbar, as described by McDougall and ! Krzysik (2015). This routine is based on the computationally-efficient ! expression for specific volume in terms of SA, CT and p (Roquet et al., ! 2015). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! spiciness0 = spiciness referenced to a pressure of 0 dbar, ! i.e. the surface [ kg/m^3 ] ! */ double gsw_spiciness0(double sa, double ct) { GSW_TEOS10_CONSTANTS; double s01 = -9.22982898371678e1, s02 = -1.35727873628866e1, s03 = 1.87353650994010e1, s04 = -1.61360047373455e1, s05 = 3.76112762286425e1, s06 = -4.27086671461257e1, s07 = 2.00820111041594e1, s08 = 2.87969717584045e2, s09 = 1.13747111959674e1, s10 = 6.07377192990680e1, s11 = -7.37514033570187e1, s12 = -7.51171878953574e1, s13 = 1.63310989721504e2, s14 = -8.83222751638095e1, s15 = -6.41725302237048e2, s16 = 2.79732530789261e1, s17 = -2.49466901993728e2, s18 = 3.26691295035416e2, s19 = 2.66389243708181e1, s20 = -2.93170905757579e2, s21 = 1.76053907144524e2, s22 = 8.27634318120224e2, s23 = -7.02156220126926e1, s24 = 3.82973336590803e2, s25 = -5.06206828083959e2, s26 = 6.69626565169529e1, s27 = 3.02851235050766e2, s28 = -1.96345285604621e2, s29 = -5.74040806713526e2, s30 = 7.03285905478333e1, s31 = -2.97870298879716e2, s32 = 3.88340373735118e2, s33 = -8.29188936089122e1, s34 = -1.87602137195354e2, s35 = 1.27096944425793e2, s36 = 2.11671167892147e2, s37 = -3.15140919876285e1, s38 = 1.16458864953602e2, s39 = -1.50029730802344e2, s40 = 3.76293848660589e1, s41 = 6.47247424373200e1, s42 = -4.47159994408867e1, s43 = -3.23533339449055e1, s44 = 5.30648562097667, s45 = -1.82051249177948e1, s46 = 2.33184351090495e1, s47 = -6.22909903460368, s48 = -9.55975464301446, s49 = 6.61877073960113; double xs, ys, spiciness0; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; spiciness0= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys))))) +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys))))) +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys))))) +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys))))) +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys))))) +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys))))) +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys))))) )))))); return (spiciness0); } /* !========================================================================== function gsw_spiciness1(sa,ct) !========================================================================== ! ! Calculates spiciness from Absolute Salinity and Conservative ! Temperature at a pressure of 1000 dbar, as described by McDougall and ! Krzysik (2015). This routine is based on the computationally-efficient ! expression for specific volume in terms of SA, CT and p (Roquet et al., ! 2015). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! spiciness1 = spiciness referenced to a pressure of 1000 dbar [ kg/m^3 ] ! */ double gsw_spiciness1(double sa, double ct) { GSW_TEOS10_CONSTANTS; double s01 = -9.19874584868912e1, s02 = -1.33517268529408e1, s03 = 2.18352211648107e1, s04 = -2.01491744114173e1, s05 = 3.70004204355132e1, s06 = -3.78831543226261e1, s07 = 1.76337834294554e1, s08 = 2.87838842773396e2, s09 = 2.14531420554522e1, s10 = 3.14679705198796e1, s11 = -4.04398864750692e1, s12 = -7.70796428950487e1, s13 = 1.36783833820955e2, s14 = -7.36834317044850e1, s15 = -6.41753415180701e2, s16 = 1.33701981685590, s17 = -1.75289327948412e2, s18 = 2.42666160657536e2, s19 = 3.17062400799114e1, s20 = -2.28131490440865e2, s21 = 1.39564245068468e2, s22 = 8.27747934506435e2, s23 = -3.50901590694775e1, s24 = 2.87473907262029e2, s25 = -4.00227341144928e2, s26 = 6.48307189919433e1, s27 = 2.16433334701578e2, s28 = -1.48273032774305e2, s29 = -5.74545648799754e2, s30 = 4.50446431127421e1, s31 = -2.30714981343772e2, s32 = 3.15958389253065e2, s33 = -8.60635313930106e1, s34 = -1.22978455069097e2, s35 = 9.18287282626261e1, s36 = 2.12120473062203e2, s37 = -2.21528216973820e1, s38 = 9.19013417923270e1, s39 = -1.24400776026014e2, s40 = 4.08512871163839e1, s41 = 3.91127352213516e1, s42 = -3.10508021853093e1, s43 = -3.24790035899152e1, s44 = 3.91029016556786, s45 = -1.45362719385412e1, s46 = 1.96136194246355e1, s47 = -7.06035474689088, s48 = -5.36884688614009, s49 = 4.43247303092448; double xs, ys, spiciness1; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; spiciness1= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys))))) +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys))))) +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys))))) +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys))))) +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys))))) +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys))))) +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys))))) )))))); return (spiciness1); } /* !========================================================================== function gsw_spiciness2(sa,ct) !========================================================================== ! ! Calculates spiciness from Absolute Salinity and Conservative ! Temperature at a pressure of 2000 dbar, as described by McDougall and ! Krzysik (2015). This routine is based on the computationally-efficient ! expression for specific volume in terms of SA, CT and p (Roquet et al., ! 2015). ! ! SA = Absolute Salinity [ g/kg ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! ! spiciness2 = spiciness referenced to a pressure of 2000 dbar [ kg/m^3 ] ! */ double gsw_spiciness2(double sa, double ct) { GSW_TEOS10_CONSTANTS; double s01 = -9.17327320732265e1, s02 = -1.31200235147912e1, s03 = 2.49574345782503e1, s04 = -2.41678075247398e1, s05 = 3.61654631402053e1, s06 = -3.22582164667710e1, s07 = 1.45092623982509e1, s08 = 2.87776645983195e2, s09 = 3.13902307672447e1, s10 = 1.69777467534459, s11 = -5.69630115740438, s12 = -7.97586359017987e1, s13 = 1.07507460387751e2, s14 = -5.58234404964787e1, s15 = -6.41708068766557e2, s16 = -2.53494801286161e1, s17 = -9.86755437385364e1, s18 = 1.52406930795842e2, s19 = 4.23888258264105e1, s20 = -1.60118811141438e2, s21 = 9.67497898053989e1, s22 = 8.27674355478637e2, s23 = 5.27561234412133e-1, s24 = 1.87440206992396e2, s25 = -2.83295392345171e2, s26 = 5.14485994597635e1, s27 = 1.29975755062696e2, s28 = -9.36526588377456e1, s29 = -5.74911728972948e2, s30 = 1.91175851862772e1, s31 = -1.59347231968841e2, s32 = 2.33884725744938e2, s33 = -7.87744010546157e1, s34 = -6.04757235443685e1, s35 = 5.27869695599657e1, s36 = 2.12517758478878e2, s37 = -1.24351794740528e1, s38 = 6.53904308937490e1, s39 = -9.44804080763788e1, s40 = 3.93874257887364e1, s41 = 1.49425448888996e1, s42 = -1.62350721656367e1, s43 = -3.25936844276669e1, s44 = 2.44035700301595, s45 = -1.05079633683795e1, s46 = 1.51515796259082e1, s47 = -7.06609886460683, s48 = -1.48043337052968, s49 = 2.10066653978515; double xs, ys, spiciness2; xs = sqrt(gsw_sfac*sa + offset); ys = ct*0.025; spiciness2= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys))))) +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys))))) +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys))))) +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys))))) +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys))))) +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys))))) +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys))))) )))))); return (spiciness2); } /* !========================================================================== function gsw_sr_from_sp(sp) !========================================================================== ! Calculates Reference Salinity, SR, from Practical Salinity, SP. ! ! sp : Practical Salinity [unitless] ! ! gsw_sr_from_sp : Reference Salinity [g/kg] */ double gsw_sr_from_sp(double sp) { GSW_TEOS10_CONSTANTS; return (sp*gsw_ups); } /* !========================================================================== function gsw_sstar_from_sa(sa,p,lon,lat) !========================================================================== ! Calculates Preformed Salinity, Sstar, from Absolute Salinity, SA. ! ! sa : Absolute Salinity [g/kg] ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_sstar_from_sa : Preformed Salinity [g/kg] */ double gsw_sstar_from_sa(double sa, double p, double lon, double lat) { double saar; saar = gsw_saar(p,lon,lat); /* ! In the Baltic Sea, Sstar = sa, and note that gsw_saar returns zero ! for saar in the Baltic. */ if (saar == GSW_INVALID_VALUE) return (saar); return (sa*(1e0 - 0.35e0*saar)/(1e0 + saar)); } /* !========================================================================== function gsw_sstar_from_sp(sp,p,lon,lat) !========================================================================== ! Calculates Preformed Salinity, Sstar, from Practical Salinity, SP. ! ! sp : Practical Salinity [unitless] ! p : sea pressure [dbar] ! lon : longitude [deg E] ! lat : latitude [deg N] ! ! gsw_sstar_from_sp : Preformed Salinity [g/kg] */ double gsw_sstar_from_sp(double sp, double p, double lon, double lat) { GSW_TEOS10_CONSTANTS; double saar, sstar_baltic; /* !In the Baltic Sea, Sstar = SA. */ sstar_baltic = gsw_sa_from_sp_baltic(sp,lon,lat); if (sstar_baltic < GSW_ERROR_LIMIT) return (sstar_baltic); saar = gsw_saar(p,lon,lat); if (saar == GSW_INVALID_VALUE) return (saar); return (gsw_ups*sp*(1 - 0.35e0*saar)); } /* !========================================================================== elemental function gsw_t_deriv_chem_potential_water_t_exact (sa, t, p) !========================================================================== ! ! Calculates the temperature derivative of the chemical potential of water ! in seawater so that it is valid at exactly SA = 0. ! ! SA = Absolute Salinity [ g/kg ] ! t = in-situ temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! ! chem_potential_water_dt = temperature derivative of the chemical ! potential of water in seawater [ J g^-1 K^-1 ] !-------------------------------------------------------------------------- */ double gsw_t_deriv_chem_potential_water_t_exact(double sa, double t, double p) { GSW_TEOS10_CONSTANTS; double g03_t, g08_sa_t, x, x2, y, z, g08_t, kg2g = 1e-3; /* ! Note. The kg2g, a factor of 1e-3, is needed to convert the output of this ! function into units of J/g. See section (2.9) of the TEOS-10 Manual. */ x2 = gsw_sfac*sa; x = sqrt(x2); y = t*0.025; z = p*rec_db2pa; /* the input pressure (p) is sea pressure in units of dbar. */ g03_t = 5.90578347909402 + z*(-270.983805184062 + z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 - 2.13290083518327*z)*z))) + y*(-24715.571866078 + z*(2910.0729080936 + z*(-1513.116771538718 + z*(546.959324647056 + z*(-111.1208127634436 + 8.68841343834394*z)))) + y*(2210.2236124548363 + z*(-2017.52334943521 + z*(1498.081172457456 + z*(-718.6359919632359 + (146.4037555781616 - 4.9892131862671505*z)*z))) + y*(-592.743745734632 + z*(1591.873781627888 + z*(-1207.261522487504 + (608.785486935364 - 105.4993508931208*z)*z)) + y*(290.12956292128547 + z*(-973.091553087975 + z*(602.603274510125 + z*(-276.361526170076 + 32.40953340386105*z))) + y*(-113.90630790850321 + y*(21.35571525415769 - 67.41756835751434*z) + z*(381.06836198507096 + z*(-133.7383902842754 + 49.023632509086724*z))))))); g08_t = x2*(168.072408311545 + x*(-493.407510141682 + x*(543.835333000098 + x*(-196.028306689776 + 36.7571622995805*x) + y*(-137.1145018408982 + y*(148.10030845687618 + y*(-68.5590309679152 + 12.4848504784754*y))) - 22.6683558512829*z) + z*(-175.292041186547 + (83.1923927801819 - 29.483064349429*z)*z) + y*(-86.1329351956084 + z*(766.116132004952 + z*(-108.3834525034224 + 51.2796974779828*z)) + y*(-30.0682112585625 - 1380.9597954037708*z + y*(3.50240264723578 + 938.26075044542*z))))); g08_sa_t = 1187.3715515697959 + x*(-1480.222530425046 + x*(2175.341332000392 + x*(-980.14153344888 + 220.542973797483*x) + y*(-548.4580073635929 + y*(592.4012338275047 + y*(-274.2361238716608 + 49.9394019139016*y))) - 90.6734234051316*z) + z*(-525.876123559641 + (249.57717834054571 - 88.449193048287*z)*z) + y*(-258.3988055868252 + z*(2298.348396014856 + z*(-325.1503575102672 + 153.8390924339484*z)) + y*(-90.2046337756875 - 4142.8793862113125*z + y*(10.50720794170734 + 2814.78225133626*z)))); return (kg2g*((g03_t + g08_t)*0.025 - 0.5*gsw_sfac*0.025*sa*g08_sa_t)); } /* !========================================================================== function gsw_t_freezing(sa,p,saturation_fraction) !========================================================================== ! Calculates the in-situ temperature at which seawater freezes ! ! sa : Absolute Salinity [g/kg] ! p : sea pressure [dbar] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction : the saturation fraction of dissolved air ! in seawater ! ! t_freezing : in-situ temperature at which seawater freezes.[deg C] */ double gsw_t_freezing(double sa, double p, double saturation_fraction) { GSW_TEOS10_CONSTANTS; GSW_FREEZING_POLY_COEFFICIENTS; double sa_r, x, p_r; double df_dt, tf, tfm, tf_old, f, return_value; /* The initial value of t_freezing_exact (for air-free seawater) */ sa_r = sa*1e-2; x = sqrt(sa_r); p_r = p*1e-4; tf = t0 + sa_r*(t1 + x*(t2 + x*(t3 + x*(t4 + x*(t5 + t6*x))))) + p_r*(t7 + p_r*(t8 + t9*p_r)) + sa_r*p_r*(t10 + p_r*(t12 + p_r*(t15 + t21*sa_r)) + sa_r*(t13 + t17*p_r + t19*sa_r) + x*(t11 + p_r*(t14 + t18*p_r) + sa_r*(t16 + t20*p_r + t22*sa_r))); /* Adjust for the effects of dissolved air */ tf -= saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso)); df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p) - gsw_gibbs_ice(1,0,tf,p); /* ! df_dt here is the initial value of the derivative of the function f whose ! zero (f = 0) we are finding (see Eqn. (3.33.2) of IOC et al (2010)). */ tf_old = tf; f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) - gsw_gibbs_ice(0,0,tf_old,p); tf = tf_old - f/df_dt; tfm = 0.5*(tf + tf_old); df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tfm,p) - gsw_gibbs_ice(1,0,tfm,p); tf = tf_old - f/df_dt; tf_old = tf; f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) - gsw_gibbs_ice(0,0,tf_old,p); tf = tf_old - f/df_dt; /* Adjust for the effects of dissolved air */ return_value = tf - saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso)); return (return_value); } /* !========================================================================== elemental subroutine gsw_t_freezing_first_derivatives (sa, p, & saturation_fraction, tfreezing_sa, tfreezing_p) !========================================================================== ! ! Calculates the first derivatives of the in-situ temperature at which ! seawater freezes with respect to Absolute Salinity SA and pressure P (in ! Pa). These expressions come from differentiating the expression that ! defines the freezing temperature, namely the equality between the ! chemical potentials of water in seawater and in ice. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! tfreezing_SA = the derivative of the in-situ freezing temperature ! (ITS-90) with respect to Absolute Salinity at fixed ! pressure [ K/(g/kg) ] i.e. [ K kg/g ] ! ! tfreezing_P = the derivative of the in-situ freezing temperature ! (ITS-90) with respect to pressure (in Pa) at fixed ! Absolute Salinity [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_t_freezing_first_derivatives(double sa, double p, double saturation_fraction, double *tfreezing_sa, double *tfreezing_p) { GSW_TEOS10_CONSTANTS; double rec_denom, tf, g_per_kg = 1000.0; tf = gsw_t_freezing(sa,p,saturation_fraction); rec_denom = 1.0/ (g_per_kg*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p) + gsw_entropy_ice(tf,p)); if (tfreezing_sa != NULL) *tfreezing_sa = gsw_dilution_coefficient_t_exact(sa,tf,p)*rec_denom + saturation_fraction*(1e-3)/(2.0*gsw_sso); if (tfreezing_p != NULL) *tfreezing_p = -(gsw_specvol_t_exact(sa,tf,p) - sa*gsw_gibbs(1,0,1,sa,tf,p) - gsw_specvol_ice(tf,p))*rec_denom; return; } /* !========================================================================== elemental subroutine gsw_t_freezing_first_derivatives_poly (sa, p, & saturation_fraction, tfreezing_sa, tfreezing_p) !========================================================================== ! ! Calculates the first derivatives of the in-situ temperature at which ! seawater freezes with respect to Absolute Salinity SA and pressure P (in ! Pa). These expressions come from differentiating the expression that ! defines the freezing temperature, namely the equality between the ! chemical potentials of water in seawater and in ice. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! tfreezing_SA = the derivative of the in-situ freezing temperature ! (ITS-90) with respect to Absolute Salinity at fixed ! pressure [ K/(g/kg) ] i.e. [ K kg/g ] ! ! tfreezing_P = the derivative of the in-situ freezing temperature ! (ITS-90) with respect to pressure (in Pa) at fixed ! Absolute Salinity [ K/Pa ] !-------------------------------------------------------------------------- */ void gsw_t_freezing_first_derivatives_poly(double sa, double p, double saturation_fraction, double *tfreezing_sa, double *tfreezing_p) { GSW_TEOS10_CONSTANTS; GSW_FREEZING_POLY_COEFFICIENTS; double p_r, sa_r, x, c = 1e-3/(2.0*gsw_sso); sa_r = sa*1e-2; x = sqrt(sa_r); p_r = p*1e-4; if (tfreezing_sa != NULL) *tfreezing_sa = (t1 + x*(1.5*t2 + x*(2.0*t3 + x*(2.5*t4 + x*(3.0*t5 + 3.5*t6*x)))) + p_r*(t10 + x*(1.5*t11 + x*(2.0*t13 + x*(2.5*t16 + x*(3.0*t19 + 3.5*t22*x)))) + p_r*(t12 + x*(1.5*t14 + x*(2.0*t17 + 2.5*t20*x)) + p_r*(t15 + x*(1.5*t18 + 2.0*t21*x)))))*1e-2 + saturation_fraction*c; if (tfreezing_p != NULL) *tfreezing_p = (t7 + sa_r*(t10 + x*(t11 + x*(t13 + x*(t16 + x*(t19 + t22*x))))) + p_r*(2.0*t8 + sa_r*(2.0*t12 + x*(2.0*t14 + x*(2.0*t17 + 2.0*t20*x))) + p_r*(3.0*t9 + sa_r*(3.0*t15 + x*(3.0*t18 + 3.0*t21*x)))))*1e-8; return; } /* !========================================================================== elemental function gsw_t_freezing_poly (sa, p, saturation_fraction) !========================================================================== ! ! Calculates the in-situ temperature at which seawater freezes from a ! computationally efficient polynomial. ! ! SA = Absolute Salinity [ g/kg ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! saturation_fraction = the saturation fraction of dissolved air in ! seawater ! ! t_freezing = in-situ temperature at which seawater freezes. [ deg C ] ! (ITS-90) !-------------------------------------------------------------------------- */ double gsw_t_freezing_poly(double sa, double p, double saturation_fraction) { GSW_TEOS10_CONSTANTS; double ctf, return_value; ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction); return_value = gsw_t_from_ct(sa,ctf,p); return (return_value); } /* !========================================================================== function gsw_t_from_ct(sa,ct,p) !========================================================================== ! Calculates in-situ temperature from Conservative Temperature of seawater ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature [deg C] ! ! gsw_t_from_ct : in-situ temperature [deg C] */ double gsw_t_from_ct(double sa, double ct, double p) { double pt0, p0=0.0; pt0 = gsw_pt_from_ct(sa,ct); return (gsw_pt_from_t(sa,pt0,p0,p)); } /* ! ========================================================================= elemental function gsw_t_from_pt0_ice (pt0_ice, p) ! ========================================================================= ! ! Calculates in-situ temperature from the potential temperature of ice Ih ! with reference pressure, p_ref, of 0 dbar (the surface), and the ! in-situ pressure. ! ! pt0_ice = potential temperature of ice Ih with reference pressure of ! zero dbar (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) !-------------------------------------------------------------------------- */ double gsw_t_from_pt0_ice(double pt0_ice, double p) { double p0 = 0.0; return (gsw_pt_from_t_ice(pt0_ice,p0,p)); } /* !========================================================================== function gsw_thermobaric(sa,ct,p) !========================================================================== ! Calculates the thermobaric coefficient of seawater with respect to ! Conservative Temperature. This routine is based on the ! computationally-efficient expression for specific volume in terms of ! SA, CT and p (Roquet et al., 2014). ! ! sa : Absolute Salinity [g/kg] ! ct : Conservative Temperature (ITS-90) [deg C] ! p : sea pressure [dbar] ! ! thermobaric : thermobaric coefficient with [1/(K Pa)] ! respect to Conservative Temperature (48 term equation) */ double gsw_thermobaric(double sa, double ct, double p) { double v_ct, v_ct_p, v_sa, v_sa_p; gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,NULL); gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,NULL,&v_sa_p,&v_ct_p); return (gsw_rho(sa,ct,p)*(v_ct_p - (v_ct/v_sa)*v_sa_p)); } /* !========================================================================== subroutine gsw_tracer_CT_interp (tracer,ct,p,p_i,factor) !========================================================================== ! ! Tracer and CT interpolation to p_i on a cast ! ! tracer = tracer [ ? ] ! CT = Conservative Temperature (ITS-90) [ deg C ] ! p = sea pressure [ dbar ] ! ( i.e. absolute pressure - 10.1325 dbar ) ! p_i = specific query points at which the interpolated tracer_i ! and CT_i are required [ dbar ] ! factor = ratio between the ranges of Conservative Temperature ! and tracer in the world ocean. [ ? ] ! ! tracer_i = interpolated tracer values at pressures p_i [ g/kg ] ! CT_i = interpolated CT values at pressures p_i [ deg C ] ! !-------------------------------------------------------------------------- */ int gsw_tracer_ct_interp(double *tracer, double *ct, double *p, int m, double *p_i, int m_i, double factor, double *tracer_i, double *ct_i) { double rec_factor = 1./factor, sin_kpi_on_16[] = { 1.950903220161283e-1, 3.826834323650898e-1, 5.555702330196022e-1, 7.071067811865475e-1, 8.314696123025452e-1, 9.238795325112867e-1, 9.807852804032304e-1 }, cos_kpi_on_16[] = { 9.807852804032304e-1, 9.238795325112867e-1, 8.314696123025452e-1, 7.071067811865476e-1, 5.555702330196023e-1, 3.826834323650898e-1, 1.950903220161283e-1 }; int i, k, prof_len, not_monotonic, unique_count, new_len, p_all_len, i_min_p_obs, i_obs_plus_interp_len, i_surf_and_obs_plus_interp_len, i_out_len; int *p_idx, *p_all_idx, *i_obs_plus_interp, *i_surf_and_obs_plus_interp, *i_out, *i_1, *i_2, *i_3; double d, unique_p, ct_sum, tracer_sum, min_p_obs, max_p_obs; double *tracer_obs, *ct_obs, *p_obs, *p_i_tmp, *p_sort, *tracer_sort, *ct_sort, *p_all, *p_all_sort, *p_obs_plus_interp, *p_surf_and_obs_plus_interp, *independent_variable, *independent_variable_obs_plus_interp, *scaled_tracer_obs, *v_tmp, *q_tmp, *v_i, *q_i, *tracer_i_obs_plus_interp, *ct_i_obs_plus_interp, *tracer_i_tooutput, *ct_i_tooutput; if (m < 4) return 1; // There must be at least 4 bottles' // Check if interpolating pressure is monotonic for (i=0; i 0) { gsw_util_sort_real(p_obs, prof_len, p_idx); for (i=0; i= min_p_obs && p_all[i] <= max_p_obs) { i_obs_plus_interp[i_obs_plus_interp_len] = i; p_obs_plus_interp[i_obs_plus_interp_len] = p_all[i]; i_obs_plus_interp_len++; } if (p_all[i] <= max_p_obs) { i_surf_and_obs_plus_interp[i_surf_and_obs_plus_interp_len] = i; p_surf_and_obs_plus_interp[i_surf_and_obs_plus_interp_len] = p_all[i]; i_surf_and_obs_plus_interp_len++; } } i_out_len = gsw_util_intersect(p_i_tmp, m_i, p_surf_and_obs_plus_interp, i_surf_and_obs_plus_interp_len, i_out, i_1); gsw_util_intersect(p_obs, prof_len, p_obs_plus_interp, i_obs_plus_interp_len, i_2, i_3); independent_variable = (double *) malloc(prof_len*sizeof (double)); independent_variable_obs_plus_interp = (double *) malloc(i_obs_plus_interp_len*sizeof (double)); for(i=0; i x[0] && z < x[n-1]) { kl = 0; ku = n-1; while (ku-kl > 1) { km = (ku+kl)>>1; if (z > x[km]) kl = km; else ku = km; } k = kl; if (z == x[k+1]) k++; } else if (z <= x[0]) k = 0; else k = n-2; return (k); } /* !========================================================================== pure function gsw_util_interp1q_int (x, iy, x_i) result(y_i) !========================================================================== ! Returns the value of the 1-D function iy (integer) at the points of column ! vector x_i using linear interpolation. The vector x specifies the ! coordinates of the underlying interval. !========================================================================== */ double * gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi, double *x_i, double *y_i) { char *in_rng; int *j, *k, *r, *jrev, *ki, imax_x, imin_x, i, n, m, ii; double *xi, *xxi, u, max_x, min_x; if (nx <= 0 || nxi <= 0) return (NULL); min_x = max_x = x[0]; imin_x = imax_x = 0; for (i=0; i max_x) { max_x = x[i]; imax_x = i; } } in_rng = (char *) malloc(nxi*sizeof (char)); memset(in_rng, 0, nxi*sizeof (char)); for (i=n=0; i= max_x) { y_i[i] = iy[imax_x]; } else { in_rng[i] = 1; n++; } } if (n==0) return (y_i); xi = (double *) malloc(n*sizeof (double)); k = (int *) malloc(3*n*sizeof (int)); ki = k+n; r = ki+n; m = nx + n; xxi = (double *) malloc(m*sizeof (double)); j = (int *) malloc(2*m*sizeof (int)); jrev = j+m; ii = 0; for (i = 0; i max_x) { max_x = x[i]; imax_x = i; } } in_rng = (char *) malloc(nxi*sizeof (char)); memset(in_rng, 0, nxi*sizeof (char)); for (i=n=0; i= max_x) { for (jy=jy0=jyi0=0; jy 0) ? 1 : (((x) < 0) ? -1 : 0)) static double pchip_edge_case(double h0, double h1, double m0, double m1) { double d; int mask, mask2; d = ((2*h0 + h1)*m0 - h0*m1) / (h0 + h1); mask = sgn(d) != sgn(m0); mask2 = (sgn(m0) != sgn(m1)) && (fabs(d) > 3.0*fabs(m0)); if (mask) { return 0.0; } if (!mask && mask2) { return 3.0*m0; } return d; } /* Calculation of the derivatives is the key to the shape-preservation. There are other algorithms that could be used, but this appears to be the simplest, and adequate for our purposes. At minimal computational cost, we include here a check for increasing x. Returns 0 on success, 1 if x is not strictly increasing. */ static int pchip_derivs(double *x, double *y, int n, double *d) { double mm, mp; /* slopes bracketing x */ double hm, hp; /* bracketing delta-x values */ int smm, smp; /* slope signs */ double w1, w2; int i; if (n == 2) { d[0] = d[1] = (y[1] - y[0]) / (x[1] - x[0]); return 0; } hm = x[1] - x[0]; hp = x[2] - x[1]; mm = (y[1] - y[0]) / hm; mp = (y[2] - y[1]) / hp; d[0] = pchip_edge_case(hm, hp, mm, mp); smm = sgn(mm); smp = sgn(mp); for (i=1; i 0) { j0--; } while (xx > x[j0+1] && j0 < n - 2) { j0++; } j1 = j0 + 1; if (xx >= x[j0] && xx <= x[j1]) { dx = x[j1] - x[j0]; t = (xx - x[j0]) / dx; tt = t * t; ttt = tt * t; /* Using intermediate variables for readability. */ h00 = (2*ttt - 3*tt + 1); h10 = (ttt - 2*tt + t); h01 = (-2*ttt + 3*tt); h11 = (ttt - tt); yi[i] = y[j0] * h00 + d[j0] * dx * h10 + y[j1] * h01 + d[j1] * dx * h11; } else { /* extrapolate with constant end values */ yi[i] = (xx < x[0]) ? y[0] : y[n-1]; } } free(d); return 0; } /* End of the pchip interpolation. ******************************* */ /* pure function gsw_util_sort_real (rarray) result(iarray) */ typedef struct { double d; int i; } DI; /* * Rank two items, by value if possible, * and by inverse index, if the values are * equal. * FIXME: decide if index method matches docs. */ int compareDI(const void *a, const void *b) { DI *A = (DI*)a; DI *B = (DI*)b; if (A->d < B->d) return (-1); if (A->d > B->d) return (1); if (A->i < B->i) return (1); return (-1); } /* ** Sort the double array rarray into ascending value sequence ** returning an index array of the sorted result. This function ** is thread-safe. */ void gsw_util_sort_real(double *rarray, int nx, int *iarray) { int i; DI* di = (DI*)malloc(nx*sizeof(DI)); for (i=0; i yy) { ++ity; } else { ix[ni] = unique_ix[itx]; iy[ni] = unique_iy[ity]; ++itx; ++ity; ++ni; } } free(sort_ix); free(sort_iy); free(unique_ix); free(unique_iy); return ni; } /* ** The End **!========================================================================== */ gsw-3.6.21/src/c_gsw/gswteos-10.h0000644000175000017500000004710115147371315016552 0ustar alastairalastair/* ** $Id: gswteos-10.h,v 045882f2da27 2015/09/13 23:47:38 fdelahoyde $ ** $Version: 3.05.0-2 $ ** ** GSW TEOS-10 V3.05 definitions and prototypes. */ #ifndef GSWTEOS_10_H #define GSWTEOS_10_H #ifdef __cplusplus # include #else # include #endif #ifdef _WIN32 # define DECLSPEC __declspec(dllexport) #else # define DECLSPEC #endif #ifdef __cplusplus extern "C" { #endif #include #include #include #include #include #define GSW_INVALID_VALUE 9e15 /* error return from gsw_saar et al. */ #define GSW_ERROR_LIMIT 1e10 #define INTERP_METHOD_LINEAR 1 #define INTERP_METHOD_PCHIP 2 #define INTERP_METHOD_MRST 3 /* ** Prototypes: */ DECLSPEC extern void gsw_add_barrier(double *input_data, double lon, double lat, double long_grid, double lat_grid, double dlong_grid, double dlat_grid, double *output_data); DECLSPEC extern void gsw_add_mean(double *data_in, double *data_out); DECLSPEC extern int gsw_infunnel(double sa, double ct, double p); DECLSPEC extern double gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p); DECLSPEC extern double gsw_adiabatic_lapse_rate_ice(double t, double p); DECLSPEC extern double gsw_alpha(double sa, double ct, double p); DECLSPEC extern double gsw_alpha_on_beta(double sa, double ct, double p); DECLSPEC extern double gsw_alpha_wrt_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_alpha_wrt_t_ice(double t, double p); DECLSPEC extern double gsw_beta_const_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_beta(double sa, double ct, double p); DECLSPEC extern double gsw_cabbeling(double sa, double ct, double p); DECLSPEC extern double gsw_c_from_sp(double sp, double t, double p); DECLSPEC extern double gsw_chem_potential_water_ice(double t, double p); DECLSPEC extern double gsw_chem_potential_water_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_cp_ice(double t, double p); DECLSPEC extern double gsw_cp_t_exact(double sa, double t, double p); DECLSPEC extern void gsw_ct_first_derivatives (double sa, double pt, double *ct_sa, double *ct_pt); DECLSPEC extern void gsw_ct_first_derivatives_wrt_t_exact(double sa, double t, double p, double *ct_sa_wrt_t, double *ct_t_wrt_t, double *ct_p_wrt_t); DECLSPEC extern double gsw_ct_freezing(double sa, double p, double saturation_fraction); DECLSPEC extern void gsw_ct_freezing_first_derivatives(double sa, double p, double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p); DECLSPEC extern void gsw_ct_freezing_first_derivatives_poly(double sa, double p, double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p); DECLSPEC extern double gsw_ct_freezing_poly(double sa, double p, double saturation_fraction); DECLSPEC extern double gsw_ct_from_enthalpy(double sa, double h, double p); DECLSPEC extern double gsw_ct_from_enthalpy_exact(double sa, double h, double p); DECLSPEC extern double gsw_ct_from_entropy(double sa, double entropy); DECLSPEC extern double gsw_ct_from_pt(double sa, double pt); DECLSPEC extern void gsw_ct_from_rho(double rho, double sa, double p, double *ct, double *ct_multiple); DECLSPEC extern double gsw_ct_from_t(double sa, double t, double p); DECLSPEC extern double gsw_ct_maxdensity(double sa, double p); DECLSPEC extern void gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa, double *ct_sa_pt, double *ct_pt_pt); DECLSPEC extern double gsw_deltasa_atlas(double p, double lon, double lat); DECLSPEC extern double gsw_deltasa_from_sp(double sp, double p, double lon, double lat); DECLSPEC extern double gsw_dilution_coefficient_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_dynamic_enthalpy(double sa, double ct, double p); DECLSPEC extern double gsw_enthalpy_ct_exact(double sa, double ct, double p); DECLSPEC extern double gsw_enthalpy_diff(double sa, double ct, double p_shallow, double p_deep); DECLSPEC extern double gsw_enthalpy(double sa, double ct, double p); DECLSPEC extern void gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct, double p, double *h_sa, double *h_ct); DECLSPEC extern void gsw_enthalpy_first_derivatives(double sa, double ct, double p, double *h_sa, double *h_ct); DECLSPEC extern double gsw_enthalpy_ice(double t, double p); DECLSPEC extern void gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct, double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct); DECLSPEC extern void gsw_enthalpy_second_derivatives(double sa, double ct, double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct); DECLSPEC extern double gsw_enthalpy_sso_0(double p); DECLSPEC extern double gsw_enthalpy_t_exact(double sa, double t, double p); DECLSPEC extern void gsw_entropy_first_derivatives(double sa, double ct, double *eta_sa, double *eta_ct); DECLSPEC extern double gsw_entropy_from_ct(double sa, double ct); DECLSPEC extern double gsw_entropy_from_pt(double sa, double pt); DECLSPEC extern double gsw_entropy_from_t(double sa, double t, double p); DECLSPEC extern double gsw_entropy_ice(double t, double p); DECLSPEC extern double gsw_entropy_part(double sa, double t, double p); DECLSPEC extern double gsw_entropy_part_zerop(double sa, double pt0); DECLSPEC extern void gsw_entropy_second_derivatives(double sa, double ct, double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct); DECLSPEC extern double gsw_fdelta(double p, double lon, double lat); DECLSPEC extern void gsw_frazil_properties(double sa_bulk, double h_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final); DECLSPEC extern void gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final); DECLSPEC extern void gsw_frazil_properties_potential_poly(double sa_bulk, double h_pot_bulk, double p, double *sa_final, double *ct_final, double *w_ih_final); DECLSPEC extern void gsw_frazil_ratios_adiabatic(double sa, double p, double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil); DECLSPEC extern void gsw_frazil_ratios_adiabatic_poly(double sa, double p, double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil); DECLSPEC extern double *gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref, int n_levels, double *dyn_height); DECLSPEC extern int gsw_geo_strf_dyn_height_1(double *sa, double *ct, double *p, double p_ref, int n_levels, double *dyn_height, double max_dp_i, int interp_method); DECLSPEC extern double *gsw_geo_strf_dyn_height_pc(double *sa, double *ct, double *delta_p, int n_levels, double *geo_strf_dyn_height_pc, double *p_mid); DECLSPEC extern double gsw_gibbs_ice (int nt, int np, double t, double p); DECLSPEC extern double gsw_gibbs_ice_part_t(double t, double p); DECLSPEC extern double gsw_gibbs_ice_pt0(double pt0); DECLSPEC extern double gsw_gibbs_ice_pt0_pt0(double pt0); DECLSPEC extern double gsw_gibbs(int ns, int nt, int np, double sa, double t, double p); DECLSPEC extern double gsw_gibbs_pt0_pt0(double sa, double pt0); DECLSPEC extern double gsw_grav(double lat, double p); DECLSPEC extern double gsw_helmholtz_energy_ice(double t, double p); DECLSPEC extern double gsw_hill_ratio_at_sp2(double t); DECLSPEC extern void gsw_ice_fraction_to_freeze_seawater(double sa, double ct, double p, double t_ih, double *sa_freeze, double *ct_freeze, double *w_ih); DECLSPEC extern double gsw_internal_energy(double sa, double ct, double p); DECLSPEC extern double gsw_internal_energy_ice(double t, double p); DECLSPEC extern void gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p, double p_ref, int nz, double *ipv_vs_fnsquared_ratio, double *p_mid); DECLSPEC extern double gsw_kappa_const_t_ice(double t, double p); DECLSPEC extern double gsw_kappa(double sa, double ct, double p); DECLSPEC extern double gsw_kappa_ice(double t, double p); DECLSPEC extern double gsw_kappa_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_latentheat_evap_ct(double sa, double ct); DECLSPEC extern double gsw_latentheat_evap_t(double sa, double t); DECLSPEC extern double gsw_latentheat_melting(double sa, double p); DECLSPEC extern void gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np, double *p_i, int npi, double *sa_i, double *ct_i); DECLSPEC extern double gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p); DECLSPEC extern double gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p); DECLSPEC extern void gsw_melting_ice_into_seawater(double sa, double ct, double p, double w_ih, double t_ih, double *sa_final, double *ct_final, double *w_ih_final); DECLSPEC extern double gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p, double t_ih); DECLSPEC extern double gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p, double t_ih); DECLSPEC extern double gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p); DECLSPEC extern double gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa, double p); DECLSPEC extern void gsw_melting_seaice_into_seawater(double sa, double ct, double p, double w_seaice, double sa_seaice, double t_seaice, double *sa_final, double *ct_final); DECLSPEC extern double gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p, double sa_seaice, double t_seaice); DECLSPEC extern double gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct, double p, double sa_seaice, double t_seaice); DECLSPEC extern void gsw_nsquared(double *sa, double *ct, double *p, double *lat, int nz, double *n2, double *p_mid); DECLSPEC extern double gsw_o2sol(double sa, double ct, double p, double lon, double lat); DECLSPEC extern double gsw_o2sol_sp_pt(double sp, double pt); DECLSPEC extern double gsw_pot_enthalpy_from_pt_ice(double pt0_ice); DECLSPEC extern double gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice); DECLSPEC extern double gsw_pot_enthalpy_ice_freezing(double sa, double p); DECLSPEC extern void gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa, double p, double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p); DECLSPEC extern void gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa, double p, double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p); DECLSPEC extern double gsw_pot_enthalpy_ice_freezing_poly(double sa, double p); DECLSPEC extern double gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref); DECLSPEC extern double gsw_pressure_coefficient_ice(double t, double p); DECLSPEC extern double gsw_pressure_freezing_ct(double sa, double ct, double saturation_fraction); DECLSPEC extern double gsw_pt0_cold_ice_poly(double pot_enthalpy_ice); DECLSPEC extern double gsw_pt0_from_t(double sa, double t, double p); DECLSPEC extern double gsw_pt0_from_t_ice(double t, double p); DECLSPEC extern void gsw_pt_first_derivatives (double sa, double ct, double *pt_sa, double *pt_ct); DECLSPEC extern double gsw_pt_from_ct(double sa, double ct); DECLSPEC extern double gsw_pt_from_entropy(double sa, double entropy); DECLSPEC extern double gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice); DECLSPEC extern double gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice); DECLSPEC extern double gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice); DECLSPEC extern double gsw_pt_from_t(double sa, double t, double p, double p_ref); DECLSPEC extern double gsw_pt_from_t_ice(double t, double p, double p_ref); DECLSPEC extern void gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa, double *pt_sa_ct, double *pt_ct_ct); DECLSPEC extern void gsw_rho_alpha_beta (double sa, double ct, double p, double *rho, double *alpha, double *beta); DECLSPEC extern double gsw_rho(double sa, double ct, double p); DECLSPEC extern void gsw_rho_first_derivatives(double sa, double ct, double p, double *drho_dsa, double *drho_dct, double *drho_dp); DECLSPEC extern void gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct, double p, double *rho_sa, double *rho_h); DECLSPEC extern double gsw_rho_ice(double t, double p); DECLSPEC extern void gsw_rho_second_derivatives(double sa, double ct, double p, double *rho_sa_sa, double *rho_sa_ct, double *rho_ct_ct, double *rho_sa_p, double *rho_ct_p); DECLSPEC extern void gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct, double p, double *rho_sa_sa, double *rho_sa_h, double *rho_h_h); DECLSPEC extern double gsw_rho_t_exact(double sa, double t, double p); DECLSPEC extern void gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp, double *p_i, int mp_i, double *sa_i, double *ct_i); DECLSPEC extern double gsw_saar(double p, double lon, double lat); DECLSPEC extern int gsw_sa_ct_interp(double *sa, double *ct, double *p, int m, double *p_i, int m_i, double *sa_i, double *ct_i); DECLSPEC extern double gsw_sa_freezing_estimate(double p, double saturation_fraction, double *ct, double *t); DECLSPEC extern double gsw_sa_freezing_from_ct(double ct, double p, double saturation_fraction); DECLSPEC extern double gsw_sa_freezing_from_ct_poly(double ct, double p, double saturation_fraction); DECLSPEC extern double gsw_sa_freezing_from_t(double t, double p, double saturation_fraction); DECLSPEC extern double gsw_sa_freezing_from_t_poly(double t, double p, double saturation_fraction); DECLSPEC extern double gsw_sa_from_rho(double rho, double ct, double p); DECLSPEC extern double gsw_sa_from_sp_baltic(double sp, double lon, double lat); DECLSPEC extern double gsw_sa_from_sp(double sp, double p, double lon, double lat); DECLSPEC extern double gsw_sa_from_sstar(double sstar, double p,double lon,double lat); DECLSPEC extern int gsw_sa_p_inrange(double sa, double p); DECLSPEC extern void gsw_seaice_fraction_to_freeze_seawater(double sa, double ct, double p, double sa_seaice, double t_seaice, double *sa_freeze, double *ct_freeze, double *w_seaice); DECLSPEC extern double gsw_sigma0(double sa, double ct); DECLSPEC extern double gsw_sigma1(double sa, double ct); DECLSPEC extern double gsw_sigma2(double sa, double ct); DECLSPEC extern double gsw_sigma3(double sa, double ct); DECLSPEC extern double gsw_sigma4(double sa, double ct); DECLSPEC extern double gsw_sound_speed(double sa, double ct, double p); DECLSPEC extern double gsw_sound_speed_ice(double t, double p); DECLSPEC extern double gsw_sound_speed_t_exact(double sa, double t, double p); DECLSPEC extern void gsw_specvol_alpha_beta(double sa, double ct, double p, double *specvol, double *alpha, double *beta); DECLSPEC extern double gsw_specvol_anom_standard(double sa, double ct, double p); DECLSPEC extern double gsw_specvol(double sa, double ct, double p); DECLSPEC extern void gsw_specvol_first_derivatives(double sa, double ct, double p, double *v_sa, double *v_ct, double *v_p); DECLSPEC extern void gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct, double p, double *v_sa, double *v_h); DECLSPEC extern double gsw_specvol_ice(double t, double p); DECLSPEC extern void gsw_specvol_second_derivatives (double sa, double ct, double p, double *v_sa_sa, double *v_sa_ct, double *v_ct_ct, double *v_sa_p, double *v_ct_p); DECLSPEC extern void gsw_specvol_second_derivatives_wrt_enthalpy(double sa, double ct, double p, double *v_sa_sa, double *v_sa_h, double *v_h_h); DECLSPEC extern double gsw_specvol_sso_0(double p); DECLSPEC extern double gsw_specvol_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_sp_from_c(double c, double t, double p); DECLSPEC extern double gsw_sp_from_sa_baltic(double sa, double lon, double lat); DECLSPEC extern double gsw_sp_from_sa(double sa, double p, double lon, double lat); DECLSPEC extern double gsw_sp_from_sk(double sk); DECLSPEC extern double gsw_sp_from_sr(double sr); DECLSPEC extern double gsw_sp_from_sstar(double sstar, double p,double lon,double lat); DECLSPEC extern double gsw_sp_salinometer(double rt, double t); DECLSPEC extern double gsw_spiciness0(double sa, double ct); DECLSPEC extern double gsw_spiciness1(double sa, double ct); DECLSPEC extern double gsw_spiciness2(double sa, double ct); DECLSPEC extern double gsw_sr_from_sp(double sp); DECLSPEC extern double gsw_sstar_from_sa(double sa, double p, double lon, double lat); DECLSPEC extern double gsw_sstar_from_sp(double sp, double p, double lon, double lat); DECLSPEC extern double gsw_t_deriv_chem_potential_water_t_exact(double sa, double t, double p); DECLSPEC extern double gsw_t_freezing(double sa, double p, double saturation_fraction); DECLSPEC extern void gsw_t_freezing_first_derivatives_poly(double sa, double p, double saturation_fraction, double *tfreezing_sa, double *tfreezing_p); DECLSPEC extern void gsw_t_freezing_first_derivatives(double sa, double p, double saturation_fraction, double *tfreezing_sa, double *tfreezing_p); DECLSPEC extern double gsw_t_freezing_poly(double sa, double p, double saturation_fraction); DECLSPEC extern double gsw_t_from_ct(double sa, double ct, double p); DECLSPEC extern double gsw_t_from_pt0_ice(double pt0_ice, double p); DECLSPEC extern double gsw_thermobaric(double sa, double ct, double p); DECLSPEC extern int gsw_tracer_ct_interp(double *tracer, double *ct, double *p, int m, double *p_i, int m_i, double factor, double *sa_i, double *ct_i); DECLSPEC extern void gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz, double *tu, double *rsubrho, double *p_mid); DECLSPEC extern int gsw_util_indx(double *x, int n, double z); DECLSPEC extern double *gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi, double *x_i, double *y_i); DECLSPEC extern int gsw_util_intersect(double *x, int nx, double *y, int ny, int *ix, int *iy); DECLSPEC extern double *gsw_util_linear_interp(int nx, double *x, int ny, double *y, int nxi, double *x_i, double *y_i); DECLSPEC extern void gsw_util_sort_real(double *rarray, int nx, int *iarray); DECLSPEC extern double gsw_util_xinterp1(double *x, double *y, int n, double x0); DECLSPEC extern int gsw_util_pchip_interp(double *x, double *y, int n, double *xi, double *yi, int ni); DECLSPEC extern double gsw_z_from_p(double p, double lat, double geo_strf_dyn_height, double sea_surface_geopotential); DECLSPEC extern double gsw_p_from_z(double z, double lat, double geo_strf_dyn_height, double sea_surface_geopotential); DECLSPEC extern int refine_grid_for_dh(double *p, double p_ref, int nz, double dp, double *p_i, int ni_max, int *p_indices, int *p_ref_ind_ptr); #ifdef __cplusplus } #endif #endif /* GSWTEOS_10_H */ gsw-3.6.21/src/method_def_entries.c0000644000175000017500000000077615147371315017370 0ustar alastairalastair/* Entries in the GswMethods table. */ {"geo_strf_dyn_height", geo_strf_dyn_height, METH_VARARGS, "geostrophic streamfunction dynamic height"}, {"geo_strf_dyn_height_1", geo_strf_dyn_height_1, METH_VARARGS, "geostrophic streamfunction dynamic height"}, {"util_pchip_interp", util_pchip_interp, METH_VARARGS, "PCHIP interpolation"}, {"sa_ct_interp", sa_ct_interp, METH_VARARGS, "SA and CT interpolation"}, {"tracer_ct_interp", tracer_ct_interp, METH_VARARGS, "Tracer and CT interpolation"}, gsw-3.6.21/LICENSE.txt0000644000175000017500000000347215147371315014425 0ustar alastairalastairLicence for the use of the Gibbs SeaWater (GSW) Oceanographic Toolbox, covering this Python implementation with C components Copyright (c) 2011, SCOR/IAPSO WG127 (Scientific Committee on Oceanic Research/ International Association for the Physical Sciences of the Oceans, Working Group 127). Copyright 2017-2020 Eric Firing and contributors All rights reserved. Redistribution and use, in source and binary forms, without modification, is permitted provided that the following conditions are met: • Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. • Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. • Neither the name of SCOR/IAPSO WG127 nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. The software is available from http://www.TEOS-10.org gsw-3.6.21/MANIFEST.in0000644000175000017500000000042415147371315014332 0ustar alastairalastairinclude *.txt include README.md graft gsw recursive-include src *.c recursive-include src *.h prune docs prune .github prune tools prune notebooks prune *.egg-info global-exclude *.so exclude *.yml exclude *.yaml exclude .gitignore exclude .isort.cfg exclude .zenodo.json gsw-3.6.21/gsw/0000755000175000017500000000000015147371330013371 5ustar alastairalastairgsw-3.6.21/gsw/stability.py0000644000175000017500000001372615147371315015763 0ustar alastairalastair""" Vertical stability functions. These work with ndarrays of profiles; use the `axis` keyword argument to specify the axis along which pressure varies. For example, the default, following the Matlab versions, is `axis=0`, meaning the pressure varies along the first dimension. Use `axis=-1` if pressure varies along the last dimension--that is, along a row, as the column index increases, in the 2-D case. Docstrings will be added later, either manually or via an automated mechanism. """ import numpy as np from ._gsw_ufuncs import grav, specvol_alpha_beta from ._utilities import axis_slicer, match_args_return __all__ = ['Nsquared', 'Turner_Rsubrho', 'IPV_vs_fNsquared_ratio', ] # In the following, axis=0 matches the Matlab behavior. @match_args_return def Nsquared(SA, CT, p, lat=None, axis=0): """ Calculate the square of the buoyancy frequency. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lat : array-like, 1-D, optional Latitude, degrees. axis : int, optional The dimension along which pressure increases. Returns ------- N2 : array Buoyancy frequency-squared at pressure midpoints, 1/s^2. The shape along the pressure axis dimension is one less than that of the inputs. (Frequency N is in radians per second.) p_mid : array Pressure at midpoints of p, dbar. The array shape matches N2. """ if lat is not None: if np.any((lat < -90) | (lat > 90)): raise ValueError('lat is out of range') SA, CT, p, lat = np.broadcast_arrays(SA, CT, p, lat) g = grav(lat, p) else: SA, CT, p = np.broadcast_arrays(SA, CT, p) g = 9.7963 # (Griffies, 2004) db_to_pa = 1e4 shallow = axis_slicer(SA.ndim, slice(-1), axis) deep = axis_slicer(SA.ndim, slice(1, None), axis) if lat is not None: g_local = 0.5 * (g[shallow] + g[deep]) else: g_local = g dSA = SA[deep] - SA[shallow] dCT = CT[deep] - CT[shallow] dp = p[deep] - p[shallow] SA_mid = 0.5 * (SA[shallow] + SA[deep]) CT_mid = 0.5 * (CT[shallow] + CT[deep]) p_mid = 0.5 * (p[shallow] + p[deep]) specvol_mid, alpha_mid, beta_mid = specvol_alpha_beta(SA_mid, CT_mid, p_mid) N2 = ((g_local**2) / (specvol_mid * db_to_pa * dp)) N2 *= (beta_mid*dSA - alpha_mid*dCT) return N2, p_mid @match_args_return def Turner_Rsubrho(SA, CT, p, axis=0): """ Calculate the Turner Angle and the Stability Ratio. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar axis : int, optional The dimension along which pressure increases. Returns ------- Tu : array Turner Angle at pressure midpoints, degrees. The shape along the pressure axis dimension is one less than that of the inputs. Rsubrho : array Stability Ratio, dimensionless. The shape matches Tu. p_mid : array Pressure at midpoints of p, dbar. The array shape matches Tu. """ SA = np.clip(SA, 0, 50) SA, CT, p = np.broadcast_arrays(SA, CT, p) shallow = axis_slicer(SA.ndim, slice(-1), axis) deep = axis_slicer(SA.ndim, slice(1, None), axis) dSA = -SA[deep] + SA[shallow] dCT = -CT[deep] + CT[shallow] SA_mid = 0.5 * (SA[shallow] + SA[deep]) CT_mid = 0.5 * (CT[shallow] + CT[deep]) p_mid = 0.5 * (p[shallow] + p[deep]) _, alpha, beta = specvol_alpha_beta(SA_mid, CT_mid, p_mid) Tu = np.arctan2((alpha*dCT + beta*dSA), (alpha*dCT - beta*dSA)) Tu = np.degrees(Tu) igood = (dSA != 0) Rsubrho = np.zeros_like(dSA) Rsubrho.fill(np.nan) Rsubrho[igood] = (alpha[igood]*dCT[igood])/(beta[igood]*dSA[igood]) return Tu, Rsubrho, p_mid @match_args_return def IPV_vs_fNsquared_ratio(SA, CT, p, p_ref=0, axis=0): """ Calculates the ratio of the vertical gradient of potential density to the vertical gradient of locally-referenced potential density. This is also the ratio of the planetary Isopycnal Potential Vorticity (IPV) to f times N^2, hence the name for this variable, IPV_vs_fNsquared_ratio (see Eqn. (3.20.17) of IOC et al. (2010)). Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : float Reference pressure, dbar Returns ------- IPV_vs_fNsquared_ratio : array The ratio of the vertical gradient of potential density referenced to p_ref, to the vertical gradient of locally-referenced potential density, dimensionless. p_mid : array Pressure at midpoints of p, dbar. The array shape matches IPV_vs_fNsquared_ratio. """ SA = np.clip(SA, 0, 50) SA, CT, p = np.broadcast_arrays(SA, CT, p) shallow = axis_slicer(SA.ndim, slice(-1), axis) deep = axis_slicer(SA.ndim, slice(1, None), axis) dSA = -SA[deep] + SA[shallow] dCT = -CT[deep] + CT[shallow] SA_mid = 0.5 * (SA[shallow] + SA[deep]) CT_mid = 0.5 * (CT[shallow] + CT[deep]) p_mid = 0.5 * (p[shallow] + p[deep]) _, alpha, beta = specvol_alpha_beta(SA_mid, CT_mid, p_mid) _, alpha_pref, beta_pref = specvol_alpha_beta(SA_mid, CT_mid, p_ref) num = dCT*alpha_pref - dSA*beta_pref den = dCT*alpha - dSA*beta igood = (den != 0) IPV_vs_fNsquared_ratio = np.zeros_like(dSA) IPV_vs_fNsquared_ratio.fill(np.nan) IPV_vs_fNsquared_ratio[igood] = num[igood] / den[igood] return IPV_vs_fNsquared_ratio, p_mid gsw-3.6.21/gsw/_wrapped_ufuncs.py0000644000175000017500000107425215147371315017145 0ustar alastairalastair """ Auto-generated wrapper for C ufunc extension; do not edit! """ from . import _gsw_ufuncs from ._utilities import match_args_return def adiabatic_lapse_rate_from_CT(SA, CT, p): """ Calculates the adiabatic lapse rate of sea water from Conservative Temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- adiabatic_lapse_rate : array-like, K/Pa adiabatic lapse rate References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqn. (2.22.1) of this TEOS-10 Manual. """ return _gsw_ufuncs.adiabatic_lapse_rate_from_ct(SA, CT, p) adiabatic_lapse_rate_from_CT.types = _gsw_ufuncs.adiabatic_lapse_rate_from_ct.types adiabatic_lapse_rate_from_CT = match_args_return(adiabatic_lapse_rate_from_CT) def adiabatic_lapse_rate_ice(t, p): """ Calculates the adiabatic lapse rate of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- adiabatic_lapse_rate_ice : array-like, K/Pa adiabatic lapse rate References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. """ return _gsw_ufuncs.adiabatic_lapse_rate_ice(t, p) adiabatic_lapse_rate_ice.types = _gsw_ufuncs.adiabatic_lapse_rate_ice.types adiabatic_lapse_rate_ice = match_args_return(adiabatic_lapse_rate_ice) def alpha(SA, CT, p): """ Calculates the thermal expansion coefficient of seawater with respect to Conservative Temperature using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- alpha : array-like, 1/K thermal expansion coefficient with respect to Conservative Temperature Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.18.3) of this TEOS-10 manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.alpha(SA, CT, p) alpha.types = _gsw_ufuncs.alpha.types alpha = match_args_return(alpha) def alpha_on_beta(SA, CT, p): """ Calculates alpha divided by beta, where alpha is the thermal expansion coefficient and beta is the saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- alpha_on_beta : array-like, g kg^-1 K^-1 thermal expansion coefficient with respect to Conservative Temperature divided by the saline contraction coefficient at constant Conservative Temperature Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.20 and appendix K of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2014: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling. """ return _gsw_ufuncs.alpha_on_beta(SA, CT, p) alpha_on_beta.types = _gsw_ufuncs.alpha_on_beta.types alpha_on_beta = match_args_return(alpha_on_beta) def alpha_wrt_t_exact(SA, t, p): """ Calculates the thermal expansion coefficient of seawater with respect to in-situ temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- alpha_wrt_t_exact : array-like, 1/K thermal expansion coefficient with respect to in-situ temperature References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqn. (2.18.1) of this TEOS-10 manual. """ return _gsw_ufuncs.alpha_wrt_t_exact(SA, t, p) alpha_wrt_t_exact.types = _gsw_ufuncs.alpha_wrt_t_exact.types alpha_wrt_t_exact = match_args_return(alpha_wrt_t_exact) def alpha_wrt_t_ice(t, p): """ Calculates the thermal expansion coefficient of ice with respect to in-situ temperature. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- alpha_wrt_t_ice : array-like, 1/K thermal expansion coefficient of ice with respect to in-situ temperature References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqn. (2.18.1) of this TEOS-10 manual. """ return _gsw_ufuncs.alpha_wrt_t_ice(t, p) alpha_wrt_t_ice.types = _gsw_ufuncs.alpha_wrt_t_ice.types alpha_wrt_t_ice = match_args_return(alpha_wrt_t_ice) def beta(SA, CT, p): """ Calculates the saline (i.e. haline) contraction coefficient of seawater at constant Conservative Temperature using the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- beta : array-like, kg/g saline contraction coefficient at constant Conservative Temperature Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.19.3) of this TEOS-10 manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.beta(SA, CT, p) beta.types = _gsw_ufuncs.beta.types beta = match_args_return(beta) def beta_const_t_exact(SA, t, p): """ Calculates the saline (i.e. haline) contraction coefficient of seawater at constant in-situ temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- beta_const_t_exact : array-like, kg/g saline contraction coefficient at constant in-situ temperature References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.19.1) of this TEOS-10 manual. """ return _gsw_ufuncs.beta_const_t_exact(SA, t, p) beta_const_t_exact.types = _gsw_ufuncs.beta_const_t_exact.types beta_const_t_exact = match_args_return(beta_const_t_exact) def C_from_SP(SP, t, p): """ Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range 2 < SP < 42. If the input Practical Salinity is less than 2 then a modified form of the Hill et al. (1986) formula is used for Practical Salinity. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- C : array-like, mS/cm conductivity Notes ----- The conductivity ratio returned by this function is consistent with the input value of Practical Salinity, SP, to 2x10^-14 psu over the full range of input parameters (from pure fresh water up to SP = 42 psu). This error of 2x10^-14 psu is machine precision at typical seawater salinities. This accuracy is achieved by having four different polynomials for the starting value of Rtx (the square root of Rt) in four different ranges of SP, and by using one and a half iterations of a computationally efficient modified Newton-Raphson technique (McDougall and Wotherspoon, 2013) to find the root of the equation. Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical Salinity in terms of the conductivity ratio, R, without actually specifying the value of C(35,15,0) (which we currently take to be 42.9140 mS/cm). References ---------- Hill, K.D., T.M. Dauphinee and D.J. Woods, 1986: The extension of the Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng., OE-11, 1, 109 - 112. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix E of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Unesco, 1983: Algorithms for computation of fundamental properties of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp. """ return _gsw_ufuncs.c_from_sp(SP, t, p) C_from_SP.types = _gsw_ufuncs.c_from_sp.types C_from_SP = match_args_return(C_from_SP) def cabbeling(SA, CT, p): """ Calculates the cabbeling coefficient of seawater with respect to Conservative Temperature. This function uses the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- cabbeling : array-like, 1/K^2 cabbeling coefficient with respect to Conservative Temperature. Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqns. (3.9.2) and (P.4) of this TEOS-10 manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.cabbeling(SA, CT, p) cabbeling.types = _gsw_ufuncs.cabbeling.types cabbeling = match_args_return(cabbeling) def chem_potential_water_ice(t, p): """ Calculates the chemical potential of water in ice from in-situ temperature and pressure. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- chem_potential_water_ice : array-like, J/kg chemical potential of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.chem_potential_water_ice(t, p) chem_potential_water_ice.types = _gsw_ufuncs.chem_potential_water_ice.types chem_potential_water_ice = match_args_return(chem_potential_water_ice) def chem_potential_water_t_exact(SA, t, p): """ Calculates the chemical potential of water in seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- chem_potential_water_t_exact : array-like, J/g chemical potential of water in seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.chem_potential_water_t_exact(SA, t, p) chem_potential_water_t_exact.types = _gsw_ufuncs.chem_potential_water_t_exact.types chem_potential_water_t_exact = match_args_return(chem_potential_water_t_exact) def cp_ice(t, p): """ Calculates the isobaric heat capacity of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- cp_ice : array-like, J kg^-1 K^-1 heat capacity of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.cp_ice(t, p) cp_ice.types = _gsw_ufuncs.cp_ice.types cp_ice = match_args_return(cp_ice) def cp_t_exact(SA, t, p): """ Calculates the isobaric heat capacity of seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- cp_t_exact : array-like, J/(kg*K) heat capacity of seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.cp_t_exact(SA, t, p) cp_t_exact.types = _gsw_ufuncs.cp_t_exact.types cp_t_exact = match_args_return(cp_t_exact) def CT_first_derivatives(SA, pt): """ Calculates the following two derivatives of Conservative Temperature (1) CT_SA, the derivative with respect to Absolute Salinity at constant potential temperature (with pr = 0 dbar), and 2) CT_pt, the derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg pt : array-like Potential temperature referenced to a sea pressure, degrees C Returns ------- CT_SA : array-like, K/(g/kg) The derivative of Conservative Temperature with respect to Absolute Salinity at constant potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar). CT_pt : array-like, unitless The derivative of Conservative Temperature with respect to potential temperature (the regular one with pr = 0 dbar) at constant SA. CT_pt is dimensionless. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.12.3a,b) and (A.15.8) of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.ct_first_derivatives(SA, pt) CT_first_derivatives.types = _gsw_ufuncs.ct_first_derivatives.types CT_first_derivatives = match_args_return(CT_first_derivatives) def CT_first_derivatives_wrt_t_exact(SA, t, p): """ Calculates the following three derivatives of Conservative Temperature. These derivatives are done with respect to in-situ temperature t (in the case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of CT_SA_wrt_t and CT_P_wrt_t). (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity at constant t and p, and (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t at constant SA and p. (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at constant SA and t. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT_SA_wrt_t : array-like, K kg/g The first derivative of Conservative Temperature with respect to Absolute Salinity at constant t and p. [ K/(g/kg)] i.e. CT_T_wrt_t : array-like, unitless The first derivative of Conservative Temperature with respect to in-situ temperature, t, at constant SA and p. CT_P_wrt_t : array-like, K/Pa The first derivative of Conservative Temperature with respect to pressure P (in Pa) at constant SA and t. Notes ----- This function uses the full Gibbs function. Note that this function avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were evaluated in the straightforward way from the derivatives of the Gibbs function function. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.15.3) and (A.15.8) of this TEOS-10 Manual for CT_T_wrt_t and CT_SA_wrt_t respectively. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.ct_first_derivatives_wrt_t_exact(SA, t, p) CT_first_derivatives_wrt_t_exact.types = _gsw_ufuncs.ct_first_derivatives_wrt_t_exact.types CT_first_derivatives_wrt_t_exact = match_args_return(CT_first_derivatives_wrt_t_exact) def CT_freezing(SA, p, saturation_fraction): """ Calculates the Conservative Temperature at which seawater freezes. The Conservative Temperature freezing point is calculated from the exact in-situ freezing temperature which is found by a modified Newton-Raphson iteration (McDougall and Wotherspoon, 2014) of the equality of the chemical potentials of water in seawater and in ice. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- CT_freezing : array-like, deg C Conservative Temperature at freezing of seawater That is, the freezing temperature expressed in terms of Conservative Temperature (ITS-90). Notes ----- An alternative GSW function, gsw_CT_freezing_poly, it is based on a computationally-efficient polynomial, and is accurate to within -5e-4 K and 6e-4 K, when compared with this function. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.ct_freezing(SA, p, saturation_fraction) CT_freezing.types = _gsw_ufuncs.ct_freezing.types CT_freezing = match_args_return(CT_freezing) def CT_freezing_first_derivatives(SA, p, saturation_fraction): """ Calculates the first derivatives of the Conservative Temperature at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa). Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- CTfreezing_SA : array-like, K kg/g the derivative of the Conservative Temperature at freezing (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e. CTfreezing_P : array-like, K/Pa the derivative of the Conservative Temperature at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. """ return _gsw_ufuncs.ct_freezing_first_derivatives(SA, p, saturation_fraction) CT_freezing_first_derivatives.types = _gsw_ufuncs.ct_freezing_first_derivatives.types CT_freezing_first_derivatives = match_args_return(CT_freezing_first_derivatives) def CT_freezing_first_derivatives_poly(SA, p, saturation_fraction): """ Calculates the first derivatives of the Conservative Temperature at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa) of the comptationally efficient polynomial fit of the freezing temperature (McDougall et al., 2014). Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- CTfreezing_SA : array-like, K kg/g the derivative of the Conservative Temperature at freezing (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e. CTfreezing_P : array-like, K/Pa the derivative of the Conservative Temperature at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.ct_freezing_first_derivatives_poly(SA, p, saturation_fraction) CT_freezing_first_derivatives_poly.types = _gsw_ufuncs.ct_freezing_first_derivatives_poly.types CT_freezing_first_derivatives_poly = match_args_return(CT_freezing_first_derivatives_poly) def CT_freezing_poly(SA, p, saturation_fraction): """ Calculates the Conservative Temperature at which seawater freezes. The error of this fit ranges between -5e-4 K and 6e-4 K when compared with the Conservative Temperature calculated from the exact in-situ freezing temperature which is found by a Newton-Raphson iteration of the equality of the chemical potentials of water in seawater and in ice. Note that the Conservative Temperature freezing temperature can be found by this exact method using the function gsw_CT_freezing. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- CT_freezing : array-like, deg C Conservative Temperature at freezing of seawater That is, the freezing temperature expressed in terms of Conservative Temperature (ITS-90). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.ct_freezing_poly(SA, p, saturation_fraction) CT_freezing_poly.types = _gsw_ufuncs.ct_freezing_poly.types CT_freezing_poly = match_args_return(CT_freezing_poly) def CT_from_enthalpy(SA, h, p): """ Calculates the Conservative Temperature of seawater, given the Absolute Salinity, specific enthalpy, h, and pressure p. The specific enthalpy input is the one calculated from the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg h : array-like Specific enthalpy, J/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT : array-like, deg C Conservative Temperature ( ITS-90) Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.ct_from_enthalpy(SA, h, p) CT_from_enthalpy.types = _gsw_ufuncs.ct_from_enthalpy.types CT_from_enthalpy = match_args_return(CT_from_enthalpy) def CT_from_enthalpy_exact(SA, h, p): """ Calculates the Conservative Temperature of seawater, given the Absolute Salinity, SA, specific enthalpy, h, and pressure p. The specific enthalpy input is calculated from the full Gibbs function of seawater, gsw_enthalpy_t_exact. Parameters ---------- SA : array-like Absolute Salinity, g/kg h : array-like Specific enthalpy, J/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT : array-like, deg C Conservative Temperature ( ITS-90) Notes ----- Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_CT_from_enthalpy(SA,h,p), which uses the computationally efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. McDougall T.J. and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.ct_from_enthalpy_exact(SA, h, p) CT_from_enthalpy_exact.types = _gsw_ufuncs.ct_from_enthalpy_exact.types CT_from_enthalpy_exact = match_args_return(CT_from_enthalpy_exact) def CT_from_entropy(SA, entropy): """ Calculates Conservative Temperature with entropy as an input variable. Parameters ---------- SA : array-like Absolute Salinity, g/kg entropy : array-like Specific entropy, J/(kg*K) Returns ------- CT : array-like, deg C Conservative Temperature (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.10 of this TEOS-10 Manual. """ return _gsw_ufuncs.ct_from_entropy(SA, entropy) CT_from_entropy.types = _gsw_ufuncs.ct_from_entropy.types CT_from_entropy = match_args_return(CT_from_entropy) def CT_from_pt(SA, pt): """ Calculates Conservative Temperature of seawater from potential temperature (whose reference sea pressure is zero dbar). Parameters ---------- SA : array-like Absolute Salinity, g/kg pt : array-like Potential temperature referenced to a sea pressure, degrees C Returns ------- CT : array-like, deg C Conservative Temperature (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.3 of this TEOS-10 Manual. """ return _gsw_ufuncs.ct_from_pt(SA, pt) CT_from_pt.types = _gsw_ufuncs.ct_from_pt.types CT_from_pt = match_args_return(CT_from_pt) def CT_from_rho(rho, SA, p): """ Calculates the Conservative Temperature of a seawater sample, for given values of its density, Absolute Salinity and sea pressure (in dbar), using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- rho : array-like Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3. SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT : array-like, deg C Conservative Temperature (ITS-90) CT_multiple : array-like, deg C Conservative Temperature (ITS-90) Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43. """ return _gsw_ufuncs.ct_from_rho(rho, SA, p) CT_from_rho.types = _gsw_ufuncs.ct_from_rho.types CT_from_rho = match_args_return(CT_from_rho) def CT_from_t(SA, t, p): """ Calculates Conservative Temperature of seawater from in-situ temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT : array-like, deg C Conservative Temperature (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.3 of this TEOS-10 Manual. """ return _gsw_ufuncs.ct_from_t(SA, t, p) CT_from_t.types = _gsw_ufuncs.ct_from_t.types CT_from_t = match_args_return(CT_from_t) def CT_maxdensity(SA, p): """ Calculates the Conservative Temperature of maximum density of seawater. This function returns the Conservative temperature at which the density of seawater is a maximum, at given Absolute Salinity, SA, and sea pressure, p (in dbar). This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- CT_maxdensity : array-like, deg C Conservative Temperature at which the density of seawater is a maximum for given Absolute Salinity and pressure. Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.42 of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.ct_maxdensity(SA, p) CT_maxdensity.types = _gsw_ufuncs.ct_maxdensity.types CT_maxdensity = match_args_return(CT_maxdensity) def CT_second_derivatives(SA, pt): """ Calculates the following three, second-order derivatives of Conservative Temperature (1) CT_SA_SA, the second derivative with respect to Absolute Salinity at constant potential temperature (with p_ref = 0 dbar), (2) CT_SA_pt, the derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) and Absolute Salinity, and (3) CT_pt_pt, the second derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg pt : array-like Potential temperature referenced to a sea pressure, degrees C Returns ------- CT_SA_SA : array-like, K/((g/kg)^2) The second derivative of Conservative Temperature with respect to Absolute Salinity at constant potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar). CT_SA_pt : array-like, The derivative of Conservative Temperature with respect to potential temperature (the regular one with p_ref : array-like, 1/(g/kg) 0 dbar) and Absolute Salinity. CT_pt_pt : array-like, The second derivative of Conservative Temperature with respect to potential temperature (the regular one with p_ref : array-like, 1/K 0 dbar) at constant SA. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See appendix A.12 of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.ct_second_derivatives(SA, pt) CT_second_derivatives.types = _gsw_ufuncs.ct_second_derivatives.types CT_second_derivatives = match_args_return(CT_second_derivatives) def deltaSA_atlas(p, lon, lat): """ Calculates the Absolute Salinity Anomaly atlas value, SA - SR, in the open ocean by spatially interpolating the global reference data set of deltaSA_atlas to the location of the seawater sample. Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- deltaSA_atlas : array-like, g/kg Absolute Salinity Anomaly atlas value Notes ----- The Absolute Salinity Anomaly atlas value in the Baltic Sea is evaluated separately, since it is a function of Practical Salinity, not of space. The present function returns a deltaSA_atlas of zero for data in the Baltic Sea. The correct way of calculating Absolute Salinity in the Baltic Sea is by calling gsw_SA_from_SP. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.deltasa_atlas(p, lon, lat) deltaSA_atlas.types = _gsw_ufuncs.deltasa_atlas.types deltaSA_atlas = match_args_return(deltaSA_atlas) def deltaSA_from_SP(SP, p, lon, lat): """ Calculates Absolute Salinity Anomaly from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- deltaSA : array-like, g/kg Absolute Salinity Anomaly References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1117-1128. https://os.copernicus.org/articles/8/1117/2012/os-8-1117-2012.pdf """ return _gsw_ufuncs.deltasa_from_sp(SP, p, lon, lat) deltaSA_from_SP.types = _gsw_ufuncs.deltasa_from_sp.types deltaSA_from_SP = match_args_return(deltaSA_from_SP) def dilution_coefficient_t_exact(SA, t, p): """ Calculates the dilution coefficient of seawater. The dilution coefficient of seawater is defined as the Absolute Salinity times the second derivative of the Gibbs function with respect to Absolute Salinity, that is, SA.*g_SA_SA. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- dilution_coefficient_t_exact : array-like, (J/kg)(kg/g) dilution coefficient References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.dilution_coefficient_t_exact(SA, t, p) dilution_coefficient_t_exact.types = _gsw_ufuncs.dilution_coefficient_t_exact.types dilution_coefficient_t_exact = match_args_return(dilution_coefficient_t_exact) def dynamic_enthalpy(SA, CT, p): """ Calculates dynamic enthalpy of seawater using the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Dynamic enthalpy is defined as enthalpy minus potential enthalpy (Young, 2010). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- dynamic_enthalpy : array-like, J/kg dynamic enthalpy Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.2 of this TEOS-10 Manual. McDougall, T. J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and the seawater Boussinesq approximation. Journal of Physical Oceanography, 40, 394-400. """ return _gsw_ufuncs.dynamic_enthalpy(SA, CT, p) dynamic_enthalpy.types = _gsw_ufuncs.dynamic_enthalpy.types dynamic_enthalpy = match_args_return(dynamic_enthalpy) def enthalpy(SA, CT, p): """ Calculates specific enthalpy of seawater using the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- enthalpy : array-like, J/kg specific enthalpy Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.6) of this TEOS-10 Manual. McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.enthalpy(SA, CT, p) enthalpy.types = _gsw_ufuncs.enthalpy.types enthalpy = match_args_return(enthalpy) def enthalpy_CT_exact(SA, CT, p): """ Calculates specific enthalpy of seawater from Absolute Salinity and Conservative Temperature and pressure. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- enthalpy_CT_exact : array-like, J/kg specific enthalpy Notes ----- Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_enthalpy(SA,CT,p), which uses the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.11 of this TEOS-10 Manual. McDougall, T. J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.enthalpy_ct_exact(SA, CT, p) enthalpy_CT_exact.types = _gsw_ufuncs.enthalpy_ct_exact.types enthalpy_CT_exact = match_args_return(enthalpy_CT_exact) def enthalpy_diff(SA, CT, p_shallow, p_deep): """ Calculates the difference of the specific enthalpy of seawater between two different pressures, p_deep (the deeper pressure) and p_shallow (the shallower pressure), at the same values of SA and CT. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). The output (enthalpy_diff) is the specific enthalpy evaluated at (SA,CT,p_deep) minus the specific enthalpy at (SA,CT,p_shallow). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p_shallow : array-like Upper sea pressure (absolute pressure minus 10.1325 dbar), dbar p_deep : array-like Lower sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- enthalpy_diff : array-like, J/kg difference of specific enthalpy (deep minus shallow) Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqns. (3.32.2) and (A.30.6) of this TEOS-10 Manual. McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.enthalpy_diff(SA, CT, p_shallow, p_deep) enthalpy_diff.types = _gsw_ufuncs.enthalpy_diff.types enthalpy_diff = match_args_return(enthalpy_diff) def enthalpy_first_derivatives(SA, CT, p): """ Calculates the following two derivatives of specific enthalpy (h) of seawater using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). (1) h_SA, the derivative with respect to Absolute Salinity at constant CT and p, and (2) h_CT, derivative with respect to CT at constant SA and p. Note that h_P is specific volume (1/rho) it can be calculated by calling gsw_specvol(SA,CT,p). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- h_SA : array-like, J/g The first derivative of specific enthalpy with respect to Absolute Salinity at constant CT and p. [ J/(kg (g/kg))] i.e. h_CT : array-like, J/(kg K) The first derivative of specific enthalpy with respect to CT at constant SA and p. Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual. McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_first_derivatives(SA, CT, p) enthalpy_first_derivatives.types = _gsw_ufuncs.enthalpy_first_derivatives.types enthalpy_first_derivatives = match_args_return(enthalpy_first_derivatives) def enthalpy_first_derivatives_CT_exact(SA, CT, p): """ Calculates the following two derivatives of specific enthalpy, h, (1) h_SA, the derivative with respect to Absolute Salinity at constant CT and p, and (2) h_CT, derivative with respect to CT at constant SA and p. Note that h_P is specific volume, v, it can be calculated by calling gsw_specvol_CT_exact(SA,CT,p). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- h_SA : array-like, J/g The first derivative of specific enthalpy with respect to Absolute Salinity at constant CT and p. [ J/(kg (g/kg))] i.e. h_CT : array-like, J/(kg K) The first derivative of specific enthalpy with respect to CT at constant SA and p. Notes ----- Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_enthalpy_first_derivatives(SA,CT,p) which uses the computationally efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual. McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_first_derivatives_ct_exact(SA, CT, p) enthalpy_first_derivatives_CT_exact.types = _gsw_ufuncs.enthalpy_first_derivatives_ct_exact.types enthalpy_first_derivatives_CT_exact = match_args_return(enthalpy_first_derivatives_CT_exact) def enthalpy_ice(t, p): """ Calculates the specific enthalpy of ice (h_Ih). Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- enthalpy_ice : array-like, J/kg specific enthalpy of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_ice(t, p) enthalpy_ice.types = _gsw_ufuncs.enthalpy_ice.types enthalpy_ice = match_args_return(enthalpy_ice) def enthalpy_second_derivatives(SA, CT, p): """ Calculates the following three second-order derivatives of specific enthalpy (h),using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). (1) h_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) h_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) h_CT_CT, second-order derivative with respect to CT at constant SA and p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- h_SA_SA : array-like, J/(kg (g/kg)^2) The second derivative of specific enthalpy with respect to Absolute Salinity at constant CT & p. h_SA_CT : array-like, J/(kg K(g/kg)) The second derivative of specific enthalpy with respect to SA and CT at constant p. h_CT_CT : array-like, J/(kg K^2) The second derivative of specific enthalpy with respect to CT at constant SA and p. Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_second_derivatives(SA, CT, p) enthalpy_second_derivatives.types = _gsw_ufuncs.enthalpy_second_derivatives.types enthalpy_second_derivatives = match_args_return(enthalpy_second_derivatives) def enthalpy_second_derivatives_CT_exact(SA, CT, p): """ Calculates the following three second-order derivatives of specific enthalpy (h), (1) h_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) h_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) h_CT_CT, second-order derivative with respect to CT at constant SA and p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- h_SA_SA : array-like, J/(kg (g/kg)^2) The second derivative of specific enthalpy with respect to Absolute Salinity at constant CT & p. h_SA_CT : array-like, J/(kg K(g/kg)) The second derivative of specific enthalpy with respect to SA and CT at constant p. h_CT_CT : array-like, J/(kg K^2) The second derivative of specific enthalpy with respect to CT at constant SA and p. Notes ----- Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_enthalpy_second_derivatives(SA,CT,p) which uses the computationally efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T. J., 2003: Potential enthalpy: A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963. See Eqns. (18) and (22) Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_second_derivatives_ct_exact(SA, CT, p) enthalpy_second_derivatives_CT_exact.types = _gsw_ufuncs.enthalpy_second_derivatives_ct_exact.types enthalpy_second_derivatives_CT_exact = match_args_return(enthalpy_second_derivatives_CT_exact) def enthalpy_SSO_0(p): """ enthalpy at (SSO,CT=0,p) Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- double, array Notes ----- gsw_enthalpy_SSO_0 enthalpy at (SSO,CT=0,p) (75-term eqn.) This function calculates enthalpy at the Standard Ocean Salinity, SSO, and at a Conservative Temperature of zero degrees C, as a function of pressure, p, in dbar, using a streamlined version of the 75-term computationally-efficient expression for specific volume, that is, a streamlined version of the code "gsw_enthalpy(SA,CT,p)". VERSION NUMBER: 3.06.12 (25th May, 2020) References ---------- Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.enthalpy_sso_0(p) enthalpy_SSO_0.types = _gsw_ufuncs.enthalpy_sso_0.types enthalpy_SSO_0 = match_args_return(enthalpy_SSO_0) def enthalpy_t_exact(SA, t, p): """ Calculates the specific enthalpy of seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- enthalpy_t_exact : array-like, J/kg specific enthalpy References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.enthalpy_t_exact(SA, t, p) enthalpy_t_exact.types = _gsw_ufuncs.enthalpy_t_exact.types enthalpy_t_exact = match_args_return(enthalpy_t_exact) def entropy_first_derivatives(SA, CT): """ Calculates the following two partial derivatives of specific entropy (eta) (1) eta_SA, the derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) eta_CT, the derivative with respect to Conservative Temperature at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- eta_SA : array-like, J/(g K) The derivative of specific entropy with respect to Absolute Salinity (in units of g kg^-1) at constant Conservative Temperature. eta_CT : array-like, J/(kg K^2) The derivative of specific entropy with respect to Conservative Temperature at constant Absolute Salinity. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.12.8) and (P.14a,c) of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.entropy_first_derivatives(SA, CT) entropy_first_derivatives.types = _gsw_ufuncs.entropy_first_derivatives.types entropy_first_derivatives = match_args_return(entropy_first_derivatives) def entropy_from_CT(SA, CT): """ Calculates specific entropy of seawater from Conservative Temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- entropy : array-like, J/(kg*K) specific entropy References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.10 of this TEOS-10 Manual. """ return _gsw_ufuncs.entropy_from_ct(SA, CT) entropy_from_CT.types = _gsw_ufuncs.entropy_from_ct.types entropy_from_CT = match_args_return(entropy_from_CT) def entropy_from_pt(SA, pt): """ Calculates specific entropy of seawater as a function of potential temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg pt : array-like Potential temperature referenced to a sea pressure, degrees C Returns ------- entropy : array-like, J/(kg*K) specific entropy References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.10 of this TEOS-10 Manual. """ return _gsw_ufuncs.entropy_from_pt(SA, pt) entropy_from_pt.types = _gsw_ufuncs.entropy_from_pt.types entropy_from_pt = match_args_return(entropy_from_pt) def entropy_from_t(SA, t, p): """ Calculates specific entropy of seawater from in-situ temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- entropy : array-like, J/(kg*K) specific entropy References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.entropy_from_t(SA, t, p) entropy_from_t.types = _gsw_ufuncs.entropy_from_t.types entropy_from_t = match_args_return(entropy_from_t) def entropy_ice(t, p): """ Calculates specific entropy of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- ice_entropy : array-like, J kg^-1 K^-1 specific entropy of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.entropy_ice(t, p) entropy_ice.types = _gsw_ufuncs.entropy_ice.types entropy_ice = match_args_return(entropy_ice) def entropy_part(SA, t, p): """ entropy minus the terms that are a function of only SA Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- double, array Notes ----- sw_entropy_part entropy minus the terms that are a function of only SA This function calculates entropy, except that it does not evaluate any terms that are functions of Absolute Salinity alone. By not calculating these terms, which are a function only of Absolute Salinity, several unnecessary computations are avoided (including saving the computation of a natural logarithm). These terms are a necessary part of entropy, but are not needed when calculating potential temperature from in-situ temperature. VERSION NUMBER: 3.06.12 (25th May, 2020) """ return _gsw_ufuncs.entropy_part(SA, t, p) entropy_part.types = _gsw_ufuncs.entropy_part.types entropy_part = match_args_return(entropy_part) def entropy_part_zerop(SA, pt0): """ entropy_part evaluated at the sea surface Parameters ---------- SA : array-like Absolute Salinity, g/kg pt0 : array-like Potential temperature with reference pressure of 0 dbar, degrees C Returns ------- double, array Notes ----- gsw_entropy_part_zerop entropy_part evaluated at the sea surface This function calculates entropy at a sea pressure of zero, except that it does not evaluate any terms that are functions of Absolute Salinity alone. By not calculating these terms, which are a function only of Absolute Salinity, several unnecessary computations are avoided (including saving the computation of a natural logarithm). These terms are a necessary part of entropy, but are not needed when calculating potential temperature from in-situ temperature. The inputs to "gsw_entropy_part_zerop(SA,pt0)" are Absolute Salinity and potential temperature with reference sea pressure of zero dbar. VERSION NUMBER: 3.06.12 (25th May, 2020) """ return _gsw_ufuncs.entropy_part_zerop(SA, pt0) entropy_part_zerop.types = _gsw_ufuncs.entropy_part_zerop.types entropy_part_zerop = match_args_return(entropy_part_zerop) def entropy_second_derivatives(SA, CT): """ Calculates the following three second-order partial derivatives of specific entropy (eta) (1) eta_SA_SA, the second derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) eta_SA_CT, the derivative with respect to Absolute Salinity and Conservative Temperature. (3) eta_CT_CT, the second derivative with respect to Conservative Temperature at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- eta_SA_SA : array-like, J/(kg K(g/kg)^2) The second derivative of specific entropy with respect to Absolute Salinity (in units of g kg^-1) at constant Conservative Temperature. eta_SA_CT : array-like, J/(kg (g/kg) K^2) The second derivative of specific entropy with respect to Conservative Temperature at constant Absolute eta_CT_CT : array-like, J/(kg K^3) The second derivative of specific entropy with respect to Conservative Temperature at constant Absolute References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (P.14b) and (P.15a,b) of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.entropy_second_derivatives(SA, CT) entropy_second_derivatives.types = _gsw_ufuncs.entropy_second_derivatives.types entropy_second_derivatives = match_args_return(entropy_second_derivatives) def Fdelta(p, lon, lat): """ Calculates Fdelta from the Absolute Salinity Anomaly Ratio (SAAR). It finds SAAR by calling the function "gsw_SAAR(p,long,lat)" and then simply calculates Fdelta from Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- Fdelta : array-like, unitless ratio of SA to Sstar, minus 1 Notes ----- Fdelta = (1 + r1)SAAR/(1 - r1*SAAR) = (SA/Sstar) - 1 with r1 being the constant 0.35 based on the work of Pawlowicz et al. (2011). Note that since SAAR is everywhere less than 0.001 in the global ocean, Fdelta is only slightly different to 1.35*SAAR. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf Pawlawicz, R., D.G. Wright and F.J. Millero, 2011; The effects of biogeochemical processes on oceanic conductivity/salinty/density relationships and the characterization of real seawater. Ocean Science, 7, 363-387. https://os.copernicus.org/articles/7/363/2011/os-7-363-2011.pdf """ return _gsw_ufuncs.fdelta(p, lon, lat) Fdelta.types = _gsw_ufuncs.fdelta.types Fdelta = match_args_return(Fdelta) def frazil_properties(SA_bulk, h_bulk, p): """ Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_final, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occurring at pressure p. The final values of Absolute Salinity, SA_final, and Conservative Temperature, CT_final, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero throughout the code). Parameters ---------- SA_bulk : array-like bulk Absolute Salinity of the seawater and ice mixture, g/kg h_bulk : array-like bulk enthalpy of the seawater and ice mixture, J/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- SA_final : array-like, g/kg Absolute Salinity of the seawater in the final state, whether or not any ice is present. CT_final : array-like, deg C Conservative Temperature of the seawater in the final state, whether or not any ice is present. w_Ih_final : array-like, unitless mass fraction of ice in the final seawater-ice mixture. If this ice mass fraction is positive, the system is at thermodynamic equilibrium. If this ice mass fraction is zero there is no ice in the final state which consists only of seawater which is warmer than the freezing temperature. Notes ----- When the mass fraction w_Ih_final is calculated as being a positive value, the seawater-ice mixture is at thermodynamic equilibrium. This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, is sufficiently large (i.e. sufficiently "warm") so that there is no ice present in the final state. In this case the final state consists of only seawater rather than being an equilibrium mixture of seawater and ice which occurs when w_Ih_final is positive. Note that when w_Ih_final = 0, the final seawater is not at the freezing temperature. Note that there is another GSW code, gsw_frazil_properties_potential_poly(SA_bulk,h_pot_bulk,p) which treats potential enthalpy as the conservative variable, while, in contrast, the present code treats in situ enthalpy as the conservative variable during the interaction of seawater and ice Ih. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of ice and sea ice into seawater, and frazil ice formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Anonymous, 2014: Modelling the interaction between seawater and frazil ice. Manuscript, March 2015. See Eqns. (8) - (15) of this manuscript. """ return _gsw_ufuncs.frazil_properties(SA_bulk, h_bulk, p) frazil_properties.types = _gsw_ufuncs.frazil_properties.types frazil_properties = match_args_return(frazil_properties) def frazil_properties_potential(SA_bulk, h_pot_bulk, p): """ Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_eq, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, occurring at pressure p. The final equilibrium values of Absolute Salinity, SA_eq, and Conservative Temperature, CT_eq, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero throughout the code). Parameters ---------- SA_bulk : array-like bulk Absolute Salinity of the seawater and ice mixture, g/kg h_pot_bulk : array-like bulk enthalpy of the seawater and ice mixture, J/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- SA_final : array-like, g/kg Absolute Salinity of the seawater in the final state, whether or not any ice is present. CT_final : array-like, deg C Conservative Temperature of the seawater in the final state, whether or not any ice is present. w_Ih_final : array-like, unitless mass fraction of ice in the final seawater-ice mixture. If this ice mass fraction is positive, the system is at thermodynamic equilibrium. If this ice mass fraction is zero there is no ice in the final state which consists only of seawater which is warmer than the freezing temperature. Notes ----- When the mass fraction w_Ih_final is calculated as being a positive value, the seawater-ice mixture is at thermodynamic equilibrium. This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, is sufficiently large (i.e. sufficiently "warm") so that there is no ice present in the final state. In this case the final state consists of only seawater rather than being an equilibrium mixture of seawater and ice which occurs when w_Ih_final is positive. Note that when w_Ih_final = 0, the final seawater is not at the freezing temperature. Note that this code uses the exact forms of CT_freezing and pot_enthalpy_ice_freezing. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of ice and sea ice into seawater, and frazil ice formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Anonymous, 2014: Modelling the interaction between seawater and frazil ice. Manuscript, March 2015. See Eqns. (8)-(15) of this manuscript. """ return _gsw_ufuncs.frazil_properties_potential(SA_bulk, h_pot_bulk, p) frazil_properties_potential.types = _gsw_ufuncs.frazil_properties_potential.types frazil_properties_potential = match_args_return(frazil_properties_potential) def frazil_properties_potential_poly(SA_bulk, h_pot_bulk, p): """ Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_eq, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, occurring at pressure p. The final equilibrium values of Absolute Salinity, SA_eq, and Conservative Temperature, CT_eq, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero throughout the code). Parameters ---------- SA_bulk : array-like bulk Absolute Salinity of the seawater and ice mixture, g/kg h_pot_bulk : array-like bulk enthalpy of the seawater and ice mixture, J/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- SA_final : array-like, g/kg Absolute Salinity of the seawater in the final state, whether or not any ice is present. CT_final : array-like, deg C Conservative Temperature of the seawater in the final state, whether or not any ice is present. w_Ih_final : array-like, unitless mass fraction of ice in the final seawater-ice mixture. If this ice mass fraction is positive, the system is at thermodynamic equilibrium. If this ice mass fraction is zero there is no ice in the final state which consists only of seawater which is warmer than the freezing temperature. Notes ----- When the mass fraction w_Ih_final is calculated as being a positive value, the seawater-ice mixture is at thermodynamic equilibrium. This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, is sufficiently large (i.e. sufficiently "warm") so that there is no ice present in the final state. In this case the final state consists of only seawater rather than being an equilibrium mixture of seawater and ice which occurs when w_Ih_final is positive. Note that when w_Ih_final = 0, the final seawater is not at the freezing temperature. Note that this code uses the polynomial forms of CT_freezing and pot_enthalpy_ice_freezing. This code is intended to be used in ocean models where the model prognostic variables are SA_bulk and h_pot_bulk. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of ice and sea ice into seawater, and frazil ice formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Anonymous, 2014: Modelling the interaction between seawater and frazil ice. Manuscript, March 2015. See Eqns. (8)-(15) of this manuscript. """ return _gsw_ufuncs.frazil_properties_potential_poly(SA_bulk, h_pot_bulk, p) frazil_properties_potential_poly.types = _gsw_ufuncs.frazil_properties_potential_poly.types frazil_properties_potential_poly = match_args_return(frazil_properties_potential_poly) def frazil_ratios_adiabatic(SA, p, w_Ih): """ Calculates the ratios of SA, CT and P changes when frazil ice forms or melts in response to an adiabatic change in pressure of a mixture of seawater and frazil ice crystals. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar w_Ih : array-like mass fraction of ice: the mass of ice divided by the sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless. Returns ------- dSA_dCT_frazil : array-like, g/(kg K) the ratio of the changes in Absolute Salinity to that of Conservative Temperature dSA_dP_frazil : array-like, g/(kg Pa) the ratio of the changes in Absolute Salinity to that of pressure (in Pa) dCT_dP_frazil : array-like, K/Pa the ratio of the changes in Conservative Temperature to that of pressure (in Pa) Notes ----- Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero whereas dCT/dSA would then be infinite. Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure derivatives with the pressure measured in Pa not dbar. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqns. (47), (48) and (49) of this manuscript. """ return _gsw_ufuncs.frazil_ratios_adiabatic(SA, p, w_Ih) frazil_ratios_adiabatic.types = _gsw_ufuncs.frazil_ratios_adiabatic.types frazil_ratios_adiabatic = match_args_return(frazil_ratios_adiabatic) def frazil_ratios_adiabatic_poly(SA, p, w_Ih): """ Calculates the ratios of SA, CT and P changes when frazil ice forms or melts in response to an adiabatic change in pressure of a mixture of seawater and frazil ice crystals. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar w_Ih : array-like mass fraction of ice: the mass of ice divided by the sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless. Returns ------- dSA_dCT_frazil : array-like, g/(kg K) the ratio of the changes in Absolute Salinity to that of Conservative Temperature dSA_dP_frazil : array-like, g/(kg Pa) the ratio of the changes in Absolute Salinity to that of pressure (in Pa) dCT_dP_frazil : array-like, K/Pa the ratio of the changes in Conservative Temperature to that of pressure (in Pa) Notes ----- Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero whereas dCT/dSA would then be infinite. Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure derivatives with the pressure measured in Pa not dbar. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015) and the polynomial expression for freezing temperature based on Conservative Temperature (McDougall et al., 2015). References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqns. (47), (48) and (49) of this manuscript. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.frazil_ratios_adiabatic_poly(SA, p, w_Ih) frazil_ratios_adiabatic_poly.types = _gsw_ufuncs.frazil_ratios_adiabatic_poly.types frazil_ratios_adiabatic_poly = match_args_return(frazil_ratios_adiabatic_poly) def gibbs(ns, nt, np, SA, t, p): """ Calculates specific Gibbs energy and its derivatives up to order 3 for seawater. The Gibbs function for seawater is that of TEOS-10 (IOC et al., 2010), being the sum of IAPWS-08 for the saline part and IAPWS-09 for the pure water part. These IAPWS releases are the officially blessed IAPWS descriptions of Feistel (2008) and the pure water part of Feistel (2003). Absolute Salinity, SA, in all of the GSW routines is expressed on the Reference-Composition Salinity Scale of 2008 (RCSS-08) of Millero et al. (2008). Parameters ---------- ns : array-like order of SA derivative, integer in (0, 1, 2) nt : array-like order of t derivative, integer in (0, 1, 2) np : array-like order of p derivative, integer in (0, 1, 2) SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- gibbs : array-like Specific Gibbs energy or its derivatives. The Gibbs energy (when ns = nt = np = 0) has units of J/kg. The Absolute Salinity derivatives are output in units of (J/kg) (g/kg)^(-ns). The temperature derivatives are output in units of (J/kg) (K)^(-nt). The pressure derivatives are output in units of (J/kg) (Pa)^(-np). The mixed derivatives are output in units of (J/kg) (g/kg)^(-ns) (K)^(-nt) (Pa)^(-np). Note: The derivatives are taken with respect to pressure in Pa, not withstanding that the pressure input into this routine is in dbar. References ---------- Feistel, R., 2003: A new extended Gibbs thermodynamic potential of seawater, Progr. Oceanogr., 58, 43-114. Feistel, R., 2008: A Gibbs function for seawater thermodynamics for -6 to 80°C and salinity up to 120 g kg–1, Deep-Sea Res. I, 55, 1639-1671. IAPWS, 2008: Release on the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater. The International Association for the Properties of Water and Steam. Berlin, Germany, September 2008, available from https://iapws.org/. This Release is referred to as IAPWS-08. IAPWS, 2009: Supplementary Release on a Computationally Efficient Thermodynamic Formulation for Liquid Water for Oceanographic Use. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009, available from https://iapws.org/. This Release is referred to as IAPWS-09. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.6 and appendices A.6, G and H of this TEOS-10 Manual. Millero, F.J., R. Feistel, D.G. Wright, and T.J. McDougall, 2008: The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72. Reference page in Help browser doc gsw_gibbs Note that this reference page includes the code contained in gsw_gibbs. We have opted to encode this programme as it is a global standard and such we cannot allow anyone to change it. """ return _gsw_ufuncs.gibbs(ns, nt, np, SA, t, p) gibbs.types = _gsw_ufuncs.gibbs.types gibbs = match_args_return(gibbs) def gibbs_ice(nt, np, t, p): """ Ice specific Gibbs energy and derivatives up to order 2. Parameters ---------- nt : array-like order of t derivative, integer in (0, 1, 2) np : array-like order of p derivative, integer in (0, 1, 2) t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- gibbs_ice : array-like Specific Gibbs energy of ice or its derivatives. The Gibbs energy (when nt = np = 0) has units of J/kg. The temperature derivatives are output in units of (J/kg) (K)^(-nt). The pressure derivatives are output in units of (J/kg) (Pa)^(-np). The mixed derivatives are output in units of (J/kg) (K)^(-nt) (Pa)^(-np). Note. The derivatives are taken with respect to pressure in Pa, not withstanding that the pressure input into this routine is in dbar. References ---------- IAPWS, 2009: Revised release on the Equation of State 2006 for H2O Ice Ih. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See appendix I. Reference page in Help browser doc gsw_gibbs_ice Note that this reference page includes the code contained in gsw_gibbs_ice. We have opted to encode this programme as it is a global standard and such we cannot allow anyone to change it. """ return _gsw_ufuncs.gibbs_ice(nt, np, t, p) gibbs_ice.types = _gsw_ufuncs.gibbs_ice.types gibbs_ice = match_args_return(gibbs_ice) def gibbs_ice_part_t(t, p): """ part of the first temperature derivative of Gibbs energy of ice that is the output is gibbs_ice(1,0,t,p) + S0 Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- gibbs_ice_part_t : array-like, J kg^-1 K^-1 part of temperature derivative References ---------- IAPWS, 2009: Revised Release on the Equation of State 2006 for H2O Ice Ih. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See appendix I. """ return _gsw_ufuncs.gibbs_ice_part_t(t, p) gibbs_ice_part_t.types = _gsw_ufuncs.gibbs_ice_part_t.types gibbs_ice_part_t = match_args_return(gibbs_ice_part_t) def gibbs_ice_pt0(pt0): """ part of the first temperature derivative of Gibbs energy of ice that is the output is "gibbs_ice(1,0,pt0,0) + s0" Parameters ---------- pt0 : array-like Potential temperature with reference pressure of 0 dbar, degrees C Returns ------- gibbs_ice_part_pt0 : array-like, J kg^-1 K^-1 part of temperature derivative References ---------- IAPWS, 2009: Revised Release on the Equation of State 2006 for H2O Ice Ih. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See appendix I. """ return _gsw_ufuncs.gibbs_ice_pt0(pt0) gibbs_ice_pt0.types = _gsw_ufuncs.gibbs_ice_pt0.types gibbs_ice_pt0 = match_args_return(gibbs_ice_pt0) def gibbs_ice_pt0_pt0(pt0): """ The second temperature derivative of Gibbs energy of ice at the potential temperature with reference sea pressure of zero dbar. That is the output is gibbs_ice(2,0,pt0,0). Parameters ---------- pt0 : array-like Potential temperature with reference pressure of 0 dbar, degrees C Returns ------- gibbs_ice_pt0_pt0 : array-like, J kg^-1 K^-2 temperature second derivative at pt0 References ---------- IAPWS, 2009: Revised Release on the Equation of State 2006 for H2O Ice Ih. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See appendix I. """ return _gsw_ufuncs.gibbs_ice_pt0_pt0(pt0) gibbs_ice_pt0_pt0.types = _gsw_ufuncs.gibbs_ice_pt0_pt0.types gibbs_ice_pt0_pt0 = match_args_return(gibbs_ice_pt0_pt0) def gibbs_pt0_pt0(SA, pt0): """ gibbs_tt at (SA,pt,0) Parameters ---------- SA : array-like Absolute Salinity, g/kg pt0 : array-like Potential temperature with reference pressure of 0 dbar, degrees C Returns ------- double, array Notes ----- gsw_gibbs_pt0_pt0 gibbs_tt at (SA,pt,0) This function calculates the second derivative of the specific Gibbs function with respect to temperature at zero sea pressure. The inputs are Absolute Salinity and potential temperature with reference sea pressure of zero dbar. VERSION NUMBER: 3.06.13 (7th September, 2020) """ return _gsw_ufuncs.gibbs_pt0_pt0(SA, pt0) gibbs_pt0_pt0.types = _gsw_ufuncs.gibbs_pt0_pt0.types gibbs_pt0_pt0 = match_args_return(gibbs_pt0_pt0) def grav(lat, p): """ Calculates acceleration due to gravity as a function of latitude and as a function of pressure in the ocean. Parameters ---------- lat : array-like Latitude, -90 to 90 degrees p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- grav : array-like, m s^-2 gravitational acceleration References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix D of this TEOS-10 Manual. Moritz, H., 2000: Geodetic reference system 1980. J. Geodesy, 74, pp. 128-133. Saunders, P.M., and N.P. Fofonoff, 1976: Conversion of pressure to depth in the ocean. Deep-Sea Res., pp. 109-111. """ return _gsw_ufuncs.grav(lat, p) grav.types = _gsw_ufuncs.grav.types grav = match_args_return(grav) def Helmholtz_energy_ice(t, p): """ Calculates the Helmholtz energy of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- Helmholtz_energy_ice : array-like, J/kg Helmholtz energy of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.helmholtz_energy_ice(t, p) Helmholtz_energy_ice.types = _gsw_ufuncs.helmholtz_energy_ice.types Helmholtz_energy_ice = match_args_return(Helmholtz_energy_ice) def Hill_ratio_at_SP2(t): """ Calculates the Hill ratio, which is the adjustment needed to apply for Practical Salinities smaller than 2. This ratio is defined at a Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill ratio is the ratio of 2 to the output of the Hill et al. (1986) formula for Practical Salinity at the conductivity ratio, Rt, at which Practical Salinity on the PSS-78 scale is exactly 2. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C Returns ------- Hill_ratio : array-like, unitless Hill ratio at SP of 2 References ---------- Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng., 11, 109 - 112. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix E of this TEOS-10 Manual. McDougall T.J. and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. Unesco, 1983: Algorithms for computation of fundamental properties of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp. """ return _gsw_ufuncs.hill_ratio_at_sp2(t) Hill_ratio_at_SP2.types = _gsw_ufuncs.hill_ratio_at_sp2.types Hill_ratio_at_SP2 = match_args_return(Hill_ratio_at_SP2) def ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih): """ Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), which, when melted into seawater having (SA,CT,p) causes the final dilute seawater to be at the freezing temperature. The other outputs are the Absolute Salinity and Conservative Temperature of the final diluted seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar t_Ih : array-like In-situ temperature of ice (ITS-90), degrees C Returns ------- SA_freeze : array-like, g/kg Absolute Salinity of seawater after the mass fraction of ice, ice_fraction, at temperature t_Ih has melted into the original seawater, and the final mixture is at the freezing temperature of seawater. CT_freeze : array-like, deg C Conservative Temperature of seawater after the mass fraction, w_Ih, of ice at temperature t_Ih has melted into the original seawater, and the final mixture is at the freezing temperature of seawater. w_Ih : array-like, unitless mass fraction of ice, having in-situ temperature t_Ih, which, when melted into seawater at (SA,CT,p) leads to the final diluted seawater being at the freezing temperature. This output must be between 0 and 1. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (9) of this manuscript. """ return _gsw_ufuncs.ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih) ice_fraction_to_freeze_seawater.types = _gsw_ufuncs.ice_fraction_to_freeze_seawater.types ice_fraction_to_freeze_seawater = match_args_return(ice_fraction_to_freeze_seawater) def infunnel(SA, CT, p): """ "oceanographic funnel" check for the 75-term equation Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- in_funnel : array-like, 0, if SA, CT and p are outside the "funnel" = 1, if SA, CT and p are inside the "funnel" Notes ----- gsw_infunnel "oceanographic funnel" check for the 75-term equation USAGE: in_funnel = gsw_infunnel(SA,CT,p) INPUT: SA = Absolute Salinity [ g kg^-1 ] CT = Conservative Temperature (ITS-90) [ deg C ] p = sea pressure [ dbar ] ( i.e. absolute pressure - 10.1325 dbar ) SA & CT need to have the same dimensions. p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN. OUTPUT: in_funnel = 0, if SA, CT and p are outside the "funnel" = 1, if SA, CT and p are inside the "funnel" Note. The term "funnel" (McDougall et al., 2003) describes the range of SA, CT and p over which the error in the fit of the computationally efficient 75-term expression for specific volume in terms of SA, CT and p was calculated (Roquet et al., 2015). AUTHOR: Trevor McDougall and Paul Barker [ help@teos-10.org ] VERSION NUMBER: 3.06.13 (23rd May, 2021) """ return _gsw_ufuncs.infunnel(SA, CT, p) infunnel.types = _gsw_ufuncs.infunnel.types infunnel = match_args_return(infunnel) def internal_energy(SA, CT, p): """ Calculates specific internal energy of seawater using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- internal_energy : array-like, J/kg specific internal energy Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.internal_energy(SA, CT, p) internal_energy.types = _gsw_ufuncs.internal_energy.types internal_energy = match_args_return(internal_energy) def internal_energy_ice(t, p): """ Calculates the specific internal energy of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- internal_energy_ice : array-like, J/kg specific internal energy (u) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.internal_energy_ice(t, p) internal_energy_ice.types = _gsw_ufuncs.internal_energy_ice.types internal_energy_ice = match_args_return(internal_energy_ice) def kappa(SA, CT, p): """ Calculates the isentropic compressibility of seawater. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- kappa : array-like, 1/Pa isentropic compressibility of seawater Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.17.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.kappa(SA, CT, p) kappa.types = _gsw_ufuncs.kappa.types kappa = match_args_return(kappa) def kappa_const_t_ice(t, p): """ Calculates isothermal compressibility of ice. Note. This is the compressibility of ice AT CONSTANT IN-SITU TEMPERATURE Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- kappa_const_t_ice : array-like, 1/Pa isothermal compressibility References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.kappa_const_t_ice(t, p) kappa_const_t_ice.types = _gsw_ufuncs.kappa_const_t_ice.types kappa_const_t_ice = match_args_return(kappa_const_t_ice) def kappa_ice(t, p): """ Calculates the isentropic compressibility of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- kappa_ice : array-like, 1/Pa isentropic compressibility References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.kappa_ice(t, p) kappa_ice.types = _gsw_ufuncs.kappa_ice.types kappa_ice = match_args_return(kappa_ice) def kappa_t_exact(SA, t, p): """ Calculates the isentropic compressibility of seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- kappa_t_exact : array-like, 1/Pa isentropic compressibility References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqns. (2.16.1) and the row for kappa in Table P.1 of appendix P of this TEOS-10 Manual. """ return _gsw_ufuncs.kappa_t_exact(SA, t, p) kappa_t_exact.types = _gsw_ufuncs.kappa_t_exact.types kappa_t_exact = match_args_return(kappa_t_exact) def latentheat_evap_CT(SA, CT): """ Calculates latent heat, or enthalpy, of evaporation at p = 0 (the surface). It is defined as a function of Absolute Salinity, SA, and Conservative Temperature, CT, and is valid in the ranges 0 < SA < 42 g/kg and 0 < CT < 40 deg C. The errors range between -0.4 and 0.6 J/kg. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- latentheat_evap : array-like, J/kg latent heat of evaporation References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.39 of this TEOS-10 Manual. """ return _gsw_ufuncs.latentheat_evap_ct(SA, CT) latentheat_evap_CT.types = _gsw_ufuncs.latentheat_evap_ct.types latentheat_evap_CT = match_args_return(latentheat_evap_CT) def latentheat_evap_t(SA, t): """ Calculates latent heat, or enthalpy, of evaporation at p = 0 (the surface). It is defined as a function of Absolute Salinity, SA, and in-situ temperature, t, and is valid in the ranges 0 < SA < 40 g/kg and 0 < CT < 42 deg C. The errors range between -0.4 and 0.6 J/kg. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C Returns ------- latentheat_evap : array-like, J/kg latent heat of evaporation References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.39 of this TEOS-10 Manual. """ return _gsw_ufuncs.latentheat_evap_t(SA, t) latentheat_evap_t.types = _gsw_ufuncs.latentheat_evap_t.types latentheat_evap_t = match_args_return(latentheat_evap_t) def latentheat_melting(SA, p): """ Calculates latent heat, or enthalpy, of melting. It is defined in terms of Absolute Salinity, SA, and sea pressure, p, and is valid in the ranges 0 < SA < 42 g kg^-1 and 0 < p < 10,000 dbar. This is based on the IAPWS Releases IAPWS-09 (for pure water), IAPWS-08 (for the saline compoonent of seawater and IAPWS-06 for ice Ih. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- latentheat_melting : array-like, J/kg latent heat of melting References ---------- IAPWS, 2008: Release on the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater. The International Association for the Properties of Water and Steam. Berlin, Germany, September 2008. This Release is known as IAPWS-09. IAPWS, 2009a: Revised Release on the Equation of State 2006 for H2O Ice Ih. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. This Release is known as IAPWS-06 IAPWS, 2009b: Supplementary Release on a Computationally Efficient Thermodynamic Formulation for Liquid Water for Oceanographic Use. The International Association for the Properties of Water and Steam. Doorwerth, The Netherlands, September 2009. This Release is known as IAPWS-09. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.34 of this TEOS-10 Manual. """ return _gsw_ufuncs.latentheat_melting(SA, p) latentheat_melting.types = _gsw_ufuncs.latentheat_melting.types latentheat_melting = match_args_return(latentheat_melting) def melting_ice_equilibrium_SA_CT_ratio(SA, p): """ Calculates the ratio of SA to CT changes when ice melts into seawater with both the seawater and the seaice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of ice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the ice temperature, and (3) the freezing temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- melting_ice_equilibrium_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when ice melts into seawater, with the seawater and seaice being close to the freezing temperature. Notes ----- The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (16) of this manuscript. """ return _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio(SA, p) melting_ice_equilibrium_SA_CT_ratio.types = _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio.types melting_ice_equilibrium_SA_CT_ratio = match_args_return(melting_ice_equilibrium_SA_CT_ratio) def melting_ice_equilibrium_SA_CT_ratio_poly(SA, p): """ Calculates the ratio of SA to CT changes when ice melts into seawater with both the seawater and the seaice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of ice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the ice temperature, and (3) the freezing temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- melting_ice_equilibrium_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when ice melts into seawater, with the seawater and seaice being close to the freezing temperature. Notes ----- The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (16) of this manuscript. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio_poly(SA, p) melting_ice_equilibrium_SA_CT_ratio_poly.types = _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio_poly.types melting_ice_equilibrium_SA_CT_ratio_poly = match_args_return(melting_ice_equilibrium_SA_CT_ratio_poly) def melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih): """ Calculates the final Absolute Salinity, final Conservative Temperature and final ice mass fraction that results when a given mass fraction of ice melts and is mixed into seawater whose properties are (SA,CT,p). This code takes the seawater to contain no dissolved air. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar w_Ih : array-like mass fraction of ice: the mass of ice divided by the sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless. t_Ih : array-like In-situ temperature of ice (ITS-90), degrees C Returns ------- SA_final : array-like, g/kg Absolute Salinity of the seawater in the final state, whether or not any ice is present. CT_final : array-like, deg C Conservative Temperature of the seawater in the final state, whether or not any ice is present. w_Ih_final : array-like, unitless mass fraction of ice in the final seawater-ice mixture. If this ice mass fraction is positive, the system is at thermodynamic equilibrium. If this ice mass fraction is zero there is no ice in the final state which consists only of seawater which is warmer than the freezing temperature. Notes ----- When the mass fraction w_Ih_final is calculated as being a positive value, the seawater-ice mixture is at thermodynamic equilibrium. This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, is sufficiently large (i.e. sufficiently "warm") so that there is no ice present in the final state. In this case the final state consists of only seawater rather than being an equilibrium mixture of seawater and ice which occurs when w_Ih_final is positive. Note that when w_Ih_final = 0, the final seawater is not at the freezing temperature. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of ice and sea ice into seawater, and frazil ice formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih) melting_ice_into_seawater.types = _gsw_ufuncs.melting_ice_into_seawater.types melting_ice_into_seawater = match_args_return(melting_ice_into_seawater) def melting_ice_SA_CT_ratio(SA, CT, p, t_Ih): """ Calculates the ratio of SA to CT changes when ice melts into seawater. It is assumed that a small mass of ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the ice will always melt. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar t_Ih : array-like In-situ temperature of ice (ITS-90), degrees C Returns ------- melting_ice_SA_CT_ratio : array-like, g kg^-1 K^-1 the ratio of SA to CT changes when ice melts into a large mass of seawater Notes ----- The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (13) of this manuscript. """ return _gsw_ufuncs.melting_ice_sa_ct_ratio(SA, CT, p, t_Ih) melting_ice_SA_CT_ratio.types = _gsw_ufuncs.melting_ice_sa_ct_ratio.types melting_ice_SA_CT_ratio = match_args_return(melting_ice_SA_CT_ratio) def melting_ice_SA_CT_ratio_poly(SA, CT, p, t_Ih): """ Calculates the ratio of SA to CT changes when ice melts into seawater. It is assumed that a small mass of ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the ice will always melt. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar t_Ih : array-like In-situ temperature of ice (ITS-90), degrees C Returns ------- melting_ice_SA_CT_ratio : array-like, g kg^-1 K^-1 the ratio of SA to CT changes when ice melts into a large mass of seawater Notes ----- The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (13) of this manuscript. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.melting_ice_sa_ct_ratio_poly(SA, CT, p, t_Ih) melting_ice_SA_CT_ratio_poly.types = _gsw_ufuncs.melting_ice_sa_ct_ratio_poly.types melting_ice_SA_CT_ratio_poly = match_args_return(melting_ice_SA_CT_ratio_poly) def melting_seaice_equilibrium_SA_CT_ratio(SA, p): """ Calculates the ratio of SA to CT changes when sea ice melts into seawater with both the seawater and the sea ice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of seaice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the sea ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the sea ice temperature, and (3) the freezing temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- melting_seaice_equilibrium_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when sea ice melts into seawater, with the seawater and sea ice being close to the freezing temperature. Notes ----- Note that the output of this function, dSA/dCT is independent of the sea ice salinity, SA_seaice. That is, the output applies equally to pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result is proven in McDougall et al. (2014). The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (29) of this manuscript. """ return _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio(SA, p) melting_seaice_equilibrium_SA_CT_ratio.types = _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio.types melting_seaice_equilibrium_SA_CT_ratio = match_args_return(melting_seaice_equilibrium_SA_CT_ratio) def melting_seaice_equilibrium_SA_CT_ratio_poly(SA, p): """ Calculates the ratio of SA to CT changes when sea ice melts into seawater with both the seawater and the sea ice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of seaice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the sea ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the sea ice temperature, and (3) the freezing temperature. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- melting_seaice_equilibrium_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when sea ice melts into seawater, with the seawater and sea ice being close to the freezing temperature. Notes ----- Note that the output of this function, dSA/dCT is independent of the sea ice salinity, SA_seaice. That is, the output applies equally to pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result is proven in McDougall et al. (2014). The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (29) of this manuscript. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio_poly(SA, p) melting_seaice_equilibrium_SA_CT_ratio_poly.types = _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio_poly.types melting_seaice_equilibrium_SA_CT_ratio_poly = match_args_return(melting_seaice_equilibrium_SA_CT_ratio_poly) def melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice): """ Calculates the Absolute Salinity and Conservative Temperature that results when a given mass of sea ice (or ice) melts and is mixed into a known mass of seawater (whose properties are (SA,CT,p)). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar w_seaice : array-like mass fraction of ice: the mass of sea-ice divided by the sum of the masses of sea-ice and seawater. 0 <= wIh <= 1. unitless. SA_seaice : array-like Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice. t_seaice : array-like In-situ temperature of the sea ice at pressure p (ITS-90), degrees C Returns ------- SA_final : array-like, g/kg Absolute Salinity of the mixture of the melted sea ice (or ice) and the original seawater CT_final : array-like, deg C Conservative Temperature of the mixture of the melted sea ice (or ice) and the original seawater Notes ----- If the ice contains no salt (e.g. if it is of glacial origin), then the input 'SA_seaice' should be set to zero. Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN's if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user. The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the sea ice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. Eqns. (8) and (9) are the simplifications when SA_seaice = 0. """ return _gsw_ufuncs.melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice) melting_seaice_into_seawater.types = _gsw_ufuncs.melting_seaice_into_seawater.types melting_seaice_into_seawater = match_args_return(melting_seaice_into_seawater) def melting_seaice_SA_CT_ratio(SA, CT, p, SA_seaice, t_seaice): """ Calculates the ratio of SA to CT changes when sea ice melts into seawater. It is assumed that a small mass of sea ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the sea ice will always melt. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar SA_seaice : array-like Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice. t_seaice : array-like In-situ temperature of the sea ice at pressure p (ITS-90), degrees C Returns ------- melting_seaice_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when sea ice melts into a large mass of seawater Notes ----- Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN's if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user. The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the seaice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA. The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (28) of this manuscript. """ return _gsw_ufuncs.melting_seaice_sa_ct_ratio(SA, CT, p, SA_seaice, t_seaice) melting_seaice_SA_CT_ratio.types = _gsw_ufuncs.melting_seaice_sa_ct_ratio.types melting_seaice_SA_CT_ratio = match_args_return(melting_seaice_SA_CT_ratio) def melting_seaice_SA_CT_ratio_poly(SA, CT, p, SA_seaice, t_seaice): """ Calculates the ratio of SA to CT changes when sea ice melts into seawater. It is assumed that a small mass of sea ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the sea ice will always melt. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar SA_seaice : array-like Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice. t_seaice : array-like In-situ temperature of the sea ice at pressure p (ITS-90), degrees C Returns ------- melting_seaice_SA_CT_ratio : array-like, g/(kg K) the ratio dSA/dCT of SA to CT changes when sea ice melts into a large mass of seawater Notes ----- Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN's if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user. The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the seaice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA. The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite. Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (31) of this manuscript. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.melting_seaice_sa_ct_ratio_poly(SA, CT, p, SA_seaice, t_seaice) melting_seaice_SA_CT_ratio_poly.types = _gsw_ufuncs.melting_seaice_sa_ct_ratio_poly.types melting_seaice_SA_CT_ratio_poly = match_args_return(melting_seaice_SA_CT_ratio_poly) def O2sol(SA, CT, p, lon, lat): """ Calculates the oxygen concentration expected at equilibrium with air at an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including saturated water vapor. This function uses the solubility coefficients derived from the data of Benson and Krause (1984), as fitted by Garcia and Gordon (1992, 1993). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- O2sol : array-like, umol/kg solubility of oxygen in micro-moles per kg Notes ----- Note that this algorithm has not been approved by IOC and is not work from SCOR/IAPSO Working Group 127. It is included in the GSW Oceanographic Toolbox as it seems to be oceanographic best practice. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ Benson, B.B., and D. Krause, 1984: The concentration and isotopic fractionation of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere. Limnology and Oceanography, 29, 620-632. Garcia, H.E., and L.I. Gordon, 1992: Oxygen solubility in seawater: Better fitting equations. Limnology and Oceanography, 37, 1307-1312. Garcia, H.E., and L.I. Gordon, 1993: Erratum: Oxygen solubility in seawater: better fitting equations. Limnology and Oceanography, 38, 656. """ return _gsw_ufuncs.o2sol(SA, CT, p, lon, lat) O2sol.types = _gsw_ufuncs.o2sol.types O2sol = match_args_return(O2sol) def O2sol_SP_pt(SP, pt): """ Calculates the oxygen concentration expected at equilibrium with air at an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including saturated water vapor. This function uses the solubility coefficients derived from the data of Benson and Krause (1984), as fitted by Garcia and Gordon (1992, 1993). Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless pt : array-like Potential temperature referenced to a sea pressure, degrees C Returns ------- O2sol : array-like, umol/kg solubility of oxygen in micro-moles per kg Notes ----- Note that this algorithm has not been approved by IOC and is not work from SCOR/IAPSO Working Group 127. It is included in the GSW Oceanographic Toolbox as it seems to be oceanographic best practice. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ Benson, B.B., and D. Krause, 1984: The concentration and isotopic fractionation of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere. Limnology and Oceanography, 29, 620-632. Garcia, H.E., and L.I. Gordon, 1992: Oxygen solubility in seawater: Better fitting equations. Limnology and Oceanography, 37, 1307-1312. Garcia, H.E., and L.I. Gordon, 1993: Erratum: Oxygen solubility in seawater: better fitting equations. Limnology and Oceanography, 38, 656. """ return _gsw_ufuncs.o2sol_sp_pt(SP, pt) O2sol_SP_pt.types = _gsw_ufuncs.o2sol_sp_pt.types O2sol_SP_pt = match_args_return(O2sol_SP_pt) def p_from_z(z, lat, geo_strf_dyn_height, sea_surface_geopotential): """ Calculates sea pressure from height using computationally-efficient 75-term expression for density, in terms of SA, CT and p (Roquet et al., 2015). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be computed with its p_ref = 0 (the surface). Also if provided, sea_surface_geopotental is the geopotential at zero sea pressure. This function solves Eqn.(3.32.3) of IOC et al. (2010) iteratively for p. Parameters ---------- z : array-like Depth, positive up, m lat : array-like Latitude, -90 to 90 degrees geo_strf_dyn_height : array-like dynamic height anomaly, m^2/s^2 Note that the reference pressure, p_ref, of geo_strf_dyn_height must be zero (0) dbar. sea_surface_geopotential : array-like geopotential at zero sea pressure, m^2/s^2 Returns ------- p : array-like, dbar sea pressure ( i.e. absolute pressure - 10.1325 dbar ) Notes ----- Note. Height (z) is NEGATIVE in the ocean. Depth is -z. Depth is not used in the GSW computer software library. Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. McDougall, T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, pp. 20-25. Moritz, H., 2000: Geodetic reference system 1980. J. Geodesy, 74, pp. 128-133. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43. Saunders, P.M., 1981: Practical conversion of pressure to depth. Journal of Physical Oceanography, 11, pp. 573-574. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.p_from_z(z, lat, geo_strf_dyn_height, sea_surface_geopotential) p_from_z.types = _gsw_ufuncs.p_from_z.types p_from_z = match_args_return(p_from_z) def pot_enthalpy_from_pt_ice(pt0_ice): """ Calculates the potential enthalpy of ice from potential temperature of ice (whose reference sea pressure is zero dbar). Parameters ---------- pt0_ice : array-like Potential temperature of ice (ITS-90), degrees C Returns ------- pot_enthalpy_ice : array-like, J/kg potential enthalpy of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.pot_enthalpy_from_pt_ice(pt0_ice) pot_enthalpy_from_pt_ice.types = _gsw_ufuncs.pot_enthalpy_from_pt_ice.types pot_enthalpy_from_pt_ice = match_args_return(pot_enthalpy_from_pt_ice) def pot_enthalpy_from_pt_ice_poly(pt0_ice): """ Calculates the potential enthalpy of ice from potential temperature of ice (whose reference sea pressure is zero dbar). This is a compuationally efficient polynomial fit to the potential enthalpy of ice. Parameters ---------- pt0_ice : array-like Potential temperature of ice (ITS-90), degrees C Returns ------- pot_enthalpy_ice : array-like, J/kg potential enthalpy of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.pot_enthalpy_from_pt_ice_poly(pt0_ice) pot_enthalpy_from_pt_ice_poly.types = _gsw_ufuncs.pot_enthalpy_from_pt_ice_poly.types pot_enthalpy_from_pt_ice_poly = match_args_return(pot_enthalpy_from_pt_ice_poly) def pot_enthalpy_ice_freezing(SA, p): """ Calculates the potential enthalpy of ice at which seawater freezes. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pot_enthalpy_ice_freezing : array-like, J/kg potential enthalpy of ice at freezing of seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.pot_enthalpy_ice_freezing(SA, p) pot_enthalpy_ice_freezing.types = _gsw_ufuncs.pot_enthalpy_ice_freezing.types pot_enthalpy_ice_freezing = match_args_return(pot_enthalpy_ice_freezing) def pot_enthalpy_ice_freezing_first_derivatives(SA, p): """ Calculates the first derivatives of the potential enthalpy of ice at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa). Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pot_enthalpy_ice_freezing_SA : array-like, K kg/g the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to Absolute salinity at fixed pressure [ K/(g/kg) ] i.e. pot_enthalpy_ice_freezing_P : array-like, K/Pa the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives(SA, p) pot_enthalpy_ice_freezing_first_derivatives.types = _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives.types pot_enthalpy_ice_freezing_first_derivatives = match_args_return(pot_enthalpy_ice_freezing_first_derivatives) def pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p): """ Calculates the first derivatives of the potential enthalpy of ice Ih at which ice melts into seawater with Absolute Salinity SA and at pressure p. This code uses the computationally efficient polynomial fit of the freezing potential enthalpy of ice Ih (McDougall et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pot_enthalpy_ice_freezing_SA : array-like, J/g the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to Absolute salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e. pot_enthalpy_ice_freezing_P : array-like, (J/kg)/Pa the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall et al. 2015: A reference for this polynomial. """ return _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p) pot_enthalpy_ice_freezing_first_derivatives_poly.types = _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives_poly.types pot_enthalpy_ice_freezing_first_derivatives_poly = match_args_return(pot_enthalpy_ice_freezing_first_derivatives_poly) def pot_enthalpy_ice_freezing_poly(SA, p): """ Calculates the potential enthalpy of ice at which seawater freezes. The error of this fit ranges between -2.5 and 1 J/kg with an rms of 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the error in the fit is between -0.7 and 0.7 with an rms of 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when compared with the potential enthalpy calculated from the exact in-situ freezing temperature which is found by a Newton-Raphson iteration of the equality of the chemical potentials of water in seawater and in ice. Note that the potential enthalpy at freezing can be found by this exact method using the function gsw_pot_enthalpy_ice_freezing. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pot_enthalpy_ice_freezing : array-like, J/kg potential enthalpy of ice at freezing of seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.pot_enthalpy_ice_freezing_poly(SA, p) pot_enthalpy_ice_freezing_poly.types = _gsw_ufuncs.pot_enthalpy_ice_freezing_poly.types pot_enthalpy_ice_freezing_poly = match_args_return(pot_enthalpy_ice_freezing_poly) def pot_rho_t_exact(SA, t, p, p_ref): """ Calculates potential density of seawater. Note. This function outputs potential density, not potential density anomaly; that is, 1000 kg/m^3 is not subtracted. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : array-like Reference pressure, dbar Returns ------- pot_rho_t_exact : array-like, kg/m^3 potential density (not potential density anomaly) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.4 of this TEOS-10 Manual. """ return _gsw_ufuncs.pot_rho_t_exact(SA, t, p, p_ref) pot_rho_t_exact.types = _gsw_ufuncs.pot_rho_t_exact.types pot_rho_t_exact = match_args_return(pot_rho_t_exact) def pressure_coefficient_ice(t, p): """ Calculates pressure coefficient of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pressure_coefficient_ice : array-like, Pa/K pressure coefficient of ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.15.1) of this TEOS-10 Manual. """ return _gsw_ufuncs.pressure_coefficient_ice(t, p) pressure_coefficient_ice.types = _gsw_ufuncs.pressure_coefficient_ice.types pressure_coefficient_ice = match_args_return(pressure_coefficient_ice) def pressure_freezing_CT(SA, CT, saturation_fraction): """ Calculates the pressure (in dbar) of seawater at the freezing temperature. That is, the output is the pressure at which seawater, with Absolute Salinity SA, Conservative Temperature CT, and with saturation_fraction of dissolved air, freezes. If the input values are such that there is no value of pressure in the range between 0 dbar and 10,000 dbar for which seawater is at the freezing temperature, the output, pressure_freezing, is put equal to NaN. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- pressure_freezing : array-like, dbar sea pressure at which the seawater freezes ( i.e. absolute pressure - 10.1325 dbar ) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pressure_freezing_ct(SA, CT, saturation_fraction) pressure_freezing_CT.types = _gsw_ufuncs.pressure_freezing_ct.types pressure_freezing_CT = match_args_return(pressure_freezing_CT) def pt0_from_t(SA, t, p): """ Calculates potential temperature with reference pressure, p_ref = 0 dbar. The present routine is computationally faster than the more general function "gsw_pt_from_t(SA,t,p,p_ref)" which can be used for any reference pressure value. This subroutine calls "gsw_entropy_part(SA,t,p)", "gsw_entropy_part_zerop(SA,pt0)" and "gsw_gibbs_pt0_pt0(SA,pt0)". Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pt0 : array-like, deg C potential temperature with reference sea pressure (p_ref) = 0 dbar. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.1 of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt0_from_t(SA, t, p) pt0_from_t.types = _gsw_ufuncs.pt0_from_t.types pt0_from_t = match_args_return(pt0_from_t) def pt0_from_t_ice(t, p): """ Calculates potential temperature of ice Ih with a reference pressure of 0 dbar, from in-situ temperature, t. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- pt0_ice : array-like, deg C potential temperature of ice Ih with reference pressure of zero dbar (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix I of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt0_from_t_ice(t, p) pt0_from_t_ice.types = _gsw_ufuncs.pt0_from_t_ice.types pt0_from_t_ice = match_args_return(pt0_from_t_ice) def pt_first_derivatives(SA, CT): """ Calculates the following two partial derivatives of potential temperature (the regular potential temperature whose reference sea pressure is 0 dbar) (1) pt_SA, the derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) pt_CT, the derivative with respect to Conservative Temperature at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- pt_SA : array-like, K/(g/kg) The derivative of potential temperature with respect to Absolute Salinity at constant Conservative Temperature. pt_CT : array-like, unitless The derivative of potential temperature with respect to Conservative Temperature at constant Absolute Salinity. pt_CT is dimensionless. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.12.6), (A.12.3), (P.6) and (P.8) of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.pt_first_derivatives(SA, CT) pt_first_derivatives.types = _gsw_ufuncs.pt_first_derivatives.types pt_first_derivatives = match_args_return(pt_first_derivatives) def pt_from_CT(SA, CT): """ Calculates potential temperature (with a reference sea pressure of zero dbar) from Conservative Temperature. This function uses 1.5 iterations through a modified Newton-Raphson (N-R) iterative solution procedure, starting from a rational-function-based initial condition for both pt and dCT_dpt. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- pt : array-like, deg C potential temperature referenced to a sea pressure of zero dbar (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See sections 3.1 and 3.3 of this TEOS-10 Manual. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt_from_ct(SA, CT) pt_from_CT.types = _gsw_ufuncs.pt_from_ct.types pt_from_CT = match_args_return(pt_from_CT) def pt_from_entropy(SA, entropy): """ Calculates potential temperature with reference pressure p_ref = 0 dbar and with entropy as an input variable. Parameters ---------- SA : array-like Absolute Salinity, g/kg entropy : array-like Specific entropy, J/(kg*K) Returns ------- pt : array-like, deg C potential temperature with reference sea pressure (p_ref) = 0 dbar. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.10 of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt_from_entropy(SA, entropy) pt_from_entropy.types = _gsw_ufuncs.pt_from_entropy.types pt_from_entropy = match_args_return(pt_from_entropy) def pt_from_pot_enthalpy_ice(pot_enthalpy_ice): """ Calculates the potential temperature of ice from the potential enthalpy of ice. The reference sea pressure of both the potential temperature and the potential enthalpy is zero dbar. Parameters ---------- pot_enthalpy_ice : array-like Potential enthalpy of ice, J/kg Returns ------- pt0_ice : array-like, deg C potential temperature of ice (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt_from_pot_enthalpy_ice(pot_enthalpy_ice) pt_from_pot_enthalpy_ice.types = _gsw_ufuncs.pt_from_pot_enthalpy_ice.types pt_from_pot_enthalpy_ice = match_args_return(pt_from_pot_enthalpy_ice) def pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice): """ Calculates the potential temperature of ice (whose reference sea pressure is zero dbar) from the potential enthalpy of ice. This is a compuationally efficient polynomial fit to the potential enthalpy of ice. Parameters ---------- pot_enthalpy_ice : array-like Potential enthalpy of ice, J/kg Returns ------- pt0_ice : array-like, deg C potential temperature of ice (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice) pt_from_pot_enthalpy_ice_poly.types = _gsw_ufuncs.pt_from_pot_enthalpy_ice_poly.types pt_from_pot_enthalpy_ice_poly = match_args_return(pt_from_pot_enthalpy_ice_poly) def pt_from_t(SA, t, p, p_ref): """ Calculates potential temperature with the general reference pressure, p_ref, from in-situ temperature, t. This function calls "gsw_entropy_part" which evaluates entropy except for the parts which are a function of Absolute Salinity alone. A faster gsw routine exists if p_ref is indeed zero dbar. This routine is "gsw_pt0_from_t(SA,t,p)". Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : array-like Reference pressure, dbar Returns ------- pt : array-like, deg C potential temperature with reference pressure, p_ref, on the ITS-90 temperature scale References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 3.1 of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt_from_t(SA, t, p, p_ref) pt_from_t.types = _gsw_ufuncs.pt_from_t.types pt_from_t = match_args_return(pt_from_t) def pt_from_t_ice(t, p, p_ref): """ Calculates potential temperature of ice Ih with the general reference pressure, p_ref, from in-situ temperature, t. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : array-like Reference pressure, dbar Returns ------- pt_ice : array-like, deg C potential temperature of ice Ih with reference pressure, p_ref, on the ITS-90 temperature scale Notes ----- A faster gsw routine exists if p_ref is indeed zero dbar. This routine is "gsw_pt0_from_t_ice(t,p)". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix I of this TEOS-10 Manual. McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.pt_from_t_ice(t, p, p_ref) pt_from_t_ice.types = _gsw_ufuncs.pt_from_t_ice.types pt_from_t_ice = match_args_return(pt_from_t_ice) def pt_second_derivatives(SA, CT): """ Calculates the following three second-order derivatives of potential temperature (the regular potential temperature which has a reference sea pressure of 0 dbar), (1) pt_SA_SA, the second derivative with respect to Absolute Salinity at constant Conservative Temperature, (2) pt_SA_CT, the derivative with respect to Conservative Temperature and Absolute Salinity, and (3) pt_CT_CT, the second derivative with respect to Conservative Temperature at constant Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- pt_SA_SA : array-like, K/((g/kg)^2) The second derivative of potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar) with respect to Absolute Salinity at constant Conservative Temperature. pt_SA_CT : array-like, 1/(g/kg) The derivative of potential temperature with respect to Absolute Salinity and Conservative Temperature. pt_CT_CT : array-like, 1/K The second derivative of potential temperature (the regular one with p_ref = 0 dbar) with respect to Conservative Temperature at constant SA. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See Eqns. (A.12.9) and (A.12.10) of this TEOS-10 Manual. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.pt_second_derivatives(SA, CT) pt_second_derivatives.types = _gsw_ufuncs.pt_second_derivatives.types pt_second_derivatives = match_args_return(pt_second_derivatives) def rho(SA, CT, p): """ Calculates in-situ density from Absolute Salinity and Conservative Temperature, using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho : array-like, kg/m^3 in-situ density Notes ----- Note that potential density with respect to reference pressure, pr, is obtained by calling this function with the pressure argument being pr (i.e. "gsw_rho(SA,CT,pr)"). Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.20 and appendix K of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43. """ return _gsw_ufuncs.rho(SA, CT, p) rho.types = _gsw_ufuncs.rho.types rho = match_args_return(rho) def rho_alpha_beta(SA, CT, p): """ Calculates in-situ density, the appropriate thermal expansion coefficient and the appropriate saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho : array-like, kg/m^3 in-situ density alpha : array-like, 1/K thermal expansion coefficient with respect to Conservative Temperature beta : array-like, kg/g saline (i.e. haline) contraction coefficient at constant Conservative Temperature Notes ----- Note that potential density (pot_rho) with respect to reference pressure p_ref is obtained by calling this function with the pressure argument being p_ref as in [pot_rho, ~, ~] = gsw_rho_alpha_beta(SA,CT,p_ref). Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.20 and appendix K of this TEOS-10 Manual. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.rho_alpha_beta(SA, CT, p) rho_alpha_beta.types = _gsw_ufuncs.rho_alpha_beta.types rho_alpha_beta = match_args_return(rho_alpha_beta) def rho_first_derivatives(SA, CT, p): """ Calculates the three (3) partial derivatives of in-situ density with respect to Absolute Salinity, Conservative Temperature and pressure. Note that the pressure derivative is done with respect to pressure in Pa, not dbar. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_SA : array-like, (kg/m^3)(g/kg)^-1 partial derivative of density with respect to Absolute Salinity rho_CT : array-like, kg/(m^3 K) partial derivative of density with respect to Conservative Temperature rho_P : array-like, kg/(m^3 Pa) partial derivative of density with respect to pressure in Pa Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.20 and appendix K of this TEOS-10 Manual. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.rho_first_derivatives(SA, CT, p) rho_first_derivatives.types = _gsw_ufuncs.rho_first_derivatives.types rho_first_derivatives = match_args_return(rho_first_derivatives) def rho_first_derivatives_wrt_enthalpy(SA, CT, p): """ Calculates the following two first-order derivatives of rho, (1) rho_SA_wrt_h, first-order derivative with respect to Absolute Salinity at constant h & p. (2) rho_h, first-order derivative with respect to h at constant SA & p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_SA_wrt_h : array-like, ((kg/m^3)(g/kg)^-1 The first derivative of rho with respect to Absolute Salinity at constant CT & p. rho_h : array-like, (m^3/kg)(J/kg)^-1 The first derivative of rho with respect to SA and CT at constant p. Notes ----- Note that this function uses the using the computationally-efficient 75 term expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2010). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.rho_first_derivatives_wrt_enthalpy(SA, CT, p) rho_first_derivatives_wrt_enthalpy.types = _gsw_ufuncs.rho_first_derivatives_wrt_enthalpy.types rho_first_derivatives_wrt_enthalpy = match_args_return(rho_first_derivatives_wrt_enthalpy) def rho_ice(t, p): """ Calculates in-situ density of ice from in-situ temperature and pressure. Note that the output, rho_ice, is density, not density anomaly; that is, 1000 kg/m^3 is not subtracted from it. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_ice : array-like, kg/m^3 in-situ density of ice (not density anomaly) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.rho_ice(t, p) rho_ice.types = _gsw_ufuncs.rho_ice.types rho_ice = match_args_return(rho_ice) def rho_second_derivatives(SA, CT, p): """ Calculates the following five second-order derivatives of rho, (1) rho_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) rho_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) rho_CT_CT, second-order derivative with respect to CT at constant SA & p. (4) rho_SA_P, second-order derivative with respect to SA & P at constant CT. (5) rho_CT_P, second-order derivative with respect to CT & P at constant SA. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_SA_SA : array-like, (kg/m^3)(g/kg)^-2 The second-order derivative of rho with respect to Absolute Salinity at constant CT & p. rho_SA_CT : array-like, (kg/m^3)(g/kg)^-1 K^-1 The second-order derivative of rho with respect to SA and CT at constant p. rho_CT_CT : array-like, (kg/m^3) K^-2 The second-order derivative of rho with respect to CT at constant SA & p rho_SA_P : array-like, (kg/m^3)(g/kg)^-1 Pa^-1 The second-order derivative with respect to SA & P at constant CT. rho_CT_P : array-like, (kg/m^3) K^-1 Pa^-1 The second-order derivative with respect to CT & P at constant SA. Notes ----- Note that this function uses the using the computationally-efficient expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_rho_second_derivatives_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.rho_second_derivatives(SA, CT, p) rho_second_derivatives.types = _gsw_ufuncs.rho_second_derivatives.types rho_second_derivatives = match_args_return(rho_second_derivatives) def rho_second_derivatives_wrt_enthalpy(SA, CT, p): """ Calculates the following three second-order derivatives of rho with respect to enthalpy, (1) rho_SA_SA, second-order derivative with respect to Absolute Salinity at constant h & p. (2) rho_SA_h, second-order derivative with respect to SA & h at constant p. (3) rho_h_h, second-order derivative with respect to h at constant SA & p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_SA_SA : array-like, (kg/m^3)(g/kg)^-2 The second-order derivative of rho with respect to Absolute Salinity at constant h & p. rho_SA_h : array-like, J/(kg K(g/kg)) The second-order derivative of rho with respect to SA and h at constant p. rho_h_h : array-like, The second-order derivative of rho with respect to h at constant SA & p Notes ----- Note that this function uses the using the computationally-efficient expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.rho_second_derivatives_wrt_enthalpy(SA, CT, p) rho_second_derivatives_wrt_enthalpy.types = _gsw_ufuncs.rho_second_derivatives_wrt_enthalpy.types rho_second_derivatives_wrt_enthalpy = match_args_return(rho_second_derivatives_wrt_enthalpy) def rho_t_exact(SA, t, p): """ Calculates in-situ density of seawater from Absolute Salinity and in-situ temperature. Note that the output, rho, is density, not density anomaly; that is, 1000 kg/m^3 is not subtracted from it. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- rho_t_exact : array-like, kg/m^3 in-situ density (not density anomaly) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.8 of this TEOS-10 Manual. """ return _gsw_ufuncs.rho_t_exact(SA, t, p) rho_t_exact.types = _gsw_ufuncs.rho_t_exact.types rho_t_exact = match_args_return(rho_t_exact) def SA_freezing_from_CT(CT, p, saturation_fraction): """ Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with Conservative Temperature CT, pressure p and the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at the same in situ temperature and pressure. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is made a NaN. Parameters ---------- CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- SA_freezing : array-like, g/kg Absolute Salinity of seawater when it freezes, for given input values of its Conservative Temperature, pressure and air saturation fraction. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.sa_freezing_from_ct(CT, p, saturation_fraction) SA_freezing_from_CT.types = _gsw_ufuncs.sa_freezing_from_ct.types SA_freezing_from_CT = match_args_return(SA_freezing_from_CT) def SA_freezing_from_CT_poly(CT, p, saturation_fraction): """ Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at Conservative Temperature CT and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is put equal to NaN. Parameters ---------- CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- SA_freezing : array-like, g/kg Absolute Salinity of seawater when it freezes, for given input values of Conservative Temperature pressure and air saturation fraction. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.sa_freezing_from_ct_poly(CT, p, saturation_fraction) SA_freezing_from_CT_poly.types = _gsw_ufuncs.sa_freezing_from_ct_poly.types SA_freezing_from_CT_poly = match_args_return(SA_freezing_from_CT_poly) def SA_freezing_from_t(t, p, saturation_fraction): """ Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at in-situ temperature t and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is set to NaN. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- SA_freezing : array-like, g/kg Absolute Salinity of seawater when it freezes, for given input values of in situ temperature, pressure and air saturation fraction. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall, T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.sa_freezing_from_t(t, p, saturation_fraction) SA_freezing_from_t.types = _gsw_ufuncs.sa_freezing_from_t.types SA_freezing_from_t = match_args_return(SA_freezing_from_t) def SA_freezing_from_t_poly(t, p, saturation_fraction): """ Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at in-situ temperature t and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is put equal to NaN. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- SA_freezing : array-like, g/kg Absolute Salinity of seawater when it freezes, for given input values of in situ temperature, pressure and air saturation fraction. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.sa_freezing_from_t_poly(t, p, saturation_fraction) SA_freezing_from_t_poly.types = _gsw_ufuncs.sa_freezing_from_t_poly.types SA_freezing_from_t_poly = match_args_return(SA_freezing_from_t_poly) def SA_from_rho(rho, CT, p): """ Calculates the Absolute Salinity of a seawater sample, for given values of its density, Conservative Temperature and sea pressure (in dbar). This function uses the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- rho : array-like Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3. CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- SA : array-like, g/kg Absolute Salinity. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.5 of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Millero, F.J., R. Feistel, D.G. Wright, and T.J. McDougall, 2008: The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale. Deep-Sea Res. I, 55, 50-72. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sa_from_rho(rho, CT, p) SA_from_rho.types = _gsw_ufuncs.sa_from_rho.types SA_from_rho = match_args_return(SA_from_rho) def SA_from_SP(SP, p, lon, lat): """ Calculates Absolute Salinity from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SA : array-like, g/kg Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sa_from_sp(SP, p, lon, lat) SA_from_SP.types = _gsw_ufuncs.sa_from_sp.types SA_from_SP = match_args_return(SA_from_SP) def SA_from_SP_Baltic(SP, lon, lat): """ Calculates Absolute Salinity in the Baltic Sea, from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero. Note. This programme will only produce Absolute Salinity values for the Baltic Sea. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SA_baltic : array-like, g kg^-1 Absolute Salinity in the Baltic Sea References ---------- Feistel, R., S. Weinreben, H. Wolf, S. Seitz, P. Spitzer, B. Adel, G. Nausch, B. Schneider and D. G. Wright, 2010: Density and Absolute Salinity of the Baltic Sea 2006-2009. Ocean Science, 6, 3-24. https://os.copernicus.org/articles/6/3/2010/os-6-3-2010.pdf IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sa_from_sp_baltic(SP, lon, lat) SA_from_SP_Baltic.types = _gsw_ufuncs.sa_from_sp_baltic.types SA_from_SP_Baltic = match_args_return(SA_from_SP_Baltic) def SA_from_Sstar(Sstar, p, lon, lat): """ Calculates Absolute Salinity from Preformed Salinity. Parameters ---------- Sstar : array-like Preformed Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SA : array-like, g/kg Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sa_from_sstar(Sstar, p, lon, lat) SA_from_Sstar.types = _gsw_ufuncs.sa_from_sstar.types SA_from_Sstar = match_args_return(SA_from_Sstar) def SAAR(p, lon, lat): """ Calculates the Absolute Salinity Anomaly Ratio, SAAR, in the open ocean by spatially interpolating the global reference data set of SAAR to the location of the seawater sample. Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SAAR : array-like, unitless Absolute Salinity Anomaly Ratio Notes ----- This function uses version 3.0 of the SAAR look up table (15th May 2011). The Absolute Salinity Anomaly Ratio in the Baltic Sea is evaluated separately, since it is a function of Practical Salinity, not of space. The present function returns a SAAR of zero for data in the Baltic Sea. The correct way of calculating Absolute Salinity in the Baltic Sea is by calling gsw_SA_from_SP. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf See also gsw_SA_from_SP, gsw_deltaSA_atlas Reference page in Help browser doc gsw_SAAR Note that this reference page includes the code contained in gsw_SAAR. We have opted to encode this programme as it is a global standard and such we cannot allow anyone to change it. """ return _gsw_ufuncs.saar(p, lon, lat) SAAR.types = _gsw_ufuncs.saar.types SAAR = match_args_return(SAAR) def seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice): """ Calculates the mass fraction of sea ice (mass of sea ice divided by mass of sea ice plus seawater), which, when melted into seawater having the properties (SA,CT,p) causes the final seawater to be at the freezing temperature. The other outputs are the Absolute Salinity and Conservative Temperature of the final seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar SA_seaice : array-like Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice. t_seaice : array-like In-situ temperature of the sea ice at pressure p (ITS-90), degrees C Returns ------- SA_freeze : array-like, g/kg Absolute Salinity of seawater after the mass fraction of sea ice, w_seaice, at temperature t_seaice has melted into the original seawater, and the final mixture is at the freezing temperature of seawater. CT_freeze : array-like, deg C Conservative Temperature of seawater after the mass fraction, w_seaice, of sea ice at temperature t_seaice has melted into the original seawater, and the final mixture is at the freezing temperature of seawater. w_seaice : array-like, unitless mass fraction of sea ice, at SA_seaice and t_seaice, which, when melted into seawater at (SA,CT,p) leads to the final mixed seawater being at the freezing temperature. This output is between 0 and 1. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall T.J. and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. See Eqn. (23) of this manuscript. """ return _gsw_ufuncs.seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice) seaice_fraction_to_freeze_seawater.types = _gsw_ufuncs.seaice_fraction_to_freeze_seawater.types seaice_fraction_to_freeze_seawater = match_args_return(seaice_fraction_to_freeze_seawater) def sigma0(SA, CT): """ Calculates potential density anomaly with reference pressure of 0 dbar, this being this particular potential density minus 1000 kg/m^3. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- sigma0 : array-like, kg/m^3 potential density anomaly with respect to a reference pressure of 0 dbar, that is, this potential density - 1000 kg/m^3. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sigma0(SA, CT) sigma0.types = _gsw_ufuncs.sigma0.types sigma0 = match_args_return(sigma0) def sigma1(SA, CT): """ Calculates potential density anomaly with reference pressure of 1000 dbar, this being this particular potential density minus 1000 kg/m^3. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- sigma1 : array-like, kg/m^3 potential density anomaly with respect to a reference pressure of 1000 dbar, that is, this potential density - 1000 kg/m^3. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sigma1(SA, CT) sigma1.types = _gsw_ufuncs.sigma1.types sigma1 = match_args_return(sigma1) def sigma2(SA, CT): """ Calculates potential density anomaly with reference pressure of 2000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- sigma2 : array-like, kg/m^3 potential density anomaly with respect to a reference pressure of 2000 dbar, that is, this potential density - 1000 kg/m^3. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sigma2(SA, CT) sigma2.types = _gsw_ufuncs.sigma2.types sigma2 = match_args_return(sigma2) def sigma3(SA, CT): """ Calculates potential density anomaly with reference pressure of 3000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- sigma3 : array-like, kg/m^3 potential density anomaly with respect to a reference pressure of 3000 dbar, that is, this potential density - 1000 kg/m^3. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sigma3(SA, CT) sigma3.types = _gsw_ufuncs.sigma3.types sigma3 = match_args_return(sigma3) def sigma4(SA, CT): """ Calculates potential density anomaly with reference pressure of 4000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- sigma4 : array-like, kg/m^3 potential density anomaly with respect to a reference pressure of 4000 dbar, that is, this potential density - 1000 kg/m^3. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (A.30.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sigma4(SA, CT) sigma4.types = _gsw_ufuncs.sigma4.types sigma4 = match_args_return(sigma4) def sound_speed(SA, CT, p): """ Calculates the speed of sound in seawater. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- sound_speed : array-like, m/s speed of sound in seawater Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.17.1) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.sound_speed(SA, CT, p) sound_speed.types = _gsw_ufuncs.sound_speed.types sound_speed = match_args_return(sound_speed) def sound_speed_ice(t, p): """ Calculates the compression speed of sound in ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- sound_speed_ice : array-like, m/s compression speed of sound in ice References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.sound_speed_ice(t, p) sound_speed_ice.types = _gsw_ufuncs.sound_speed_ice.types sound_speed_ice = match_args_return(sound_speed_ice) def sound_speed_t_exact(SA, t, p): """ Calculates the speed of sound in seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- sound_speed_t_exact : array-like, m/s speed of sound in seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (2.17.1) of this TEOS-10 Manual. """ return _gsw_ufuncs.sound_speed_t_exact(SA, t, p) sound_speed_t_exact.types = _gsw_ufuncs.sound_speed_t_exact.types sound_speed_t_exact = match_args_return(sound_speed_t_exact) def SP_from_C(C, t, p): """ Calculates Practical Salinity, SP, from conductivity, C, primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm produces a Practical Salinity that is less than 2 then the Practical Salinity is recalculated with a modified form of the Hill et al. (1986) formula. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2. Note that the input values of conductivity need to be in units of mS/cm (not S/m). Parameters ---------- C : array-like Conductivity, mS/cm t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- SP : array-like, unitless Practical Salinity on the PSS-78 scale References ---------- Culkin and Smith, 1980: Determination of the Concentration of Potassium Chloride Solution Having the Same Electrical Conductivity, at 15C and Infinite Frequency, as Standard Seawater of Salinity 35.0000 (Chlorinity 19.37394), IEEE J. Oceanic Eng, 5, 22-23. Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng., 11, 109 - 112. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix E of this TEOS-10 Manual. Unesco, 1983: Algorithms for computation of fundamental properties of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp. """ return _gsw_ufuncs.sp_from_c(C, t, p) SP_from_C.types = _gsw_ufuncs.sp_from_c.types SP_from_C = match_args_return(SP_from_C) def SP_from_SA(SA, p, lon, lat): """ Calculates Practical Salinity from Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SP : array-like, unitless Practical Salinity (PSS-78) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sp_from_sa(SA, p, lon, lat) SP_from_SA.types = _gsw_ufuncs.sp_from_sa.types SP_from_SA = match_args_return(SP_from_SA) def SP_from_SA_Baltic(SA, lon, lat): """ Calculates Practical Salinity for the Baltic Sea, from a value computed analytically from Absolute Salinity. Note. This programme will only produce Practical Salinty values for the Baltic Sea. Parameters ---------- SA : array-like Absolute Salinity, g/kg lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SP_baltic : array-like, unitless Practical Salinity References ---------- Feistel, R., S. Weinreben, H. Wolf, S. Seitz, P. Spitzer, B. Adel, G. Nausch, B. Schneider and D. G. Wright, 2010c: Density and Absolute Salinity of the Baltic Sea 2006-2009. Ocean Science, 6, 3-24. https://os.copernicus.org/articles/6/3/2010/os-6-3-2010.pdf IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sp_from_sa_baltic(SA, lon, lat) SP_from_SA_Baltic.types = _gsw_ufuncs.sp_from_sa_baltic.types SP_from_SA_Baltic = match_args_return(SP_from_SA_Baltic) def SP_from_SK(SK): """ Calculates Practical Salinity from Knudsen Salinity. Parameters ---------- SK : array-like Knudsen Salinity, ppt Returns ------- SP : array-like, unitless Practical Salinity (PSS-78) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Appendix A.3 of this TEOS-10 Manual. """ return _gsw_ufuncs.sp_from_sk(SK) SP_from_SK.types = _gsw_ufuncs.sp_from_sk.types SP_from_SK = match_args_return(SP_from_SK) def SP_from_SR(SR): """ Calculates Practical Salinity from Reference Salinity. Parameters ---------- SR : array-like Reference Salinity, g/kg Returns ------- SP : array-like, unitless Practical Salinity (PSS-78) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.sp_from_sr(SR) SP_from_SR.types = _gsw_ufuncs.sp_from_sr.types SP_from_SR = match_args_return(SP_from_SR) def SP_from_Sstar(Sstar, p, lon, lat): """ Calculates Practical Salinity from Preformed Salinity. Parameters ---------- Sstar : array-like Preformed Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- SP : array-like, unitless Practical Salinity (PSS-78) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sp_from_sstar(Sstar, p, lon, lat) SP_from_Sstar.types = _gsw_ufuncs.sp_from_sstar.types SP_from_Sstar = match_args_return(SP_from_Sstar) def SP_salinometer(Rt, t): """ Calculates Practical Salinity SP from a salinometer, primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm produces a Practical Salinity that is less than 2 then the Practical Salinity is recalculated with a modified form of the Hill et al. (1986) formula. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2. Parameters ---------- Rt : array-like C(SP,t_68,0)/C(SP=35,t_68,0), unitless t : array-like In-situ temperature (ITS-90), degrees C Returns ------- SP : array-like, unitless Practical Salinity on the PSS-78 scale t may have dimensions 1x1 or Mx1 or 1xN or MxN, where Rt is MxN. Notes ----- A laboratory salinometer has the ratio of conductivities, Rt, as an output, and the present function uses this conductivity ratio and the temperature t of the salinometer bath as the two input variables. References ---------- Fofonoff, P. and R.C. Millard Jr. 1983: Algorithms for computation of fundamental properties of seawater. Unesco Tech. Pap. in Mar. Sci., 44, 53 pp. Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng., 11, 109 - 112. IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix E of this TEOS-10 Manual, and in particular, Eqns. (E.2.1) and (E.2.6). """ return _gsw_ufuncs.sp_salinometer(Rt, t) SP_salinometer.types = _gsw_ufuncs.sp_salinometer.types SP_salinometer = match_args_return(SP_salinometer) def specvol(SA, CT, p): """ Calculates specific volume from Absolute Salinity, Conservative Temperature and pressure, using the computationally-efficient 75-term polynomial expression for specific volume (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- specvol : array-like, m^3/kg specific volume Notes ----- Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmos. Ocean. Tech., 20, 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol(SA, CT, p) specvol.types = _gsw_ufuncs.specvol.types specvol = match_args_return(specvol) def specvol_alpha_beta(SA, CT, p): """ Calculates specific volume, the appropriate thermal expansion coefficient and the appropriate saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- specvol : array-like, m/kg specific volume alpha : array-like, 1/K thermal expansion coefficient with respect to Conservative Temperature beta : array-like, kg/g saline (i.e. haline) contraction coefficient at constant Conservative Temperature Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix A.20 and appendix K of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.specvol_alpha_beta(SA, CT, p) specvol_alpha_beta.types = _gsw_ufuncs.specvol_alpha_beta.types specvol_alpha_beta = match_args_return(specvol_alpha_beta) def specvol_anom_standard(SA, CT, p): """ Calculates specific volume anomaly from Absolute Salinity, Conservative Temperature and pressure. It uses the computationally-efficient expression for specific volume as a function of SA, CT and p (Roquet et al., 2015). The reference value to which the anomaly is calculated has an Absolute Salinity of SSO and Conservative Temperature equal to 0 degrees C. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- specvol_anom : array-like, m^3/kg specific volume anomaly Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqn. (3.7.3) of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.specvol_anom_standard(SA, CT, p) specvol_anom_standard.types = _gsw_ufuncs.specvol_anom_standard.types specvol_anom_standard = match_args_return(specvol_anom_standard) def specvol_first_derivatives(SA, CT, p): """ Calculates the following three first-order derivatives of specific volume (v), (1) v_SA, first-order derivative with respect to Absolute Salinity at constant CT & p. (2) v_CT, first-order derivative with respect to CT at constant SA & p. (3) v_P, first-order derivative with respect to P at constant SA and CT. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- v_SA : array-like, (m^3/kg)(g/kg)^-1 The first derivative of specific volume with respect to Absolute Salinity at constant CT & p. v_CT : array-like, m^3/(K kg) The first derivative of specific volume with respect to CT at constant SA and p. v_P : array-like, m^3/(Pa kg) The first derivative of specific volume with respect to P at constant SA and CT. Notes ----- Note that this function uses the using the computationally-efficient 75-term expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_specvol_first_derivatives_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2010). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol_first_derivatives(SA, CT, p) specvol_first_derivatives.types = _gsw_ufuncs.specvol_first_derivatives.types specvol_first_derivatives = match_args_return(specvol_first_derivatives) def specvol_first_derivatives_wrt_enthalpy(SA, CT, p): """ Calculates the following two first-order derivatives of specific volume (v), (1) v_SA_wrt_h, first-order derivative with respect to Absolute Salinity at constant h & p. (2) v_h, first-order derivative with respect to h at constant SA & p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- v_SA_wrt_h : array-like, (m^3/kg)(g/kg)^-1 The first derivative of specific volume with respect to Absolute Salinity at constant CT & p. v_h : array-like, (m^3/kg)(J/kg)^-1 The first derivative of specific volume with respect to SA and CT at constant p. Notes ----- Note that this function uses the using the computationally-efficient 75 term expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2010). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol_first_derivatives_wrt_enthalpy(SA, CT, p) specvol_first_derivatives_wrt_enthalpy.types = _gsw_ufuncs.specvol_first_derivatives_wrt_enthalpy.types specvol_first_derivatives_wrt_enthalpy = match_args_return(specvol_first_derivatives_wrt_enthalpy) def specvol_ice(t, p): """ Calculates the specific volume of ice. Parameters ---------- t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- specvol_ice : array-like, m^3/kg specific volume References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol_ice(t, p) specvol_ice.types = _gsw_ufuncs.specvol_ice.types specvol_ice = match_args_return(specvol_ice) def specvol_second_derivatives(SA, CT, p): """ Calculates the following five second-order derivatives of specific volume (v), (1) v_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) v_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) v_CT_CT, second-order derivative with respect to CT at constant SA and p. (4) v_SA_P, second-order derivative with respect to SA & P at constant CT. (5) v_CT_P, second-order derivative with respect to CT & P at constant SA. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- v_SA_SA : array-like, (m^3/kg)(g/kg)^-2 The second derivative of specific volume with respect to Absolute Salinity at constant CT & p. v_SA_CT : array-like, (m^3/kg)(g/kg)^-1 K^-1 The second derivative of specific volume with respect to SA and CT at constant p. v_CT_CT : array-like, (m^3/kg) K^-2) The second derivative of specific volume with respect to CT at constant SA and p. v_SA_P : array-like, (m^3/kg)(g/kg)^-1 Pa^-1 The second derivative of specific volume with respect to SA and P at constant CT. v_CT_P : array-like, (m^3/kg) K^-1 Pa^-1 The second derivative of specific volume with respect to CT and P at constant SA. Notes ----- Note that this function uses the using the computationally-efficient 75-term expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_specvol_second_derivatives_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol_second_derivatives(SA, CT, p) specvol_second_derivatives.types = _gsw_ufuncs.specvol_second_derivatives.types specvol_second_derivatives = match_args_return(specvol_second_derivatives) def specvol_second_derivatives_wrt_enthalpy(SA, CT, p): """ Calculates the following three first-order derivatives of specific volume (v) with respect to enthalpy, (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute Salinity at constant h & p. (2) v_SA_h, second-order derivative with respect to SA & h at constant p. (3) v_h_h, second-order derivative with respect to h at constant SA & p. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- v_SA_SA_wrt_h : array-like, (m^3/kg)(g/kg)^-2 The second-order derivative of specific volume with respect to Absolute Salinity at constant h & p. v_SA_h : array-like, (m^3/kg)(g/kg)^-1 (J/kg)^-1 The second-order derivative of specific volume with respect to SA and h at constant p. v_h_h : array-like, (m^3/kg)(J/kg)^-2 The second-order derivative with respect to h at constant SA & p. Notes ----- Note that this function uses the using the computationally-efficient 75 term expression for specific volume (Roquet et al., 2015). There is an alternative to calling this function, namely gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p) which uses the full Gibbs function (IOC et al., 2010). This 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2010). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.specvol_second_derivatives_wrt_enthalpy(SA, CT, p) specvol_second_derivatives_wrt_enthalpy.types = _gsw_ufuncs.specvol_second_derivatives_wrt_enthalpy.types specvol_second_derivatives_wrt_enthalpy = match_args_return(specvol_second_derivatives_wrt_enthalpy) def specvol_SSO_0(p): """ specific volume at (SSO,CT=0,p) Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- double, array Notes ----- sw_specvol_SSO_0 specific volume at (SSO,CT=0,p) (75-term equation) This function calculates specific volume at the Standard Ocean Salinity, SSO, and at a Conservative Temperature of zero degrees C, as a function of pressure, p, in dbar, using a streamlined version of the 75-term CT version of specific volume, that is, a streamlined version of the code "gsw_specvol(SA,CT,p)". VERSION NUMBER: 3.06.12 (25th May, 2020) References ---------- Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.specvol_sso_0(p) specvol_SSO_0.types = _gsw_ufuncs.specvol_sso_0.types specvol_SSO_0 = match_args_return(specvol_SSO_0) def specvol_t_exact(SA, t, p): """ Calculates the specific volume of seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- specvol_t_exact : array-like, m^3/kg specific volume References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.7 of this TEOS-10 Manual. """ return _gsw_ufuncs.specvol_t_exact(SA, t, p) specvol_t_exact.types = _gsw_ufuncs.specvol_t_exact.types specvol_t_exact = match_args_return(specvol_t_exact) def spiciness0(SA, CT): """ Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 0 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- spiciness0 : array-like, kg/m^3 spiciness referenced to a pressure of 0 dbar, i.e. the surface Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. McDougall, T.J., and O.A. Krzysik, 2015: Spiciness. Journal of Marine Research, 73, 141-152. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.spiciness0(SA, CT) spiciness0.types = _gsw_ufuncs.spiciness0.types spiciness0 = match_args_return(spiciness0) def spiciness1(SA, CT): """ Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 1000 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- spiciness1 : array-like, kg/m^3 spiciness referenced to a pressure of 1000 dbar Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. McDougall, T.J., and O.A. Krzysik, 2015: Spiciness. Journal of Marine Research, 73, 141-152. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.spiciness1(SA, CT) spiciness1.types = _gsw_ufuncs.spiciness1.types spiciness1 = match_args_return(spiciness1) def spiciness2(SA, CT): """ Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 2000 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C Returns ------- spiciness2 : array-like, kg/m^3 spiciness referenced to a pressure of 2000 dbar Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. McDougall, T.J., and O.A. Krzysik, 2015: Spiciness. Journal of Marine Research, 73, 141-152. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.spiciness2(SA, CT) spiciness2.types = _gsw_ufuncs.spiciness2.types spiciness2 = match_args_return(spiciness2) def SR_from_SP(SP): """ Calculates Reference Salinity from Practical Salinity. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless Returns ------- SR : array-like, g/kg Reference Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.sr_from_sp(SP) SR_from_SP.types = _gsw_ufuncs.sr_from_sp.types SR_from_SP = match_args_return(SR_from_SP) def Sstar_from_SA(SA, p, lon, lat): """ Converts Preformed Salinity from Absolute Salinity. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- Sstar : array-like, g/kg Preformed Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sstar_from_sa(SA, p, lon, lat) Sstar_from_SA.types = _gsw_ufuncs.sstar_from_sa.types Sstar_from_SA = match_args_return(Sstar_from_SA) def Sstar_from_SP(SP, p, lon, lat): """ Calculates Preformed Salinity from Absolute Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero. Parameters ---------- SP : array-like Practical Salinity (PSS-78), unitless p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lon : array-like Longitude, -360 to 360 degrees lat : array-like Latitude, -90 to 90 degrees Returns ------- Sstar : array-like, g/kg Preformed Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual. McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity. Ocean Science, 8, 1123-1134. https://os.copernicus.org/articles/8/1123/2012/os-8-1123-2012.pdf """ return _gsw_ufuncs.sstar_from_sp(SP, p, lon, lat) Sstar_from_SP.types = _gsw_ufuncs.sstar_from_sp.types Sstar_from_SP = match_args_return(Sstar_from_SP) def t_deriv_chem_potential_water_t_exact(SA, t, p): """ Calculates the temperature derivative of the chemical potential of water in seawater so that it is valid at exactly SA = 0. Parameters ---------- SA : array-like Absolute Salinity, g/kg t : array-like In-situ temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- chem_potential_water_dt : array-like, J g^-1 K^-1 temperature derivative of the chemical potential of water in seawater References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ """ return _gsw_ufuncs.t_deriv_chem_potential_water_t_exact(SA, t, p) t_deriv_chem_potential_water_t_exact.types = _gsw_ufuncs.t_deriv_chem_potential_water_t_exact.types t_deriv_chem_potential_water_t_exact = match_args_return(t_deriv_chem_potential_water_t_exact) def t_freezing(SA, p, saturation_fraction): """ Calculates the in-situ temperature at which seawater freezes. The in-situ temperature freezing point is calculated from the exact in-situ freezing temperature which is found by a modified Newton-Raphson iteration (McDougall and Wotherspoon, 2013) of the equality of the chemical potentials of water in seawater and in ice. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- t_freezing : array-like, deg C in-situ temperature at which seawater freezes. (ITS-90) Notes ----- An alternative GSW function, gsw_t_freezing_poly, it is based on a computationally-efficient polynomial, and is accurate to within -5e-4 K and 6e-4 K, when compared with this function. References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton's method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25. """ return _gsw_ufuncs.t_freezing(SA, p, saturation_fraction) t_freezing.types = _gsw_ufuncs.t_freezing.types t_freezing = match_args_return(t_freezing) def t_freezing_first_derivatives(SA, p, saturation_fraction): """ Calculates the first derivatives of the in-situ temperature at which seawater freezes with respect to Absolute Salinity SA and pressure P (in Pa). These expressions come from differentiating the expression that defines the freezing temperature, namely the equality between the chemical potentials of water in seawater and in ice. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- tfreezing_SA : array-like, K kg/g the derivative of the in-situ freezing temperature (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e. tfreezing_P : array-like, K/Pa the derivative of the in-situ freezing temperature (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. """ return _gsw_ufuncs.t_freezing_first_derivatives(SA, p, saturation_fraction) t_freezing_first_derivatives.types = _gsw_ufuncs.t_freezing_first_derivatives.types t_freezing_first_derivatives = match_args_return(t_freezing_first_derivatives) def t_freezing_first_derivatives_poly(SA, p, saturation_fraction): """ Calculates the first derivatives of the in-situ temperature at which seawater freezes with respect to Absolute Salinity SA and pressure P (in Pa). These expressions come from differentiating the expression that defines the freezing temperature, namely the equality between the chemical potentials of water in seawater and in ice. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- tfreezing_SA : array-like, K kg/g the derivative of the in-situ freezing temperature (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e. tfreezing_P : array-like, K/Pa the derivative of the in-situ freezing temperature (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.t_freezing_first_derivatives_poly(SA, p, saturation_fraction) t_freezing_first_derivatives_poly.types = _gsw_ufuncs.t_freezing_first_derivatives_poly.types t_freezing_first_derivatives_poly = match_args_return(t_freezing_first_derivatives_poly) def t_freezing_poly(SA, p, saturation_fraction): """ Calculates the in-situ temperature at which seawater freezes from a comptationally efficient polynomial. Parameters ---------- SA : array-like Absolute Salinity, g/kg p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar saturation_fraction : array-like Saturation fraction of dissolved air in seawater. (0..1) Returns ------- t_freezing : array-like, deg C in-situ temperature at which seawater freezes. (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual. McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775. """ return _gsw_ufuncs.t_freezing_poly(SA, p, saturation_fraction) t_freezing_poly.types = _gsw_ufuncs.t_freezing_poly.types t_freezing_poly = match_args_return(t_freezing_poly) def t_from_CT(SA, CT, p): """ Calculates in-situ temperature from the Conservative Temperature of seawater. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- t : array-like, deg C in-situ temperature (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See sections 3.1 and 3.3 of this TEOS-10 Manual. """ return _gsw_ufuncs.t_from_ct(SA, CT, p) t_from_CT.types = _gsw_ufuncs.t_from_ct.types t_from_CT = match_args_return(t_from_CT) def t_from_pt0_ice(pt0_ice, p): """ Calculates in-situ temperature from the potential temperature of ice Ih with reference pressure, p_ref, of 0 dbar (the surface), and the in-situ pressure. Parameters ---------- pt0_ice : array-like Potential temperature of ice (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- t : array-like, deg C in-situ temperature (ITS-90) References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See appendix I of this TEOS-10 Manual. """ return _gsw_ufuncs.t_from_pt0_ice(pt0_ice, p) t_from_pt0_ice.types = _gsw_ufuncs.t_from_pt0_ice.types t_from_pt0_ice = match_args_return(t_from_pt0_ice) def thermobaric(SA, CT, p): """ Calculates the thermobaric coefficient of seawater with respect to Conservative Temperature. This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar Returns ------- thermobaric : array-like, 1/(K Pa) thermobaric coefficient with respect to Conservative Temperature. Notes ----- Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ See Eqns. (3.8.2) and (P.2) of this TEOS-10 manual. McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43. """ return _gsw_ufuncs.thermobaric(SA, CT, p) thermobaric.types = _gsw_ufuncs.thermobaric.types thermobaric = match_args_return(thermobaric) def z_from_p(p, lat, geo_strf_dyn_height, sea_surface_geopotential): """ Calculates height from sea pressure using the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be computed with its p_ref = 0 (the surface). Also if provided, sea_surface_geopotental is the geopotential at zero sea pressure. This function solves Eqn.(3.32.3) of IOC et al. (2010). Parameters ---------- p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar lat : array-like Latitude, -90 to 90 degrees geo_strf_dyn_height : array-like dynamic height anomaly, m^2/s^2 Note that the reference pressure, p_ref, of geo_strf_dyn_height must be zero (0) dbar. sea_surface_geopotential : array-like geopotential at zero sea pressure, m^2/s^2 Returns ------- z : array-like, m height Notes ----- Note. Height z is NEGATIVE in the ocean. i.e. Depth is -z. Depth is not used in the GSW computer software library. Note that this 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is available to be used if one wants to test if some of one's data lies outside this "funnel". References ---------- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/ McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741. Moritz, H., 2000: Geodetic reference system 1980. J. Geodesy, 74, pp. 128-133. Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90, pp. 29-43. This software is available from https://www.teos-10.org/ """ return _gsw_ufuncs.z_from_p(p, lat, geo_strf_dyn_height, sea_surface_geopotential) z_from_p.types = _gsw_ufuncs.z_from_p.types z_from_p = match_args_return(z_from_p) gsw-3.6.21/gsw/geostrophy.py0000644000175000017500000002676015147371315016164 0ustar alastairalastair""" Functions for calculating geostrophic currents. """ import numpy as np from . import _gsw_ufuncs from ._utilities import indexer, match_args_return from .conversions import z_from_p __all__ = ['geo_strf_dyn_height', 'geo_strf_steric_height', 'distance', 'f', 'geostrophic_velocity', ] @match_args_return def geo_strf_dyn_height(SA, CT, p, p_ref=0, axis=0, max_dp=1.0, interp_method='pchip'): """ Dynamic height anomaly as a function of pressure. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : float or array-like, optional Reference pressure, dbar axis : int, optional, default is 0 The index of the pressure dimension in SA and CT. max_dp : float If any pressure interval in the input p exceeds max_dp, the dynamic height will be calculated after interpolating to a grid with this spacing. interp_method : string {'mrst', 'pchip', 'linear'} Interpolation algorithm. Returns ------- dynamic_height : array This is the integral of specific volume anomaly with respect to pressure, from each pressure in p to the specified reference pressure. It is the geostrophic streamfunction in an isobaric surface, relative to the reference surface. """ interp_methods = {'mrst' : 3, 'pchip' : 2, 'linear' : 1} if interp_method not in interp_methods: raise ValueError(f'interp_method must be one of {interp_methods.keys()}') if SA.shape != CT.shape: raise ValueError(f'Shapes of SA and CT must match; found {SA.shape} and {CT.shape}') if p.ndim == 1 and SA.ndim > 1: if len(p) != SA.shape[axis]: raise ValueError( f'With 1-D p, len(p) must be SA.shape[axis];\n' f' found {len(p)} versus {SA.shape[axis]} on specified axis, {axis}' ) ind = [np.newaxis] * SA.ndim ind[axis] = slice(None) p = p[tuple(ind)] p_ref = float(p_ref) with np.errstate(invalid='ignore'): # The need for this context seems to be a bug in np.ma.any. if np.ma.any(np.ma.diff(np.ma.masked_invalid(p), axis=axis) <= 0): raise ValueError('p must be increasing along the specified axis') p = np.broadcast_to(p, SA.shape) goodmask = ~(np.isnan(SA) | np.isnan(CT) | np.isnan(p)) dh = np.empty(SA.shape, dtype=float) dh.fill(np.nan) try: order = 'F' if SA.flags.fortran else 'C' except AttributeError: order = 'C' # e.g., xarray DataArray doesn't have flags for ind in indexer(SA.shape, axis, order=order): # this is needed to support xarray inputs for numpy < 1.23 igood = np.asarray(goodmask[ind]) # If p_ref is below the deepest value, skip the profile. pgood = p[ind][igood] if len(pgood) > 1 and pgood[-1] >= p_ref: sa = SA[ind][igood] ct = CT[ind][igood] # Temporarily add a top (typically surface) point and mixed layer # if p_ref is above the shallowest pressure. if pgood[0] > p_ref: ptop = np.arange(p_ref, pgood[0], max_dp) ntop = len(ptop) sa = np.hstack(([sa[0]]*ntop, sa)) ct = np.hstack(([ct[0]]*ntop, ct)) pgood = np.hstack((ptop, pgood)) else: ntop = 0 dh_all = _gsw_ufuncs.geo_strf_dyn_height_1( sa, ct, pgood, p_ref, max_dp, interp_methods[interp_method]) if ntop > 0: dh[ind][igood] = dh_all[ntop:] else: dh[ind][igood] = dh_all return dh @match_args_return def geo_strf_steric_height(SA, CT, p, p_ref=0, axis=0, max_dp=1.0, interp_method="pchip"): """ Steric height anomaly as a function of pressure. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_ref : float or array-like, optional Reference pressure, dbar axis : int, optional, default is 0 The index of the pressure dimension in SA and CT. max_dp : float If any pressure interval in the input p exceeds max_dp, the dynamic height will be calculated after interpolating to a grid with this spacing. interp_method : string {'mrst', 'pchip', 'linear'} Interpolation algorithm. Returns ------- steric_height : array This is the integral of specific volume anomaly with respect to pressure, from each pressure in p to the specified reference pressure, divided by the global mean surface value of gravitational acceleration, 9.7963 m s^-2. (see page 46 of Griffies, 2004) It is not exactly the height of an isobaric surface above a geopotential surface, but is an exact geostrophic streamfunction. References ---------- Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton, NJ: Princeton University Press, 518 pp + xxxiv. """ return ( geo_strf_dyn_height(SA, CT, p, p_ref, axis=axis, max_dp=max_dp, interp_method=interp_method) / 9.7963 ) def unwrap(lon, centered=True, copy=True): """ Unwrap a sequence of longitudes or headings in degrees. Optionally center it as close to zero as possible By default, return a copy; if *copy* is False, avoid a copy when possible. Returns a masked array only if the input is a masked array. """ # From pycurrents.data.ocean. It could probably be simplified # for use here. masked_input = np.ma.isMaskedArray(lon) if masked_input: fill_value = lon.fill_value # masked_invalid loses the original fill_value (ma bug, 2011/01/20) lon = np.ma.masked_invalid(lon).astype(float) if lon.ndim != 1: raise ValueError("Only 1-D sequences are supported") if lon.shape[0] < 2: return lon x = lon.compressed() if len(x) < 2: return lon w = np.zeros(x.shape[0]-1, int) ld = np.diff(x) np.putmask(w, ld > 180, -1) np.putmask(w, ld < -180, 1) x[1:] += (w.cumsum() * 360.0) if centered: x -= 360 * np.round(x.mean() / 360.0) if lon.mask is np.ma.nomask: lon[:] = x else: lon[~lon.mask] = x if masked_input: lon.fill_value = fill_value return lon else: return lon.filled(np.nan) @match_args_return def distance(lon, lat, p=0, axis=-1): """ Great-circle distance in m between lon, lat points. Parameters ---------- lon, lat : array-like, 1-D or 2-D (shapes must match) Longitude, latitude, in degrees. p : array-like, scalar, 1-D or 2-D, optional, default is 0 Sea pressure (absolute pressure minus 10.1325 dbar), dbar axis : int, -1, 0, 1, optional The axis or dimension along which *lat and lon* vary. This differs from most functions, for which axis is the dimension along which p increases. Returns ------- distance : 1-D or 2-D array distance in meters between adjacent points. """ earth_radius = 6371e3 if not lon.shape == lat.shape: raise ValueError(f'lon, lat shapes must match; found {lon.shape}, {lat.shape}') if not (lon.ndim in (1, 2) and lon.shape[axis] > 1): raise ValueError('lon, lat must be 1-D or 2-D with more than one point' f' along axis; found shape {lon.shape} and axis {axis}') if lon.ndim == 1: one_d = True # xarray requires expand_dims() rather than [newaxis, :] lon = np.expand_dims(lon, 0) lat = np.expand_dims(lat, 0) axis = -1 else: one_d = False # Handle scalar default; match_args_return doesn't see it. p = np.atleast_1d(p) one_d = (one_d and p.ndim == 1) if axis == 0: indm = (slice(0, -1), slice(None)) indp = (slice(1, None), slice(None)) else: indm = (slice(None), slice(0, -1)) indp = (slice(None), slice(1, None)) if np.all(p == 0): z = 0 else: lon, lat, p = np.broadcast_arrays(lon, lat, p) p_mid = 0.5 * (p[indm] + p[indp]) lat_mid = 0.5 * (lat[indm] + lat[indp]) z = z_from_p(p_mid, lat_mid) lon = np.radians(lon) lat = np.radians(lat) dlon = np.diff(lon, axis=axis) dlat = np.diff(lat, axis=axis) a = ((np.sin(dlat / 2)) ** 2 + np.cos(lat[indm]) * np.cos(lat[indp]) * (np.sin(dlon / 2)) ** 2) angles = 2 * np.arctan2(np.sqrt(a), np.sqrt(1 - a)) distance = (earth_radius + z) * angles if one_d: distance = distance[0] return distance @match_args_return def f(lat): """ Coriolis parameter in 1/s for latitude in degrees. """ omega = 7.292115e-5 # (1/s) (Groten, 2004). f = 2 * omega * np.sin(np.radians(lat)) return f @match_args_return def geostrophic_velocity(geo_strf, lon, lat, p=0, axis=0): """ Calculate geostrophic velocity from a streamfunction. Calculates geostrophic velocity relative to a reference pressure, given a geostrophic streamfunction and the position of each station in sequence along an ocean section. The data can be from a single isobaric or "density" surface, or from a series of such surfaces. Parameters ---------- geo_strf : array-like, 1-D or 2-D geostrophic streamfunction; see Notes below. lon : array-like, 1-D Longitude, -360 to 360 degrees lat : array-like, 1-D Latitude, degrees p : float or array-like, optional Sea pressure (absolute pressure minus 10.1325 dbar), dbar. This used only for a tiny correction in the distance calculation; it is safe to omit it. axis : int, 0 or 1, optional The axis or dimension along which pressure increases in geo_strf. If geo_strf is 1-D, it is ignored. Returns ------- velocity : array, 2-D or 1-D Geostrophic velocity in m/s relative to the sea surface, averaged between each successive pair of positions. mid_lon, mid_lat : array, 1-D Midpoints of input lon and lat. Notes ----- The geostrophic streamfunction can be: - geo_strf_dyn_height (in an isobaric surface) - geo_strf_Montgomery (in a specific volume anomaly surface) - geo_strf_Cunninhgam (in an approximately neutral surface such as a potential density surface). - geo_strf_isopycnal (in an approximately neutral surface such as a potential density surface, a Neutral Density surface, or an omega surface (Klocker et al., 2009)). Only :func:`geo_strf_dyn_height` is presently implemented in GSW-Python. """ lon = unwrap(lon) if lon.shape != lat.shape or lon.ndim != 1: raise ValueError(f'lon, lat must be 1-D and matching; found shapes {lon.shape} and {lat.shape}') if geo_strf.ndim not in (1, 2): raise ValueError(f'geo_strf must be 1-D or 2-d; found shape {geo_strf.shape}') laxis = 0 if axis else -1 ds = distance(lon, lat, p) mid_lon = 0.5 * (lon[:-1] + lon[1:]) mid_lat = 0.5 * (lat[:-1] + lat[1:]) u = np.diff(geo_strf, axis=laxis) / (ds * f(mid_lat)) return u, mid_lon, mid_lat gsw-3.6.21/gsw/tests/0000755000175000017500000000000015147371330014533 5ustar alastairalastairgsw-3.6.21/gsw/tests/check_functions.py0000644000175000017500000002576315147371315020272 0ustar alastairalastair""" Module with functions and script to generate tests directly from our local version of gsw_check_functions.m. Usage (run from this test directory): python check_functions.py A primary use for this script is to see which functions are missing from GSW-Python; they appear in the NameError category. TypeError category can include functions that are incomplete or otherwise not working correctly. For functions that run but yield results that fail the check, the error arrays are printed. This can be improved--we should get less information from the matlab script and more from our own functions. We probably should not need the matlab script at all, or maybe use it only to extract the list of functions being tested in matlab. This module is also imported by test_check_functions.py, which is run by py.test. """ import os import re import sys import numpy as np from gsw import * # noqa from gsw._utilities import Bunch # If we switch to using the logging module, uncomment: # import logging # log = logging.getLogger() # logging.basicConfig() # The following re patterns are for the "alternative" parsing of # the test line to support using numpy assert_allclose. This is # not presently in use, but aspects of this method, here and in # _WIP_test_ufuncs.py, might replace some of the original code here. # # pattern for a single test line after it has been pre-processed to # remove spaces, the square brackets, and semicolon testlinepat = r"(\w+\.\w+)=find\(\w*\((\w+\.\w+)-(\w+\.\w+)\)>=(\w+\.\w+)\)" # # pattern for the inner test when there is a sequence separated by '|' testpat = r"\(+\w*\((\w+\.\w+)-(\w+\.\w+)\)+>=(\w+\.\w+)\)" def find(x): """ Numpy equivalent to Matlab find. """ return np.nonzero(np.asarray(x).flatten())[0] def group_or(line): """ Translate matlab 'find' functions including logical or operators. Example: the test for gsw_rho_alpha_beta Numpy wart: using bitwise or as a fake elementwise logical or, we need to add parentheses. """ if not ('find(' in line and '|' in line): return line i0 = line.index('find(') + 5 head = line[:i0] tail = line[i0:] parts = tail.replace('|', ') | (') new = head + '(' + parts + ')' return new class FunctionCheck: """ Parse the line-pair for checks in gsw_check_functions. """ def __init__(self, linepair): """ *linepair* is the sequence of two lines; the first runs the function and assigns the output, and the second generates an array of indices where the output error exceeds a tolerance. """ self.linepair = linepair self.runline = linepair[0] self.testline = linepair[1] # parse the line that runs the function head, tail = self.runline.split('=') self.outstrings = [s.strip() for s in head.split(',')] self.outstr = ','.join(self.outstrings) funcstr, argpart = tail.split('(', 1) self.name = funcstr.strip() self.argstrings = [s.strip() for s in argpart[:-1].split(',')] self.argstr = ','.join(self.argstrings) # parse the line that checks the results head, tail = self.testline.split('=', 1) self.resultstr = head.strip() # cv.I* head, tail = tail.split('(', 1) self.teststr = tail.strip()[:-1] # argument of "find()" self.teststr = self.teststr.replace('abs(', 'np.abs(') # alternative parsing of testline testline = self.testline.replace(' ', '') if '|' in testline: diffstr, test_str = testline.split('=', 1) # Chop off the leading 'find('. tests = test_str[5:].split('|') self.test_varstrings = [diffstr] for test in tests: m = re.match(testpat, test) if m is None: print(self.name, testpat, test, m) if m is not None: self.test_varstrings.extend(list(m.groups())) else: m = re.match(testlinepat, testline) if m is not None: self.test_varstrings = m.groups() else: print("no match") self.test_varstrings = None # To be set when run() is successful self.outlist = None self.result = None # will be a reference to the cv.I* array self.passed = None # will be set to True or False # To be set if run() is not successful self.exception = None def __str__(self): return self.runline def record_details(self, evalargs): tline = self.testline i0 = 5 + tline.index('find(') tline = tline[i0:-1] checks = tline.split('|') parts = [] for check in checks: check = check.replace(' ', '') if check.startswith('('): check = check[1:-1] part = Bunch(check=check) LHS, RHS = check.split('>=') part.tolerance = eval(RHS, *evalargs) # Sometimes there is an extra set of (). if LHS.startswith('('): LHS = LHS[1:-1] LHS = LHS[4:-1] # chop off abs(...) target, calculated = LHS.split('-') part.checkval = eval(target, *evalargs) part.val = eval(calculated, *evalargs) parts.append(part) self.details = parts def run(self, locals_=None): try: if locals_ is not None: _globals = globals() #dict(**globals()) _globals.update(locals_) evalargs = (_globals,) else: evalargs = () # The following is needed for melting_ice_into_seawater. if len(self.outstrings) > 1: rl_ind = f"[:{len(self.outstrings)}]" else: rl_ind = "" exec(self.runline + rl_ind, *evalargs) if len(self.outstrings) == 1: if isinstance(eval(self.outstr, *evalargs), tuple): exec(f"{self.outstr} = {self.outstr}[0]", *evalargs) self.outlist = [eval(s, *evalargs) for s in self.outstrings] exec(self.testline, *evalargs) self.result = eval(self.resultstr, *evalargs) self.passed = (len(self.result) == 0) # The following has trouble with CT_first_derivatives if self.name not in ['CT_first_derivatives',]: self.record_details(evalargs) # print("%s passed? %s" % (self.name, self.passed)) except Exception as e: self.exception = e def find_arguments(checks): """ For a sequence of FunctionCheck instances, return the set of unique arguments as a sorted list. """ argset = set() for c in checks: argset.update(c.argstrings) argsetlist = list(argset) argsetlist.sort() return argsetlist def find_arglists(checks): """ For a sequence of FunctionCheck instances, return the set of unique argument lists as a sorted list. """ alset = set() for c in checks: alset.update([c.argstr]) arglists = list(alset) arglists.sort() return arglists def parse_check_functions(mfile): """ Return a list of FunctionCheck instances from gsw_check_functions.m """ with open(mfile) as fid: mfilelines = fid.readlines() first_pass = [] concat = False for line in mfilelines: line = line.strip() if concat: if line.endswith('...'): line = line[:-3] first_pass[-1] += line if line.endswith(';'): concat = False continue if '=' in line and (line.startswith('gsw_') or line.startswith('[gsw_')): if line.endswith('...'): line = line[:-3] concat = True first_pass.append(line) second_pass = [] for line in first_pass: if not '(' in line: continue if 'which' in line: continue line = line.replace('gsw_', '') if line.startswith('['): line = line[1:].replace(']', '') if line.endswith(';'): line = line[:-1] line = line.replace('(I)', '') # For deltaSA_atlas. second_pass.append(line) pairs = [] for i in range(len(second_pass)): if 'find(' in second_pass[i] and not 'find(' in second_pass[i-1]: pairs.extend(second_pass[i-1:i+1]) final = [group_or(line) for line in pairs] checks = [] for i in range(0, len(final), 2): pair = final[i:i+2] checks.append(FunctionCheck(pair)) return checks if __name__ == '__main__': import argparse parser = argparse.ArgumentParser( description='Run checks from gsw_check_functions.m') parser.add_argument('--path', dest='mfiledir', default="", help='path to external gsw_check_functions.m') parser.add_argument('-v', '--verbose', action='store_true', help='print output mismatch arrays') parser.add_argument('--find', help='run functions with this substring') args = parser.parse_args() if args.mfiledir: mfile = os.path.join(args.mfiledir, "gsw_check_functions.m") else: mfile = "gsw_check_functions_save.m" checks = parse_check_functions(mfile) #datadir = os.path.join(os.path.dirname(gsw.utilities.__file__), 'data') datadir = './' cv = Bunch(np.load(os.path.join(datadir, 'gsw_cv_v3_0.npz'))) cf = Bunch() if args.find: checks = [c for c in checks if args.find in c.runline] for fc in checks: fc.run() passes = [f for f in checks if f.passed] failures = [f for f in checks if f.passed is False] run_problems = [f for f in checks if f.exception is not None] etypes = [NameError, UnboundLocalError, TypeError, AttributeError] ex_dict = {} for exc in etypes: elist = [(f.name, f.exception) for f in checks if isinstance(f.exception, exc)] ex_dict[exc] = elist print(f"\n{len(checks)} tests were translated from gsw_check_functions.m") print(f"\n{len(passes)} tests ran with no error and with correct output") if args.verbose: for f in passes: print(f.name) print(f"\n{len(failures)} tests had an output mismatch:") for f in failures: print(f.name) print(f.runline) print(f.testline) if args.verbose: print(f.result) for part in f.details: print("tolerance: ", part.tolerance) print("error:") print(part.checkval - part.val) print('') print('') print(f"\n{len(run_problems)} exceptions were raised as follows:") for exc in etypes: print(" ", exc.__name__) strings = [" {} : {}".format(*e) for e in ex_dict[exc]] print("\n".join(strings)) print("") checkbunch = Bunch([(c.name, c) for c in checks]) gsw-3.6.21/gsw/tests/test_xarray.py0000644000175000017500000001231215147371315017454 0ustar alastairalastair""" Tests functions with xarray inputs. This version is a copy of the original test_check_functions but with an import of xarray, and conversion of the 3 main check cast arrays into DataArray objects. An additional xarray-dask test is added. """ import os import numpy as np import pandas as pd import pytest from check_functions import parse_check_functions from numpy.testing import assert_allclose import gsw from gsw._utilities import Bunch xr = pytest.importorskip('xarray') # Most of the tests have some nan values, so we need to suppress the warning. # Any more careful fix would likely require considerable effort. np.seterr(invalid='ignore') root_path = os.path.abspath(os.path.dirname(__file__)) # Function checks that we can't handle automatically yet. blacklist = ['deltaSA_atlas', # the test is complicated; doesn't fit the pattern. 'geostrophic_velocity', # test elsewhere; we changed the API #'CT_from_entropy', # needs prior entropy_from_CT; don't have it in C #'CT_first_derivatives', # passes, but has trouble in "details"; # see check_functions.py #'entropy_second_derivatives', # OK now; handling extra parens. #'melting_ice_into_seawater', # OK now; fixed nargs mismatch. ] # We get an overflow from ct_from_enthalpy_exact, but the test passes. cv = Bunch(np.load(os.path.join(root_path, 'gsw_cv_v3_0.npz'))) # Substitute new check values for the pchip interpolation version. cv.geo_strf_dyn_height = np.load(os.path.join(root_path,'geo_strf_dyn_height.npy')) cv.geo_strf_steric_height = np.load(os.path.join(root_path,'geo_strf_steric_height.npy')) cv.geo_strf_velocity = np.load(os.path.join(root_path,'geo_strf_velocity.npy')) for name in ['SA_chck_cast', 't_chck_cast', 'p_chck_cast']: cv[name] = xr.DataArray(cv[name]) cf = Bunch() d = dir(gsw) funcnames = [name for name in d if '__' not in name] mfuncs = parse_check_functions(os.path.join(root_path, 'gsw_check_functions_save.m')) mfuncs = [mf for mf in mfuncs if mf.name in d and mf.name not in blacklist] mfuncnames = [mf.name for mf in mfuncs] @pytest.fixture(scope='session', params=mfuncs) def cfcf(request): return cv, cf, request.param def test_check_function(cfcf): cv, cf, mfunc = cfcf mfunc.run(locals()) if mfunc.exception is not None or not mfunc.passed: print('\n', mfunc.name) print(' ', mfunc.runline) print(' ', mfunc.testline) if mfunc.exception is None: mfunc.exception = ValueError('Calculated values are different from the expected matlab results.') raise mfunc.exception else: print(mfunc.name) assert mfunc.passed def test_dask_chunking(): dsa = pytest.importorskip('dask.array') # define some input data shape = (100, 1000) chunks = (100, 200) sp = xr.DataArray(dsa.full(shape, 35., chunks=chunks), dims=['time', 'depth']) p = xr.DataArray(np.arange(shape[1]), dims=['depth']) lon = 0 lat = 45 sa = gsw.SA_from_SP(sp, p, lon, lat) sa_dask = sa.compute() sa_numpy = gsw.SA_from_SP(np.full(shape, 35.0), p.values, lon, lat) assert_allclose(sa_dask, sa_numpy) # Additional tests from Graeme MacGilchrist # https://nbviewer.jupyter.org/github/gmacgilchrist/wmt_bgc/blob/master/notebooks/test_gsw-xarray.ipynb # Define dimensions and coordinates dims = ['y','z','t'] # 2x2x2 y = np.arange(0,2) z = np.arange(0,2) t = np.arange(0,2) # Define numpy arrays of salinity, temperature and pressure SA_vals = np.array([[[34.7,34.8],[34.9,35]],[[35.1,35.2],[35.3,35.4]]]) CT_vals = np.array([[[7,8],[9,10]],[[11,12],[13,14]]]) p_vals = np.array([10,20]) lat_vals = np.array([0,10]) # Plug in to xarray objects SA = xr.DataArray(SA_vals,dims=dims,coords={'y':y,'z':z,'t':t}) CT = xr.DataArray(CT_vals,dims=dims,coords={'y':y,'z':z,'t':t}) p = xr.DataArray(p_vals,dims=['z'],coords={'z':z}) lat = xr.DataArray(lat_vals,dims=['y'],coords={'y':y}) def test_xarray_with_coords(): pytest.importorskip('dask') SA_chunk = SA.chunk(chunks={'y':1,'t':1}) CT_chunk = CT.chunk(chunks={'y':1,'t':1}) lat_chunk = lat.chunk(chunks={'y':1}) # Dimensions and coordinates match: expected = gsw.sigma0(SA_vals, CT_vals) xarray = gsw.sigma0(SA, CT) chunked = gsw.sigma0(SA_chunk, CT_chunk) assert_allclose(xarray, expected) assert_allclose(chunked, expected) # Broadcasting along dimension required (dimensions known) expected = gsw.alpha(SA_vals, CT_vals, p_vals[np.newaxis, :, np.newaxis]) xarray = gsw.alpha(SA, CT, p) chunked = gsw.alpha(SA_chunk, CT_chunk, p) assert_allclose(xarray, expected) assert_allclose(chunked, expected) # Broadcasting along dimension required (dimensions unknown/exclusive) expected = gsw.z_from_p(p_vals[:, np.newaxis], lat_vals[np.newaxis, :]) xarray = gsw.z_from_p(p, lat) chunked = gsw.z_from_p(p,lat_chunk) assert_allclose(xarray, expected) assert_allclose(chunked, expected) def test_pandas_20(): df = pd.DataFrame( { "pressure": [0, 10, 20], "latitude": [70, 70, 70], } ) depth = -1 * gsw.z_from_p(df["pressure"], df["latitude"]) assert isinstance(depth, pd.core.series.Series)gsw-3.6.21/gsw/tests/gsw_cv_v3_0.npz0000644000175000017500000234557615147371315017434 0ustar alastairalastairPK!] SA_Arctic.npyNUMPYv{'descr': '@YƑp?@ٵ{@@BQ@@63Sp@@:tV@@EH@@v) @@㭟;HA@iA@?yA@^3}A@DE;&A@A=tA@hA@uA@R0DA@b@5$A@H&A@1A@NCA@YωA@ɨA@k\6A@XCA@kߖ5A@qމA@.f^A@,A@آ9A@Q+9A@˜5A@YW<@S"&<@n.<@)t>@,IJ?@^MH@@=@7@@fإS@@Emj@@̠3@@K:|Ϙ@@m@@t/2A@-dA@NrtA@qܼ9d}A@L?KA@!vA@X6)HkA@#XKvA@vqDHA@P A@c A@ A@!:̈A@@A@~JA@K7A@H%A@dmg#A@뭏A@A@E$A@ިBA@ CA@݌;?A@aΩR=@n=@ɲ=@(=@*e>@!D@@^yT@@9a\9@@W,&O#@@Ḧ́A@GW[??9m4?zG?Pkw?OjM?镲?&S?2U0*&†W¿HPsʿ -пo_ӿhoؿJ4ڿ rhٿ qhؿ%䃞ֿŏ1w-տV/ӿh|?5ҿQIпŏ1w%CaTR'J4I +6[?߾5^I St$uV37mV}bϿ=U?( 0?q???ffffff?$(~k?m?<,Ԛ?ea?eaBi%䃞ʿy&1пJ4ҿ:MԿHؿQٿ%䃞ٿ8gDioؿׁsFֿv/տZӼӿ-C6ҿQIпPK!VLXX p_Arctic.npyXXNUMPYv{'descr': '=r@Ldo@2V~ @ܓF"@*U, @Ag?c5@n_-@m?hU@dSvt(@?WE?)L"@B!h#@ʚ"@nh#!?8`J@@ @)hsl @ f?\?]. ?fJE@4TD@Wuw-@{pu @<^@l@^@t<;?x@zֶ\?upz @5/U@ZXh5@?-?"pt"@9>L@x@@nq#1o@;i@t @ W@YMn@kf@Z @2@/Q@fI@,J; 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Ѩ[CT_T_wrt_t_ca.npyPK!&CT_P_wrt_t_ca.npyPK!JJGh_SA_wrt_t_ca.npyPK!1 h_T_wrt_t_ca.npyPK!^fRh_P_wrt_t_ca.npyPK!}.Pcp_t_exact_ca.npyPK!{!isochoric_heat_cap_t_exact_ca.npyPK!&chem_potential_relative_t_exact_ca.npyPK!PK#chem_potential_water_t_exact_ca.npyPK!+"chem_potential_salt_t_exact_ca.npyPK!$=+t_deriv_chem_potential_water_t_exact_ca.npyPK!>P=#tdilution_coefficient_t_exact_ca.npyPK!̅QGibbs_energy_t_exact_ca.npyPK!|&Helmholtz_energy_t_exact_ca.npyPK!.㘈"osmotic_coefficient_t_exact_ca.npyPK!c|osmotic_pressure_t_exact_ca.npyPK!Ȉ Fdelta_ca.npyPK!%{deltaSA_atlas_ca.npyPK!p~XXIgsw_data_file.npyPK! ujmat_zip_ver.npyPK66gsw-3.6.21/gsw/tests/gsw_check_functions_save.m0000644000175000017500000034310515147371315021765 0ustar alastairalastairif isempty(which('gsw_gibbs.html')) fprintf(2,'You need to add the GSW "html" subdirectory to your path. \n'); end if isempty(which('gsw_gibbs.m')) fprintf(2,'You need to add the GSW "library" subdirectory to your path. \n'); end if isempty(which('gibbs.pdf')) fprintf(2,'You need to add the GSW "pdf" subdirectory to your path. \n'); end if isempty(which('gsw_rho_t_exact.m')) fprintf(2,'You need to add the GSW "thermodynamics_from_t" subdirectory to your path. \n'); end if isempty(which('gsw_gibbs.html')) | isempty(which('gsw_gibbs.m')) | ... isempty(which('gibbs.pdf')) | isempty(which('gsw_rho_t_exact.m')) error('You have not added the GSW subdirectories to you MATLAB Path') end try gsw_installation_dir = which ('gsw_gibbs.html'); builddocsearchdb ([gsw_installation_dir(1:end-14)]) clear gsw_installation_dir end gsw_data = 'gsw_data_v3_0.mat'; gsw_data_file = which(gsw_data); load (gsw_data_file,'gsw_cv'); gsw_ver fprintf(1,' \n'); fprintf(1,'If you have any questions regarding this software email help@TEOS-10.org\n'); fprintf(1,' \n'); fprintf(1,'This function is running three stored vertical profiles through\n'); fprintf(1,'all the functions in the GSW Oceanographic Toolbox, and then checks\n'); fprintf(1,'that the outputs are all within pre-defined limits of the correct\n'); fprintf(1,'answers. These pre-defined limits are a factor of approximately\n'); fprintf(1,'a hundred larger than the errors expected from numerical round-off.\n'); fprintf(1,' \n'); fprintf(1,' checking '); gsw_cf.gsw_chks = 1; %% Practical Salinity (SP):- PSS-78 gsw_cf.C = gsw_C_from_SP(gsw_cv.SP_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.IC_from_SP] = find(abs(gsw_cv.C_from_SP - gsw_cf.C) >= gsw_cv.C_from_SP_ca); if ~isempty(gsw_cf.IC_from_SP) fprintf(2,'gsw_C_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_C = gsw_SP_from_C(gsw_cf.C,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ISP_from_C] = find(abs(gsw_cv.SP_from_C - gsw_cf.SP_from_C) >= gsw_cv.SP_from_C_ca); if ~isempty(gsw_cf.ISP_from_C) fprintf(2,'gsw_SP_from_C: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.R = gsw_R_from_SP(gsw_cv.SP_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.IR_from_SP] = find(abs(gsw_cv.R_from_SP - gsw_cf.R) >= gsw_cv.R_from_SP_ca); if ~isempty(gsw_cf.IR_from_SP) fprintf(2,'gsw_R_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_R = gsw_SP_from_R(gsw_cf.R,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ISP_from_R] = find(abs(gsw_cv.SP_from_R - gsw_cf.SP_from_R) >= gsw_cv.SP_from_R_ca); if ~isempty(gsw_cf.ISP_from_R) fprintf(2,'gsw_SP_from_R: Failed\n'); gsw_chks = 0; end gsw_cf.SP_salinometer = gsw_SP_salinometer(gsw_cv.Rt_chck_cast,gsw_cv.t_chck_cast); [gsw_cf.ISP_salinometer] = find(abs(gsw_cv.SP_salinometer - gsw_cf.SP_salinometer) >= gsw_cv.SP_salinometer_ca); if ~isempty(gsw_cf.ISP_salinometer) fprintf(2,'gsw_SP_salinometer: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_SK = gsw_SP_from_SK(gsw_cv.SK_chck_cast); [gsw_cf.ISP_from_SK] = find(abs(gsw_cv.SP_from_SK - gsw_cf.SP_from_SK) >= gsw_cv.SP_from_SK_ca); if ~isempty(gsw_cf.ISP_from_SK) fprintf(2,'gsw_SP_from_SK: Failed\n'); gsw_cf.gsw_chks = 0; end %% Absolute Salinity (SA), Preformed Salinity (Sstar) and Conservative Temperature (CT) gsw_cf.SA_from_SP = gsw_SA_from_SP(gsw_cv.SP_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISA_from_SP] = find(abs(gsw_cv.SA_from_SP - gsw_cf.SA_from_SP) >= gsw_cv.SA_from_SP_ca); if ~isempty(gsw_cf.ISA_from_SP) fprintf(2,'gsw_SA_from_SP: Failed. Note that this will cause many other programmes in the GSW toolbox to fail.\n'); gsw_cf.gsw_chks = 0; end gsw_cf.Sstar_from_SP = gsw_Sstar_from_SP(gsw_cv.SP_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISstar_from_SP] = find(abs(gsw_cv.Sstar_from_SP - gsw_cf.Sstar_from_SP) >= gsw_cv.Sstar_from_SP_ca); if ~isempty(gsw_cf.ISstar_from_SP) fprintf(2,'gsw_Sstar_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_chck_cast = gsw_CT_from_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_from_t] = find(abs(gsw_cv.CT_from_t - gsw_cf.CT_chck_cast) >= gsw_cv.CT_from_t_ca); if ~isempty(gsw_cf.ICT_from_t) fprintf(2,'gsw_CT_from_t: Failed. Note that this will cause many other programmes in the GSW toolbox to fail.\n'); gsw_cf.gsw_chks = 0; end %% other conversions between temperatures, salinities, pressure and height gsw_cf.deltaSA_from_SP = gsw_deltaSA_from_SP(gsw_cv.SP_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IdeltaSA_from_SP] = find(abs(gsw_cv.deltaSA_from_SP - gsw_cf.deltaSA_from_SP) >= gsw_cv.deltaSA_from_SP_ca); if ~isempty(gsw_cf.IdeltaSA_from_SP) fprintf(2,'gsw_deltaSA_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.SA_SA_Sstar_from_SP, gsw_cf.Sstar_SA_Sstar_from_SP] = gsw_SA_Sstar_from_SP(gsw_cv.SP_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISA_Sstar_from_SP] = find(abs(gsw_cv.SA_SA_Sstar_from_SP - gsw_cf.SA_SA_Sstar_from_SP) >= gsw_cv.SA_SA_Sstar_from_SP_ca | ... abs(gsw_cv.Sstar_SA_Sstar_from_SP - gsw_cf.Sstar_SA_Sstar_from_SP) >= gsw_cv.Sstar_SA_Sstar_from_SP_ca); if ~isempty(gsw_cf.ISA_Sstar_from_SP) fprintf(2,'gsw_SA_Sstar_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SR_from_SP = gsw_SR_from_SP(gsw_cv.SP_chck_cast); [gsw_cf.ISR_from_SP] = find(abs(gsw_cv.SR_from_SP - gsw_cf.SR_from_SP) >= gsw_cv.SR_from_SP_ca); if ~isempty(gsw_cf.ISR_from_SP) fprintf(2,'gsw_SR_from_SP: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_SR = gsw_SP_from_SR(gsw_cv.SR_from_SP); [gsw_cf.ISP_from_SR] = find(abs(gsw_cv.SP_from_SR - gsw_cf.SP_from_SR) >= gsw_cv.SP_from_SR_ca); if ~isempty(gsw_cf.ISP_from_SR) fprintf(2,'gsw_SP_from_SR: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_SA = gsw_SP_from_SA(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISP_from_SA] = find(abs(gsw_cv.SP_chck_cast - gsw_cf.SP_from_SA) >= gsw_cv.SP_from_SA_ca); if ~isempty(gsw_cf.ISP_from_SA) fprintf(2,'gsw_SP_from_SA: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.Sstar_from_SA = gsw_Sstar_from_SA(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISstar_from_SA] = find(abs(gsw_cv.Sstar_from_SA - gsw_cf.Sstar_from_SA) >= gsw_cv.Sstar_from_SA_ca); if ~isempty(gsw_cf.ISstar_from_SA) fprintf(2,'gsw_Sstar_from_SA: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SA_from_Sstar = gsw_SA_from_Sstar(gsw_cv.Sstar_from_SA,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISA_from_Sstar] = find(abs(gsw_cv.SA_from_Sstar - gsw_cf.SA_from_Sstar) >= gsw_cv.SA_from_Sstar_ca); if ~isempty(gsw_cf.ISA_from_Sstar) fprintf(2,'gsw_SA_from_Sstar: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SP_from_Sstar = gsw_SP_from_Sstar(gsw_cv.Sstar_from_SA,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.ISP_from_Sstar] = find(abs(gsw_cv.SP_from_Sstar - gsw_cf.SP_from_Sstar) >= gsw_cv.SP_from_Sstar_ca); if ~isempty(gsw_cf.ISP_from_Sstar) fprintf(2,'gsw_SP_from_Sstar: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.t_from_CT = gsw_t_from_CT(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.It_from_CT] = find(abs(gsw_cv.t_chck_cast - gsw_cf.t_from_CT) >= gsw_cv.t_from_CT_ca); if ~isempty(gsw_cf.It_from_CT) fprintf(2,'gsw_t_from_CT: Failed.\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pt = gsw_pt_from_CT(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ipt_from_CT] = find(abs(gsw_cv.pt_from_CT - gsw_cf.pt) >= gsw_cv.pt_from_CT_ca); if ~isempty(gsw_cf.Ipt_from_CT) fprintf(2,'gsw_pt_from_CT: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_pt = gsw_CT_from_pt(gsw_cv.SA_chck_cast,gsw_cf.pt); [gsw_cf.ICT_from_pt] = find(abs(gsw_cv.CT_from_pt - gsw_cf.CT_from_pt) >= gsw_cv.CT_from_pt_ca); if ~isempty(gsw_cf.ICT_from_pt) fprintf(2,'gsw_CT_from_pt: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pot_enthalpy_from_pt = gsw_pot_enthalpy_from_pt(gsw_cv.SA_chck_cast,gsw_cf.pt); [gsw_cf.Ipot_enthalpy] = find(abs(gsw_cv.pot_enthalpy_from_pt - gsw_cf.pot_enthalpy_from_pt) >= gsw_cv.pot_enthalpy_from_pt_ca); if ~isempty(gsw_cf.Ipot_enthalpy) fprintf(2,'gsw_pot_enthalpy_from_pt: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pt0_from_t = gsw_pt0_from_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ipt0] = find(abs(gsw_cv.pt0_from_t - gsw_cf.pt0_from_t) >= gsw_cv.pt0_from_t_ca); if ~isempty(gsw_cf.Ipt0) fprintf(2,'gsw_pt0_from_t: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pt_from_t = gsw_pt_from_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Ipt_from_t] = find(abs(gsw_cv.pt_from_t - gsw_cf.pt_from_t) >= gsw_cv.pt_from_t_ca); if ~isempty(gsw_cf.Ipt_from_t) fprintf(2,'gsw_pt_from_t: Failed\n'); gsw_cf.gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end gsw_cf.t90_from_t48 = gsw_t90_from_t48(gsw_cv.t_chck_cast); [gsw_cf.It90_from_t48] = find(abs(gsw_cv.t90_from_t48 - gsw_cf.t90_from_t48) >= gsw_cv.t90_from_t48_ca); if ~isempty(gsw_cf.It90_from_t48) fprintf(2,'gsw_t90_from_t48: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.t90_from_t68 = gsw_t90_from_t68(gsw_cv.t_chck_cast); [gsw_cf.It90_from_t68] = find(abs(gsw_cv.t90_from_t68 - gsw_cf.t90_from_t68) >= gsw_cv.t90_from_t68_ca); if ~isempty(gsw_cf.It90_from_t68) fprintf(2,'gsw_t90_from_t68: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.z_from_p = gsw_z_from_p(gsw_cv.p_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.Iz_from_p] = find(abs(gsw_cv.z_from_p - gsw_cf.z_from_p) >= gsw_cv.z_from_p_ca); if ~isempty(gsw_cf.Iz_from_p) fprintf(2,'gsw_z_from_p: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.p_from_z = gsw_p_from_z(gsw_cf.z_from_p,gsw_cv.lat_chck_cast); [gsw_cf.Ip_from_z] = find(abs(gsw_cv.p_from_z - gsw_cf.p_from_z) >= gsw_cv.p_from_z_ca); if ~isempty(gsw_cf.Ip_from_z) fprintf(2,'gsw_p_from_z: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.depth_from_z = gsw_depth_from_z(gsw_cf.z_from_p); [gsw_cf.Idepth_from_z] = find(abs(gsw_cv.depth_from_z - gsw_cf.depth_from_z) >= gsw_cv.depth_from_z_ca); if ~isempty(gsw_cf.Idepth_from_z) fprintf(2,'gsw_depth_from_z: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.z_from_depth = gsw_z_from_depth(gsw_cf.depth_from_z); [gsw_cf.Iz_from_depth] = find(abs(gsw_cv.z_from_depth - gsw_cf.z_from_depth) >= gsw_cv.z_from_depth_ca); if ~isempty(gsw_cf.Iz_from_depth) fprintf(2,'gsw_z_from_depth: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.Abs_Pressure_from_p = gsw_Abs_Pressure_from_p(gsw_cv.p_chck_cast); [gsw_cf.IAbs_Pressure_from_p] = find(abs(gsw_cv.Abs_Pressure_from_p - gsw_cf.Abs_Pressure_from_p) >= gsw_cv.Abs_Pressure_from_p_ca); if ~isempty(gsw_cf.IAbs_Pressure_from_p) fprintf(2,'gsw_Abs_Pressure_from_p: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.p_from_Abs_Pressure = gsw_p_from_Abs_Pressure(gsw_cf.Abs_Pressure_from_p); [gsw_cf.Ip_from_Abs_Pressure] = find(abs(gsw_cv.p_from_Abs_Pressure - gsw_cf.p_from_Abs_Pressure) >= gsw_cv.p_from_Abs_Pressure_ca); if ~isempty(gsw_cf.Ip_from_Abs_Pressure) fprintf(2,'gsw_p_from_Abs_Pressure: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.entropy_from_CT = gsw_entropy_from_CT(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ientropy_from_CT] = find(abs(gsw_cv.entropy_from_CT - gsw_cf.entropy_from_CT) >= gsw_cv.entropy_from_CT_ca); if ~isempty(gsw_cf.Ientropy_from_CT) fprintf(2,'gsw_entropy_from_CT: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_entropy = gsw_CT_from_entropy(gsw_cv.SA_chck_cast,gsw_cf.entropy_from_CT); [gsw_cf.ICT_from_entropy] = find(abs(gsw_cv.CT_from_entropy - gsw_cf.CT_from_entropy) >= gsw_cv.CT_from_entropy_ca); if ~isempty(gsw_cf.ICT_from_entropy) fprintf(2,'gsw_CT_from_entropy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.entropy_from_pt = gsw_entropy_from_pt(gsw_cv.SA_chck_cast,gsw_cf.pt_from_t); [gsw_cf.Ientropy_from_pt] = find(abs(gsw_cv.entropy_from_pt - gsw_cf.entropy_from_pt) >= gsw_cv.entropy_from_pt_ca); if ~isempty(gsw_cf.Ientropy_from_pt) fprintf(2,'gsw_entropy_from_pt: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pt_from_entropy = gsw_pt_from_entropy(gsw_cv.SA_chck_cast,gsw_cf.entropy_from_pt); [gsw_cf.Ipt_from_entropy] = find(abs(gsw_cv.pt_from_entropy - gsw_cf.pt_from_entropy) >= gsw_cv.pt_from_entropy_ca); if ~isempty(gsw_cf.Ipt_from_entropy) fprintf(2,'gsw_pt_from_entropy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.entropy_from_t = gsw_entropy_from_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ientropy_from_t] = find(abs(gsw_cv.entropy_from_t - gsw_cf.entropy_from_t) >= gsw_cv.entropy_from_t_ca); if ~isempty(gsw_cf.Ientropy_from_t) fprintf(2,'gsw_entropy_from_t: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.t_from_entropy = gsw_t_from_entropy(gsw_cv.SA_chck_cast,gsw_cf.entropy_from_t,gsw_cv.p_chck_cast); [gsw_cf.It_from_entropy] = find(abs(gsw_cv.t_from_entropy - gsw_cf.t_from_entropy) >= gsw_cv.t_from_entropy_ca); if ~isempty(gsw_cf.It_from_entropy) fprintf(2,'gsw_t_from_entropy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.adiabatic_lapse_rate_from_CT = gsw_adiabatic_lapse_rate_from_CT(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iadiabatic_lapse_rate_from_CT] = find(abs(gsw_cv.adiabatic_lapse_rate_from_CT - gsw_cf.adiabatic_lapse_rate_from_CT) >= gsw_cv.adiabatic_lapse_rate_from_CT_ca); if ~isempty(gsw_cf.Iadiabatic_lapse_rate_from_CT) fprintf(2,'gsw_adiabatic_lapse_rate_from_CT: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.adiabatic_lapse_rate_from_t = gsw_adiabatic_lapse_rate_from_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iadiabatic_lapse_rate_from_t] = find(abs(gsw_cv.adiabatic_lapse_rate_from_t - gsw_cf.adiabatic_lapse_rate_from_t) >= gsw_cv.adiabatic_lapse_rate_from_t_ca); if ~isempty(gsw_cf.Iadiabatic_lapse_rate_from_t) fprintf(2,'gsw_adiabatic_lapse_rate_from_t: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.molality_from_SA = gsw_molality_from_SA(gsw_cv.SA_chck_cast); [gsw_cf.Imolality_from_SA] = find(abs(gsw_cv.molality_from_SA - gsw_cf.molality_from_SA) >= gsw_cv.molality_from_SA_ca); if ~isempty(gsw_cf.Imolality_from_SA) fprintf(2,'gsw_molality_from_SA: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.ionic_strength_from_SA = gsw_ionic_strength_from_SA(gsw_cv.SA_chck_cast); [gsw_cf.Iionic_strength_from_SA] = find(abs(gsw_cv.ionic_strength_from_SA - gsw_cf.ionic_strength_from_SA) >= gsw_cv.ionic_strength_from_SA_ca); if ~isempty(gsw_cf.Iionic_strength_from_SA) fprintf(2,'gsw_ionic_strength_from_SA: Failed\n'); gsw_cf.gsw_chks = 0; end %% specific volume, density and enthalpy if gsw_cf.gsw_chks == 1; fprintf(1,'.'); end gsw_cf.specvol = gsw_specvol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol] = find(abs(gsw_cv.specvol - gsw_cf.specvol) >= gsw_cv.specvol_ca); if ~isempty(gsw_cf.Ispecvol) fprintf(2,'gsw_specvol: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha = gsw_alpha(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha] = find(abs(gsw_cv.alpha - gsw_cf.alpha) >= gsw_cv.alpha_ca); if ~isempty(gsw_cf.Ialpha) fprintf(2,'gsw_alpha: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.beta = gsw_beta(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ibeta] = find(abs(gsw_cv.beta - gsw_cf.beta) >= gsw_cv.beta_ca); if ~isempty(gsw_cf.Ibeta) fprintf(2,'gsw_beta: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha_on_beta = gsw_alpha_on_beta(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_on_beta] = find(abs(gsw_cv.alpha_on_beta - gsw_cf.alpha_on_beta) >= gsw_cv.alpha_on_beta_ca); if ~isempty(gsw_cf.Ialpha_on_beta) fprintf(2,'gsw_alpha_on_beta: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_vab, gsw_cf.alpha_vab, gsw_cf.beta_vab] = gsw_specvol_alpha_beta(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ivab] = find(abs(gsw_cv.v_vab - gsw_cf.v_vab) >= gsw_cv.v_vab_ca | ... abs(gsw_cv.alpha_vab - gsw_cf.alpha_vab) >= gsw_cv.alpha_vab_ca | ... abs(gsw_cv.beta_vab - gsw_cf.beta_vab) >= gsw_cv.beta_vab_ca); if ~isempty(gsw_cf.Ivab) fprintf(2,'gsw_specvol_alpha_beta: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA, gsw_cf.v_CT, gsw_cf.v_P] = gsw_specvol_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_fd] = find(abs(gsw_cv.v_SA - gsw_cf.v_SA) >= gsw_cv.v_SA_ca | ... abs(gsw_cv.v_CT - gsw_cf.v_CT) >= gsw_cv.v_CT_ca | ... abs(gsw_cv.v_P - gsw_cf.v_P) >= gsw_cv.v_P_ca); if ~isempty(gsw_cf.Iv_fd) fprintf(2,'gsw_specvol_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA, gsw_cf.v_SA_CT, gsw_cf.v_CT_CT, gsw_cf.v_SA_P, gsw_cf.v_CT_P] = gsw_specvol_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_sd] = find(abs(gsw_cv.v_SA_SA - gsw_cf.v_SA_SA) >= gsw_cv.v_SA_SA_ca | ... abs(gsw_cv.v_SA_CT - gsw_cf.v_SA_CT) >= gsw_cv.v_SA_CT_ca | ... abs(gsw_cv.v_CT_CT - gsw_cf.v_CT_CT) >= gsw_cv.v_CT_CT_ca | ... abs(gsw_cv.v_SA_P - gsw_cf.v_SA_P) >= gsw_cv.v_SA_P_ca | ... abs(gsw_cv.v_CT_P - gsw_cf.v_CT_P) >= gsw_cv.v_CT_P_ca); if ~isempty(gsw_cf.Iv_sd) fprintf(2,'gsw_specvol_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_wrt_h, gsw_cf.v_h] = gsw_specvol_first_derivatives_wrt_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_fd_wrt_h] = find(abs(gsw_cv.v_SA_wrt_h - gsw_cf.v_SA_wrt_h) >= gsw_cv.v_SA_wrt_h_ca | ... abs(gsw_cv.v_h - gsw_cf.v_h) >= gsw_cv.v_h_ca); if ~isempty(gsw_cf.Iv_fd_wrt_h) fprintf(2,'gsw_specvol_first_derivatives_wrt_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA_wrt_h, gsw_cf.v_SA_h, gsw_cf.v_h_h] = gsw_specvol_second_derivatives_wrt_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_sd_wrt_h] = find(abs(gsw_cv.v_SA_SA - gsw_cf.v_SA_SA) >= gsw_cv.v_SA_SA_ca | ... abs(gsw_cv.v_SA_CT - gsw_cf.v_SA_CT) >= gsw_cv.v_SA_CT_ca | ... abs(gsw_cv.v_CT_CT - gsw_cf.v_CT_CT) >= gsw_cv.v_CT_CT_ca | ... abs(gsw_cv.v_SA_P - gsw_cf.v_SA_P) >= gsw_cv.v_SA_P_ca | ... abs(gsw_cv.v_CT_P - gsw_cf.v_CT_P) >= gsw_cv.v_CT_P_ca); if ~isempty(gsw_cf.Iv_sd_wrt_h) fprintf(2,'gsw_specvol_second_derivatives_wrt_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_anom = gsw_specvol_anom(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.SA_ref,gsw_cv.CT_ref); [gsw_cf.Ispecvol_anom] = find(abs(gsw_cv.specvol_anom - gsw_cf.specvol_anom) >= gsw_cv.specvol_anom_ca); if ~isempty(gsw_cf.Ispecvol_anom) fprintf(2,'gsw_specvol_anom: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_anom_standard = gsw_specvol_anom_standard(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol_anom_standard] = find(abs(gsw_cv.specvol_anom_standard - gsw_cf.specvol_anom_standard) >= gsw_cv.specvol_anom_standard_ca); if ~isempty(gsw_cf.Ispecvol_anom_standard) fprintf(2,'gsw_specvol_anom_standard: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.rho = gsw_rho(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho] = find(abs(gsw_cv.rho - gsw_cf.rho) >= gsw_cv.rho_ca); if ~isempty(gsw_cf.Irho) fprintf(2,'gsw_rho: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_rab, gsw_cf.alpha_rab, gsw_cf.beta_rab] = gsw_rho_alpha_beta(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_rab] = find(abs(gsw_cv.rho_rab - gsw_cf.rho_rab) >= gsw_cv.rho_rab_ca | ... abs(gsw_cv.alpha_rab - gsw_cf.alpha_rab) >= gsw_cv.alpha_rab_ca | ... abs(gsw_cv.beta_rab - gsw_cf.beta_rab) >= gsw_cv.beta_rab_ca); if ~isempty(gsw_cf.Irho_rab) fprintf(2,'gsw_rho_alpha_beta: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_SA, gsw_cf.rho_CT, gsw_cf.rho_P] = gsw_rho_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_fd] = find(abs(gsw_cv.rho_SA - gsw_cf.rho_SA) >= gsw_cv.rho_SA_ca | ... abs(gsw_cv.rho_CT - gsw_cf.rho_CT) >= gsw_cv.rho_CT_ca | ... abs(gsw_cv.rho_P - gsw_cf.rho_P) >= gsw_cv.rho_P_ca); if ~isempty(gsw_cf.Irho_fd) fprintf(2,'gsw_rho_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_SA_SA, gsw_cf.rho_SA_CT, gsw_cf.rho_CT_CT, gsw_cf.rho_SA_P, gsw_cf.rho_CT_P] = gsw_rho_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_sd] = find(abs(gsw_cv.rho_SA_SA - gsw_cf.rho_SA_SA) >= gsw_cv.rho_SA_SA_ca | ... abs(gsw_cv.rho_SA_CT - gsw_cf.rho_SA_CT) >= gsw_cv.rho_SA_CT_ca | ... abs(gsw_cv.rho_CT_CT - gsw_cf.rho_CT_CT) >= gsw_cv.rho_CT_CT_ca | ... abs(gsw_cv.rho_SA_P - gsw_cf.rho_SA_P) >= gsw_cv.rho_SA_P_ca | ... abs(gsw_cv.rho_CT_P - gsw_cf.rho_CT_P) >= gsw_cv.rho_CT_P_ca); if ~isempty(gsw_cf.Irho_sd) fprintf(2,'gsw_rho_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_SA_wrt_h, gsw_cf.rho_h] = gsw_rho_first_derivatives_wrt_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_fd_wrt_h] = find(abs(gsw_cv.rho_SA_wrt_h - gsw_cf.rho_SA_wrt_h) >= gsw_cv.rho_SA_wrt_h_ca | ... abs(gsw_cv.rho_h - gsw_cf.rho_h) >= gsw_cv.rho_h_ca); if ~isempty(gsw_cf.Irho_fd_wrt_h) fprintf(2,'gsw_rho_first_derivatives_wrt_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA_wrt_h, gsw_cf.v_SA_h, gsw_cf.v_h_h] = gsw_rho_second_derivatives_wrt_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_sd_wrt_h] = find(abs(gsw_cv.rho_SA_SA - gsw_cf.rho_SA_SA) >= gsw_cv.rho_SA_SA_ca | ... abs(gsw_cv.rho_SA_CT - gsw_cf.rho_SA_CT) >= gsw_cv.rho_SA_CT_ca | ... abs(gsw_cv.rho_CT_CT - gsw_cf.rho_CT_CT) >= gsw_cv.rho_CT_CT_ca | ... abs(gsw_cv.rho_SA_P - gsw_cf.rho_SA_P) >= gsw_cv.rho_SA_P_ca | ... abs(gsw_cv.rho_CT_P - gsw_cf.rho_CT_P) >= gsw_cv.rho_CT_P_ca); if ~isempty(gsw_cf.Irho_sd_wrt_h) fprintf(2,'gsw_rho_second_derivatives_wrt_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma0 = gsw_sigma0(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma0] = find(abs(gsw_cv.sigma0 - gsw_cf.sigma0) >= gsw_cv.sigma0_ca); if ~isempty(gsw_cf.Isigma0) fprintf(2,'gsw_sigma0: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma1 = gsw_sigma1(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma1] = find(abs(gsw_cv.sigma1 - gsw_cf.sigma1) >= gsw_cv.sigma1_ca); if ~isempty(gsw_cf.Isigma1) fprintf(2,'gsw_sigma1: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma2 = gsw_sigma2(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma2] = find(abs(gsw_cv.sigma2 - gsw_cf.sigma2) >= gsw_cv.sigma2_ca); if ~isempty(gsw_cf.Isigma2) fprintf(2,'gsw_sigma2: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma3 = gsw_sigma3(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma3] = find(abs(gsw_cv.sigma3 - gsw_cf.sigma3) >= gsw_cv.sigma3_ca); if ~isempty(gsw_cf.Isigma3) fprintf(2,'gsw_sigma3: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma4 = gsw_sigma4(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma4] = find(abs(gsw_cv.sigma4 - gsw_cf.sigma4) >= gsw_cv.sigma4_ca); if ~isempty(gsw_cf.Isigma4) fprintf(2,'gsw_sigma4: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.cabbeling = gsw_cabbeling(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Icabbeling] = find(abs(gsw_cv.cabbeling - gsw_cf.cabbeling) >= gsw_cv.cabbeling_ca); if ~isempty(gsw_cf.Icabbeling) fprintf(2,'gsw_cabbeling: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.thermobaric = gsw_thermobaric(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ithermobaric] = find(abs(gsw_cv.thermobaric - gsw_cf.thermobaric) >= gsw_cv.thermobaric_ca); if ~isempty(gsw_cf.Ithermobaric) fprintf(2,'gsw_thermobaric: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.enthalpy = gsw_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy] = find(abs(gsw_cv.enthalpy - gsw_cf.enthalpy) >= gsw_cv.enthalpy_ca); if ~isempty(gsw_cf.Ienthalpy) fprintf(2,'gsw_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.enthalpy_diff = gsw_enthalpy_diff(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast_shallow,gsw_cv.p_chck_cast_deep); [gsw_cf.Ienthalpy_diff] = find(abs(gsw_cv.enthalpy_diff - gsw_cf.enthalpy_diff) >= gsw_cv.enthalpy_diff_ca); if ~isempty(gsw_cf.Ienthalpy_diff) fprintf(2,'gsw_enthalpy_diff: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.dynamic_enthalpy = gsw_dynamic_enthalpy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Idynamic_enthalpy] = find(abs(gsw_cv.dynamic_enthalpy - gsw_cf.dynamic_enthalpy) >= gsw_cv.dynamic_enthalpy_ca); if ~isempty(gsw_cf.Idynamic_enthalpy) fprintf(2,'gsw_dynamic_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.h_SA, gsw_cf.h_CT] = gsw_enthalpy_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_first_deriv] = find(abs(gsw_cv.h_SA - gsw_cf.h_SA) >= gsw_cv.h_SA_ca | ... abs(gsw_cv.h_CT - gsw_cf.h_CT) >= gsw_cv.h_CT_ca); if ~isempty(gsw_cf.Ienthalpy_first_deriv) fprintf(2,'gsw_enthalpy_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.h_SA_SA, gsw_cf.h_SA_CT, gsw_cf.h_CT_CT] = gsw_enthalpy_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_second_deriv] = find(abs(gsw_cv.h_SA_SA - gsw_cf.h_SA_SA) >= gsw_cv.h_SA_SA_ca | ... abs(gsw_cv.h_SA_CT - gsw_cf.h_SA_CT) >= gsw_cv.h_SA_CT_ca | ... abs(gsw_cv.h_CT_CT - gsw_cf.h_CT_CT) >= gsw_cv.h_CT_CT_ca); if ~isempty(gsw_cf.Ienthalpy_second_deriv) fprintf(2,'gsw_enthalpy_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sound_speed = gsw_sound_speed(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Isound_speed] = find(abs(gsw_cv.sound_speed - gsw_cf.sound_speed) >= gsw_cv.sound_speed_ca); if ~isempty(gsw_cf.Isound_speed) fprintf(2,'gsw_sound_speed: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.kappa = gsw_kappa(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ikappa] = find(abs(gsw_cv.kappa - gsw_cf.kappa) >= gsw_cv.kappa_ca); if ~isempty(gsw_cf.Ikappa) fprintf(2,'gsw_kappa: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.internal_energy = gsw_internal_energy(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iinternal_energy] = find(abs(gsw_cv.internal_energy - gsw_cf.internal_energy) >= gsw_cv.internal_energy_ca); if ~isempty(gsw_cf.Iinternal_energy) fprintf(2,'gsw_internal_energy: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.u_SA, gsw_cf.u_CT, gsw_cf.u_P] = gsw_internal_energy_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iu_fd] = find(abs(gsw_cv.u_SA - gsw_cf.u_SA) >= gsw_cv.u_SA_ca | ... abs(gsw_cv.u_CT - gsw_cf.u_CT) >= gsw_cv.u_CT_ca | ... abs(gsw_cv.u_P - gsw_cf.u_P) >= gsw_cv.u_P_ca); if ~isempty(gsw_cf.Iu_fd) fprintf(2,'gsw_rho_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.u_SA_SA, gsw_cf.u_SA_CT, gsw_cf.u_CT_CT, gsw_cf.u_SA_P, gsw_cf.u_CT_P] = gsw_internal_energy_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iu_sd] = find(abs(gsw_cv.u_SA_SA - gsw_cf.u_SA_SA) >= gsw_cv.rho_SA_SA_ca | ... abs(gsw_cv.u_SA_CT - gsw_cf.u_SA_CT) >= gsw_cv.u_SA_CT_ca | ... abs(gsw_cv.u_CT_CT - gsw_cf.u_CT_CT) >= gsw_cv.u_CT_CT_ca | ... abs(gsw_cv.u_SA_P - gsw_cf.u_SA_P) >= gsw_cv.u_SA_P_ca | ... abs(gsw_cv.u_CT_P - gsw_cf.u_CT_P) >= gsw_cv.u_CT_P_ca); if ~isempty(gsw_cf.Iu_sd) fprintf(2,'gsw_internal_energy_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_enthalpy = gsw_CT_from_enthalpy(gsw_cv.SA_chck_cast,gsw_cf.enthalpy,gsw_cv.p_chck_cast); [gsw_cf.ICT_from_h] = find(abs(gsw_cv.CT_from_enthalpy - gsw_cf.CT_from_enthalpy) >= gsw_cv.CT_from_enthalpy_ca); if ~isempty(gsw_cf.ICT_from_h) fprintf(2,'gsw_CT_from_enthalpy: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SA_from_rho = gsw_SA_from_rho(gsw_cf.rho,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ISA_from_rho] = find(abs(gsw_cv.SA_from_rho - gsw_cf.SA_from_rho) >= gsw_cv.SA_from_rho_ca); if ~isempty(gsw_cf.ISA_from_rho) fprintf(2,'gsw_SA_from_rho: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_rho = gsw_CT_from_rho(gsw_cf.rho,gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_from_rho] = find(abs(gsw_cv.CT_from_rho - gsw_cf.CT_from_rho) >= gsw_cv.CT_from_rho_ca); if ~isempty(gsw_cf.ICT_from_rho) fprintf(2,'gsw_CT_from_rho: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_maxdensity = gsw_CT_maxdensity(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_maxdensity] = find(abs(gsw_cv.CT_maxdensity - gsw_cf.CT_maxdensity) >= gsw_cv.CT_maxdensity_ca); if ~isempty(gsw_cf.ICT_maxdensity) fprintf(2,'gsw_CT_maxdensity: Failed\n'); gsw_cf.gsw_chks = 0; end %% vertical stability and interpolation [gsw_cf.Tu, gsw_cf.Rsubrho, gsw_cf.p_mid_TuRsr] = gsw_Turner_Rsubrho(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ITurner] = find(abs(gsw_cv.Tu - gsw_cf.Tu) >= gsw_cv.Tu_ca | abs(gsw_cv.Rsubrho - gsw_cf.Rsubrho) >= gsw_cv.Rsubrho_ca | ... abs(gsw_cv.p_mid_TuRsr - gsw_cf.p_mid_TuRsr) >= gsw_cv.p_mid_TuRsr_ca); if ~isempty(gsw_cf.ITurner) fprintf(2,'gsw_Turner_Rsubrho: Failed\n'); gsw_chks = 0; end [gsw_cf.n2, gsw_cf.p_mid_n2] = gsw_Nsquared(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.INsquared] = find(abs(gsw_cv.n2 - gsw_cf.n2) >= gsw_cv.n2_ca | abs(gsw_cv.p_mid_n2 - gsw_cf.p_mid_n2) >= gsw_cv.p_mid_n2_ca); if ~isempty(gsw_cf.INsquared) fprintf(2,'gsw_Nsquared: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.n2min, gsw_cf.n2min_pmid, gsw_cf.n2min_specvol, gsw_cf.n2min_alpha, gsw_cf.n2min_beta, gsw_cf.n2min_dsa, gsw_cf.n2min_dct, gsw_cf.n2min_dp] = gsw_Nsquared_min(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.INsquared_min] = find(abs(gsw_cv.n2min - gsw_cf.n2min) >= gsw_cv.n2min_ca | abs(gsw_cv.n2min_pmid - gsw_cf.n2min_pmid) >= gsw_cv.n2min_pmid_ca | ... abs(gsw_cv.n2min_specvol - gsw_cf.n2min_specvol) >= gsw_cv.n2min_specvol_ca | abs(gsw_cv.n2min_alpha - gsw_cf.n2min_alpha) >= gsw_cv.n2min_alpha_ca | ... abs(gsw_cv.n2min_beta - gsw_cf.n2min_beta) >= gsw_cv.n2min_beta_ca | abs(gsw_cv.n2min_dsa - gsw_cf.n2min_dsa) >= gsw_cv.n2min_dsa_ca | ... abs(gsw_cv.n2min_dct - gsw_cf.n2min_dct) >= gsw_cv.n2min_dct_ca | abs(gsw_cv.n2min_dp - gsw_cf.n2min_dp) >= gsw_cv.n2min_dp_ca); if ~isempty(gsw_cf.INsquared_min) fprintf(2,'gsw_Nsquared_min: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.mlp = gsw_mlp(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Imlp] = find(abs(gsw_cv.mlp - gsw_cf.mlp) >= gsw_cv.mlp_ca); if ~isempty(gsw_cf.Imlp) fprintf(2,'gsw_mlp: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.n2_lowerlimit = gsw_Nsquared_lowerlimit(gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.INsquared_lowerlimit] = find(abs(gsw_cv.n2_lowerlimit - gsw_cf.n2_lowerlimit) >= gsw_cv.n2_lowerlimit_ca); if ~isempty(gsw_cf.INsquared_lowerlimit) fprintf(2,'gsw_Nsquared_lowerlimit: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.SAi_SACTinterp, gsw_cf.CTi_SACTinterp] = gsw_SA_CT_interp(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.p_i); [gsw_cf.SACTinterp] = find(abs(gsw_cv.SAi_SACTinterp - gsw_cf.SAi_SACTinterp) >= gsw_cv.SAi_SACTinterp_ca | ... abs(gsw_cv.CTi_SACTinterp - gsw_cf.CTi_SACTinterp) >= gsw_cv.CTi_SACTinterp_ca); if ~isempty(gsw_cf.SACTinterp) fprintf(2,'gsw_SA_CT_interp: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.ti_tinterp = gsw_t_interp(gsw_cv.t_chck_cast,gsw_cv.p_chck_cast,gsw_cv.p_i); [gsw_cf.tinterp] = find(abs(gsw_cv.ti_tinterp - gsw_cf.ti_tinterp) >= gsw_cv.ti_tinterp_ca); if ~isempty(gsw_cf.tinterp) fprintf(2,'gsw_t_interp: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.traceri_tracerCTinterp, gsw_cf.CTi_tracerCTinterp] = gsw_tracer_CT_interp(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.p_i); [gsw_cf.tracerCTinterp] = find(abs(gsw_cv.traceri_tracerCTinterp - gsw_cf.traceri_tracerCTinterp) >= gsw_cv.traceri_tracerCTinterp_ca | ... abs(gsw_cv.CTi_tracerCTinterp - gsw_cf.CTi_tracerCTinterp) >= gsw_cv.CTi_tracerCTinterp_ca); if ~isempty(gsw_cf.tracerCTinterp) fprintf(2,'gsw_tracer_CT_interp: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.traceri_tracerinterp = gsw_tracer_interp(gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.p_i); [gsw_cf.tracerinterp] = find(abs(gsw_cv.traceri_tracerinterp - gsw_cf.traceri_tracerinterp) >= gsw_cv.traceri_tracerinterp_ca); if ~isempty(gsw_cf.tracerinterp) fprintf(2,'gsw_tracer_interp: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.IPVfN2, gsw_cf.p_mid_IPVfN2] = gsw_IPV_vs_fNsquared_ratio(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.IIPVfN2] = find(abs(gsw_cv.IPVfN2 - gsw_cf.IPVfN2) >= gsw_cv.IPVfN2_ca | ... abs(gsw_cv.p_mid_IPVfN2 - gsw_cf.p_mid_IPVfN2) >= gsw_cv.p_mid_IPVfN2_ca); if ~isempty(gsw_cf.IIPVfN2) fprintf(2,'gsw_IPV_vs_fNsquared_ratio: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.IPVfN2, gsw_cf.p_mid_IPVfN2] = gsw_IPV_vs_fNsquared_ratio(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.IIPVfN2] = find(abs(gsw_cv.IPVfN2 - gsw_cf.IPVfN2) >= gsw_cv.IPVfN2_ca | ... abs(gsw_cv.p_mid_IPVfN2 - gsw_cf.p_mid_IPVfN2) >= gsw_cv.p_mid_IPVfN2_ca); if ~isempty(gsw_cf.IIPVfN2) fprintf(2,'gsw_IPV_vs_fNsquared_ratio: Failed\n'); gsw_cf.gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end %% geostrophic streamfunctions and acoustic travel time gsw_cf.geo_strf_dyn_height = gsw_geo_strf_dyn_height(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Igeo_strf_dyn_height] = find(abs(gsw_cv.geo_strf_dyn_height - gsw_cf.geo_strf_dyn_height) >= gsw_cv.geo_strf_dyn_height_ca); if ~isempty(gsw_cf.Igeo_strf_dyn_height) fprintf(2,'gsw_geo_strf_dyn_height: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.geo_strf_dyn_height_pc, gsw_cf.geo_strf_dyn_height_pc_p_mid] = gsw_geo_strf_dyn_height_pc(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.delta_p_chck_cast); [gsw_cf.Igeo_strf_dyn_height_pc] = find(abs(gsw_cv.geo_strf_dyn_height_pc - gsw_cf.geo_strf_dyn_height_pc) >= gsw_cv.geo_strf_dyn_height_pc_ca | ... abs(gsw_cv.geo_strf_dyn_height_pc_p_mid - gsw_cf.geo_strf_dyn_height_pc_p_mid) >= gsw_cv.geo_strf_dyn_height_pc_p_mid_ca); if ~isempty(gsw_cf.Igeo_strf_dyn_height_pc) fprintf(2,'gsw_geo_strf_dyn_height_pc: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.geo_strf_isopycnal = gsw_geo_strf_isopycnal(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr,gsw_cv.Neutral_Density,gsw_cv.p_Neutral_Density); [gsw_cf.Igeo_strf_isopycnal] = find(abs(gsw_cv.geo_strf_isopycnal - gsw_cf.geo_strf_isopycnal) >= gsw_cv.geo_strf_isopycnal_ca); if ~isempty(gsw_cf.Igeo_strf_isopycnal) fprintf(2,'gsw_geo_strf_isopycnal: Failed\n'); gsw_chks = 0; end [gsw_cf.geo_strf_isopycnal_pc, gsw_cf.geo_strf_isopycnal_pc_p_mid] = gsw_geo_strf_isopycnal_pc(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.delta_p_chck_cast,gsw_cv.Neutral_Density(1),3); [gsw_cf.Igeo_strf_isopycnal_pc] = find(abs(gsw_cv.geo_strf_isopycnal_pc - gsw_cf.geo_strf_isopycnal_pc) >= gsw_cv.geo_strf_isopycnal_pc_ca |... abs(gsw_cv.geo_strf_isopycnal_pc_p_mid - gsw_cf.geo_strf_isopycnal_pc_p_mid) >= gsw_cv.geo_strf_isopycnal_pc_p_mid_ca); if ~isempty(gsw_cf.Igeo_strf_isopycnal_pc) fprintf(2,'gsw_geo_strf_isopycnal_pc: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.geo_strf_Montgomery = gsw_geo_strf_Montgomery(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Igeo_strf_Montgomery] = find(abs(gsw_cv.geo_strf_Montgomery - gsw_cf.geo_strf_Montgomery) >= gsw_cv.geo_strf_Montgomery_ca); if ~isempty(gsw_cf.Igeo_strf_Montgomery) fprintf(2,'gsw_geo_strf_Montgomery: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.geo_strf_Cunningham = gsw_geo_strf_Cunningham(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Igeo_strf_Cunningham] = find(abs(gsw_cv.geo_strf_Cunningham - gsw_cf.geo_strf_Cunningham) >= gsw_cv.geo_strf_Cunningham_ca); if ~isempty(gsw_cf.Igeo_strf_Cunningham) fprintf(2,'gsw_geo_strf_Cunningham: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.geo_strf_steric_height = gsw_geo_strf_steric_height(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Igeo_strf_steric_height] = find(abs(gsw_cv.geo_strf_steric_height - gsw_cf.geo_strf_steric_height) >= gsw_cv.geo_strf_steric_height_ca); if ~isempty(gsw_cf.Igeo_strf_steric_height) fprintf(2,'gsw_geo_strf_steric_height: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.geo_strf_PISH = gsw_geo_strf_PISH(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr_05); [gsw_cf.Igeo_strf_PISH] = find(abs(gsw_cv.geo_strf_PISH - gsw_cf.geo_strf_PISH) >= gsw_cv.geo_strf_PISH_ca); if ~isempty(gsw_cf.Igeo_strf_PISH) fprintf(2,'gsw_geo_strf_PISH: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.travel_time = gsw_travel_time(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.lat_chck_cast(1)); [gsw_cf.Itravel_time] = find(abs(gsw_cv.travel_time - gsw_cf.travel_time) >= gsw_cv.travel_time_ca); if ~isempty(gsw_cf.Itravel_time) fprintf(2,'gsw_travel_time: Failed\n'); gsw_cf.gsw_chks = 0; end %% Geostrophic velocity [gsw_cf.geo_strf_velocity, gsw_cf.geo_strf_velocity_mid_lat, gsw_cf.geo_strf_velocity_mid_long] = gsw_geostrophic_velocity(gsw_cv.geo_strf_dyn_height,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Igeostrophic_velo] = find(abs(gsw_cv.geo_strf_velocity - gsw_cf.geo_strf_velocity) >= gsw_cv.geo_strf_velocity_ca | ... abs(gsw_cv.geo_strf_velocity_mid_lat - gsw_cf.geo_strf_velocity_mid_lat) >= gsw_cv.geo_strf_velocity_mid_lat_ca | ... abs(gsw_cv.geo_strf_velocity_mid_long - gsw_cf.geo_strf_velocity_mid_long) >= gsw_cv.geo_strf_velocity_mid_long_ca); if ~isempty(gsw_cf.Igeostrophic_velo) fprintf(2,'gsw_geostrophic_velocity: Failed\n'); gsw_cf.gsw_chks = 0; end %% neutral versus isopycnal slopes and ratios if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end gsw_cf.isopycnal_slope_ratio = gsw_isopycnal_slope_ratio(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Iisopycnal_slope_ratio] = find(abs(gsw_cv.isopycnal_slope_ratio - gsw_cf.isopycnal_slope_ratio) >= gsw_cv.isopycnal_slope_ratio_ca); if ~isempty(gsw_cf.Iisopycnal_slope_ratio) fprintf(2,'gsw_isopycnal_slope_ratio: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.G_CT, gsw_cf.p_mid_G_CT] = gsw_isopycnal_vs_ntp_CT_ratio(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.IG_CT] = find(abs(gsw_cv.G_CT - gsw_cf.G_CT) >= gsw_cv.G_CT_ca | ... (gsw_cv.p_mid_G_CT - gsw_cf.p_mid_G_CT) >= gsw_cv.p_mid_G_CT_ca); if ~isempty(gsw_cf.IG_CT) fprintf(2,'gsw_isopycnal_vs_ntp_CT_ratio: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.ntpptCT = gsw_ntp_pt_vs_CT_ratio(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.IntpptCT] = find(abs(gsw_cv.ntpptCT - gsw_cf.ntpptCT) >= gsw_cv.ntpptCT_ca); if ~isempty(gsw_cf.IntpptCT) fprintf(2,'gsw_ntp_pt_vs_CT_ratio: Failed\n'); gsw_cf.gsw_chks = 0; end %% derivatives of enthalpy, entropy, CT and pt [gsw_cf.CT_SA, gsw_cf.CT_pt] = gsw_CT_first_derivatives(gsw_cv.SA_chck_cast,gsw_cf.pt); [gsw_cf.ICT_first_deriv] = find(abs(gsw_cv.CT_SA - gsw_cf.CT_SA) >= gsw_cv.CT_SA_ca | ... (gsw_cv.CT_pt - gsw_cf.CT_pt) >= gsw_cv.CT_pt_ca); if ~isempty(gsw_cf.ICT_first_deriv) fprintf(2,'gsw_CT_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.CT_SA_SA, gsw_cf.CT_SA_pt, gsw_cf.CT_pt_pt] = gsw_CT_second_derivatives(gsw_cv.SA_chck_cast,gsw_cf.pt); [gsw_cf.ICT_second_deriv] = find(abs(gsw_cv.CT_SA_SA - gsw_cf.CT_SA_SA) >= gsw_cv.CT_SA_SA_ca | ... abs(gsw_cv.CT_SA_pt - gsw_cf.CT_SA_pt) >= gsw_cv.CT_SA_pt_ca | ... abs(gsw_cv.CT_pt_pt - gsw_cf.CT_pt_pt) >= gsw_cv.CT_pt_pt_ca); if ~isempty(gsw_cf.ICT_second_deriv) fprintf(2,'gsw_CT_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.eta_SA, gsw_cf.eta_CT] = gsw_entropy_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ientropy_first_deriv] = find(abs(gsw_cv.eta_SA - gsw_cf.eta_SA) >= gsw_cv.eta_SA_ca | ... abs(gsw_cv.eta_CT - gsw_cf.eta_CT) >= gsw_cv.eta_CT_ca); if ~isempty(gsw_cf.Ientropy_first_deriv) fprintf(2,'gsw_entropy_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end [gsw_cf.eta_SA_SA, gsw_cf.eta_SA_CT, gsw_cf.eta_CT_CT] = gsw_entropy_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ientropy_second_deriv] = find((abs(gsw_cv.eta_SA_SA - gsw_cf.eta_SA_SA)) >= gsw_cv.eta_SA_SA_ca |... abs(gsw_cv.eta_SA_CT - gsw_cf.eta_SA_CT) >= gsw_cv.eta_SA_CT_ca |... abs(gsw_cv.eta_CT_CT - gsw_cf.eta_CT_CT) >= gsw_cv.eta_CT_CT_ca); if ~isempty(gsw_cf.Ientropy_second_deriv) fprintf(2,'gsw_entropy_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.pt_SA, gsw_cf.pt_CT] = gsw_pt_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ipt_first_deriv] = find(abs(gsw_cv.pt_SA - gsw_cf.pt_SA) >= gsw_cv.pt_SA_ca |... abs(gsw_cv.pt_CT - gsw_cf.pt_CT) >= gsw_cv.pt_CT_ca); if ~isempty(gsw_cf.Ipt_first_deriv) fprintf(2,'gsw_pt_first_derivatives: Failed\n'); gsw_chks = 0; end [gsw_cf.pt_SA_SA, gsw_cf.pt_SA_CT, gsw_cf.pt_CT_CT] = gsw_pt_second_derivatives(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ipt_second_deriv] = find(abs(gsw_cv.pt_SA_SA - gsw_cf.pt_SA_SA) >= gsw_cv.pt_SA_SA_ca | ... abs(gsw_cv.pt_SA_CT - gsw_cf.pt_SA_CT) >= gsw_cv.pt_SA_CT_ca | ... abs(gsw_cv.pt_CT_CT - gsw_cf.pt_CT_CT) >= gsw_cv.pt_CT_CT_ca); if ~isempty(gsw_cf.Ipt_second_deriv) fprintf(2,'gsw_pt_second_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end %% seawater properties at freezing temperatures gsw_cf.CT_freezing = gsw_CT_freezing(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.ICT_freezing] = find(abs(gsw_cv.CT_freezing - gsw_cf.CT_freezing) >= gsw_cv.CT_freezing_ca); if ~isempty(gsw_cf.ICT_freezing) fprintf(2,'gsw_CT_freezing: Failed\n'); gsw_chks = 0; end gsw_cf.CT_freezing_poly = gsw_CT_freezing_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.ICT_freezing_poly] = find(abs(gsw_cv.CT_freezing_poly - gsw_cf.CT_freezing_poly) >= gsw_cv.CT_freezing_poly_ca); if ~isempty(gsw_cf.ICT_freezing_poly) fprintf(2,'gsw_CT_freezing_poly: Failed\n'); gsw_chks = 0; end gsw_cf.t_freezing = gsw_t_freezing(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.It_freezing] = find(abs(gsw_cv.t_freezing - gsw_cf.t_freezing) >= gsw_cv.t_freezing_ca); if ~isempty(gsw_cf.It_freezing) fprintf(2,'gsw_t_freezing: Failed\n'); gsw_chks = 0; end gsw_cf.t_freezing_poly = gsw_t_freezing_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.It_freezing_poly] = find(abs(gsw_cv.t_freezing_poly - gsw_cf.t_freezing_poly) >= gsw_cv.t_freezing_poly_ca); if ~isempty(gsw_cf.It_freezing_poly) fprintf(2,'gsw_t_freezing_poly: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_ice_freezing = gsw_pot_enthalpy_ice_freezing(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ipot_enthalpy_ice_freezing] = find(abs(gsw_cv.pot_enthalpy_ice_freezing - gsw_cf.pot_enthalpy_ice_freezing) >= gsw_cv.pot_enthalpy_ice_freezing_ca); if ~isempty(gsw_cf.Ipot_enthalpy_ice_freezing) fprintf(2,'gsw_pot_enthalpy_ice_freezing: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_ice_freezing_poly = gsw_pot_enthalpy_ice_freezing_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ipot_enthalpy_ice_freezing_poly] = find(abs(gsw_cv.pot_enthalpy_ice_freezing_poly - gsw_cf.pot_enthalpy_ice_freezing_poly) >= gsw_cv.pot_enthalpy_ice_freezing_poly_ca); if ~isempty(gsw_cf.Ipot_enthalpy_ice_freezing_poly) fprintf(2,'gsw_pot_enthalpy_ice_freezing_poly: Failed\n'); gsw_chks = 0; end gsw_cf.SA_freezing_from_CT = gsw_SA_freezing_from_CT(gsw_cf.CT_freezing,gsw_cv.p_chck_cast,0.5); [gsw_cf.ISA_freezing_from_CT] = find(abs(gsw_cv.SA_freezing_from_CT - gsw_cf.SA_freezing_from_CT) >= gsw_cv.SA_freezing_from_CT_ca); if ~isempty(gsw_cf.ISA_freezing_from_CT) fprintf(2,'gsw_SA_freezing_from_CT: Failed\n'); gsw_chks = 0; end gsw_cf.SA_freezing_from_CT_poly = gsw_SA_freezing_from_CT_poly(gsw_cf.CT_freezing_poly,gsw_cv.p_chck_cast,0.5); [gsw_cf.ISA_freezing_from_CT_poly] = find(abs(gsw_cv.SA_freezing_from_CT_poly - gsw_cf.SA_freezing_from_CT_poly) >= gsw_cv.SA_freezing_from_CT_poly_ca); if ~isempty(gsw_cf.ISA_freezing_from_CT_poly) fprintf(2,'gsw_SA_freezing_from_CT_poly: Failed\n'); gsw_chks = 0; end gsw_cf.SA_freezing_from_t = gsw_SA_freezing_from_t(gsw_cf.t_freezing,gsw_cv.p_chck_cast,0.5); [gsw_cf.ISA_freezing_from_t] = find(abs(gsw_cv.SA_freezing_from_t - gsw_cf.SA_freezing_from_t) >= gsw_cv.SA_freezing_from_t_ca); if ~isempty(gsw_cf.ISA_freezing_from_t) fprintf(2,'gsw_SA_freezing_from_t: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SA_freezing_from_t_poly = gsw_SA_freezing_from_t_poly(gsw_cf.t_freezing_poly,gsw_cv.p_chck_cast,0.5); [gsw_cf.ISA_freezing_from_t_poly] = find(abs(gsw_cv.SA_freezing_from_t_poly - gsw_cf.SA_freezing_from_t_poly) >= gsw_cv.SA_freezing_from_t_poly_ca); if ~isempty(gsw_cf.ISA_freezing_from_t_poly) fprintf(2,'gsw_SA_freezing_from_t_poly: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.pressure_freezing_CT = gsw_pressure_freezing_CT(gsw_cv.SA_Arctic,(gsw_cv.CT_Arctic - 1),0.5); [gsw_cf.Ipressure_freezing_CT] = find(abs(gsw_cv.pressure_freezing_CT - gsw_cf.pressure_freezing_CT) >= gsw_cv.pressure_freezing_CT_ca); if ~isempty(gsw_cf.Ipressure_freezing_CT) fprintf(2,'gsw_pressure_freezing_CT: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.CTfreezing_SA, gsw_cf.CTfreezing_P] = gsw_CT_freezing_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.ICT_freezing_first_derivatives] = find(abs(gsw_cv.CTfreezing_SA - gsw_cf.CTfreezing_SA) >= gsw_cv.CTfreezing_SA_ca | ... abs(gsw_cv.CTfreezing_P - gsw_cf.CTfreezing_P) >= gsw_cv.CTfreezing_P_ca); if ~isempty(gsw_cf.ICT_freezing_first_derivatives) fprintf(2,'gsw_CT_freezing_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.CTfreezing_SA_poly, gsw_cf.CTfreezing_P_poly] = gsw_CT_freezing_first_derivatives_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.ICT_freezing_first_derivatives_poly] = find(abs(gsw_cv.CTfreezing_SA_poly - gsw_cf.CTfreezing_SA_poly) >= gsw_cv.CTfreezing_SA_poly_ca | ... abs(gsw_cv.CTfreezing_P_poly - gsw_cf.CTfreezing_P_poly) >= gsw_cv.CTfreezing_P_poly_ca); if ~isempty(gsw_cf.ICT_freezing_first_derivatives_poly) fprintf(2,'gsw_CT_freezing_first_derivatives_poly: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.tfreezing_SA, gsw_cf.tfreezing_P] = gsw_t_freezing_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.It_freezing_first_derivatives] = find(abs(gsw_cv.tfreezing_SA - gsw_cf.tfreezing_SA) >= gsw_cv.tfreezing_SA_ca | ... abs(gsw_cv.tfreezing_P - gsw_cf.tfreezing_P) >= gsw_cv.tfreezing_P_ca); if ~isempty(gsw_cf.It_freezing_first_derivatives) fprintf(2,'gsw_t_freezing_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.tfreezing_SA_poly, gsw_cf.tfreezing_P_poly] = gsw_t_freezing_first_derivatives_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast,0.5); [gsw_cf.It_freezing_first_derivatives_poly] = find(abs(gsw_cv.tfreezing_SA_poly - gsw_cf.tfreezing_SA_poly) >= gsw_cv.tfreezing_SA_poly_ca | ... abs(gsw_cv.tfreezing_P_poly - gsw_cf.tfreezing_P_poly) >= gsw_cv.tfreezing_P_poly_ca); if ~isempty(gsw_cf.It_freezing_first_derivatives_poly) fprintf(2,'gsw_t_freezing_first_derivatives_poly: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.pot_enthalpy_ice_freezing_SA, gsw_cf.pot_enthalpy_ice_freezing_P] = gsw_pot_enthalpy_ice_freezing_first_derivatives(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ipot_enthalpy_ice_freezing_first_derivatives] = find(abs(gsw_cv.pot_enthalpy_ice_freezing_SA - gsw_cf.pot_enthalpy_ice_freezing_SA) >= gsw_cv.pot_enthalpy_ice_freezing_SA_ca | ... abs(gsw_cv.pot_enthalpy_ice_freezing_P - gsw_cf.pot_enthalpy_ice_freezing_P) >= gsw_cv.pot_enthalpy_ice_freezing_P_ca); if ~isempty(gsw_cf.Ipot_enthalpy_ice_freezing_first_derivatives) fprintf(2,'gsw_pot_enthalpy_ice_freezing_first_derivatives: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.pot_enthalpy_ice_freezing_SA_poly, gsw_cf.pot_enthalpy_ice_freezing_P_poly] = gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ipot_enthalpy_ice_freezing_first_derivatives_poly] = find(abs(gsw_cv.pot_enthalpy_ice_freezing_SA_poly - gsw_cf.pot_enthalpy_ice_freezing_SA_poly) >= gsw_cv.pot_enthalpy_ice_freezing_SA_poly_ca | ... abs(gsw_cv.pot_enthalpy_ice_freezing_P_poly - gsw_cf.pot_enthalpy_ice_freezing_P_poly) >= gsw_cv.pot_enthalpy_ice_freezing_P_poly_ca); if ~isempty(gsw_cf.Ipot_enthalpy_ice_freezing_first_derivatives_poly) fprintf(2,'gsw_pot_enthalpy_ice_freezing_first_derivatives_poly: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.latentheat_melting = gsw_latentheat_melting(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ilatentheat_melting] = find(abs(gsw_cv.latentheat_melting - gsw_cf.latentheat_melting) >= gsw_cv.latentheat_melting_ca); if ~isempty(gsw_cf.Ilatentheat_melting) fprintf(2,'gsw_latentheat_melting: Failed\n'); gsw_cf.gsw_chks = 0; end %% thermodynamic interaction between ice and seawater gsw_cf.melting_ice_SA_CT_ratio = gsw_melting_ice_SA_CT_ratio(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.t_ice); [gsw_cf.Imelting_ice_SA_CT_ratio] = find(abs(gsw_cv.melting_ice_SA_CT_ratio - gsw_cf.melting_ice_SA_CT_ratio) >= gsw_cv.melting_ice_SA_CT_ratio_ca); if ~isempty(gsw_cf.Imelting_ice_SA_CT_ratio) fprintf(2,'gsw_melting_ice_SA_CT_ratio: Failed\n'); gsw_chks = 0; end gsw_cf.melting_ice_SA_CT_ratio_poly = gsw_melting_ice_SA_CT_ratio_poly(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.t_ice); [gsw_cf.Imelting_ice_SA_CT_ratio_poly] = find(abs(gsw_cv.melting_ice_SA_CT_ratio_poly - gsw_cf.melting_ice_SA_CT_ratio_poly) >= gsw_cv.melting_ice_SA_CT_ratio_poly_ca); if ~isempty(gsw_cf.Imelting_ice_SA_CT_ratio_poly) fprintf(2,'gsw_melting_ice_SA_CT_ratio_poly: Failed\n'); gsw_chks = 0; end gsw_cf.melting_ice_equilibrium_SA_CT_ratio = gsw_melting_ice_equilibrium_SA_CT_ratio(gsw_cv.SA_Arctic,gsw_cv.p_Arctic); [gsw_cf.Imelting_ice_equilibrium_SA_CT_ratio] = find(abs(gsw_cv.melting_ice_equilibrium_SA_CT_ratio - gsw_cf.melting_ice_equilibrium_SA_CT_ratio) >= gsw_cv.melting_ice_equilibrium_SA_CT_ratio_ca); if ~isempty(gsw_cf.Imelting_ice_equilibrium_SA_CT_ratio) fprintf(2,'gsw_melting_ice_equilibrium_SA_CT_ratio: Failed\n'); gsw_chks = 0; end gsw_cf.melting_ice_equilibrium_SA_CT_ratio_poly = gsw_melting_ice_equilibrium_SA_CT_ratio_poly(gsw_cv.SA_Arctic,gsw_cv.p_Arctic); [gsw_cf.Imelting_ice_equilibrium_SA_CT_ratio_poly] = find(abs(gsw_cv.melting_ice_equilibrium_SA_CT_ratio_poly - gsw_cf.melting_ice_equilibrium_SA_CT_ratio_poly) >= gsw_cv.melting_ice_equilibrium_SA_CT_ratio_poly_ca); if ~isempty(gsw_cf.Imelting_ice_equilibrium_SA_CT_ratio_poly) fprintf(2,'gsw_melting_ice_equilibrium_SA_CT_ratio_poly: Failed\n'); gsw_chks = 0; end [gsw_cf.melting_ice_into_seawater_SA_final, gsw_cf.melting_ice_into_seawater_CT_final] = gsw_melting_ice_into_seawater(gsw_cv.SA_Arctic,(gsw_cv.CT_Arctic+0.1),gsw_cv.p_Arctic,gsw_cv.w_ice,gsw_cv.t_ice); [gsw_cf.Imelting_ice_into_seawater] = find(abs(gsw_cv.melting_ice_into_seawater_SA_final - gsw_cf.melting_ice_into_seawater_SA_final) >= gsw_cv.melting_ice_into_seawater_SA_final_ca | ... abs(gsw_cv.melting_ice_into_seawater_CT_final - gsw_cf.melting_ice_into_seawater_CT_final) >= gsw_cv.melting_ice_into_seawater_CT_final_ca); if ~isempty(gsw_cf.Imelting_ice_into_seawater) fprintf(2,'gsw_melting_ice_into_seawater: Failed\n'); gsw_chks = 0; end [gsw_cf.ice_fraction_to_freeze_seawater_SA_freeze, gsw_cf.ice_fraction_to_freeze_seawater_CT_freeze, gsw_cf.ice_fraction_to_freeze_seawater_w_Ih] = gsw_ice_fraction_to_freeze_seawater(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.t_ice); [gsw_cf.Iice_fraction_to_freeze_seawater] = find(abs(gsw_cv.ice_fraction_to_freeze_seawater_SA_freeze - gsw_cf.ice_fraction_to_freeze_seawater_SA_freeze) >= gsw_cv.ice_fraction_to_freeze_seawater_SA_freeze_ca | ... abs(gsw_cv.ice_fraction_to_freeze_seawater_CT_freeze - gsw_cf.ice_fraction_to_freeze_seawater_CT_freeze) >= gsw_cv.ice_fraction_to_freeze_seawater_CT_freeze_ca | ... abs(gsw_cv.ice_fraction_to_freeze_seawater_w_Ih - gsw_cf.ice_fraction_to_freeze_seawater_w_Ih) >= gsw_cv.ice_fraction_to_freeze_seawater_w_Ih_ca ); if ~isempty(gsw_cf.Imelting_ice_into_seawater) fprintf(2,'gsw_melting_ice_into_seawater: Failed\n'); gsw_chks = 0; end [gsw_cf.dSA_dCT_frazil, gsw_cf.dSA_dP_frazil, gsw_cf.dCT_dP_frazil] = gsw_frazil_ratios_adiabatic(gsw_cv.SA_Arctic,gsw_cv.p_Arctic,gsw_cv.w_ice); [gsw_cf.Ifrazil_ratios] = find(abs(gsw_cv.dSA_dCT_frazil - gsw_cf.dSA_dCT_frazil) >= gsw_cv.dSA_dCT_frazil_ca | ... abs(gsw_cv.dSA_dP_frazil - gsw_cf.dSA_dP_frazil) >= gsw_cv.dSA_dP_frazil_ca | ... abs(gsw_cv.dCT_dP_frazil - gsw_cf.dCT_dP_frazil) >= gsw_cv.dCT_dP_frazil_ca ); if ~isempty(gsw_cf.Ifrazil_ratios) fprintf(2,'gsw_frazil_ratios_adiabatic: Failed\n'); gsw_chks = 0; end [gsw_cf.dSA_dCT_frazil_poly, gsw_cf.dSA_dP_frazil_poly, gsw_cf.dCT_dP_frazil_poly] = gsw_frazil_ratios_adiabatic_poly(gsw_cv.SA_Arctic,gsw_cv.p_Arctic,gsw_cv.w_ice); [gsw_cf.Ifrazil_ratios_poly] = find(abs(gsw_cv.dSA_dCT_frazil_poly - gsw_cf.dSA_dCT_frazil_poly) >= gsw_cv.dSA_dCT_frazil_poly_ca | ... abs(gsw_cv.dSA_dP_frazil_poly - gsw_cf.dSA_dP_frazil_poly) >= gsw_cv.dSA_dP_frazil_poly_ca | ... abs(gsw_cv.dCT_dP_frazil_poly - gsw_cf.dCT_dP_frazil_poly) >= gsw_cv.dCT_dP_frazil_poly_ca ); if ~isempty(gsw_cf.Ifrazil_ratios_poly) fprintf(2,'gsw_frazil_ratios_adiabatic_poly: Failed\n'); gsw_chks = 0; end [gsw_cf.frazil_properties_potential_SA_final, gsw_cf.frazil_properties_potential_CT_final, gsw_cf.frazil_properties_potential_w_Ih_final] = gsw_frazil_properties_potential(gsw_cv.SA_bulk,gsw_cv.h_pot_bulk,gsw_cv.p_Arctic); [gsw_cf.Ifrazil_properties_potential] = find(abs(gsw_cv.frazil_properties_potential_SA_final - gsw_cf.frazil_properties_potential_SA_final) >= gsw_cv.frazil_properties_potential_SA_final_ca | ... abs(gsw_cv.frazil_properties_potential_CT_final - gsw_cf.frazil_properties_potential_CT_final) >= gsw_cv.frazil_properties_potential_CT_final_ca | ... abs(gsw_cv.frazil_properties_potential_w_Ih_final - gsw_cf.frazil_properties_potential_w_Ih_final) >= gsw_cv.frazil_properties_potential_w_Ih_final_ca ); if ~isempty(gsw_cf.Ifrazil_properties_potential) fprintf(2,'gsw_frazil_properties_potential: Failed\n'); gsw_chks = 0; end [gsw_cf.frazil_properties_potential_poly_SA_final, gsw_cf.frazil_properties_potential_poly_CT_final, gsw_cf.frazil_properties_potential_poly_w_Ih_final] = gsw_frazil_properties_potential_poly(gsw_cv.SA_bulk,gsw_cv.h_pot_bulk,gsw_cv.p_Arctic); [gsw_cf.Ifrazil_properties_potential_poly] = find(abs(gsw_cv.frazil_properties_potential_poly_SA_final - gsw_cf.frazil_properties_potential_poly_SA_final) >= gsw_cv.frazil_properties_potential_poly_SA_final_ca | ... abs(gsw_cv.frazil_properties_potential_poly_CT_final - gsw_cf.frazil_properties_potential_poly_CT_final) >= gsw_cv.frazil_properties_potential_poly_CT_final_ca | ... abs(gsw_cv.frazil_properties_potential_poly_w_Ih_final - gsw_cf.frazil_properties_potential_poly_w_Ih_final) >= gsw_cv.frazil_properties_potential_poly_w_Ih_final_ca ); if ~isempty(gsw_cf.Ifrazil_properties_potential_poly) fprintf(2,'gsw_frazil_properties_potential_poly: Failed\n'); gsw_chks = 0; end [gsw_cf.frazil_properties_SA_final, gsw_cf.frazil_properties_CT_final, gsw_cf.frazil_properties_w_Ih_final] = gsw_frazil_properties(gsw_cv.SA_bulk,gsw_cv.h_bulk,gsw_cv.p_Arctic); [gsw_cf.Ifrazil_properties] = find(abs(gsw_cv.frazil_properties_SA_final - gsw_cf.frazil_properties_SA_final) >= gsw_cv.frazil_properties_SA_final_ca | ... abs(gsw_cv.frazil_properties_CT_final - gsw_cf.frazil_properties_CT_final) >= gsw_cv.frazil_properties_CT_final_ca | ... abs(gsw_cv.frazil_properties_w_Ih_final - gsw_cf.frazil_properties_w_Ih_final) >= gsw_cv.frazil_properties_w_Ih_final_ca ); if ~isempty(gsw_cf.Ifrazil_properties) fprintf(2,'gsw_frazil_properties: Failed\n'); gsw_chks = 0; end %% thermodynamic interaction between sea ice and seawater gsw_cf.melting_seaice_SA_CT_ratio = gsw_melting_seaice_SA_CT_ratio(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.SA_seaice,gsw_cv.t_seaice); [gsw_cf.Imelting_seaice_SA_CT_ratio] = find(abs(gsw_cv.melting_seaice_SA_CT_ratio - gsw_cf.melting_seaice_SA_CT_ratio) >= gsw_cv.melting_seaice_SA_CT_ratio_ca); if ~isempty(gsw_cf.Imelting_seaice_SA_CT_ratio) fprintf(2,'gsw_melting_seaice_SA_CT_ratio: Failed\n'); gsw_chks = 0; end gsw_cf.melting_seaice_SA_CT_ratio_poly = gsw_melting_seaice_SA_CT_ratio_poly(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.SA_seaice,gsw_cv.t_seaice); [gsw_cf.Imelting_seaice_SA_CT_ratio_poly] = find(abs(gsw_cv.melting_seaice_SA_CT_ratio_poly - gsw_cf.melting_seaice_SA_CT_ratio_poly) >= gsw_cv.melting_seaice_SA_CT_ratio_poly_ca); if ~isempty(gsw_cf.Imelting_seaice_SA_CT_ratio_poly) fprintf(2,'gsw_melting_seaice_SA_CT_ratio_poly: Failed\n'); gsw_chks = 0; end gsw_cf.melting_seaice_equilibrium_SA_CT_ratio = gsw_melting_seaice_equilibrium_SA_CT_ratio(gsw_cv.SA_Arctic,gsw_cv.p_Arctic); [gsw_cf.Imelting_seaice_equilibrium_SA_CT_ratio] = find(abs(gsw_cv.melting_seaice_equilibrium_SA_CT_ratio - gsw_cf.melting_seaice_equilibrium_SA_CT_ratio) >= gsw_cv.melting_seaice_equilibrium_SA_CT_ratio_ca); if ~isempty(gsw_cf.Imelting_seaice_equilibrium_SA_CT_ratio) fprintf(2,'gsw_melting_seaice_equilibrium_SA_CT_ratio: Failed\n'); gsw_chks = 0; end gsw_cf.melting_seaice_equilibrium_SA_CT_ratio_poly = gsw_melting_seaice_equilibrium_SA_CT_ratio_poly(gsw_cv.SA_Arctic,gsw_cv.p_Arctic); [gsw_cf.Imelting_seaice_equilibrium_SA_CT_ratio_poly] = find(abs(gsw_cv.melting_seaice_equilibrium_SA_CT_ratio_poly - gsw_cf.melting_seaice_equilibrium_SA_CT_ratio_poly) >= gsw_cv.melting_seaice_equilibrium_SA_CT_ratio_poly_ca); if ~isempty(gsw_cf.Imelting_seaice_equilibrium_SA_CT_ratio_poly) fprintf(2,'gsw_melting_seaice_equilibrium_SA_CT_ratio_poly: Failed\n'); gsw_chks = 0; end [gsw_cf.melting_seaice_into_seawater_SA_final, gsw_cf.melting_seaice_into_seawater_CT_final] = gsw_melting_seaice_into_seawater(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.w_seaice,gsw_cv.SA_seaice,gsw_cv.t_seaice); [gsw_cf.Imelting_seaice_into_seawater] = find(abs(gsw_cv.melting_seaice_into_seawater_SA_final - gsw_cf.melting_seaice_into_seawater_SA_final) >= gsw_cv.melting_seaice_into_seawater_SA_final_ca | ... abs(gsw_cv.melting_seaice_into_seawater_CT_final - gsw_cf.melting_seaice_into_seawater_CT_final) >= gsw_cv.melting_seaice_into_seawater_CT_final_ca); if ~isempty(gsw_cf.Imelting_seaice_into_seawater) fprintf(2,'gsw_melting_seaice_into_seawater: Failed\n'); gsw_chks = 0; end [gsw_cf.seaice_fraction_to_freeze_seawater_SA_freeze, gsw_cf.seaice_fraction_to_freeze_seawater_CT_freeze, gsw_cf.seaice_fraction_to_freeze_seawater_w_Ih] = gsw_seaice_fraction_to_freeze_seawater(gsw_cv.SA_Arctic,gsw_cv.CT_Arctic,gsw_cv.p_Arctic,gsw_cv.SA_seaice,gsw_cv.t_seaice); [gsw_cf.Iseaice_fraction_to_freeze_seawater] = find(abs(gsw_cv.seaice_fraction_to_freeze_seawater_SA_freeze - gsw_cf.seaice_fraction_to_freeze_seawater_SA_freeze) >= gsw_cv.seaice_fraction_to_freeze_seawater_SA_freeze_ca | ... abs(gsw_cv.seaice_fraction_to_freeze_seawater_CT_freeze - gsw_cf.seaice_fraction_to_freeze_seawater_CT_freeze) >= gsw_cv.seaice_fraction_to_freeze_seawater_CT_freeze_ca | ... abs(gsw_cv.seaice_fraction_to_freeze_seawater_w_Ih - gsw_cf.seaice_fraction_to_freeze_seawater_w_Ih) >= gsw_cv.seaice_fraction_to_freeze_seawater_w_Ih_ca ); if ~isempty(gsw_cf.Imelting_seaice_into_seawater) fprintf(2,'gsw_melting_seaice_into_seawater: Failed\n'); gsw_chks = 0; end %% themodynamic properties of ice Ih gsw_cf.rho_ice = gsw_rho_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Irho_ice] = find(abs(gsw_cv.rho_ice - gsw_cf.rho_ice) >= gsw_cv.rho_ice_ca); if ~isempty(gsw_cf.Irho_ice) fprintf(2,'gsw_rho_ice: Failed\n'); gsw_chks = 0; end gsw_cf.alpha_wrt_t_ice = gsw_alpha_wrt_t_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ialpha_wrt_t_ice] = find(abs(gsw_cv.alpha_wrt_t_ice - gsw_cf.alpha_wrt_t_ice) >= gsw_cv.alpha_wrt_t_ice_ca); if ~isempty(gsw_cf.Ialpha_wrt_t_ice) fprintf(2,'gsw_alpha_wrt_t_ice: Failed\n'); gsw_chks = 0; end gsw_cf.specvol_ice = gsw_specvol_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ispecvol_ice] = find(abs(gsw_cv.specvol_ice - gsw_cf.specvol_ice) >= gsw_cv.specvol_ice_ca); if ~isempty(gsw_cf.Ispecvol_ice) fprintf(2,'gsw_specvol_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pressure_coefficient_ice = gsw_pressure_coefficient_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ipressure_coefficient_ice] = find(abs(gsw_cv.pressure_coefficient_ice - gsw_cf.pressure_coefficient_ice) >= gsw_cv.pressure_coefficient_ice_ca); if ~isempty(gsw_cf.Ipressure_coefficient_ice) fprintf(2,'gsw_pressure_coefficient_ice: Failed\n'); gsw_chks = 0; end gsw_cf.sound_speed_ice = gsw_sound_speed_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Isound_speed_ice] = find(abs(gsw_cv.sound_speed_ice - gsw_cf.sound_speed_ice) >= gsw_cv.sound_speed_ice_ca); if ~isempty(gsw_cf.Isound_speed_ice) fprintf(2,'gsw_sound_speed_ice: Failed\n'); gsw_chks = 0; end gsw_cf.kappa_ice = gsw_kappa_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ikappa_ice] = find(abs(gsw_cv.kappa_ice - gsw_cf.kappa_ice) >= gsw_cv.kappa_ice_ca); if ~isempty(gsw_cf.Ikappa_ice) fprintf(2,'gsw_kappa_ice: Failed\n'); gsw_chks = 0; end gsw_cf.kappa_const_t_ice = gsw_kappa_const_t_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ikappa_const_t_ice] = find(abs(gsw_cv.kappa_const_t_ice - gsw_cf.kappa_const_t_ice) >= gsw_cv.kappa_const_t_ice_ca); if ~isempty(gsw_cf.Ikappa_const_t_ice) fprintf(2,'gsw_kappa_const_t_ice: Failed\n'); gsw_chks = 0; end gsw_cf.internal_energy_ice = gsw_internal_energy_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Iinternal_energy_ice] = find(abs(gsw_cv.internal_energy_ice - gsw_cf.internal_energy_ice) >= gsw_cv.internal_energy_ice_ca); if ~isempty(gsw_cf.Iinternal_energy_ice) fprintf(2,'gsw_internal_energy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.enthalpy_ice = gsw_enthalpy_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ienthalpy_ice] = find(abs(gsw_cv.enthalpy_ice - gsw_cf.enthalpy_ice) >= gsw_cv.enthalpy_ice_ca); if ~isempty(gsw_cf.Ienthalpy_ice) fprintf(2,'gsw_enthalpy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.entropy_ice = gsw_entropy_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ientropy_ice] = find(abs(gsw_cv.entropy_ice - gsw_cf.entropy_ice) >= gsw_cv.entropy_ice_ca); if ~isempty(gsw_cf.Ientropy_ice) fprintf(2,'gsw_entropy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.cp_ice = gsw_cp_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Icp_ice] = find(abs(gsw_cv.cp_ice - gsw_cf.cp_ice) >= gsw_cv.cp_ice_ca); if ~isempty(gsw_cf.Icp_ice) fprintf(2,'gsw_cp_ice: Failed\n'); gsw_chks = 0; end gsw_cf.chem_potential_water_ice = gsw_chem_potential_water_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ichem_potential_water_ice] = find(abs(gsw_cv.chem_potential_water_ice - gsw_cf.chem_potential_water_ice) >= gsw_cv.chem_potential_water_ice_ca); if ~isempty(gsw_cf.Ichem_potential_water_ice) fprintf(2,'gsw_chem_potential_water_ice: Failed\n'); gsw_chks = 0; end gsw_cf.Helmholtz_energy_ice = gsw_Helmholtz_energy_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.IHelmholtz_energy_ice] = find(abs(gsw_cv.Helmholtz_energy_ice - gsw_cf.Helmholtz_energy_ice) >= gsw_cv.Helmholtz_energy_ice_ca); if ~isempty(gsw_cf.IHelmholtz_energy_ice) fprintf(2,'gsw_Helmholtz_energy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.adiabatic_lapse_rate_ice = gsw_adiabatic_lapse_rate_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Iadiabatic_lapse_rate_ice] = find(abs(gsw_cv.adiabatic_lapse_rate_ice - gsw_cf.adiabatic_lapse_rate_ice) >= gsw_cv.kappa_const_t_ice_ca); if ~isempty(gsw_cf.Iadiabatic_lapse_rate_ice) fprintf(2,'gsw_adiabatic_lapse_rate_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pt0_from_t_ice = gsw_pt0_from_t_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic); [gsw_cf.Ipt0_from_t_ice] = find(abs(gsw_cv.pt0_from_t_ice - gsw_cf.pt0_from_t_ice) >= gsw_cv.pt0_from_t_ice_ca); if ~isempty(gsw_cf.Ipt0_from_t_ice) fprintf(2,'gsw_pt0_from_t_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pt_from_t_ice = gsw_pt_from_t_ice(gsw_cv.t_seaice,gsw_cv.p_Arctic,gsw_cv.pr); [gsw_cf.Ipt_from_t_ice] = find(abs(gsw_cv.pt_from_t_ice - gsw_cf.pt_from_t_ice) >= gsw_cv.pt_from_t_ice_ca); if ~isempty(gsw_cf.Ipt_from_t_ice) fprintf(2,'gsw_pt_from_t_ice: Failed\n'); gsw_chks = 0; end gsw_cf.t_from_pt0_ice = gsw_t_from_pt0_ice(gsw_cv.pt0_from_t_ice,gsw_cv.p_Arctic); [gsw_cf.It_from_pt0_ice] = find(abs(gsw_cv.t_from_pt0_ice - gsw_cf.t_from_pt0_ice) >= gsw_cv.t_from_pt0_ice_ca); if ~isempty(gsw_cf.It_from_pt0_ice) fprintf(2,'gsw_t_from_pt0_ice: Failed\n'); gsw_chks = 0; end gsw_cf.t_from_rho_ice = gsw_t_from_rho_ice(gsw_cv.rho_ice,gsw_cv.p_Arctic); [gsw_cf.It_from_rho_ice] = find(abs(gsw_cv.t_from_rho_ice - gsw_cf.t_from_rho_ice) >= gsw_cv.t_from_rho_ice_ca); if ~isempty(gsw_cf.It_from_rho_ice) fprintf(2,'gsw_t_from_rho_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_from_pt_ice = gsw_pot_enthalpy_from_pt_ice(gsw_cv.pt0_from_t_ice); [gsw_cf.Ipot_enthalpy_from_pt_ice] = find(abs(gsw_cv.pot_enthalpy_from_pt_ice - gsw_cf.pot_enthalpy_from_pt_ice) >= gsw_cv.pot_enthalpy_from_pt_ice_ca); if ~isempty(gsw_cf.Ipot_enthalpy_from_pt_ice) fprintf(2,'gsw_pot_enthalpy_from_pt_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pt_from_pot_enthalpy_ice = gsw_pt_from_pot_enthalpy_ice (gsw_cv.pot_enthalpy_from_pt_ice); [gsw_cf.Ipt_from_pot_enthalpy_ice] = find(abs(gsw_cv.pt_from_pot_enthalpy_ice - gsw_cf.pt_from_pot_enthalpy_ice) >= gsw_cv.pt_from_pot_enthalpy_ice_ca); if ~isempty(gsw_cf.Ipt_from_pot_enthalpy_ice) fprintf(2,'gsw_pt_from_pot_enthalpy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_from_pt_ice_poly = gsw_pot_enthalpy_from_pt_ice_poly(gsw_cv.pt0_from_t_ice); [gsw_cf.Ipot_enthalpy_from_pt_ice_poly] = find(abs(gsw_cv.pot_enthalpy_from_pt_ice_poly - gsw_cf.pot_enthalpy_from_pt_ice_poly) >= gsw_cv.pot_enthalpy_from_pt_ice_poly_ca); if ~isempty(gsw_cf.Ipot_enthalpy_from_pt_ice_poly) fprintf(2,'gsw_pot_enthalpy_from_pt_ice_poly: Failed\n'); gsw_chks = 0; end gsw_cf.pt_from_pot_enthalpy_ice_poly = gsw_pt_from_pot_enthalpy_ice_poly(gsw_cv.pot_enthalpy_from_pt_ice_poly); [gsw_cf.Ipt_from_pot_enthalpy_ice_poly] = find(abs(gsw_cv.pt_from_pot_enthalpy_ice_poly - gsw_cf.pt_from_pot_enthalpy_ice_poly) >= gsw_cv.pt_from_pot_enthalpy_ice_poly_ca); if ~isempty(gsw_cf.Ipt_from_pot_enthalpy_ice_poly) fprintf(2,'gsw_pt_from_pot_enthalpy_ice_poly: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_from_specvol_ice = gsw_pot_enthalpy_from_specvol_ice(gsw_cv.specvol_ice,gsw_cv.p_Arctic); [gsw_cf.Ipot_enthalpy_from_specvol_ice] = find(abs(gsw_cv.pot_enthalpy_from_specvol_ice - gsw_cf.pot_enthalpy_from_specvol_ice) >= gsw_cv.pot_enthalpy_from_pt_ice_ca); if ~isempty(gsw_cf.Ipot_enthalpy_from_specvol_ice) fprintf(2,'gsw_pot_enthalpy_from_specvol_ice: Failed\n'); gsw_chks = 0; end gsw_cf.specvol_from_pot_enthalpy_ice = gsw_specvol_from_pot_enthalpy_ice(gsw_cv.pot_enthalpy_from_specvol_ice,gsw_cv.p_Arctic); [gsw_cf.Ispecvol_from_pot_enthalpy_ice] = find(abs(gsw_cv.specvol_from_pot_enthalpy_ice - gsw_cf.specvol_from_pot_enthalpy_ice) >= gsw_cv.pt_from_pot_enthalpy_ice_ca); if ~isempty(gsw_cf.Ispecvol_from_pot_enthalpy_ice) fprintf(2,'gsw_specvol_from_pot_enthalpy_ice: Failed\n'); gsw_chks = 0; end gsw_cf.pot_enthalpy_from_specvol_ice_poly = gsw_pot_enthalpy_from_specvol_ice_poly(gsw_cv.specvol_ice,gsw_cv.p_Arctic); [gsw_cf.Ipot_enthalpy_from_specvol_ice_poly] = find(abs(gsw_cv.pot_enthalpy_from_specvol_ice_poly - gsw_cf.pot_enthalpy_from_specvol_ice_poly) >= gsw_cv.pot_enthalpy_from_pt_ice_poly_ca); if ~isempty(gsw_cf.Ipot_enthalpy_from_specvol_ice_poly) fprintf(2,'gsw_pot_enthalpy_from_specvol_ice_poly: Failed\n'); gsw_chks = 0; end gsw_cf.specvol_from_pot_enthalpy_ice_poly = gsw_specvol_from_pot_enthalpy_ice_poly(gsw_cv.pot_enthalpy_from_specvol_ice_poly,gsw_cv.p_Arctic); [gsw_cf.Ispecvol_from_pot_enthalpy_ice_poly] = find(abs(gsw_cv.specvol_from_pot_enthalpy_ice_poly - gsw_cf.specvol_from_pot_enthalpy_ice_poly) >= gsw_cv.pt_from_pot_enthalpy_ice_poly_ca); if ~isempty(gsw_cf.Ispecvol_from_pot_enthalpy_ice_poly) fprintf(2,'gsw_specvol_from_pot_enthalpy_ice_poly: Failed\n'); gsw_chks = 0; end %% isobaric evaporation enthalpy gsw_cf.latentheat_evap_CT = gsw_latentheat_evap_CT(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ilatentheat_evap_CT] = find(abs(gsw_cv.latentheat_evap_CT - gsw_cf.latentheat_evap_CT) >= gsw_cv.latentheat_evap_CT_ca); if ~isempty(gsw_cf.Ilatentheat_evap_CT) fprintf(2,'gsw_latentheat_evap_CT: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.latentheat_evap_t = gsw_latentheat_evap_t(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast); [gsw_cf.Ilatentheat_evap_t] = find(abs(gsw_cv.latentheat_evap_t - gsw_cf.latentheat_evap_t) >= gsw_cv.latentheat_evap_t_ca); if ~isempty(gsw_cf.Ilatentheat_evap_t) fprintf(2,'gsw_latentheat_evap_t: Failed\n'); gsw_cf.gsw_chks = 0; end %% spiciness gsw_cf.spiciness0 = gsw_spiciness0(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ispiciness0] = find(abs(gsw_cv.spiciness0 - gsw_cf.spiciness0) >= gsw_cv.spiciness0_ca); if ~isempty(gsw_cf.Ispiciness0) fprintf(2,'gsw_spiciness0: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.spiciness1 = gsw_spiciness1(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ispiciness1] = find(abs(gsw_cv.spiciness1 - gsw_cf.spiciness1) >= gsw_cv.spiciness1_ca); if ~isempty(gsw_cf.Ispiciness1) fprintf(2,'gsw_spiciness1: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.spiciness2 = gsw_spiciness2(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Ispiciness2] = find(abs(gsw_cv.spiciness2 - gsw_cf.spiciness2) >= gsw_cv.spiciness2_ca); if ~isempty(gsw_cf.Ispiciness2) fprintf(2,'gsw_spiciness2: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.SA_spicsig0, gsw_cf.CT_spicsig0] = gsw_SA_CT_from_sigma0_spiciness0(gsw_cv.sigma0,gsw_cv.spiciness0); [gsw_cf.Ispicsig0] = find(abs(gsw_cv.SA_spicsig0 - gsw_cf.SA_spicsig0) >= gsw_cv.SA_spicsig0_ca | ... abs(gsw_cv.CT_spicsig0 - gsw_cf.CT_spicsig0) >= gsw_cv.CT_spicsig0_ca); if ~isempty(gsw_cf.Ispicsig0) fprintf(2,'gsw_SA_CT_from_sigma0_spiciness0: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.SA_spicsig1, gsw_cf.CT_spicsig1] = gsw_SA_CT_from_sigma1_spiciness1(gsw_cv.sigma1,gsw_cv.spiciness1); [gsw_cf.Ispicsig1] = find(abs(gsw_cv.SA_spicsig1 - gsw_cf.SA_spicsig1) >= gsw_cv.SA_spicsig1_ca | ... abs(gsw_cv.CT_spicsig1 - gsw_cf.CT_spicsig1) >= gsw_cv.CT_spicsig1_ca); if ~isempty(gsw_cf.Ispicsig1) fprintf(2,'gsw_SA_CT_from_sigma1_spiciness1: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.SA_spicsig2, gsw_cf.CT_spicsig2] = gsw_SA_CT_from_sigma2_spiciness2(gsw_cv.sigma2,gsw_cv.spiciness2); [gsw_cf.Ispicsig2] = find(abs(gsw_cv.SA_spicsig2 - gsw_cf.SA_spicsig2) >= gsw_cv.SA_spicsig2_ca | ... abs(gsw_cv.CT_spicsig2 - gsw_cf.CT_spicsig2) >= gsw_cv.CT_spicsig2_ca); if ~isempty(gsw_cf.Ispicsig2) fprintf(2,'gsw_SA_CT_from_sigma2_spiciness2: Failed\n'); gsw_cf.gsw_chks = 0; end %% planet earth properties gsw_cf.f = gsw_f(gsw_cv.lat_chck_cast); [gsw_cf.If] = find(abs(gsw_cv.f - gsw_cf.f) >= gsw_cv.f_ca); if ~isempty(gsw_cf.If) fprintf(2,'gsw_f: Failed\n'); gsw_chks = 0; end gsw_cf.grav = gsw_grav(gsw_cv.lat_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Igrav] = find(abs(gsw_cv.grav - gsw_cf.grav) >= gsw_cv.grav_ca); if ~isempty(gsw_cf.Igrav) fprintf(2,'gsw_grav: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.distance = gsw_distance(gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Idistance] = find(abs(gsw_cv.distance - gsw_cf.distance) >= gsw_cv.distance_ca); if ~isempty(gsw_cf.Idistance) fprintf(2,'gsw_distance: Failed\n'); gsw_cf.gsw_chks = 0; end %% TEOS-10 constants gsw_cf.T0 = gsw_T0; [gsw_cf.IT0] = find(abs(gsw_cv.T0 - gsw_cf.T0) > 1e-13); if ~isempty(gsw_cf.IT0) fprintf(2,'gsw_T0: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.P0 = gsw_P0; [gsw_cf.IP0] = find(abs(gsw_cv.P0 - gsw_cf.P0) > 1e-13); if ~isempty(gsw_cf.IP0) fprintf(2,'gsw_P0: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SSO = gsw_SSO; [gsw_cf.ISSO] = find(abs(gsw_cv.SSO - gsw_cf.SSO) > 1e-13); if ~isempty(gsw_cf.ISSO) fprintf(2,'gsw_SSO: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.uPS = gsw_uPS; [gsw_cf.IuPS] = find(abs(gsw_cv.uPS - gsw_cf.uPS) > 1e-13); if ~isempty(gsw_cf.IuPS) fprintf(2,'gsw_uPS: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.cp0 = gsw_cp0; [gsw_cf.Icp0] = find(abs(gsw_cv.cp0 - gsw_cf.cp0) > 1e-13); if ~isempty(gsw_cf.Icp0) fprintf(2,'gsw_cp0: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.C3515 = gsw_C3515; [gsw_cf.IC3515] = find(abs(gsw_cv.C3515 - gsw_cf.C3515) > 1e-13); if ~isempty(gsw_cf.IC3515) fprintf(2,'gsw_C3515: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SonCl = gsw_SonCl; [gsw_cf.ISonCl] = find(abs(gsw_cv.SonCl - gsw_cf.SonCl) > 1e-13); if ~isempty(gsw_cf.ISonCl) fprintf(2,'gsw_SonCl: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.valence_factor = gsw_valence_factor; [gsw_cf.Ivalence_factor] = find(abs(gsw_cv.valence_factor - gsw_cf.valence_factor) > 1e-13); if ~isempty(gsw_cf.Ivalence_factor) fprintf(2,'gsw_valence_factor: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.atomic_weight = gsw_atomic_weight; [gsw_cf.Iatomic_weight] = find(abs(gsw_cv.atomic_weight - gsw_cf.atomic_weight) > 1e-13); if ~isempty(gsw_cf.Iatomic_weight) fprintf(2,'gsw_atomic_weight: Failed\n'); gsw_cf.gsw_chks = 0; end %% dissolved gasses gsw_cf.Arsol = gsw_Arsol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IArsol] = find(abs(gsw_cv.Arsol - gsw_cf.Arsol) >= gsw_cv.Arsol_ca); if ~isempty(gsw_cf.IArsol) fprintf(2,'gsw_Arsol: Failed\n'); gsw_chks = 0; end gsw_cf.Arsol_SP_pt = gsw_Arsol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.IArsol_SP_pt] = find(abs(gsw_cv.Arsol_SP_pt - gsw_cf.Arsol_SP_pt) >= gsw_cv.Arsol_SP_pt_ca); if ~isempty(gsw_cf.IArsol_SP_pt) fprintf(2,'gsw_Arsol_SP_pt: Failed\n'); gsw_chks = 0; end gsw_cf.Hesol = gsw_Hesol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IHesol] = find(abs(gsw_cv.Hesol - gsw_cf.Hesol) >= gsw_cv.Hesol_ca); if ~isempty(gsw_cf.IHesol) fprintf(2,'gsw_Hesol: Failed\n'); gsw_chks = 0; end gsw_cf.Hesol_SP_pt = gsw_Hesol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.IHesol_SP_pt] = find(abs(gsw_cv.Hesol_SP_pt - gsw_cf.Hesol_SP_pt) >= gsw_cv.Hesol_SP_pt_ca); if ~isempty(gsw_cf.IHesol_SP_pt) fprintf(2,'gsw_Hesol_SP_pt: Failed\n'); gsw_chks = 0; end gsw_cf.Krsol = gsw_Krsol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IKrsol] = find(abs(gsw_cv.Krsol - gsw_cf.Krsol) >= gsw_cv.Krsol_ca); if ~isempty(gsw_cf.IKrsol) fprintf(2,'gsw_Krsol: Failed\n'); gsw_chks = 0; end gsw_cf.Krsol_SP_pt = gsw_Krsol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.IKrsol_SP_pt] = find(abs(gsw_cv.Krsol_SP_pt - gsw_cf.Krsol_SP_pt) >= gsw_cv.Krsol_SP_pt_ca); if ~isempty(gsw_cf.IKrsol_SP_pt) fprintf(2,'gsw_Krsol_SP_pt: Failed\n'); gsw_chks = 0; end % gsw_cf.N2Osol = gsw_N2Osol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); % [gsw_cf.IN2Osol] = find(abs(gsw_cv.N2Osol - gsw_cf.N2Osol) >= gsw_cv.N2Osol_ca); % if ~isempty(gsw_cf.IN2Osol) % fprintf(2,'gsw_N2Osol: Failed\n'); % gsw_chks = 0; % end % gsw_cf.N2Osol_SP_pt = gsw_N2Osol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); % [gsw_cf.IN2Osol_SP_pt] = find(abs(gsw_cv.N2Osol_SP_pt - gsw_cf.N2Osol_SP_pt) >= gsw_cv.N2Osol_SP_pt_ca); % if ~isempty(gsw_cf.IN2Osol_SP_pt) % fprintf(2,'gsw_N2Osol_SP_pt: Failed\n'); % gsw_chks = 0; % end gsw_cf.N2sol = gsw_N2sol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IN2sol] = find(abs(gsw_cv.N2sol - gsw_cf.N2sol) >= gsw_cv.N2sol_ca); if ~isempty(gsw_cf.IN2sol) fprintf(2,'gsw_N2sol: Failed\n'); gsw_chks = 0; end gsw_cf.N2sol_SP_pt = gsw_N2sol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.IN2sol_SP_pt] = find(abs(gsw_cv.N2sol_SP_pt - gsw_cf.N2sol_SP_pt) >= gsw_cv.N2sol_SP_pt_ca); if ~isempty(gsw_cf.IN2sol_SP_pt) fprintf(2,'gsw_N2sol_SP_pt: Failed\n'); gsw_chks = 0; end gsw_cf.Nesol = gsw_Nesol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.INesol] = find(abs(gsw_cv.Nesol - gsw_cf.Nesol) >= gsw_cv.Nesol_ca); if ~isempty(gsw_cf.INesol) fprintf(2,'gsw_Nesol: Failed\n'); gsw_chks = 0; end gsw_cf.Nesol_SP_pt = gsw_Nesol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.INesol_SP_pt] = find(abs(gsw_cv.Nesol_SP_pt - gsw_cf.Nesol_SP_pt) >= gsw_cv.Nesol_SP_pt_ca); if ~isempty(gsw_cf.INesol_SP_pt) fprintf(2,'gsw_Nesol_SP_pt: Failed\n'); gsw_chks = 0; end gsw_cf.O2sol = gsw_O2sol(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IO2sol] = find(abs(gsw_cv.O2sol - gsw_cf.O2sol) >= gsw_cv.O2sol_ca); if ~isempty(gsw_cf.IO2sol) fprintf(2,'gsw_O2sol: Failed\n'); gsw_chks = 0; end gsw_cf.O2sol_SP_pt = gsw_O2sol_SP_pt(gsw_cv.SP_chck_cast,gsw_cv.pt0_from_t); [gsw_cf.IO2sol_SP_pt] = find(abs(gsw_cv.O2sol_SP_pt - gsw_cf.O2sol_SP_pt) >= gsw_cv.O2sol_SP_pt_ca); if ~isempty(gsw_cf.IO2sol_SP_pt) fprintf(2,'gsw_O2sol_SP_pt: Failed\n'); gsw_chks = 0; end %% density and enthalpy in terms of CT, derived from the exact Gibbs function gsw_cf.specvol_CT_exact = gsw_specvol_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol_CT_exact] = find(abs(gsw_cv.specvol_CT_exact - gsw_cf.specvol_CT_exact) >= gsw_cv.specvol_CT_exact_ca); if ~isempty(gsw_cf.Ispecvol_CT_exact) fprintf(2,'gsw_specvol_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha_CT_exact = gsw_alpha_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_CT_exact] = find(abs(gsw_cv.alpha_CT_exact - gsw_cf.alpha_CT_exact) >= gsw_cv.alpha_CT_exact_ca); if ~isempty(gsw_cf.Ialpha_CT_exact) fprintf(2,'gsw_alpha_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.beta_CT_exact = gsw_beta_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ibeta_CT_exact] = find(abs(gsw_cv.beta_CT_exact - gsw_cf.beta_CT_exact) >= gsw_cv.beta_CT_exact_ca); if ~isempty(gsw_cf.Ibeta_CT_exact) fprintf(2,'gsw_beta_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha_on_beta_CT_exact = gsw_alpha_on_beta_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_on_beta_CT_exact] = find(abs(gsw_cv.alpha_on_beta_CT_exact - gsw_cf.alpha_on_beta_CT_exact) >= gsw_cv.alpha_on_beta_CT_exact_ca); if ~isempty(gsw_cf.Ialpha_on_beta_CT_exact) fprintf(2,'gsw_alpha_on_beta_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_vab_CT_exact, gsw_cf.alpha_vab_CT_exact, gsw_cf.beta_vab_CT_exact] = gsw_specvol_alpha_beta_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_vab_CT_exact] = find(abs(gsw_cv.v_vab_CT_exact - gsw_cf.v_vab_CT_exact) >= gsw_cv.v_vab_CT_exact_ca | ... abs(gsw_cv.alpha_vab_CT_exact - gsw_cf.alpha_vab_CT_exact) >= gsw_cv.alpha_vab_CT_exact_ca | ... abs(gsw_cv.beta_vab_CT_exact - gsw_cf.beta_vab_CT_exact) >= gsw_cv.beta_vab_CT_exact_ca); if ~isempty(gsw_cf.Iv_vab_CT_exact) fprintf(2,'gsw_specvol_alpha_beta_CT_exact: Failed\n'); gsw_chks = 0; end [gsw_cf.v_SA_CT_exact, gsw_cf.v_CT_CT_exact, gsw_cf.v_P_CT_exact] = gsw_specvol_first_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_fd_CT_exact] = find(abs(gsw_cv.v_SA_CT_exact - gsw_cf.v_SA_CT_exact) >= gsw_cv.v_SA_CT_exact_ca | ... abs(gsw_cv.v_CT_CT_exact - gsw_cf.v_CT_CT_exact) >= gsw_cv.v_CT_CT_exact_ca | ... abs(gsw_cv.v_P_CT_exact - gsw_cf.v_P_CT_exact) >= gsw_cv.v_P_CT_exact_ca); if ~isempty(gsw_cf.Iv_fd_CT_exact) fprintf(2,'gsw_specvol_first_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA_CT_exact, gsw_cf.v_SA_CT_CT_exact, gsw_cf.v_CT_CT_CT_exact, gsw_cf.v_SA_P_CT_exact, gsw_cf.v_CT_P_CT_exact] = gsw_specvol_second_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_sd_CT_exact] = find(abs(gsw_cv.v_SA_SA_CT_exact - gsw_cf.v_SA_SA_CT_exact) >= gsw_cv.v_SA_SA_CT_exact_ca | ... abs(gsw_cv.v_SA_CT_CT_exact - gsw_cf.v_SA_CT_CT_exact) >= gsw_cv.v_SA_CT_CT_exact_ca | ... abs(gsw_cv.v_CT_CT_CT_exact - gsw_cf.v_CT_CT_CT_exact) >= gsw_cv.v_CT_CT_CT_exact_ca | ... abs(gsw_cv.v_SA_P_CT_exact - gsw_cf.v_SA_P_CT_exact) >= gsw_cv.v_SA_P_CT_exact_ca | ... abs(gsw_cv.v_CT_P_CT_exact - gsw_cf.v_CT_P_CT_exact) >= gsw_cv.v_CT_P_CT_exact_ca); if ~isempty(gsw_cf.Iv_sd_CT_exact) fprintf(2,'gsw_specvol_second_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_wrt_h_CT_exact, gsw_cf.v_h_CT_exact] = gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_fd_wrt_h_CT_exact] = find(abs(gsw_cv.v_SA_wrt_h_CT_exact - gsw_cf.v_SA_wrt_h_CT_exact) >= gsw_cv.v_SA_wrt_h_CT_exact_ca | ... abs(gsw_cv.v_h_CT_exact - gsw_cf.v_h_CT_exact) >= gsw_cv.v_h_CT_exact_ca); if ~isempty(gsw_cf.Iv_fd_wrt_h_CT_exact) fprintf(2,'gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA_wrt_h_CT_exact, gsw_cf.v_SA_h_CT_exact, gsw_cf.v_h_h_CT_exact] = gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iv_sd_wrt_h_CT_exact] = find(abs(gsw_cv.v_SA_SA_CT_exact - gsw_cf.v_SA_SA_CT_exact) >= gsw_cv.v_SA_SA_CT_exact_ca | ... abs(gsw_cv.v_SA_CT_CT_exact - gsw_cf.v_SA_CT_CT_exact) >= gsw_cv.v_SA_CT_CT_exact_ca | ... abs(gsw_cv.v_CT_CT_CT_exact - gsw_cf.v_CT_CT_CT_exact) >= gsw_cv.v_CT_CT_CT_exact_ca | ... abs(gsw_cv.v_SA_P_CT_exact - gsw_cf.v_SA_P_CT_exact) >= gsw_cv.v_SA_P_CT_exact_ca | ... abs(gsw_cv.v_CT_P_CT_exact - gsw_cf.v_CT_P_CT_exact) >= gsw_cv.v_CT_P_CT_exact_ca); if ~isempty(gsw_cf.Iv_sd_wrt_h_CT_exact) fprintf(2,'gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_anom_CT_exact = gsw_specvol_anom_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast,gsw_cv.SA_ref,gsw_cv.CT_ref); [gsw_cf.Ispecvol_anom_CT_exact] = find(abs(gsw_cv.specvol_anom_CT_exact - gsw_cf.specvol_anom_CT_exact) >= gsw_cv.specvol_anom_CT_exact_ca); if ~isempty(gsw_cf.Ispecvol_anom_CT_exact) fprintf(2,'gsw_specvol_anom_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_anom_standard_CT_exact = gsw_specvol_anom_standard_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol_anom_standard_CT_exact] = find(abs(gsw_cv.specvol_anom_standard_CT_exact - gsw_cf.specvol_anom_standard_CT_exact) >= gsw_cv.specvol_anom_standard_CT_exact_ca); if ~isempty(gsw_cf.Ispecvol_anom_standard_CT_exact) fprintf(2,'gsw_specvol_anom_standard_CT_exact: Failed\n'); gsw_chks = 0; end gsw_cf.rho_CT_exact = gsw_rho_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_CT_exact] = find(abs(gsw_cv.rho_CT_exact - gsw_cf.rho_CT_exact) >= gsw_cv.rho_CT_exact_ca); if ~isempty(gsw_cf.Irho_CT_exact) fprintf(2,'gsw_rho_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_rab_CT_exact, gsw_cf.alpha_rab_CT_exact, gsw_cf.beta_rab_CT_exact] = gsw_rho_alpha_beta_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_rab_CT_exact] = find(abs(gsw_cv.rho_rab_CT_exact - gsw_cf.rho_rab_CT_exact) >= gsw_cv.rho_rab_CT_exact_ca | ... abs(gsw_cv.alpha_rab_CT_exact - gsw_cf.alpha_rab_CT_exact) >= gsw_cv.alpha_rab_CT_exact_ca | ... abs(gsw_cv.beta_rab_CT_exact - gsw_cf.beta_rab_CT_exact) >= gsw_cv.beta_rab_CT_exact_ca); if ~isempty(gsw_cf.Irho_rab_CT_exact) fprintf(2,'gsw_rho_alpha_beta_CT_exact: Failed\n'); gsw_chks = 0; end [gsw_cf.rho_SA_CT_exact, gsw_cf.rho_CT_CT_exact, gsw_cf.rho_P_CT_exact] = gsw_rho_first_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_fd_CT_exact] = find(abs(gsw_cv.rho_SA_CT_exact - gsw_cf.rho_SA_CT_exact) >= gsw_cv.rho_SA_CT_exact_ca | ... abs(gsw_cv.rho_CT_CT_exact - gsw_cf.rho_CT_CT_exact) >= gsw_cv.rho_CT_CT_exact_ca | ... abs(gsw_cv.rho_P_CT_exact - gsw_cf.rho_P_CT_exact) >= gsw_cv.rho_P_CT_exact_ca); if ~isempty(gsw_cf.Irho_fd_CT_exact) fprintf(2,'gsw_rho_first_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_SA_SA_CT_exact, gsw_cf.rho_SA_CT_CT_exact, gsw_cf.rho_CT_CT_CT_exact, gsw_cf.rho_SA_P_CT_exact, gsw_cf.rho_CT_P_CT_exact] = gsw_rho_second_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_sd_CT_exact] = find(abs(gsw_cv.rho_SA_SA_CT_exact - gsw_cf.rho_SA_SA_CT_exact) >= gsw_cv.rho_SA_SA_CT_exact_ca | ... abs(gsw_cv.rho_SA_CT_CT_exact - gsw_cf.rho_SA_CT_CT_exact) >= gsw_cv.rho_SA_CT_CT_exact_ca | ... abs(gsw_cv.rho_CT_CT_CT_exact - gsw_cf.rho_CT_CT_CT_exact) >= gsw_cv.rho_CT_CT_CT_exact_ca | ... abs(gsw_cv.rho_SA_P_CT_exact - gsw_cf.rho_SA_P_CT_exact) >= gsw_cv.rho_SA_P_CT_exact_ca | ... abs(gsw_cv.rho_CT_P_CT_exact - gsw_cf.rho_CT_P_CT_exact) >= gsw_cv.rho_CT_P_CT_exact_ca); if ~isempty(gsw_cf.Irho_sd_CT_exact) fprintf(2,'gsw_rho_second_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.rho_SA_wrt_h_CT_exact, gsw_cf.rho_h_CT_exact] = gsw_rho_first_derivatives_wrt_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_fd_wrt_h_CT_exact] = find(abs(gsw_cv.rho_SA_wrt_h_CT_exact - gsw_cf.rho_SA_wrt_h_CT_exact) >= gsw_cv.rho_SA_wrt_h_CT_exact_ca | ... abs(gsw_cv.rho_h_CT_exact - gsw_cf.rho_h_CT_exact) >= gsw_cv.rho_h_CT_exact_ca); if ~isempty(gsw_cf.Irho_fd_wrt_h_CT_exact) fprintf(2,'gsw_rho_first_derivatives_wrt_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.v_SA_SA_wrt_h_CT_exact, gsw_cf.v_SA_h_CT_exact, gsw_cf.v_h_h_CT_exact] = gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_sd_wrt_h_CT_exact] = find(abs(gsw_cv.rho_SA_SA_CT_exact - gsw_cf.rho_SA_SA_CT_exact) >= gsw_cv.rho_SA_SA_CT_exact_ca | ... abs(gsw_cv.rho_SA_CT_CT_exact - gsw_cf.rho_SA_CT_CT_exact) >= gsw_cv.rho_SA_CT_CT_exact_ca | ... abs(gsw_cv.rho_CT_CT_CT_exact - gsw_cf.rho_CT_CT_CT_exact) >= gsw_cv.rho_CT_CT_CT_exact_ca | ... abs(gsw_cv.rho_SA_P_CT_exact - gsw_cf.rho_SA_P_CT_exact) >= gsw_cv.rho_SA_P_CT_exact_ca | ... abs(gsw_cv.rho_CT_P_CT_exact - gsw_cf.rho_CT_P_CT_exact) >= gsw_cv.rho_CT_P_CT_exact_ca); if ~isempty(gsw_cf.Irho_sd_wrt_h_CT_exact) fprintf(2,'gsw_rho_second_derivatives_wrt_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma0_CT_exact = gsw_sigma0_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma0_CT_exact] = find(abs(gsw_cv.sigma0_CT_exact - gsw_cf.sigma0_CT_exact) >= gsw_cv.sigma0_CT_exact_ca); if ~isempty(gsw_cf.Isigma0_CT_exact) fprintf(2,'gsw_sigma0_CT_exact: Failed\n'); gsw_chks = 0; end gsw_cf.sigma1_CT_exact = gsw_sigma1_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma1_CT_exact] = find(abs(gsw_cv.sigma1_CT_exact - gsw_cf.sigma1_CT_exact) >= gsw_cv.sigma1_CT_exact_ca); if ~isempty(gsw_cf.Isigma1_CT_exact) fprintf(2,'gsw_sigma1_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma2_CT_exact = gsw_sigma2_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma2_CT_exact] = find(abs(gsw_cv.sigma2_CT_exact - gsw_cf.sigma2_CT_exact) >= gsw_cv.sigma2_CT_exact_ca); if ~isempty(gsw_cf.Isigma2_CT_exact) fprintf(2,'gsw_sigma2_CT_exact: Failed\n'); gsw_chks = 0; end gsw_cf.sigma3_CT_exact = gsw_sigma3_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma3_CT_exact] = find(abs(gsw_cv.sigma3_CT_exact - gsw_cf.sigma3_CT_exact) >= gsw_cv.sigma3_CT_exact_ca); if ~isempty(gsw_cf.Isigma3_CT_exact) fprintf(2,'gsw_sigma3_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sigma4_CT_exact = gsw_sigma4_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast); [gsw_cf.Isigma4_CT_exact] = find(abs(gsw_cv.sigma4_CT_exact - gsw_cf.sigma4_CT_exact) >= gsw_cv.sigma4_CT_exact_ca); if ~isempty(gsw_cf.Isigma4_CT_exact) fprintf(2,'gsw_sigma4_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.cabbeling_CT_exact = gsw_cabbeling_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Icabbeling_CT_exact] = find(abs(gsw_cv.cabbeling_CT_exact - gsw_cf.cabbeling_CT_exact) >= gsw_cv.cabbeling_CT_exact_ca); if ~isempty(gsw_cf.Icabbeling_CT_exact) fprintf(2,'gsw_cabbeling_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.thermobaric_CT_exact = gsw_thermobaric_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ithermobaric_CT_exact] = find(abs(gsw_cv.thermobaric_CT_exact - gsw_cf.thermobaric_CT_exact) >= gsw_cv.thermobaric_CT_exact_ca); if ~isempty(gsw_cf.Ithermobaric_CT_exact) fprintf(2,'gsw_thermobaric_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.enthalpy_CT_exact = gsw_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_CT_exact] = find(abs(gsw_cv.enthalpy_CT_exact - gsw_cf.enthalpy_CT_exact) >= gsw_cv.enthalpy_CT_exact_ca); if ~isempty(gsw_cf.Ienthalpy_CT_exact) fprintf(2,'gsw_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.enthalpy_diff_CT_exact = gsw_enthalpy_diff_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast_shallow,gsw_cv.p_chck_cast_deep); [gsw_cf.Ienthalpy_diff_CT_exact] = find(abs(gsw_cv.enthalpy_diff_CT_exact - gsw_cf.enthalpy_diff_CT_exact) >= gsw_cv.enthalpy_diff_CT_exact_ca); if ~isempty(gsw_cf.Ienthalpy_diff_CT_exact) fprintf(2,'gsw_enthalpy_diff_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.dynamic_enthalpy_CT_exact = gsw_dynamic_enthalpy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Idynamic_enthalpy_CT_exact] = find(abs(gsw_cv.dynamic_enthalpy_CT_exact - gsw_cf.dynamic_enthalpy_CT_exact) >= gsw_cv.dynamic_enthalpy_CT_exact_ca); if ~isempty(gsw_cf.Idynamic_enthalpy_CT_exact) fprintf(2,'gsw_dynamic_enthalpy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.h_SA_CT_exact, gsw_cf.h_CT_CT_exact] = gsw_enthalpy_first_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_first_deriv_CT_exact] = find(abs(gsw_cv.h_SA_CT_exact - gsw_cf.h_SA_CT_exact) >= gsw_cv.h_SA_CT_exact_ca | ... abs(gsw_cv.h_CT_CT_exact - gsw_cf.h_CT_CT_exact) >= gsw_cv.h_CT_CT_exact_ca); if ~isempty(gsw_cf.Ienthalpy_first_deriv_CT_exact) fprintf(2,'gsw_enthalpy_first_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.h_SA_SA_CT_exact, gsw_cf.h_SA_CT_CT_exact, gsw_cf.h_CT_CT_CT_exact] = gsw_enthalpy_second_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_second_deriv_CT_exact] = find(abs(gsw_cv.h_SA_SA_CT_exact - gsw_cf.h_SA_SA_CT_exact) >= gsw_cv.h_SA_SA_CT_exact_ca | ... abs(gsw_cv.h_SA_CT_CT_exact - gsw_cf.h_SA_CT_CT_exact) >= gsw_cv.h_SA_CT_CT_exact_ca | ... abs(gsw_cv.h_CT_CT_CT_exact - gsw_cf.h_CT_CT_CT_exact) >= gsw_cv.h_CT_CT_CT_exact_ca); if ~isempty(gsw_cf.Ienthalpy_second_deriv_CT_exact) fprintf(2,'gsw_enthalpy_second_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.sound_speed_CT_exact = gsw_sound_speed_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Isound_speed_CT_exact] = find(abs(gsw_cv.sound_speed_CT_exact - gsw_cf.sound_speed_CT_exact) >= gsw_cv.sound_speed_CT_exact_ca); if ~isempty(gsw_cf.Isound_speed_CT_exact) fprintf(2,'gsw_sound_speed_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.kappa_CT_exact = gsw_kappa_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ikappa_CT_exact] = find(abs(gsw_cv.kappa_CT_exact - gsw_cf.kappa_CT_exact) >= gsw_cv.kappa_CT_exact_ca); if ~isempty(gsw_cf.Ikappa_CT_exact) fprintf(2,'gsw_kappa_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.internal_energy_CT_exact = gsw_internal_energy_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iinternal_energy_CT_exact] = find(abs(gsw_cv.internal_energy_CT_exact - gsw_cf.internal_energy_CT_exact) >= gsw_cv.internal_energy_CT_exact_ca); if ~isempty(gsw_cf.Iinternal_energy_CT_exact) fprintf(2,'gsw_internal_energy_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.u_SA_CT_exact, gsw_cf.u_CT_CT_exact, gsw_cf.u_P_CT_exact] = gsw_internal_energy_first_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iu_fd_CT_exact] = find(abs(gsw_cv.u_SA_CT_exact - gsw_cf.u_SA_CT_exact) >= gsw_cv.u_SA_CT_exact_ca | ... abs(gsw_cv.u_CT_CT_exact - gsw_cf.u_CT_CT_exact) >= gsw_cv.u_CT_CT_exact_ca | ... abs(gsw_cv.u_P_CT_exact - gsw_cf.u_P_CT_exact) >= gsw_cv.u_P_CT_exact_ca); if ~isempty(gsw_cf.Iu_fd_CT_exact) fprintf(2,'gsw_rho_first_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.u_SA_SA_CT_exact, gsw_cf.u_SA_CT_CT_exact, gsw_cf.u_CT_CT_CT_exact, gsw_cf.u_SA_P_CT_exact, gsw_cf.u_CT_P_CT_exact] = gsw_internal_energy_second_derivatives_CT_exact(gsw_cv.SA_chck_cast,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iu_sd_CT_exact] = find(abs(gsw_cv.u_SA_SA_CT_exact - gsw_cf.u_SA_SA_CT_exact) >= gsw_cv.rho_SA_SA_CT_exact_ca | ... abs(gsw_cv.u_SA_CT_CT_exact - gsw_cf.u_SA_CT_CT_exact) >= gsw_cv.u_SA_CT_CT_exact_ca | ... abs(gsw_cv.u_CT_CT_CT_exact - gsw_cf.u_CT_CT_CT_exact) >= gsw_cv.u_CT_CT_CT_exact_ca | ... abs(gsw_cv.u_SA_P_CT_exact - gsw_cf.u_SA_P_CT_exact) >= gsw_cv.u_SA_P_CT_exact_ca | ... abs(gsw_cv.u_CT_P_CT_exact - gsw_cf.u_CT_P_CT_exact) >= gsw_cv.u_CT_P_CT_exact_ca); if ~isempty(gsw_cf.Iu_sd_CT_exact) fprintf(2,'gsw_internal_energy_second_derivatives_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_enthalpy_exact = gsw_CT_from_enthalpy_exact(gsw_cf.enthalpy_CT_exact,gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_from_enthalpy_exact] = find(abs(gsw_cv.CT_from_enthalpy_exact - gsw_cf.CT_from_enthalpy_exact) >= gsw_cv.CT_from_enthalpy_exact_ca); if ~isempty(gsw_cf.ICT_from_enthalpy_exact) fprintf(2,'gsw_CT_from_enthalpy_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SA_from_rho_CT_exact = gsw_SA_from_rho_CT_exact(gsw_cf.rho_CT_exact,gsw_cv.CT_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ISA_from_rho_CT_exact] = find(abs(gsw_cv.SA_from_rho_CT_exact - gsw_cf.SA_from_rho_CT_exact) >= gsw_cv.SA_from_rho_CT_exact_ca); if ~isempty(gsw_cf.ISA_from_rho_CT_exact) fprintf(2,'gsw_SA_from_rho_CT_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_from_rho_exact = gsw_CT_from_rho_exact(gsw_cf.rho_CT_exact,gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_from_rho_exact] = find(abs(gsw_cv.CT_from_rho_exact - gsw_cf.CT_from_rho_exact) >= gsw_cv.CT_from_rho_exact_ca); if ~isempty(gsw_cf.ICT_from_rho_exact) fprintf(2,'gsw_CT_from_rho_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.CT_maxdensity_exact = gsw_CT_maxdensity_exact(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_maxdensity_exact] = find(abs(gsw_cv.CT_maxdensity_exact - gsw_cf.CT_maxdensity_exact) >= gsw_cv.CT_maxdensity_exact_ca); if ~isempty(gsw_cf.ICT_maxdensity_exact) fprintf(2,'gsw_CT_maxdensity_exact: Failed\n'); gsw_cf.gsw_chks = 0; end %% Labrortory functions gsw_cf.rho_t_exact = gsw_rho_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Irho_t_exact] = find(abs(gsw_cv.rho_t_exact - gsw_cf.rho_t_exact) >= gsw_cv.rho_t_exact_ca); if ~isempty(gsw_cf.Irho_t_exact) fprintf(2,'gsw_rho_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.SA_from_rho_t_exact = gsw_SA_from_rho_t_exact(gsw_cf.rho_t_exact,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ISA_from_rho_t_exact] = find(abs(gsw_cv.SA_from_rho_t_exact - gsw_cf.SA_from_rho_t_exact) >= gsw_cv.SA_from_rho_t_exact_ca); if ~isempty(gsw_cf.ISA_from_rho_t_exact) fprintf(2,'gsw_SA_from_rho_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.deltaSA_from_rho_t_exact = gsw_deltaSA_from_rho_t_exact(gsw_cf.rho_t_exact,gsw_cv.SP_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.IdeltaSA_from_rho_t_exact] = find(abs(gsw_cv.deltaSA_from_rho_t_exact - gsw_cf.deltaSA_from_rho_t_exact) >= gsw_cv.deltaSA_from_rho_t_exact_ca); if ~isempty(gsw_cf.IdeltaSA_from_rho_t_exact) fprintf(2,'gsw_deltaSA_from_rho_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end %% basic thermodynamic properties interms of in-situ t, derived from the exact Gibbs function % gsw_cf.rho_t_exact = gsw_rho_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); % [gsw_cf.Irho_t_exact] = find(abs(gsw_cv.rho_t_exact - gsw_cf.rho_t_exact) >= gsw_cv.rho_t_exact_ca); % if ~isempty(gsw_cf.Irho_t_exact) % fprintf(2,'gsw_rho_t_exact: Failed\n'); % gsw_cf.gsw_chks = 0; % end gsw_cf.pot_rho_t_exact = gsw_pot_rho_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast,gsw_cv.pr); [gsw_cf.Ipot_rho_t_exact] = find(abs(gsw_cv.pot_rho_t_exact - gsw_cf.pot_rho_t_exact) >= gsw_cv.pot_rho_t_exact_ca); if ~isempty(gsw_cf.Ipot_rho_t_exact) fprintf(2,'gsw_pot_rho_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.sigma0_pt0_exact = gsw_sigma0_pt0_exact(gsw_cv.SA_chck_cast,gsw_cf.pt0_from_t); [gsw_cf.Isigma0_pt0_exact] = find(abs(gsw_cv.sigma0_pt0_exact - gsw_cf.sigma0_pt0_exact) >= gsw_cv.sigma0_pt0_exact_ca); if ~isempty(gsw_cf.Isigma0_pt0_exact) fprintf(2,'gsw_sigma0_pt0_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha_wrt_CT_t_exact = gsw_alpha_wrt_CT_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_wrt_CT_t_exact] = find(abs(gsw_cv.alpha_wrt_CT_t_exact - gsw_cf.alpha_wrt_CT_t_exact) >= gsw_cv.alpha_wrt_CT_t_exact_ca); if ~isempty(gsw_cf.Ialpha_wrt_CT_t_exact) fprintf(2,'gsw_alpha_wrt_CT_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.alpha_wrt_pt_t_exact = gsw_alpha_wrt_pt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_wrt_pt_t_exact] = find(abs(gsw_cv.alpha_wrt_pt_t_exact - gsw_cf.alpha_wrt_pt_t_exact) >= gsw_cv.alpha_wrt_pt_t_exact_ca); if ~isempty(gsw_cf.Ialpha_wrt_pt_t_exact) fprintf(2,'gsw_alpha_wrt_pt_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.alpha_wrt_t_exact = gsw_alpha_wrt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ialpha_wrt_t_exact] = find(abs(gsw_cv.alpha_wrt_t_exact - gsw_cf.alpha_wrt_t_exact) >= gsw_cv.alpha_wrt_t_exact_ca); if ~isempty(gsw_cf.Ialpha_wrt_t_exact) fprintf(2,'gsw_alpha_wrt_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.beta_const_CT_t_exact = gsw_beta_const_CT_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ibeta_const_CT_t_exact] = find(abs(gsw_cv.beta_const_CT_t_exact - gsw_cf.beta_const_CT_t_exact) >= gsw_cv.beta_const_CT_t_exact_ca); if ~isempty(gsw_cf.Ibeta_const_CT_t_exact) fprintf(2,'gsw_beta_const_CT_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.beta_const_pt_t_exact = gsw_beta_const_pt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ibeta_const_pt_t_exact] = find(abs(gsw_cv.beta_const_pt_t_exact - gsw_cf.beta_const_pt_t_exact) >= gsw_cv.beta_const_pt_t_exact_ca); if ~isempty(gsw_cf.Ibeta_const_pt_t_exact) fprintf(2,'gsw_beta_const_pt_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.beta_const_t_exact = gsw_beta_const_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ibeta_const_t_exact] = find(abs(gsw_cv.beta_const_t_exact - gsw_cf.beta_const_t_exact) >= gsw_cv.beta_const_t_exact_ca); if ~isempty(gsw_cf.Ibeta_const_t_exact) fprintf(2,'gsw_beta_const_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_t_exact = gsw_specvol_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol_t_exact] = find(abs(gsw_cv.specvol_t_exact - gsw_cf.specvol_t_exact) >= gsw_cv.specvol_t_exact_ca); if ~isempty(gsw_cf.Ispecvol_t_exact) fprintf(2,'gsw_specvol_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.specvol_anom_standard_t_exact = gsw_specvol_anom_standard_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ispecvol_anom_standard_t_exact] = find(abs(gsw_cv.specvol_anom_standard_t_exact - gsw_cf.specvol_anom_standard_t_exact) >= gsw_cv.specvol_anom_standard_t_exact_ca); if ~isempty(gsw_cf.Ispecvol_anom_standard_t_exact) fprintf(2,'gsw_specvol_anom_standard_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end gsw_cf.sound_speed_t_exact = gsw_sound_speed_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Isound_speed_t_exact] = find(abs(gsw_cv.sound_speed_t_exact - gsw_cf.sound_speed_t_exact) >= gsw_cv.sound_speed_t_exact_ca); if ~isempty(gsw_cf.Isound_speed_t_exact) fprintf(2,'gsw_sound_speed_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.kappa_t_exact = gsw_kappa_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ikappa_t_exact] = find(abs(gsw_cv.kappa_t_exact - gsw_cf.kappa_t_exact) >= gsw_cv.kappa_t_exact_ca); if ~isempty(gsw_cf.Ikappa_t_exact) fprintf(2,'gsw_kappa_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.kappa_const_t_exact = gsw_kappa_const_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ikappa_const_t_exact] = find(abs(gsw_cv.kappa_const_t_exact - gsw_cf.kappa_const_t_exact) >= gsw_cv.kappa_const_t_exact_ca); if ~isempty(gsw_cf.Ikappa_const_t_exact) fprintf(2,'gsw_kappa_const_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.t_from_rho_exact = gsw_t_from_rho_exact(gsw_cf.rho_t_exact,gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.It_from_rho_exact] = find(abs(gsw_cv.t_from_rho_exact - gsw_cf.t_from_rho_exact) >= gsw_cv.t_from_rho_exact_ca); if ~isempty(gsw_cf.It_from_rho_exact) fprintf(2,'gsw_t_from_rho_exact: Failed\n'); gsw_chks = 0; end gsw_cf.t_maxdensity_exact = gsw_t_maxdensity_exact(gsw_cv.SA_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.It_maxdensity_exact] = find(abs(gsw_cv.t_maxdensity_exact - gsw_cf.t_maxdensity_exact) >= gsw_cv.t_maxdensity_exact_ca); if ~isempty(gsw_cf.It_maxdensity_exact) fprintf(2,'gsw_t_maxdensity_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.internal_energy_t_exact = gsw_internal_energy_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iinternal_energy_t_exact] = find(abs(gsw_cv.internal_energy_t_exact - gsw_cf.internal_energy_t_exact) >= gsw_cv.internal_energy_t_exact_ca); if ~isempty(gsw_cf.Iinternal_energy_t_exact) fprintf(2,'gsw_internal_energy_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.enthalpy_t_exact = gsw_enthalpy_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_t_exact] = find(abs(gsw_cv.enthalpy_t_exact - gsw_cf.enthalpy_t_exact) >= gsw_cv.enthalpy_t_exact_ca); if ~isempty(gsw_cf.Ienthalpy_t_exact) fprintf(2,'gsw_enthalpy_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.dynamic_enthalpy_t_exact = gsw_dynamic_enthalpy_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Idynamic_enthalpy_t_exact] = find(abs(gsw_cv.dynamic_enthalpy_t_exact - gsw_cf.dynamic_enthalpy_t_exact) >= gsw_cv.dynamic_enthalpy_t_exact_ca); if ~isempty(gsw_cf.Idynamic_enthalpy_t_exact) fprintf(2,'gsw_dynamic_enthalpy_t_exact: Failed\n'); gsw_chks = 0; end % gsw_cf.SA_from_rho_t_exact = gsw_SA_from_rho_t_exact(gsw_cf.rho_t_exact,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); % [gsw_cf.ISA_from_rho_t_exact] = find(abs(gsw_cv.SA_from_rho_t_exact - gsw_cf.SA_from_rho_t_exact) >= gsw_cv.SA_from_rho_t_exact_ca); % if ~isempty(gsw_cf.ISA_from_rho_t_exact) % fprintf(2,'gsw_SA_from_rho_t_exact: Failed\n'); % gsw_cf.gsw_chks = 0; % end [gsw_cf.CT_SA_wrt_t, gsw_cf.CT_T_wrt_t, gsw_cf.CT_P_wrt_t] = gsw_CT_first_derivatives_wrt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.ICT_first_derivatives_wrt_t_exact] = find(abs(gsw_cv.CT_SA_wrt_t - gsw_cf.CT_SA_wrt_t) >= gsw_cv.CT_SA_wrt_t_ca | ... abs(gsw_cv.CT_T_wrt_t - gsw_cf.CT_T_wrt_t) >= gsw_cv.CT_T_wrt_t_ca | ... abs(gsw_cv.CT_P_wrt_t - gsw_cf.CT_P_wrt_t) >= gsw_cv.CT_P_wrt_t_ca); if ~isempty(gsw_cf.ICT_first_derivatives_wrt_t_exact) fprintf(2,'gsw_CT_first_derivatives_wrt_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end [gsw_cf.h_SA_wrt_t, gsw_cf.h_T_wrt_t, gsw_cf.h_P_wrt_t] = gsw_enthalpy_first_derivatives_wrt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ienthalpy_first_derivatives_wrt_t_exact] = find(abs(gsw_cv.h_SA_wrt_t - gsw_cf.h_SA_wrt_t) >= gsw_cv.h_SA_wrt_t_ca | ... abs(gsw_cv.h_T_wrt_t - gsw_cf.h_T_wrt_t) >= gsw_cv.h_T_wrt_t_ca | ... abs(gsw_cv.h_P_wrt_t - gsw_cf.h_P_wrt_t) >= gsw_cv.h_P_wrt_t_ca); if ~isempty(gsw_cf.Ienthalpy_first_derivatives_wrt_t_exact) fprintf(2,'gsw_enthalpy_first_derivatives_wrt_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.cp_t_exact = gsw_cp_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Icp_t_exact] = find(abs(gsw_cv.cp_t_exact - gsw_cf.cp_t_exact) >= gsw_cv.cp_t_exact_ca); if ~isempty(gsw_cf.Icp_t_exact) fprintf(2,'gsw_cp_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.isochoric_heat_cap_t_exact = gsw_isochoric_heat_cap_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iisochoric_heat_cap_t_exact] = find(abs(gsw_cv.isochoric_heat_cap_t_exact - gsw_cf.isochoric_heat_cap_t_exact) >= gsw_cv.isochoric_heat_cap_t_exact_ca); if ~isempty(gsw_cf.Iisochoric_heat_cap_t_exact) fprintf(2,'gsw_isochoric_heat_cap_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.chem_potential_relative_t_exact = gsw_chem_potential_relative_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ichem_potential_relative_t_exact] = find(abs(gsw_cv.chem_potential_relative_t_exact - gsw_cf.chem_potential_relative_t_exact) >= gsw_cv.chem_potential_relative_t_exact_ca); if ~isempty(gsw_cf.Ichem_potential_relative_t_exact) fprintf(2,'gsw_chem_potential_relative_t_exact: Failed\n'); gsw_chks = 0; end gsw_cf.chem_potential_water_t_exact = gsw_chem_potential_water_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ichem_potential_water_t_exact] = find(abs(gsw_cv.chem_potential_water_t_exact - gsw_cf.chem_potential_water_t_exact) >= gsw_cv.chem_potential_water_t_exact_ca); if ~isempty(gsw_cf.Ichem_potential_water_t_exact) fprintf(2,'gsw_chem_potential_water_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end gsw_cf.chem_potential_salt_t_exact = gsw_chem_potential_salt_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Ichem_potential_salt_t_exact] = find(abs(gsw_cv.chem_potential_salt_t_exact - gsw_cf.chem_potential_salt_t_exact) >= gsw_cv.chem_potential_salt_t_exact_ca); if ~isempty(gsw_cf.Ichem_potential_salt_t_exact) fprintf(2,'gsw_chem_potential_salt_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.t_deriv_chem_potential_water_t_exact = gsw_t_deriv_chem_potential_water_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.It_deriv_chem_potential_water_t_exact] = find(abs(gsw_cv.t_deriv_chem_potential_water_t_exact - gsw_cf.t_deriv_chem_potential_water_t_exact) >= gsw_cv.t_deriv_chem_potential_water_t_exact_ca); if ~isempty(gsw_cf.It_deriv_chem_potential_water_t_exact) fprintf(2,'gsw_t_deriv_chem_potential_water_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.dilution_coefficient_t_exact = gsw_dilution_coefficient_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Idilution_coefficient_t_exact] = find(abs(gsw_cv.dilution_coefficient_t_exact - gsw_cf.dilution_coefficient_t_exact) >= gsw_cv.dilution_coefficient_t_exact_ca); if ~isempty(gsw_cf.Idilution_coefficient_t_exact) fprintf(2,'gsw_dilution_coefficient_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.Helmholtz_energy_t_exact = gsw_Helmholtz_energy_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.IHelmholtz_energy_t_exact] = find(abs(gsw_cv.Helmholtz_energy_t_exact - gsw_cf.Helmholtz_energy_t_exact) >= gsw_cv.Helmholtz_energy_t_exact_ca); if ~isempty(gsw_cf.IHelmholtz_energy_t_exact) fprintf(2,'gsw_Helmholtz_energy_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.osmotic_coefficient_t_exact = gsw_osmotic_coefficient_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iosmotic_coefficient_t_exact] = find(abs(gsw_cv.osmotic_coefficient_t_exact - gsw_cf.osmotic_coefficient_t_exact) >= gsw_cv.osmotic_coefficient_t_exact_ca); if ~isempty(gsw_cf.Iosmotic_coefficient_t_exact) fprintf(2,'gsw_osmotic_coefficient_t_exact: Failed\n'); gsw_cf.gsw_chks = 0; end gsw_cf.osmotic_pressure_t_exact = gsw_osmotic_pressure_t_exact(gsw_cv.SA_chck_cast,gsw_cv.t_chck_cast,gsw_cv.p_chck_cast); [gsw_cf.Iosmotic_pressure_t_exact] = find(abs(gsw_cv.osmotic_pressure_t_exact - gsw_cf.osmotic_pressure_t_exact) >= gsw_cv.osmotic_pressure_t_exact_ca); if ~isempty(gsw_cf.Iosmotic_pressure_t_exact) fprintf(2,'gsw_osmotic_pressure_t_exact: Failed\n'); gsw_chks = 0; end if gsw_cf.gsw_chks == 1 ; fprintf(1,'.'); end %% library gsw_cf.Fdelta = gsw_Fdelta(gsw_cv.p_chck_cast,gsw_cv.long_chck_cast,gsw_cv.lat_chck_cast); [gsw_cf.IFdelta] = find(abs(gsw_cv.Fdelta - gsw_cf.Fdelta) >= gsw_cv.Fdelta_ca); if ~isempty(gsw_cf.IFdelta) fprintf(2,'gsw_Fdelta: Failed. \n'); gsw_cf.gsw_chks = 0; end for I = 1:45 gsw_cf.long_chck_cast_temp(I,:) = gsw_cv.long_chck_cast(1,:); gsw_cf.lat_chck_cast_temp(I,:) = gsw_cv.lat_chck_cast(1,:); end [I] = find(~isnan(gsw_cv.p_chck_cast)); gsw_cf.deltaSA_atlas = nan(45,3); gsw_cf.deltaSA_atlas(I) = gsw_deltaSA_atlas(gsw_cv.p_chck_cast(I),gsw_cf.long_chck_cast_temp(I),gsw_cf.lat_chck_cast_temp(I)); [gsw_cf.IdeltaSA_atlas] = find(abs(gsw_cv.deltaSA_atlas - gsw_cf.deltaSA_atlas) >= gsw_cv.deltaSA_atlas_ca); if ~isempty(gsw_cf.IdeltaSA_atlas) fprintf(2,'gsw_deltaSA_atlas: Failed. \n'); gsw_cf.gsw_chks = 0; end clear I %% if gsw_cf.gsw_chks == 1 ; fprintf(1,' Finished.\n'); fprintf(1,'\n'); end if gsw_cf.gsw_chks == 0 fprintf(2,'Your installation of the Gibbs SeaWater (GSW) Oceanographic Toolbox has errors !\n'); demo = 0; else fprintf(1,'Well done! The gsw_check_functions confirms that the \n'); fprintf(1,'Gibbs SeaWater (GSW) Oceanographic Toolbox is installed correctly.\n'); fprintf(1,'\n'); fprintf(1,'If you use the GSW Oceanographic Toolbox we ask that you include\n'); fprintf(1,'a reference to McDougall and Barker (2011), whose full citation is: \n'); fprintf(1,' \n'); fprintf(1,'McDougall, T.J., and P.M. Barker, 2011: Getting started with TEOS-10 \n'); fprintf(1,'and the Gibbs Seawater (GSW) Oceanographic Toolbox, 28pp., \n'); fprintf(1,'SCOR/IAPSO WG127, ISBN 978-0-646-55621-5.\n'); fprintf(1,' \n'); demo = gsw_cf.gsw_chks; clear gsw_cf gsw_cv gsw_data gsw_data_file end if demo == 1 fprintf(1,'A demo will now follow. \n'); fprintf(1,'Press enter to continue. \n'); pause gsw_demo end clear demo gsw-3.6.21/gsw/tests/test_geostrophy.py0000644000175000017500000001150315147371315020352 0ustar alastairalastairimport os import numpy as np from numpy.testing import assert_allclose, assert_almost_equal, assert_array_equal import gsw from gsw._utilities import Bunch root_path = os.path.abspath(os.path.dirname(__file__)) cv = Bunch(np.load(os.path.join(root_path, 'gsw_cv_v3_0.npz'))) # Override the original with what we calculate using pchip interp cv.geo_strf_velocity = np.load(os.path.join(root_path,'geo_strf_velocity.npy')) lon = [1, 2] lat = [45, 45] expected = 78626.18767687 # distance tests def test_list(): value = gsw.distance(lon, lat, p=0, axis=-1) assert_almost_equal(expected, value) def test_1darray(): value = gsw.distance(np.array(lon), np.array(lat), p=0, axis=-1) assert_almost_equal(expected, value) def test_1darray_default_p(): # @match_args_return doesn't see the default p. value = gsw.distance(np.array(lon), np.array(lat)) assert_almost_equal(expected, value) def test_2dlist(): value = gsw.distance(np.atleast_2d(lon), np.atleast_2d(lat), p=0, axis=1) assert_almost_equal(expected, value) # geostrophic streamfunction tests def test_strf_no_good(): # revised geo_strf_dyn_height requires 2 valid points shape = (5,) SA = np.ma.masked_all(shape, dtype=float) CT = np.ma.masked_all(shape, dtype=float) p = np.array([0.0, 10.0, 20.0, 30.0, 40.0]) # No valid points. strf = gsw.geo_strf_dyn_height(SA, CT, p, p_ref=0, axis=0) expected = np.zeros(shape, float) + np.nan assert_array_equal(strf.filled(np.nan), expected) # 1 valid point: not enough. SA[:1] = 35 CT[:1] = 5 strf = gsw.geo_strf_dyn_height(SA, CT, p, p_ref=0, axis=0) expected = np.zeros(shape, float) + np.nan assert_array_equal(strf.filled(np.nan), expected) # 2 valid points: enough for the calculation to proceed. SA[:2] = 35 CT[:2] = [5, 4] strf = gsw.geo_strf_dyn_height(SA, CT, p, p_ref=0, axis=0) assert strf.count() == 2 def test_geostrophy(): lon = cv.long_chck_cast lat = cv.lat_chck_cast p = cv.p_chck_cast CT = cv.CT_chck_cast SA = cv.SA_chck_cast strf = gsw.geo_strf_dyn_height(SA, CT, p) geovel, midlon, midlat = gsw.geostrophic_velocity(strf, lon, lat) assert_almost_equal(geovel, cv.geo_strf_velocity) assert_almost_equal(midlon, cv.geo_strf_velocity_mid_long[0]) assert_almost_equal(midlat, cv.geo_strf_velocity_mid_lat[0]) def test_dyn_height_shallower_pref(): """ Check that we can handle a p_ref that is shallower than the top of the cast. To make the results from bin 1 on down independent of whether bin 0 has been deleted, we need to use linear interpolation. """ p = cv.p_chck_cast CT = cv.CT_chck_cast SA = cv.SA_chck_cast strf0 = gsw.geo_strf_dyn_height(SA, CT, p, p_ref=0, interp_method='linear') strf1 = gsw.geo_strf_dyn_height(SA[1:], CT[1:], p[1:], p_ref=0, interp_method='linear') found = strf1 - strf1[0] expected = strf0[1:] - strf0[1] assert_almost_equal(found, expected) def test_dyn_height_grid_bug(): """ The C toolbox had a bug in the interpolation grid generation, triggered under specific circumstances demonstrated in issue #225. The fix was copied from https://github.com/TEOS-10/GSW-C/pull/87. """ SA = np.array([34.17634373, 34.17633109, 34.17725485, 34.90704565]) CT = np.array([ 0.02005831, 0.02003146, 0.01868686, 1.7676452 ]) pres = np.array([ 4.9000001 , 5.69999981, 15.80000019, 995.90002441]) # Last 2 args: grid delta-p is 1; interp method is 3 (mrst). dh1 = gsw._gsw_ufuncs.geo_strf_dyn_height_1(SA, CT, pres, pres[-1], 1, 3) assert dh1[-1] == 0 dh2 = gsw.geo_strf_dyn_height(SA, CT, pres, p_ref = pres[-1], interp_method="mrst") assert_array_equal(dh1, dh2) def test_pz_roundtrip(): """ The p_z conversion functions have Matlab-based checks that use only the first two arguments. Here we verify that the functions are also inverses when the optional arguments are used. """ z = np.array([-10, -100, -1000, -5000], dtype=float) p = gsw.p_from_z(z, 30, 0.5, 0.25) zz = gsw.z_from_p(p, 30, 0.5, 0.25) assert_almost_equal(z, zz) def test_dyn_height_mrst(): """ Tests the MRST-PCHIP interpolation method. """ p = cv.p_chck_cast CT = cv.CT_chck_cast SA = cv.SA_chck_cast pr = cv.pr strf = gsw.geo_strf_dyn_height(SA, CT, p, p_ref=pr, interp_method='mrst') assert_allclose(strf, cv.geo_strf_dyn_height, rtol=0, atol=cv.geo_strf_dyn_height_ca) def test_steric_height_mrst(): """ Tests the MRST-PCHIP interpolation method. """ p = cv.p_chck_cast CT = cv.CT_chck_cast SA = cv.SA_chck_cast pr = cv.pr strf = gsw.geo_strf_steric_height(SA, CT, p, p_ref=pr, interp_method='mrst') assert_allclose(strf, cv.geo_strf_steric_height, rtol=0, atol=cv.geo_strf_steric_height_ca) gsw-3.6.21/gsw/tests/geo_strf_steric_height.npy0000644000175000017500000000227015147371315022000 0ustar alastairalastairNUMPYv{'descr': '䰳e}$[ʒC{N<wQYFCՠ _Ό0 *B)ɳ+84zmEó*KP1S;㟠TA>2}9}NG+B~Z{1=c TXDYf n{G^t+ 5t*wIFiA>$[ɟ51-6q wEYr$]kAOB1 Ғfdc3~J1"8=~3B< zM _P +r_1 ?bY]  zL Zd5G2 WOT z  VDž ݐ cèG Hp/G~^) UȓWqUT }-U\-F\q/@!,gsw-3.6.21/gsw/tests/test_gibbs.py0000644000175000017500000000512515147371315017240 0ustar alastairalastairimport numpy as np from numpy.testing import assert_almost_equal import gsw def test_gibbs_0(): SA = np.array([35, 34])[:, np.newaxis] p = np.array([0, 1000])[np.newaxis, :] out = gsw.gibbs(0, 0, 0, SA, 15, p) expected = np.array([[-1624.830331610998, 8102.300078026374], [-1694.143599586675, 8040.219363411558]]) assert_almost_equal(out, expected) def test_gibbs_1(): ns = np.array([0, 1])[:, np.newaxis, np.newaxis] nt = np.array([0, 1])[np.newaxis, :, np.newaxis] np_ = np.array([0, 1])[np.newaxis, np.newaxis, :] out = gsw.gibbs(ns, nt, np_, 35, 15, 0) expected = np.array([[[-1624.830331610998, 9.748019262990162e-04], [-213.3508284006898, 2.083180196723266e-07]], [[70.39427245333731, -7.288938619915955e-07], [0.590312110989411, 2.083180196723266e-07]]]) expected[1, 1, 1] = np.nan # Unless we add this case to GSW-C. print(out) assert_almost_equal(out, expected) def test_gibbs_2(): params = [ (2, 0, 0, 35, 15, 0, 2.144088568168594), (0, 2, 0, 35, 15, 0, -13.86057508638656), (0, 0, 2, 35, 15, 0, -4.218331910346273e-13) ] for p in params: assert_almost_equal(gsw.gibbs(*p[:6]), p[6]) def test_gibbs_ice(): out = gsw.gibbs_ice(1, 0, 0, [0, 100]) expected = np.array([1220.788661299953, 1220.962914882458]) assert_almost_equal(out, expected) # Source, on an Intel Mac: # octave:3> gsw_gibbs(0, 0, 0, 35, 15, 0) # ans = -1624.830331610998 # octave:4> gsw_gibbs(0, 0, 0, 35, 15, 1000) # ans = 8102.300078026374 # octave:5> gsw_gibbs(0, 0, 0, 34, 15, 0) # ans = -1694.143599586675 # octave:6> gsw_gibbs(0, 0, 0, 34, 15, 1000) # ans = 8040.219363411558 # octave:7> gsw_gibbs(1, 0, 0, 35, 15, 0) # ans = 70.39427245333731 # octave:8> gsw_gibbs(0, 1, 0, 35, 15, 0) # ans = -213.3508284006898 # octave:9> gsw_gibbs(0, 0, 1, 35, 15, 0) # ans = 9.748019262990162e-04 # octave:10> gsw_gibbs(2, 0, 0, 35, 15, 0) # ans = 2.144088568168594 # octave:11> gsw_gibbs(0, 2, 0, 35, 15, 0) # ans = -13.86057508638656 # octave:12> gsw_gibbs(0, 0, 2, 35, 15, 0) # ans = -4.218331910346273e-13 # octave:13> gsw_gibbs(1, 0, 1, 35, 15, 0) # ans = -7.288938619915955e-07 # octave:14> gsw_gibbs(1, 1, 0, 35, 15, 0) # ans = 0.590312110989411 # octave:15> gsw_gibbs(0, 1, 1, 35, 15, 0) # ans = 2.083180196723266e-07 # octave:16> # octave:16> gsw_gibbs(1, 1, 1, 35, 15, 0) # ans = 1.420449745181019e-09 # octave:7> gsw_gibbs_ice(1, 0, 0, 0) # ans = 1220.788661299953 # octave:8> gsw_gibbs_ice(1, 0, 0, 100) # ans = 1220.962914882458gsw-3.6.21/gsw/tests/write_geo_npyfiles.py0000644000175000017500000000260515147371315021010 0ustar alastairalastair""" Generate our own test values for geostrophic calculations. We are presently using simple pchip interpolation for geostrophy rather than trying to mimic the ever-changing Matlab functions. Therefore we have to make our own test values, using the current test cast inputs. This is a minimal script for that purpose, to be run in the tests directory in which it lives. It should be run only if we change to a different calculation algorithm, or we update the cast input and general check value file. """ import numpy as np import gsw from gsw._utilities import Bunch cv = Bunch(np.load('gsw_cv_v3_0.npz')) dyn_height = gsw.geo_strf_dyn_height(cv.SA_chck_cast, cv.CT_chck_cast, cv.p_chck_cast, cv.pr) np.save('geo_strf_dyn_height.npy', dyn_height) steric_height = gsw.geo_strf_steric_height(cv.SA_chck_cast, cv.CT_chck_cast, cv.p_chck_cast, cv.pr) np.save('geo_strf_steric_height.npy', steric_height) lon = cv.long_chck_cast lat = cv.lat_chck_cast p = cv.p_chck_cast CT = cv.CT_chck_cast SA = cv.SA_chck_cast strf = gsw.geo_strf_dyn_height(SA, CT, p) geovel, midlon, midlat = gsw.geostrophic_velocity(strf, lon, lat) np.save('geo_strf_velocity.npy', geovel) # midlon, midlat are OK gsw-3.6.21/gsw/tests/list_check_functions.py0000644000175000017500000000204115147371315021305 0ustar alastairalastair""" Lists functions checked by test_check_functions, and functions that are in gsw_check_functions but are not in gsw. """ import os import numpy as np from check_functions import parse_check_functions import gsw root_path = os.path.abspath(os.path.dirname(__file__)) # Function checks that we can't handle automatically yet. blacklist = ['deltaSA_atlas', # the test is complicated; doesn't fit the pattern. ] d = dir(gsw) funcnames = [name for name in d if '__' not in name] mfuncs_all = parse_check_functions(os.path.join(root_path, 'gsw_check_functions_save.m')) mfuncs = [mf for mf in mfuncs_all if mf.name in d and mf.name not in blacklist] mfuncnames = sorted([mf.name for mf in mfuncs]) missingnames = [mf for mf in mfuncs_all if mf.name not in d] missingnames = sorted([mf.name for mf in missingnames]) print('Functions being checked:') for i, name in enumerate(mfuncnames): print(i, name) print('Functions not in gsw:') for i, name in enumerate(missingnames): print(i, name) gsw-3.6.21/gsw/tests/geo_strf_velocity.npy0000644000175000017500000000152015147371315021012 0ustar alastairalastairNUMPYv{'descr': '?po1&kcuF? ^$5t.N?S"ztS?ul/B盀rc? ㈿Q/Bg/r?b _ª{?םǂ?,?^ؿ"?ݔ7?f(?Dk?P]z?z)њ?+)?"iՑ?Uqv6I?rn[?a A\&?nS^??;ݏ?ʶ;b?r3r?^D?t%|?i%V?0?@\̛c? 3JP?q h?Ō?mjk?).?lF? K?|]w?ΰc\쾒??$/,?2h?gsw-3.6.21/gsw/tests/test_dll_export.py0000644000175000017500000000056115147371315020325 0ustar alastairalastairimport ctypes import gsw def test_ctypes_access(): dllname = gsw._gsw_ufuncs.__file__ gswlib = ctypes.cdll.LoadLibrary(dllname) rho_gsw_ctypes = gswlib.gsw_rho # In-situ density. rho_gsw_ctypes.argtypes = [ctypes.c_double] * 3 rho_gsw_ctypes.restype = ctypes.c_double stp = (35.0, 10.0, 0.0) assert rho_gsw_ctypes(*stp) == gsw.rho(*stp) gsw-3.6.21/gsw/tests/test_check_functions.py0000644000175000017500000000511115147371315021312 0ustar alastairalastair""" Tests functions with pytest, using the machinery from check_functions.py """ import os import numpy as np import pytest from check_functions import parse_check_functions from numpy.testing import assert_allclose import gsw from gsw._utilities import Bunch # Most of the tests have some nan values, so we need to suppress the warning. # Any more careful fix would likely require considerable effort. # We get an overflow from ct_from_enthalpy_exact, but the test passes. np.seterr(invalid='ignore', over='ignore') root_path = os.path.abspath(os.path.dirname(__file__)) # Function checks that we can't handle automatically yet. blacklist = ['deltaSA_atlas', # the test is complicated; doesn't fit the pattern. 'geostrophic_velocity', # test elsewhere; we changed the API #'CT_from_entropy', # needs prior entropy_from_CT; don't have it in C #'CT_first_derivatives', # passes, but has trouble in "details"; # see check_functions.py #'entropy_second_derivatives', # OK now; handling extra parens. #'melting_ice_into_seawater', # OK now; fixed nargs mismatch. ] cv = Bunch(np.load(os.path.join(root_path, 'gsw_cv_v3_0.npz'))) # Substitute new check values for the pchip interpolation version. cv.geo_strf_dyn_height = np.load(os.path.join(root_path,'geo_strf_dyn_height.npy')) cv.geo_strf_steric_height = np.load(os.path.join(root_path,'geo_strf_steric_height.npy')) cv.geo_strf_velocity = np.load(os.path.join(root_path,'geo_strf_velocity.npy')) cf = Bunch() d = dir(gsw) funcnames = [name for name in d if '__' not in name] mfuncs = parse_check_functions(os.path.join(root_path, 'gsw_check_functions_save.m')) mfuncs = [mf for mf in mfuncs if mf.name in d and mf.name not in blacklist] mfuncnames = [mf.name for mf in mfuncs] @pytest.fixture(params=[-360., 0., 360.]) def lonshift(request): return request.param @pytest.fixture(params=mfuncs, ids=mfuncnames) def setup(request, lonshift): cvshift = Bunch(**cv) cvshift.long_chck_cast = cv.long_chck_cast + lonshift return cvshift, cf, request.param def test_check_function(setup): cv, cf, mfunc = setup mfunc.run(locals()) if mfunc.exception is not None or not mfunc.passed: print('\n', mfunc.name) print(' ', mfunc.runline) print(' ', mfunc.testline) if mfunc.exception is None: mfunc.exception = ValueError('Calculated values are different from the expected matlab results.') raise mfunc.exception else: print(mfunc.name) assert mfunc.passed gsw-3.6.21/gsw/tests/_WIP_test_ufuncs.py0000644000175000017500000000533515147371315020336 0ustar alastairalastair""" Tests for the unwrapped ufuncs. This is a WIP; it doesn't work yet for all cases, and might not be a good approach anyway. For now, test_check_functions is adequate, handling the wrapped ufuncs via check_functions "eval" and "exec" machinery. """ import numpy as np import pytest from numpy.testing import assert_allclose import gsw from gsw._utilities import Bunch from gsw.tests.check_functions import parse_check_functions cv = Bunch(np.load('gsw_cv_v3_0.npz')) cf = Bunch() d = dir(gsw._gsw_ufuncs) funcnames = [name for name in d if '__' not in name] mfuncs = parse_check_functions('gsw_check_functions_save.m') mfuncs = [mf for mf in mfuncs if mf.name in d] mfuncnames = [mf.name for mf in mfuncs] @pytest.fixture(scope='session', params=mfuncs) def cfcf(request): return cv, cf, request.param def test_mechanism(cfcf): cv, cf, mfunc = cfcf print(f"<{mfunc.name}>") def value_from_name(vname): b, name = vname.split('.') if b == 'cf': return cf[name] elif b == 'cv': return cv[name] else: raise ValueError(f"Can't find cf. or cv. in {vname}") def set_from_name(vname, value): b, name = vname.split('.') if b == 'cf': cf[name] = value else: raise ValueError(f"attempting to set value in {b}") func = getattr(gsw._gsw_ufuncs, mfunc.name) args = [eval(a) for a in mfunc.argstrings] #print("<<%s>>" % (args,)) out = func(*args) #print("<<<%s>>>" % (out,)) if isinstance(out, tuple): nout = len(out) else: nout = 1 out = (out,) n = min(nout, len(mfunc.outstrings)) for i, s in enumerate(mfunc.outstrings[:n]): set_from_name(s, out[i]) if mfunc.test_varstrings is not None: ntests = (len(mfunc.test_varstrings) - 1) // 3 for i in range(ntests): expected = value_from_name(mfunc.test_varstrings[3*i+1]) found = value_from_name(mfunc.test_varstrings[3*i+2]) tolerance = value_from_name(mfunc.test_varstrings[3*i+3]) #print(expected) #print(found) print(tolerance) try: assert_allclose(expected, found, atol=tolerance) except TypeError: print(mfunc.test_varstrings[3*i+3], tolerance.shape) print(mfunc.test_varstrings) # The following is not right, but this step is unimportant. #set_from_name(mfunc.test_varstrings[0], expected - found) else: print(f">>{mfunc.testline}<<") print("missing mfunc.test_varstrings") mfunc.run() if hasattr(mfunc, "exception"): print(f">>>{mfunc.exception}<<<") else: assert mfunc.passed gsw-3.6.21/gsw/tests/geo_strf_dyn_height.npy0000644000175000017500000000227015147371315021301 0ustar alastairalastairNUMPYv{'descr': 'ј0[,4 0K+-:11;/}X냱2̜a_0+8u361,x/4i߆L2xj4@|3El5'ػ3GT6cS4P&7mF5P|D8>m9 7:njX8a]~H-;ď89 Hծh<.Ku?bP=NB:>@A>EC(@'6?^JtCAg>b@RȌA@iD&IBPA6KB)AަGMC[{") first_double = argtypes.index("d") int_return = ret_types[0] == 'i' else: first_double = 0 int_return = False def fixup(ret): if hasduck: return ret if hasmasked and not int_return: ret = np.ma.masked_invalid(ret) if not hasarray and isinstance(ret, np.ndarray) and ret.size == 1: try: ret = ret[0] except IndexError: pass return ret newargs = [] for i, arg in enumerate(args): if i < first_double: newargs.append(arg) # for gibbs and gibbs_ice elif ismasked[i]: newargs.append(masked_to_nan(arg)) elif isduck[i]: newargs.append(arg) else: newargs.append(np.asarray(arg, dtype=float)) if p is not None: kw['p'] = newargs.pop() ret = f(*newargs, **kw) if isinstance(ret, tuple): retlist = [fixup(arg) for arg in ret] ret = tuple(retlist) else: ret = fixup(ret) return ret wrapper.__wrapped__ = f return wrapper def axis_slicer(n, sl, axis): """ Return an indexing tuple for an array with `n` dimensions, with slice `sl` taken on `axis`. """ itup = [slice(None)] * n itup[axis] = sl return tuple(itup) def indexer(shape, axis, order='C'): """ Generator of indexing tuples for "apply_along_axis" usage. The generator cycles through all axes other than `axis`. The numpy np.apply_along_axis function only works with functions of a single array; this generator allows us work with a function of more than one array. """ ndim = len(shape) ind_shape = list(shape) ind_shape[axis] = 1 # "axis" and any dim of 1 will not be incremented # list of indices, with a slice at "axis" inds = [0] * ndim inds[axis] = slice(None) kmax = np.prod(ind_shape) if order == 'C': index_position = list(reversed(range(ndim))) else: index_position = list(range(ndim)) for _k in range(kmax): yield tuple(inds) for i in index_position: if ind_shape[i] == 1: continue inds[i] += 1 if inds[i] == ind_shape[i]: inds[i] = 0 else: break # This is straight from pycurrents.system. We can trim out # the parts we don't need, but there is no rush to do so. class Bunch(dict): """ A dictionary that also provides access via attributes. Additional methods update_values and update_None provide control over whether new keys are added to the dictionary when updating, and whether an attempt to add a new key is ignored or raises a KeyError. The Bunch also prints differently than a normal dictionary, using str() instead of repr() for its keys and values, and in key-sorted order. The printing format can be customized by subclassing with a different str_ftm class attribute. Do not assign directly to this class attribute, because that would substitute an instance attribute which would then become part of the Bunch, and would be reported as such by the keys() method. To output a string representation with a particular format, without subclassing, use the formatted() method. """ str_fmt = "{0!s:<{klen}} : {1!s:>{vlen}}\n" def __init__(self, *args, **kwargs): """ *args* can be dictionaries, bunches, or sequences of key,value tuples. *kwargs* can be used to initialize or add key, value pairs. """ dict.__init__(self) for arg in args: self.update(arg) self.update(kwargs) def __getattr__(self, name): try: return self[name] except KeyError as err: raise AttributeError(f"'Bunch' object has no attribute {name}. {err}") def __setattr__(self, name, value): self[name] = value def __str__(self): return self.formatted() def formatted(self, fmt=None, types=False): """ Return a string with keys and/or values or types. *fmt* is a format string as used in the str.format() method. The str.format() method is called with key, value as positional arguments, and klen, vlen as kwargs. The latter are the maxima of the string lengths for the keys and values, respectively, up to respective maxima of 20 and 40. """ if fmt is None: fmt = self.str_fmt items = list(self.items()) items.sort() klens = [] vlens = [] for i, (k, v) in enumerate(items): lenk = len(str(k)) if types: v = type(v).__name__ lenv = len(str(v)) items[i] = (k, v) klens.append(lenk) vlens.append(lenv) klen = min(20, max(klens)) vlen = min(40, max(vlens)) slist = [fmt.format(k, v, klen=klen, vlen=vlen) for k, v in items] return ''.join(slist) def from_pyfile(self, filename): """ Read in variables from a python code file. """ # We can't simply exec the code directly, because in # Python 3 the scoping for list comprehensions would # lead to a NameError. Wrapping the code in a function # fixes this. d = {} lines = ["def _temp_func():\n"] with open(filename) as f: lines.extend([" " + line for line in f]) lines.extend(["\n return(locals())\n", "_temp_out = _temp_func()\n", "del(_temp_func)\n"]) codetext = "".join(lines) code = compile(codetext, filename, 'exec') exec(code, globals(), d) self.update(d["_temp_out"]) return self def update_values(self, *args, **kw): """ arguments are dictionary-like; if present, they act as additional sources of kwargs, with the actual kwargs taking precedence. One reserved optional kwarg is "strict". If present and True, then any attempt to update with keys that are not already in the Bunch instance will raise a KeyError. """ strict = kw.pop("strict", False) newkw = {} for d in args: newkw.update(d) newkw.update(kw) self._check_strict(strict, newkw) dsub = {k: v for (k, v) in newkw.items() if k in self} self.update(dsub) def update_None(self, *args, **kw): """ Similar to update_values, except that an existing value will be updated only if it is None. """ strict = kw.pop("strict", False) newkw = {} for d in args: newkw.update(d) newkw.update(kw) self._check_strict(strict, newkw) dsub = {k: v for (k, v) in newkw.items() if k in self and self[k] is None} self.update(dsub) def _check_strict(self, strict, kw): if strict: bad = set(kw.keys()) - set(self.keys()) if bad: bk = list(bad) bk.sort() ek = list(self.keys()) ek.sort() raise KeyError( f"Update keys {bk} don't match existing keys {ek}") gsw-3.6.21/gsw/energy.py0000644000175000017500000000026615147371315015243 0ustar alastairalastair""" Functions involving internal energy, enthalpy, latent heat. """ from ._wrapped_ufuncs import ( enthalpy, enthalpy_diff, internal_energy, latentheat_evap_CT, latentheat_evap_t, ) gsw-3.6.21/gsw/freezing.py0000644000175000017500000000107715147371315015564 0ustar alastairalastair""" Freezing-point functions. """ from ._wrapped_ufuncs import ( CT_freezing, CT_freezing_first_derivatives, CT_freezing_first_derivatives_poly, CT_freezing_poly, SA_freezing_from_CT, SA_freezing_from_CT_poly, SA_freezing_from_t, SA_freezing_from_t_poly, pot_enthalpy_ice_freezing, pot_enthalpy_ice_freezing_first_derivatives, pot_enthalpy_ice_freezing_first_derivatives_poly, pot_enthalpy_ice_freezing_poly, pressure_freezing_CT, t_freezing, t_freezing_first_derivatives, t_freezing_first_derivatives_poly, ) gsw-3.6.21/gsw/conversions.py0000644000175000017500000000354715147371315016327 0ustar alastairalastair""" Conversions involving temperature, salinity, entropy, pressure, and height. Those most commonly used probably include: - :func:`gsw.CT_from_t` - :func:`gsw.SA_from_SP` - :func:`gsw.SP_from_C` - :func:`gsw.p_from_z` - :func:`gsw.z_from_p` """ __all__ = ['t90_from_t68', 'adiabatic_lapse_rate_from_CT', 'C_from_SP', 'CT_from_enthalpy', 'CT_from_entropy', 'CT_from_pt', 'CT_from_rho', 'CT_from_t', 'deltaSA_from_SP', 'entropy_from_pt', 'entropy_from_t', 'pt0_from_t', 'pt_from_CT', 'pt_from_entropy', 'pt_from_t', 'SA_from_rho', 'SA_from_SP', 'SA_from_Sstar', 'SP_from_C', 'SP_from_SA', 'SP_from_SK', 'SP_from_SR', 'SP_from_Sstar', 'SR_from_SP', 'Sstar_from_SA', 'Sstar_from_SP', 't_from_CT', 'p_from_z', 'z_from_p', ] from ._fixed_wrapped_ufuncs import ( C_from_SP, CT_from_enthalpy, CT_from_entropy, CT_from_pt, CT_from_rho, CT_from_t, SA_from_rho, SA_from_SP, SA_from_Sstar, SP_from_C, SP_from_SA, SP_from_SK, SP_from_SR, SP_from_Sstar, SR_from_SP, Sstar_from_SA, Sstar_from_SP, adiabatic_lapse_rate_from_CT, deltaSA_from_SP, entropy_from_pt, entropy_from_t, p_from_z, pt0_from_t, pt_from_CT, pt_from_entropy, pt_from_t, t_from_CT, z_from_p, ) from ._utilities import match_args_return @match_args_return def t90_from_t68(t68): """ ITS-90 temperature from IPTS-68 temperature This conversion should be applied to all in-situ data collected between 1/1/1968 and 31/12/1989. """ return t68 / 1.00024 gsw-3.6.21/gsw/utility.py0000644000175000017500000000357515147371315015463 0ustar alastairalastair""" Functions not specific to the TEOS-10 realm of variables. """ import numpy as np from . import _gsw_ufuncs from ._utilities import indexer, match_args_return @match_args_return def pchip_interp(x, y, xi, axis=0): """ Interpolate using Piecewise Cubic Hermite Interpolating Polynomial This is a shape-preserving algorithm; it does not introduce new local extrema. The implementation in C that is wrapped here is largely taken from the scipy implementation, https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.PchipInterpolator.html. Points outside the range of the interpolation table are filled using the end values in the table. (In contrast, scipy.interpolate.pchip_interpolate() extrapolates using the end polynomials.) Parameters ---------- x, y : array-like Interpolation table x and y; n-dimensional, must be broadcastable to the same dimensions. xi : array-like One-dimensional array of new x values. axis : int, optional, default is 0 Axis along which xi is taken. Returns ------- yi : array Values of y interpolated to xi along the specified axis. """ xi = np.array(xi, dtype=float, copy=False, order='C', ndmin=1) if xi.ndim > 1: raise ValueError('xi must be no more than 1-dimensional') nxi = xi.size x, y = np.broadcast_arrays(x, y) out_shape = list(x.shape) out_shape[axis] = nxi yi = np.empty(out_shape, dtype=float) yi.fill(np.nan) goodmask = ~(np.isnan(x) | np.isnan(y)) order = 'F' if y.flags.fortran else 'C' for ind in indexer(y.shape, axis, order=order): igood = goodmask[ind] # If p_ref is below the deepest value, skip the profile. xgood = x[ind][igood] ygood = y[ind][igood] yi[ind] = _gsw_ufuncs.util_pchip_interp(xgood, ygood, xi) return yi gsw-3.6.21/gsw/ice.py0000644000175000017500000000202415147371315014504 0ustar alastairalastair""" Functions about ice and melting, but not the freezing point. """ from ._wrapped_ufuncs import ( Helmholtz_energy_ice, adiabatic_lapse_rate_ice, alpha_wrt_t_ice, chem_potential_water_ice, cp_ice, enthalpy_ice, entropy_ice, ice_fraction_to_freeze_seawater, internal_energy_ice, kappa_const_t_ice, kappa_ice, melting_ice_equilibrium_SA_CT_ratio, melting_ice_equilibrium_SA_CT_ratio_poly, melting_ice_into_seawater, melting_ice_SA_CT_ratio, melting_ice_SA_CT_ratio_poly, melting_seaice_equilibrium_SA_CT_ratio, melting_seaice_equilibrium_SA_CT_ratio_poly, melting_seaice_into_seawater, melting_seaice_SA_CT_ratio, melting_seaice_SA_CT_ratio_poly, pot_enthalpy_from_pt_ice, pot_enthalpy_from_pt_ice_poly, pressure_coefficient_ice, pt0_from_t_ice, pt_from_pot_enthalpy_ice, pt_from_pot_enthalpy_ice_poly, pt_from_t_ice, rho_ice, seaice_fraction_to_freeze_seawater, sound_speed_ice, specvol_ice, t_from_pt0_ice, ) gsw-3.6.21/gsw/_fixed_wrapped_ufuncs.py0000644000175000017500000000257215147371315020317 0ustar alastairalastair""" Internally import from this, not from _wrapped_ufuncs. Users should import only from non-private modules, of course. """ import numpy from ._wrapped_ufuncs import * _p_from_z = p_from_z def p_from_z(z, lat, geo_strf_dyn_height=0, sea_surface_geopotential=0): return _p_from_z(z, lat, geo_strf_dyn_height, sea_surface_geopotential) p_from_z.__doc__ = _p_from_z.__doc__ _z_from_p = z_from_p def z_from_p(p, lat, geo_strf_dyn_height=0, sea_surface_geopotential=0): return _z_from_p(p, lat, geo_strf_dyn_height, sea_surface_geopotential) z_from_p.__doc__ = _z_from_p.__doc__ _gibbs = gibbs def gibbs(ns, nt, np, SA, t, p): params = {"ns": ns, "nt": nt, "np": np} for k, v in params.items(): u = numpy.unique(v) if u.min() < 0 or u.max() > 2 or u.dtype.kind != "i": raise ValueError("ns, nt, np must contain integers 0, 1, or 2;" f" found {k}={v}") return _gibbs(ns, nt, np, SA, t, p) gibbs.__doc__ = _gibbs.__doc__ _gibbs_ice = gibbs_ice def gibbs_ice(nt, np, t, p): params = {"nt": nt, "np": np} for k, v in params.items(): u = numpy.unique(v) if u.min() < 0 or u.max() > 2 or u.dtype.kind != "i": raise ValueError("nt, np must contain integers 0, 1, or 2;" f" found {k}={v}") return _gibbs_ice(nt, np, t, p) gibbs_ice.__doc__ = _gibbs_ice.__doc__ gsw-3.6.21/gsw/_version.py0000644000175000017500000000002615147371330015565 0ustar alastairalastair__version__ = '3.6.21'gsw-3.6.21/gsw/interpolation.py0000644000175000017500000001535415147371315016645 0ustar alastairalastair""" Functions for vertical interpolation. """ import numpy as np from . import _gsw_ufuncs from ._utilities import indexer, match_args_return __all__ = ['sa_ct_interp', 'tracer_ct_interp', ] @match_args_return def sa_ct_interp(SA, CT, p, p_i, axis=0): """ Interpolates vertical casts of values of Absolute Salinity and Conservative Temperature to the arbitrary pressures p_i. Parameters ---------- SA : array-like Absolute Salinity, g/kg CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_i : array-like Sea pressure to interpolate on, dbar axis : int, optional, default is 0 The index of the pressure dimension in SA and CT. Returns ------- SA_i : array Values of SA interpolated to p_i along the specified axis. CT_i : array Values of CT interpolated to p_i along the specified axis. """ if SA.shape != CT.shape: raise ValueError(f'Shapes of SA and CT must match; found {SA.shape} and {CT.shape}') if p.ndim != p_i.ndim: raise ValueError(f'p and p_i must have the same number of dimensions;\n' f' found {p.ndim} versus {p_i.ndim}') if p.ndim == 1 and SA.ndim > 1: if len(p) != SA.shape[axis]: raise ValueError( f'With 1-D p, len(p) must be SA.shape[axis];\n' f' found {len(p)} versus {SA.shape[axis]} on specified axis, {axis}' ) ind = [np.newaxis] * SA.ndim ind[axis] = slice(None) p = p[tuple(ind)] p_i = p_i[tuple(ind)] elif p.ndim > 1: if p.shape != SA.shape: raise ValueError(f'With {p.ndim}-D p, shapes of p and SA must match;\n' f'found {p.shape} and {SA.shape}') if any(p.shape[i] != p_i.shape[i] for i in range(p.ndim) if i != axis): raise ValueError(f'With {p.ndim}-D p, p and p_i must have the same dimensions outside of axis {axis};\n' f' found {p.shape} versus {p_i.shape}') with np.errstate(invalid='ignore'): # The need for this context seems to be a bug in np.ma.any. if np.ma.any(np.ma.diff(np.ma.masked_invalid(p_i), axis=axis) <= 0) \ or np.ma.any(np.ma.diff(np.ma.masked_invalid(p), axis=axis) <= 0): raise ValueError('p and p_i must be increasing along the specified axis') p = np.broadcast_to(p, SA.shape) goodmask = ~(np.isnan(SA) | np.isnan(CT) | np.isnan(p)) SA_i = np.empty(p_i.shape, dtype=float) CT_i = np.empty(p_i.shape, dtype=float) SA_i.fill(np.nan) CT_i.fill(np.nan) try: order = 'F' if SA.flags.fortran else 'C' except AttributeError: order = 'C' # e.g., xarray DataArray doesn't have flags for ind in indexer(SA.shape, axis, order=order): # this is needed to support xarray inputs for numpy < 1.23 igood = np.asarray(goodmask[ind]) pgood = p[ind][igood] pi = p_i[ind] # There must be at least 2 non-NaN values for interpolation if len(pgood) > 2: sa = SA[ind][igood] ct = CT[ind][igood] sai, cti = _gsw_ufuncs.sa_ct_interp(sa, ct, pgood, pi) SA_i[ind] = sai CT_i[ind] = cti return (SA_i, CT_i) @match_args_return def tracer_ct_interp(tracer, CT, p, p_i, factor=9., axis=0): """ Interpolates vertical casts of values of a tracer and Conservative Temperature to the arbitrary pressures p_i. Parameters ---------- tracer : array-like tracer CT : array-like Conservative Temperature (ITS-90), degrees C p : array-like Sea pressure (absolute pressure minus 10.1325 dbar), dbar p_i : array-like Sea pressure to interpolate on, dbar factor: float, optional, default is 9. Ratio between the ranges of Conservative Temperature and tracer in the world ocean. axis : int, optional, default is 0 The index of the pressure dimension in tracer and CT. Returns ------- tracer_i : array Values of tracer interpolated to p_i along the specified axis. CT_i : array Values of CT interpolated to p_i along the specified axis. """ if tracer.shape != CT.shape: raise ValueError(f'Shapes of tracer and CT must match; found {tracer.shape} and {CT.shape}') if p.ndim != p_i.ndim: raise ValueError(f'p and p_i must have the same number of dimensions;\n' f' found {p.ndim} versus {p_i.ndim}') if p.ndim == 1 and tracer.ndim > 1: if len(p) != tracer.shape[axis]: raise ValueError( f'With 1-D p, len(p) must be tracer.shape[axis];\n' f' found {len(p)} versus {tracer.shape[axis]} on specified axis, {axis}' ) ind = [np.newaxis] * tracer.ndim ind[axis] = slice(None) p = p[tuple(ind)] p_i = p_i[tuple(ind)] elif p.ndim > 1: if p.shape != tracer.shape: raise ValueError(f'With {p.ndim}-D p, shapes of p and tracer must match;\n' f'found {p.shape} and {tracer.shape}') if any(p.shape[i] != p_i.shape[i] for i in range(p.ndim) if i != axis): raise ValueError(f'With {p.ndim}-D p, p and p_i must have the same dimensions outside of axis {axis};\n' f' found {p.shape} versus {p_i.shape}') with np.errstate(invalid='ignore'): # The need for this context seems to be a bug in np.ma.any. if np.ma.any(np.ma.diff(np.ma.masked_invalid(p_i), axis=axis) <= 0) \ or np.ma.any(np.ma.diff(np.ma.masked_invalid(p), axis=axis) <= 0): raise ValueError('p and p_i must be increasing along the specified axis') p = np.broadcast_to(p, tracer.shape) goodmask = ~(np.isnan(tracer) | np.isnan(CT) | np.isnan(p)) tracer_i = np.empty(p_i.shape, dtype=float) CT_i = np.empty(p_i.shape, dtype=float) tracer_i.fill(np.nan) CT_i.fill(np.nan) try: order = 'F' if tracer.flags.fortran else 'C' except AttributeError: order = 'C' # e.g., xarray DataArray doesn't have flags for ind in indexer(tracer.shape, axis, order=order): # this is needed to support xarray inputs for numpy < 1.23 igood = np.asarray(goodmask[ind]) pgood = p[ind][igood] pi = p_i[ind] # There must be at least 2 non-NaN values for interpolation if len(pgood) > 2: tr = tracer[ind][igood] ct = CT[ind][igood] tri, cti = _gsw_ufuncs.tracer_ct_interp(tr, ct, pgood, pi, factor) tracer_i[ind] = tri CT_i[ind] = cti return (tracer_i, CT_i) gsw-3.6.21/gsw/density.py0000644000175000017500000000101215147371315015417 0ustar alastairalastair""" Functions related to density and specific volume. These are a subset of the TEOS-10 table category "specific volume, density, and enthalpy". We are grouping the functions related to enthalpy and internal energy in their own "energy" module. """ from ._wrapped_ufuncs import ( alpha, alpha_on_beta, beta, kappa, rho, rho_alpha_beta, rho_t_exact, sigma0, sigma1, sigma2, sigma3, sigma4, sound_speed, specvol, specvol_alpha_beta, specvol_anom_standard, ) gsw-3.6.21/gsw/__init__.py0000644000175000017500000000351615147371315015512 0ustar alastairalastair""" This is a Python implementation of the Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10. Extensive documentation is available from https://www.teos-10.org/; users of this Python package are strongly encouraged to study the documents posted there. This implementation is based on GSW-C for core functions, with additional functions written in Python. GSW-C is the work of Frank Delahoyde and Glenn Hyland (author of GSW-Fortran, on which GSW-C is based), who translated and re-implemented the algorithms originally written in Matlab by David Jackett, Trevor McDougall, and Paul Barker. The present Python library has an interface that is similar to the original Matlab code, but with a few important differences: - Many functions in the GSW-Matlab toolbox are not yet available here. - Taking advantage of Python namespaces, we omit the "gsw" prefix from the function names. - Missing values may be handled using `numpy.ma` masked arrays, or using `nan` values. - All functions follow numpy broadcasting rules; function arguments must be broadcastable to the dimensions of the highest-dimensioned argument. Recall that with numpy broadcasting, extra dimensions are automatically added as needed on the left, but must be added explicitly as needed on the right. - Functions such as `Nsquared` that operate on profiles rather than scalars have an `axis` keyword argument to specify the index that is incremented along the pressure (depth) axis. """ from . import conversions, density, energy, geostrophy, ice, stability, utility from ._fixed_wrapped_ufuncs import * # noqa from .conversions import t90_from_t68 from .geostrophy import * # noqa from .interpolation import * # noqa from .stability import * # noqa from .utility import * # noqa try: from ._version import __version__ except ImportError: __version__ = "unknown" gsw-3.6.21/requirements-dev.txt0000644000175000017500000000012215147371315016627 0ustar alastairalastairdask numpydoc pandas>=2 pytest scipy setuptools_scm sphinx sphinx_rtd_theme xarray