.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_16_teos10_seawater_density.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_oceanography_plot_16_teos10_seawater_density.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_oceanography_plot_16_teos10_seawater_density.py:


TEOS-10 (2010)
==============

The Thermodynamic Equation of Seawater 2010 replaced the 1980 equation of
state with one derived from a Gibbs function, in Absolute Salinity and
Conservative Temperature. Its density is curved in temperature: mixing two
waters of equal density gives a denser mixture (cabbeling), which no linear
equation of state can show. Here the simplified fit of Roquet et al. (2015)
stands in for the full TEOS-10 polynomial.

.. GENERATED FROM PYTHON SOURCE LINES 12-53



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_16_teos10_seawater_density_001.png
   :alt: Cabbeling: mixing makes water denser
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_16_teos10_seawater_density_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    mixing two waters of 1026.69 kg/m^3 gives 1027.14 kg/m^3






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.optimize import brentq

    from earthsciencekit.oceanography import linear_density, simplified_seawater_density
    from earthsciencekit.units import convert

    alpha, beta = 0.16550 / 1026, 0.76554 / 1026
    cold = (convert(2.0, "degC", "K"), 34.6)
    target = simplified_seawater_density(*cold, 0)
    warm_salinity = brentq(lambda s: simplified_seawater_density(convert(20.0, "degC", "K"), s, 0) - target, 30, 45, xtol=1e-14)
    warm = (convert(20.0, "degC", "K"), warm_salinity)
    mixed = simplified_seawater_density((cold[0] + warm[0]) / 2, (cold[1] + warm[1]) / 2, 0)
    assert mixed > target + 0.1
    linear_cold = linear_density(1026, cold[0] - 283.15, cold[1] - 35, alpha, beta)
    linear_warm = linear_density(1026, warm[0] - 283.15, warm[1] - 35, alpha, beta)
    linear_mix = linear_density(1026, (cold[0] + warm[0]) / 2 - 283.15, (cold[1] + warm[1]) / 2 - 35, alpha, beta)
    assert np.isclose(linear_mix, (linear_cold + linear_warm) / 2)
    print(f"mixing two waters of {target:.2f} kg/m^3 gives {mixed:.2f} kg/m^3")

    salinity, celsius = np.meshgrid(np.linspace(33, 40, 141), np.linspace(-2, 28, 121))
    kelvin = convert(celsius, "degC", "K")
    fig, ax = plt.subplots()
    ax.contour(salinity, celsius, simplified_seawater_density(kelvin, salinity, 0), levels=[target], colors="tab:blue")
    ax.contour(
        salinity,
        celsius,
        linear_density(1026, kelvin - 283.15, salinity - 35, alpha, beta),
        levels=[target],
        colors="tab:orange",
        linestyles="--",
    )
    ax.plot([cold[1], warm[1]], [2, 20], "k:o")
    ax.plot((cold[1] + warm[1]) / 2, 11, "r*", markersize=12, label=f"mixture, +{mixed - target:.2f} kg/m^3")
    ax.plot([], [], color="tab:blue", label="isopycnal, simplified TEOS-10")
    ax.plot([], [], color="tab:orange", ls="--", label="isopycnal, linear")
    ax.set(xlabel="Absolute Salinity [g/kg]", ylabel="Conservative Temperature [degC]", title="Cabbeling: mixing makes water denser")
    ax.legend(loc="lower right")

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.099 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_16_teos10_seawater_density.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/oceanography/plot_16_teos10_seawater_density.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_16_teos10_seawater_density.ipynb <plot_16_teos10_seawater_density.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_16_teos10_seawater_density.py <plot_16_teos10_seawater_density.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_16_teos10_seawater_density.zip <plot_16_teos10_seawater_density.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_