.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_06_knudsen_equation_of_state.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_06_knudsen_equation_of_state.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_06_knudsen_equation_of_state.py:


Knudsen's equation of state (1901)
==================================

Martin Knudsen, with Carl Forch and Søren Sørensen, measured seawater density
against temperature and salinity and published the Hydrographical Tables used
for the next 70 years. Near a reference state the density is linear in both:
warming makes water lighter and salt makes it heavier, so lines of equal
density in the temperature-salinity plane have slope ``alpha / beta``.

.. GENERATED FROM PYTHON SOURCE LINES 11-28



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_06_knudsen_equation_of_state_001.png
   :alt: Isopycnals of the linear equation of state [kg/m^3]
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_06_knudsen_equation_of_state_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.oceanography import linear_density

    alpha, beta = 2e-4, 7.6e-4
    temperature, salinity = np.meshgrid(np.linspace(-10, 15, 101), np.linspace(-3, 3, 101))
    density = linear_density(1027, temperature, salinity, alpha, beta)
    assert np.isclose(linear_density(1027, 1.0, alpha / beta, alpha, beta), 1027)

    fig, ax = plt.subplots()
    contours = ax.contour(salinity, temperature, density, levels=12, cmap="viridis")
    ax.clabel(contours, fmt="%.1f", fontsize=7)
    ax.set(xlabel="salinity anomaly [g/kg]", ylabel="temperature anomaly [K]", title="Isopycnals of the linear equation of state [kg/m^3]")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.106 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_06_knudsen_equation_of_state.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_06_knudsen_equation_of_state.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_knudsen_equation_of_state.ipynb <plot_06_knudsen_equation_of_state.ipynb>`

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

      :download:`Download Python source code: plot_06_knudsen_equation_of_state.py <plot_06_knudsen_equation_of_state.py>`

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

      :download:`Download zipped: plot_06_knudsen_equation_of_state.zip <plot_06_knudsen_equation_of_state.zip>`


.. only:: html

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

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