.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_14_stommel_thermohaline_boxes.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_14_stommel_thermohaline_boxes.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_14_stommel_thermohaline_boxes.py:


Stommel's two-box thermohaline circulation (1961)
=================================================

Stommel connected a warm, salty equatorial box with a cold polar box. Heat
makes the polar water dense and drives sinking there; salt works against it.
For moderate freshwater forcing the boxes have two stable states, a strong
thermal overturning and a weak reversed haline one, and which one the ocean
settles in depends on where it starts.

.. GENERATED FROM PYTHON SOURCE LINES 11-40



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_14_stommel_thermohaline_boxes_001.png
   :alt: Equilibria fold at q = q_T / 2, Same forcing, two outcomes
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_14_stommel_thermohaline_boxes_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.oceanography import simulate_thermohaline_boxes, thermohaline_forcing
    from earthsciencekit.units import convert

    thermal, haline, volume = 3e7, 6e6, 1e16
    forcing = 0.8 * thermal**2 / (4 * haline)
    flow = np.linspace(-1.5 * thermal, thermal, 501)
    time = convert(np.linspace(0, 1500, 301), "year", "s")
    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    left.plot(thermohaline_forcing(flow, thermal, haline), convert(flow, "m^3/s", "Sv"))
    left.axvline(forcing, color="0.5", ls="--")
    for initial in [0.0, 4.0, 8.0]:
        result = simulate_thermohaline_boxes(thermal, haline, forcing, volume, time, initial_salinity_difference=initial)
        final = result.values[-1, 1]
        assert np.isclose(thermohaline_forcing(final, thermal, haline), forcing, rtol=1e-5)
        right.plot(convert(time, "s", "year"), convert(result.values[:, 1], "m^3/s", "Sv"), label=f"initial dS = {initial:g} g/kg")
        left.plot(forcing, convert(final, "m^3/s", "Sv"), "ko")
    assert simulate_thermohaline_boxes(thermal, haline, forcing, volume, time).values[-1, 1] > 0
    assert simulate_thermohaline_boxes(thermal, haline, forcing, volume, time, initial_salinity_difference=8).values[-1, 1] < 0
    left.set(xlabel="salt forcing [g/kg m^3/s]", ylabel="steady overturning [Sv]", title="Equilibria fold at q = q_T / 2")
    right.axhline(0, color="k", lw=0.5)
    right.set(xlabel="time [years]", ylabel="overturning [Sv]", title="Same forcing, two outcomes")
    right.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.307 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_14_stommel_thermohaline_boxes.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_14_stommel_thermohaline_boxes.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_14_stommel_thermohaline_boxes.ipynb <plot_14_stommel_thermohaline_boxes.ipynb>`

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

      :download:`Download Python source code: plot_14_stommel_thermohaline_boxes.py <plot_14_stommel_thermohaline_boxes.py>`

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

      :download:`Download zipped: plot_14_stommel_thermohaline_boxes.zip <plot_14_stommel_thermohaline_boxes.zip>`


.. only:: html

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

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