.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/climate/plot_10_budyko_sellers_ice_albedo.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_climate_plot_10_budyko_sellers_ice_albedo.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_climate_plot_10_budyko_sellers_ice_albedo.py:


Budyko and Sellers's ice-albedo feedback (1969)
===============================================

Mikhail Budyko and William Sellers independently built energy-balance models
in which ice reflects more sunlight than ocean or land. Colder climates grow
more ice and absorb less, which cools them further. Both found that a drop of
a few percent in sunlight could freeze the whole planet, and that a frozen
Earth would stay frozen until the Sun grew far brighter: a hysteresis loop.
Inverting the energy balance gives the solar constant that holds each
temperature, which traces every equilibrium at once.

.. GENERATED FROM PYTHON SOURCE LINES 13-43



.. image-sg:: /api/gallery/climate/images/sphx_glr_plot_10_budyko_sellers_ice_albedo_001.png
   :alt: Snowball hysteresis
   :srcset: /api/gallery/climate/images/sphx_glr_plot_10_budyko_sellers_ice_albedo_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.climate import equilibrium_solar_constant

    parameters = (0.62, 0.62, 0.3, 265.0, 8.0)
    temperature = np.linspace(220, 310, 2001)
    solar = equilibrium_solar_constant(temperature, *parameters)
    slope = np.diff(solar)
    folds = np.where(np.sign(slope[1:]) != np.sign(slope[:-1]))[0] + 1
    escape, collapse = solar[folds]
    assert escape > 1361 > collapse
    crossings = np.where(np.diff(np.sign(solar - 1361)))[0]
    assert crossings.size == 3

    stable = np.r_[slope > 0, True]
    fig, ax = plt.subplots()
    ax.plot(np.where(stable, solar, np.nan), temperature, "C0", label="stable")
    ax.plot(np.where(~stable, solar, np.nan), temperature, "C0--", label="unstable")
    cold, warm = slice(None, folds[0]), slice(folds[1], None)
    freeze = temperature[cold][np.argmin(abs(solar[cold] - collapse))]
    thaw = temperature[warm][np.argmin(abs(solar[warm] - escape))]
    ax.annotate("", xy=(collapse, freeze), xytext=(collapse, temperature[folds[1]]), arrowprops={"arrowstyle": "->", "color": "tab:blue"})
    ax.annotate("", xy=(escape, thaw), xytext=(escape, temperature[folds[0]]), arrowprops={"arrowstyle": "->", "color": "tab:red"})
    ax.axvline(1361, color="0.5", ls=":", label="present Sun")
    ax.set(xlabel="solar constant [W/m²]", ylabel="equilibrium temperature [K]", title="Snowball hysteresis")
    ax.legend(loc="lower right")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.079 seconds)


.. _sphx_glr_download_api_gallery_climate_plot_10_budyko_sellers_ice_albedo.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/climate/plot_10_budyko_sellers_ice_albedo.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_10_budyko_sellers_ice_albedo.ipynb <plot_10_budyko_sellers_ice_albedo.ipynb>`

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

      :download:`Download Python source code: plot_10_budyko_sellers_ice_albedo.py <plot_10_budyko_sellers_ice_albedo.py>`

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

      :download:`Download zipped: plot_10_budyko_sellers_ice_albedo.zip <plot_10_budyko_sellers_ice_albedo.zip>`


.. only:: html

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

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