.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_16_schoof_grounding_line_flux.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_glaciology_plot_16_schoof_grounding_line_flux.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_glaciology_plot_16_schoof_grounding_line_flux.py:


Schoof's grounding-line flux (2007)
===================================

Christian Schoof resolved the boundary layer where a sliding ice sheet meets
its shelf and found that the flux across the grounding line is a power of
the flotation thickness, about 4.75 for Glen's n = 3 and a sliding exponent
of 1/3. A grounding line is steady where this flux equals the snowfall
upstream, and stable only where the bed rises inland. On an overdeepened bed
the steady states come in pairs, and the inner one is unstable.

.. GENERATED FROM PYTHON SOURCE LINES 12-43



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_16_schoof_grounding_line_flux_001.png
   :alt: An overdeepened marine bed, Schoof: filled stable, open unstable
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_16_schoof_grounding_line_flux_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY, ICE_DENSITY, SECONDS_PER_YEAR
    from earthsciencekit.glaciology import flotation_thickness, schoof_grounding_line_flux

    parameters = (2.4e-25, 3, 7.6e6, 1 / 3, ICE_DENSITY, 1028, GRAVITY)
    x = np.linspace(100e3, 1400e3, 1301)
    bed_depth = 200 + 700 * np.exp(-(((x - 800e3) / 250e3) ** 2)) + 2e-4 * x  # an overdeepening
    flux = schoof_grounding_line_flux(flotation_thickness(bed_depth, ICE_DENSITY, 1028), *parameters)
    supply = 0.2 / SECONDS_PER_YEAR * x
    ratio = schoof_grounding_line_flux(2000, *parameters) / schoof_grounding_line_flux(1000, *parameters)
    assert np.isclose(ratio, 2**4.75)
    imbalance = flux - supply
    crossings = np.flatnonzero(np.diff(np.sign(imbalance)))
    stable = np.gradient(imbalance, x)[crossings] > 0
    assert crossings.size >= 2 and stable.any() and not stable.all()

    fig, (top, bottom) = plt.subplots(2, 1, figsize=(8, 7), sharex=True)
    top.plot(x / 1e3, -bed_depth, color="saddlebrown")
    top.set(ylabel="bed elevation [m]", title="An overdeepened marine bed")
    bottom.semilogy(x / 1e3, flux * SECONDS_PER_YEAR / 1e6, label="grounding-line flux")
    bottom.semilogy(x / 1e3, supply * SECONDS_PER_YEAR / 1e6, "k--", label="snowfall upstream")
    for index, ok in zip(crossings, stable):
        bottom.plot(x[index] / 1e3, supply[index] * SECONDS_PER_YEAR / 1e6, "o", color="k", mfc="k" if ok else "white")
    bottom.set(xlabel="grounding-line position [km]", ylabel="flux [km^2/year]", title="Schoof: filled stable, open unstable")
    bottom.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.264 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_16_schoof_grounding_line_flux.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/glaciology/plot_16_schoof_grounding_line_flux.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_16_schoof_grounding_line_flux.ipynb <plot_16_schoof_grounding_line_flux.ipynb>`

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

      :download:`Download Python source code: plot_16_schoof_grounding_line_flux.py <plot_16_schoof_grounding_line_flux.py>`

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

      :download:`Download zipped: plot_16_schoof_grounding_line_flux.zip <plot_16_schoof_grounding_line_flux.zip>`


.. only:: html

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

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