.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_10_meier_glacier_mass_balance.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_10_meier_glacier_mass_balance.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_10_meier_glacier_mass_balance.py:


Meier's glacier mass balance (1962)
===================================

Mark Meier proposed the definitions of glacier mass budget still in use: the
net balance at each point, the equilibrium line where it is zero, and the
accumulation-area ratio. With a balance rising linearly with altitude, a
glacier is in balance with its climate when the ablation below the
equilibrium line cancels the accumulation above it, which on this synthetic
valley glacier leaves about 60% of its area in the accumulation zone.

.. GENERATED FROM PYTHON SOURCE LINES 12-44



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_10_meier_glacier_mass_balance_001.png
   :alt: Hypsometry, Meier: balance zero at the equilibrium line
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_10_meier_glacier_mass_balance_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


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

    from earthsciencekit.constants import SECONDS_PER_YEAR
    from earthsciencekit.glaciology import accumulation_area_ratio, linear_mass_balance

    elevation = np.linspace(2000, 3400, 141)  # m, centres of 10 m bands
    area = 4e4 * np.exp(-(((elevation - 2900) / 350) ** 2))  # m^2 per band, a wide upper basin
    gradient = 0.007 / SECONDS_PER_YEAR


    def net_balance(ela):
        return np.sum(linear_mass_balance(elevation, ela, gradient) * area)


    balanced = brentq(net_balance, 2000, 3400)
    ratio = accumulation_area_ratio(area[elevation > balanced].sum(), area.sum())
    assert abs(net_balance(balanced)) < 1e-9 and 0.5 < ratio < 0.7

    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
    left.barh(elevation, area / 1e3, height=10, color="lightblue")
    left.axhline(balanced, color="k", ls="--", label=f"equilibrium line, AAR = {ratio:.2f}")
    left.set(xlabel="area per 10 m band [10^3 m^2]", ylabel="elevation [m]", title="Hypsometry")
    left.legend()
    right.plot(linear_mass_balance(elevation, balanced, gradient) * SECONDS_PER_YEAR, elevation)
    right.axvline(0, color="0.5", ls=":")
    right.set(xlabel="mass balance [m ice/year]", title="Meier: balance zero at the equilibrium line")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.304 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_10_meier_glacier_mass_balance.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_10_meier_glacier_mass_balance.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_10_meier_glacier_mass_balance.ipynb <plot_10_meier_glacier_mass_balance.ipynb>`

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

      :download:`Download Python source code: plot_10_meier_glacier_mass_balance.py <plot_10_meier_glacier_mass_balance.py>`

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

      :download:`Download zipped: plot_10_meier_glacier_mass_balance.zip <plot_10_meier_glacier_mass_balance.zip>`


.. only:: html

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

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