.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_10_horton_infiltration_capacity.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_hydrology_plot_10_horton_infiltration_capacity.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_hydrology_plot_10_horton_infiltration_capacity.py:


Horton's infiltration capacity (1933)
=====================================

Robert Horton described the soil surface as a separator: rain up to the
infiltration capacity enters the soil and feeds groundwater, and rain beyond
it runs off over the surface. The capacity falls exponentially during a storm
from an initial to a steady value. Overland flow produced this way, Hortonian
or infiltration-excess runoff, is the shaded area where the rain exceeds the
capacity.

.. GENERATED FROM PYTHON SOURCE LINES 12-34



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_10_horton_infiltration_capacity_001.png
   :alt: Horton: 16.2 mm runs off over the surface
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_10_horton_infiltration_capacity_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import horton_cumulative_infiltration, horton_infiltration_rate

    time = np.linspace(0, 3 * 3600, 361)
    capacity = horton_infiltration_rate(time, 25 / 3.6e6, 4 / 3.6e6, 1 / 1800)  # mm/h converted to m/s
    rain = np.full_like(time, 12 / 3.6e6)
    infiltration = np.minimum(rain, capacity)
    runoff_depth = np.trapezoid(rain - infiltration, time)
    total = horton_cumulative_infiltration(time[-1], 25 / 3.6e6, 4 / 3.6e6, 1 / 1800)
    assert np.isclose(total, np.trapezoid(capacity, time), rtol=1e-4) and runoff_depth > 0

    fig, ax = plt.subplots()
    ax.plot(time / 3600, capacity * 3.6e6, label="infiltration capacity")
    ax.plot(time / 3600, rain * 3.6e6, "k--", label="rain, 12 mm/h")
    ax.fill_between(time / 3600, capacity * 3.6e6, rain * 3.6e6, where=rain > capacity, alpha=0.3, label="overland flow")
    ax.set(xlabel="time [h]", ylabel="rate [mm/h]", title=f"Horton: {runoff_depth * 1e3:.1f} mm runs off over the surface")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.081 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_10_horton_infiltration_capacity.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/hydrology/plot_10_horton_infiltration_capacity.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_10_horton_infiltration_capacity.ipynb <plot_10_horton_infiltration_capacity.ipynb>`

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

      :download:`Download Python source code: plot_10_horton_infiltration_capacity.py <plot_10_horton_infiltration_capacity.py>`

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

      :download:`Download zipped: plot_10_horton_infiltration_capacity.zip <plot_10_horton_infiltration_capacity.zip>`


.. only:: html

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

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