.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_09_sherman_unit_hydrograph.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_09_sherman_unit_hydrograph.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_09_sherman_unit_hydrograph.py:


Sherman's unit hydrograph (1932)
================================

LeRoy Sherman proposed that a catchment responds linearly to rain: one
centimetre of excess rainfall in a given interval always produces the same
hydrograph, and a storm produces the sum of these responses, shifted and
scaled by its bursts of rain. The example takes a Nash (1957) cascade of
reservoirs as the unit hydrograph of a 50 km^2 catchment, convolves it with a
three-hour storm, and checks that the flood carries the volume of the excess
rain.

.. GENERATED FROM PYTHON SOURCE LINES 13-34



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_09_sherman_unit_hydrograph_001.png
   :alt: Sherman: the storm is a sum of unit responses
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_09_sherman_unit_hydrograph_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import nash_unit_hydrograph, unit_hydrograph_convolution

    area, step = 50e6, 3600.0
    hours = np.arange(72)
    unit = area * nash_unit_hydrograph(hours * step, 3, 4 * step)  # m^3/s per metre of excess rain
    storm = np.array([0.006, 0.015, 0.004])  # m of excess rain per hour
    flood = unit_hydrograph_convolution(storm, unit)
    assert np.isclose(flood.sum() * step, storm.sum() * area, rtol=1e-2)

    fig, ax = plt.subplots()
    for i, burst in enumerate(storm):
        ax.plot(hours + i, burst * unit, ":", label=f"hour {i + 1}: {burst * 1e3:g} mm")
    ax.plot(np.arange(flood.size), flood, "k", lw=2, label="storm hydrograph")
    ax.set(xlim=(0, 48), xlabel="time [h]", ylabel="direct runoff [m^3/s]", title="Sherman: the storm is a sum of unit responses")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.080 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_09_sherman_unit_hydrograph.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_09_sherman_unit_hydrograph.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_09_sherman_unit_hydrograph.ipynb <plot_09_sherman_unit_hydrograph.ipynb>`

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

      :download:`Download Python source code: plot_09_sherman_unit_hydrograph.py <plot_09_sherman_unit_hydrograph.py>`

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

      :download:`Download zipped: plot_09_sherman_unit_hydrograph.zip <plot_09_sherman_unit_hydrograph.zip>`


.. only:: html

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

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