.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_12_mccarthy_muskingum_routing.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_12_mccarthy_muskingum_routing.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_12_mccarthy_muskingum_routing.py:


McCarthy's Muskingum routing (1938)
===================================

Gerald McCarthy, working on flood control in the Muskingum basin of Ohio,
wrote the storage of a river reach as a weighted mix of its inflow and
outflow, ``S = K (X I + (1 - X) O)``. Combined with continuity, the outflow
becomes a fixed linear combination of the latest inflows and the previous
outflow. Routing a flood through a reach delays it by about ``K`` and lowers
its peak, more so when ``X`` is small, while conserving its volume.

.. GENERATED FROM PYTHON SOURCE LINES 12-32



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_12_mccarthy_muskingum_routing_001.png
   :alt: Muskingum: the flood is delayed and flattened
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_12_mccarthy_muskingum_routing_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import muskingum_coefficients, muskingum_routing

    step = 3600.0
    hours = np.arange(96)
    inflow = 20 + 380 * (hours / 12) ** 2 * np.exp(2 * (1 - hours / 12))  # m^3/s
    fig, ax = plt.subplots()
    ax.plot(hours, inflow, "k", lw=2, label="inflow")
    for weighting in (0.0, 0.2, 0.4):
        assert np.isclose(muskingum_coefficients(6 * step, weighting, step).sum(), 1)
        outflow = muskingum_routing(inflow, 6 * step, weighting, step)
        assert np.isclose(outflow.sum(), inflow.sum(), rtol=1e-3) and outflow.max() < inflow.max()
        ax.plot(hours, outflow, label=f"outflow, K = 6 h, X = {weighting}")
    ax.set(xlabel="time [h]", ylabel="discharge [m^3/s]", title="Muskingum: the flood is delayed and flattened")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.101 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_12_mccarthy_muskingum_routing.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_12_mccarthy_muskingum_routing.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_12_mccarthy_muskingum_routing.ipynb <plot_12_mccarthy_muskingum_routing.ipynb>`

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

      :download:`Download Python source code: plot_12_mccarthy_muskingum_routing.py <plot_12_mccarthy_muskingum_routing.py>`

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

      :download:`Download zipped: plot_12_mccarthy_muskingum_routing.zip <plot_12_mccarthy_muskingum_routing.zip>`


.. only:: html

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

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