.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_01_perrault_catchment_water_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_hydrology_plot_01_perrault_catchment_water_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_hydrology_plot_01_perrault_catchment_water_balance.py:


Perrault's catchment water balance (1674)
=========================================

Pierre Perrault measured the rain at Paris for three years and estimated the
flow of the Seine above Aignay-le-Duc. The river carried only about a sixth of
the rain that fell on its basin, so rainfall was more than enough to feed it,
against the old view that rivers rise from the sea through the ground. The
water balance makes the same bookkeeping explicit for a year of synthetic
monthly rain, evaporation and runoff: the storage it implies rises in winter,
falls in summer and returns to its starting value.

.. GENERATED FROM PYTHON SOURCE LINES 13-38



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_01_perrault_catchment_water_balance_001.png
   :alt: Perrault: the river carries a sixth of the rain
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_01_perrault_catchment_water_balance_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import runoff_coefficient, water_balance

    month = np.arange(12)
    rain = 50 + 15 * np.cos(2 * np.pi * (month - 11) / 12)  # mm per month
    evaporation = 32 + 28 * np.cos(2 * np.pi * (month - 6) / 12)
    runoff = rain.sum() / 6 * (1 + 0.5 * np.cos(2 * np.pi * (month - 1) / 12)) / 12
    evaporation *= (rain.sum() - runoff.sum()) / evaporation.sum()  # close the annual balance
    storage = np.cumsum(water_balance(rain, evaporation, runoff))
    ratio = runoff_coefficient(runoff.sum(), rain.sum())
    assert np.isclose(ratio, 1 / 6) and np.isclose(storage[-1], 0)

    fig, (top, bottom) = plt.subplots(2, 1, sharex=True)
    top.plot(month, rain, "o-", label="precipitation")
    top.plot(month, evaporation, "s-", label="evapotranspiration")
    top.plot(month, runoff, "^-", label=f"runoff ({ratio:.2f} of the rain)")
    top.set(ylabel="mm per month", title="Perrault: the river carries a sixth of the rain")
    top.legend(fontsize="small")
    bottom.bar(month, storage, color="0.6")
    bottom.set(xlabel="month (0 = January)", ylabel="storage change [mm]")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.116 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_01_perrault_catchment_water_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/hydrology/plot_01_perrault_catchment_water_balance.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_perrault_catchment_water_balance.ipynb <plot_01_perrault_catchment_water_balance.ipynb>`

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

      :download:`Download Python source code: plot_01_perrault_catchment_water_balance.py <plot_01_perrault_catchment_water_balance.py>`

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

      :download:`Download zipped: plot_01_perrault_catchment_water_balance.zip <plot_01_perrault_catchment_water_balance.zip>`


.. only:: html

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

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