.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_15_penman_evaporation.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_15_penman_evaporation.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_15_penman_evaporation.py:


Penman's evaporation (1948)
===========================

Howard Penman combined the energy balance of a wet surface with Dalton's law,
and linearized the saturation curve between the air and the surface, so the
unknown surface temperature drops out. Evaporation becomes a weighted mean of
a radiation term and a drying-power term that need only the net radiation and
standard measurements at screen height. The example solves the full energy
balance for the surface temperature and shows that Penman's equation agrees
to within a few per cent.

.. GENERATED FROM PYTHON SOURCE LINES 13-49



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_15_penman_evaporation_001.png
   :alt: Penman: no surface temperature needed
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_15_penman_evaporation_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.atmosphere import saturation_vapor_pressure
    from earthsciencekit.constants import LATENT_HEAT_VAPORIZATION
    from earthsciencekit.hydrology import dalton_evaporation, penman_evaporation, psychrometric_constant, saturation_slope

    air, pressure = 293.15, 101325.0
    vapor = 0.6 * saturation_vapor_pressure(air)
    wind_function = 3.0e-8 * (1 + 0.54 * 2.0)  # kg/(m^2 s Pa) at 2 m/s
    gamma = psychrometric_constant(pressure)
    drying = dalton_evaporation(saturation_vapor_pressure(air), vapor, wind_function)
    radiation = np.linspace(50, 400, 36)


    def surface_balance(surface, net):
        latent = LATENT_HEAT_VAPORIZATION * dalton_evaporation(saturation_vapor_pressure(surface), vapor, wind_function)
        return latent + LATENT_HEAT_VAPORIZATION * wind_function * gamma * (surface - air) - net


    surface = np.array([brentq(surface_balance, air - 20, air + 20, args=(net,)) for net in radiation])
    exact = dalton_evaporation(saturation_vapor_pressure(surface), vapor, wind_function)
    penman = penman_evaporation(radiation, air, drying, pressure)
    assert np.all(np.abs(penman / exact - 1) < 0.05)
    weight = saturation_slope(air) / (saturation_slope(air) + gamma)

    fig, ax = plt.subplots()
    ax.plot(radiation, exact * 86400, lw=4, alpha=0.4, label="energy balance solved for the surface temperature")
    ax.plot(radiation, penman * 86400, "k", label="Penman (1948)")
    ax.plot(radiation, weight * radiation / LATENT_HEAT_VAPORIZATION * 86400, ":", label=f"radiation term, weight {weight:.2f}")
    ax.set(xlabel="net radiation [W/m^2]", ylabel="evaporation [mm/day]", title="Penman: no surface temperature needed")
    ax.legend(fontsize="small")

    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_15_penman_evaporation.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_15_penman_evaporation.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_15_penman_evaporation.ipynb <plot_15_penman_evaporation.ipynb>`

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

      :download:`Download Python source code: plot_15_penman_evaporation.py <plot_15_penman_evaporation.py>`

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

      :download:`Download zipped: plot_15_penman_evaporation.zip <plot_15_penman_evaporation.zip>`


.. only:: html

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

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