.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/atmosphere/plot_07_magnus_vapour_pressure.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_atmosphere_plot_07_magnus_vapour_pressure.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_atmosphere_plot_07_magnus_vapour_pressure.py:


Magnus's vapour-pressure formula (1844)
=======================================

Gustav Magnus measured the pressure of water vapour in equilibrium with
liquid water and fitted it with an exponential in temperature. Clausius
later derived the same shape from thermodynamics. The package uses the
Clausius-Clapeyron form with a constant latent heat. Over 0-40 °C it agrees
with a modern Magnus fit (Alduchov and Eskridge, 1996) to within 5%, and both
give the 6-7% increase per kelvin that makes warm air hold so much more water.

.. GENERATED FROM PYTHON SOURCE LINES 12-36



.. image-sg:: /api/gallery/atmosphere/images/sphx_glr_plot_07_magnus_vapour_pressure_001.png
   :alt: plot 07 magnus vapour pressure
   :srcset: /api/gallery/atmosphere/images/sphx_glr_plot_07_magnus_vapour_pressure_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    relative humidity of 15 hPa vapour at 25 °C: 0.47






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import relative_humidity, saturation_vapor_pressure

    celsius = np.linspace(0, 40, 201)
    clausius = saturation_vapor_pressure(celsius + 273.15)
    magnus = 610.94 * np.exp(17.625 * celsius / (celsius + 243.04))
    assert np.all(np.abs(clausius / magnus - 1) < 0.05)
    growth = np.gradient(np.log(clausius), celsius)
    assert np.all((growth > 0.055) & (growth < 0.075))
    print(f"relative humidity of 15 hPa vapour at 25 °C: {relative_humidity(1500, saturation_vapor_pressure(298.15)):.2f}")

    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    axes[0].plot(celsius, clausius / 100, label="Clausius-Clapeyron (package)")
    axes[0].plot(celsius, magnus / 100, ls="--", label="Magnus fit")
    axes[0].set(xlabel="temperature [°C]", ylabel="saturation vapour pressure [hPa]")
    axes[0].legend()
    axes[1].plot(celsius, growth * 100)
    axes[1].set(xlabel="temperature [°C]", ylabel="increase per kelvin [%]")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.181 seconds)


.. _sphx_glr_download_api_gallery_atmosphere_plot_07_magnus_vapour_pressure.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/atmosphere/plot_07_magnus_vapour_pressure.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_07_magnus_vapour_pressure.ipynb <plot_07_magnus_vapour_pressure.ipynb>`

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

      :download:`Download Python source code: plot_07_magnus_vapour_pressure.py <plot_07_magnus_vapour_pressure.py>`

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

      :download:`Download zipped: plot_07_magnus_vapour_pressure.zip <plot_07_magnus_vapour_pressure.zip>`


.. only:: html

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

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