.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/atmosphere/plot_03_halley_barometric_altitude.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_03_halley_barometric_altitude.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_03_halley_barometric_altitude.py:


Halley's barometric altitude (1686)
===================================

Edmond Halley combined Boyle's law with the weight of the air and found that
height grows with the logarithm of pressure: equal ratios of pressure mark
equal steps of height. The step for a factor e is the scale height
``R T / g``, about 8 km. Inverting the barometric law turns a barometer into an
altimeter.

.. GENERATED FROM PYTHON SOURCE LINES 11-30



.. image-sg:: /api/gallery/atmosphere/images/sphx_glr_plot_03_halley_barometric_altitude_001.png
   :alt: Height is linear in log pressure
   :srcset: /api/gallery/atmosphere/images/sphx_glr_plot_03_halley_barometric_altitude_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import barometric_pressure, scale_height
    from earthsciencekit.constants import GRAVITY

    height = np.linspace(0, 30e3, 301)
    fig, ax = plt.subplots()
    for temperature in [230, 260, 290]:
        H = float(scale_height(temperature, GRAVITY))
        pressure = barometric_pressure(101325, height, temperature, GRAVITY)
        np.testing.assert_allclose(H * np.log(101325 / pressure), height, atol=1e-9)
        assert np.isclose(barometric_pressure(101325, H, temperature, GRAVITY), 101325 / np.e)
        ax.semilogx(pressure / 100, height / 1000, label=f"{temperature} K, H = {H / 1000:.2f} km")
    ax.set(xlabel="pressure [hPa, log scale]", ylabel="height [km]", title="Height is linear in log pressure")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.120 seconds)


.. _sphx_glr_download_api_gallery_atmosphere_plot_03_halley_barometric_altitude.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_03_halley_barometric_altitude.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_halley_barometric_altitude.ipynb <plot_03_halley_barometric_altitude.ipynb>`

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

      :download:`Download Python source code: plot_03_halley_barometric_altitude.py <plot_03_halley_barometric_altitude.py>`

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

      :download:`Download zipped: plot_03_halley_barometric_altitude.zip <plot_03_halley_barometric_altitude.zip>`


.. only:: html

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

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