.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/atmosphere/plot_06_poisson_adiabat.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_06_poisson_adiabat.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_06_poisson_adiabat.py:


Poisson's adiabat (1823)
========================

Siméon Denis Poisson showed that a gas compressed or expanded without
exchanging heat follows ``T p^(-R/c_p) = constant``. Combined with
hydrostatic balance, a rising dry parcel cools at the dry adiabatic lapse
rate ``g / c_p``, close to 10 K per kilometre. Integrating the parcel's
temperature and pressure confirms both: the cooling is linear in height and
the Poisson invariant, the potential temperature, does not change.

.. GENERATED FROM PYTHON SOURCE LINES 12-37



.. image-sg:: /api/gallery/atmosphere/images/sphx_glr_plot_06_poisson_adiabat_001.png
   :alt: plot 06 poisson adiabat
   :srcset: /api/gallery/atmosphere/images/sphx_glr_plot_06_poisson_adiabat_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    dry adiabatic lapse rate: 9.77 K/km






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import dry_adiabatic_lapse_rate, potential_temperature, simulate_dry_ascent
    from earthsciencekit.constants import CP_DRY_AIR, GRAVITY

    time = np.linspace(0, 3000, 201)
    result = simulate_dry_ascent(300, 101325, 1, time)
    T, pressure = result.values.T
    theta = potential_temperature(T, pressure, 101325)
    np.testing.assert_allclose(theta, 300, rtol=3e-8)
    np.testing.assert_allclose(T, 300 - dry_adiabatic_lapse_rate(GRAVITY, CP_DRY_AIR) * time, atol=1e-8)
    print(f"dry adiabatic lapse rate: {dry_adiabatic_lapse_rate(GRAVITY, CP_DRY_AIR) * 1000:.2f} K/km")

    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    axes[0].plot(T, time / 1000, label="parcel temperature")
    axes[0].plot(theta, time / 1000, linestyle="--", label="potential temperature")
    axes[0].set(xlabel="temperature [K]", ylabel="height [km]")
    axes[0].legend()
    axes[1].plot(pressure / 100, time / 1000)
    axes[1].set(xlabel="pressure [hPa]", ylabel="height [km]")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.169 seconds)


.. _sphx_glr_download_api_gallery_atmosphere_plot_06_poisson_adiabat.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_06_poisson_adiabat.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_poisson_adiabat.ipynb <plot_06_poisson_adiabat.ipynb>`

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

      :download:`Download Python source code: plot_06_poisson_adiabat.py <plot_06_poisson_adiabat.py>`

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

      :download:`Download zipped: plot_06_poisson_adiabat.zip <plot_06_poisson_adiabat.zip>`


.. only:: html

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

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