.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/atmosphere/plot_04_hadley_circulation.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_04_hadley_circulation.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_04_hadley_circulation.py:


Hadley's circulation (1735)
===========================

George Hadley explained the trade winds. Air heated at the equator rises and
flows poleward aloft, and air returns towards the equator near the ground.
The ground there moves eastward faster than at the latitude the air came
from, so the returning air lags behind and blows from the east. Today the
deflection is written with the Coriolis parameter ``f = 2 Omega sin(phi)``.
A ring of air that leaves the equator at rest and keeps its angular momentum
gains the westerly wind ``Omega a sin^2(phi) / cos(phi)``, whose growth with
latitude is ``f + u tan(phi) / a``.

.. GENERATED FROM PYTHON SOURCE LINES 14-37



.. image-sg:: /api/gallery/atmosphere/images/sphx_glr_plot_04_hadley_circulation_001.png
   :alt: Coriolis parameter, Upper branch conserving angular momentum
   :srcset: /api/gallery/atmosphere/images/sphx_glr_plot_04_hadley_circulation_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    angular-momentum wind at 30 degrees: 134 m/s






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import coriolis_parameter
    from earthsciencekit.constants import EARTH_RADIUS, OMEGA_EARTH

    latitude = np.deg2rad(np.linspace(0, 30, 301))
    f = coriolis_parameter(latitude)
    u = OMEGA_EARTH * EARTH_RADIUS * np.sin(latitude) ** 2 / np.cos(latitude)
    dudy = np.gradient(u, EARTH_RADIUS * latitude)
    np.testing.assert_allclose(dudy[1:-1], (f + u * np.tan(latitude) / EARTH_RADIUS)[1:-1], rtol=1e-3)
    np.testing.assert_allclose(coriolis_parameter(-latitude), -f)
    print(f"angular-momentum wind at 30 degrees: {u[-1]:.0f} m/s")

    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    axes[0].plot(np.rad2deg(latitude), f * 1e4)
    axes[0].set(xlabel="latitude [degree]", ylabel="f [10^-4 /s]", title="Coriolis parameter")
    axes[1].plot(np.rad2deg(latitude), u)
    axes[1].set(xlabel="latitude [degree]", ylabel="zonal wind [m/s]", title="Upper branch conserving angular momentum")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.188 seconds)


.. _sphx_glr_download_api_gallery_atmosphere_plot_04_hadley_circulation.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_04_hadley_circulation.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_hadley_circulation.ipynb <plot_04_hadley_circulation.ipynb>`

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

      :download:`Download Python source code: plot_04_hadley_circulation.py <plot_04_hadley_circulation.py>`

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

      :download:`Download zipped: plot_04_hadley_circulation.zip <plot_04_hadley_circulation.zip>`


.. only:: html

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

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