.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/atmosphere/plot_16_charney_eniac_forecast.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_16_charney_eniac_forecast.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_16_charney_eniac_forecast.py:


Charney, Fjørtoft and von Neumann's ENIAC forecast (1950)
=========================================================

Jule Charney, Ragnar Fjørtoft and John von Neumann ran the first computer
weather forecasts on the ENIAC in 1950. They avoided Richardson's failure by
predicting only the vorticity of a nondivergent barotropic flow, which keeps
the fast gravity waves out. Here the same equation runs on a doubly periodic
beta plane. A single Fourier mode is an exact Rossby wave and moves at the
speed of Rossby's formula; a mix of modes evolves nonlinearly while keeping
its enstrophy.

.. GENERATED FROM PYTHON SOURCE LINES 13-43



.. image-sg:: /api/gallery/atmosphere/images/sphx_glr_plot_16_charney_eniac_forecast_001.png
   :alt: analysis, 24-hour forecast
   :srcset: /api/gallery/atmosphere/images/sphx_glr_plot_16_charney_eniac_forecast_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import rossby_wave_speed, simulate_barotropic_vorticity

    n, spacing, beta = 32, 600e3, 1.6e-11
    x = np.arange(n) * spacing
    X, Y = np.meshgrid(x, x)
    length = n * spacing
    day = 86400.0
    k = 2 * np.pi * 2 / length
    single = simulate_barotropic_vorticity(1e-5 * np.sin(k * X), [0, day], beta, spacing)
    shift = float(rossby_wave_speed(0, beta, k)) * day
    np.testing.assert_allclose(single.values[-1], 1e-5 * np.sin(k * (X - shift)).ravel(), atol=1e-10)

    rng = np.random.default_rng(1950)
    modes = [(i, j) for i in range(4) for j in range(-3, 4)]
    zeta = sum(4e-6 * rng.normal() * np.cos(2 * np.pi * (i * X + j * Y) / length + rng.uniform(0, 2 * np.pi)) for i, j in modes)
    result = simulate_barotropic_vorticity(zeta, [0, day], beta, spacing)
    enstrophy = np.sum(result.values**2, axis=1)
    assert np.isclose(enstrophy[-1], enstrophy[0], rtol=1e-5)

    fig, axes = plt.subplots(1, 2, figsize=(10, 4.2))
    for ax, field, title in zip(axes, result.values, ["analysis", "24-hour forecast"]):
        image = ax.pcolormesh(X / 1e3, Y / 1e3, field.reshape(n, n) * 1e5, cmap="RdBu_r", vmin=-4, vmax=4)
        ax.set(xlabel="east [km]", ylabel="north [km]", title=title, aspect="equal")
    fig.colorbar(image, ax=axes, label="relative vorticity [10^-5 /s]")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.200 seconds)


.. _sphx_glr_download_api_gallery_atmosphere_plot_16_charney_eniac_forecast.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_16_charney_eniac_forecast.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_16_charney_eniac_forecast.ipynb <plot_16_charney_eniac_forecast.ipynb>`

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

      :download:`Download Python source code: plot_16_charney_eniac_forecast.py <plot_16_charney_eniac_forecast.py>`

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

      :download:`Download zipped: plot_16_charney_eniac_forecast.zip <plot_16_charney_eniac_forecast.zip>`


.. only:: html

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

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