.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_03_kelvin_cooling_earth.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_plate_tectonics_plot_03_kelvin_cooling_earth.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_plate_tectonics_plot_03_kelvin_cooling_earth.py:


Kelvin's cooling Earth (1862)
=============================

William Thomson (Lord Kelvin) treated the Earth as a half-space cooling from a
uniform 7000 degrees Fahrenheit. The surface gradient of the conductive
solution falls as one over the square root of age, so the measured gradient of
about 1 degree Fahrenheit per 50 feet fixes an age near 100 million years.
Kelvin did not know about radioactive heating or mantle convection.

.. GENERATED FROM PYTHON SOURCE LINES 11-42



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_03_kelvin_cooling_earth_001.png
   :alt: Kelvin's geotherm
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_03_kelvin_cooling_earth_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.plate_tectonics import halfspace_heat_flux, halfspace_temperature
    from earthsciencekit.units import convert

    surface = 273.0
    excess = 7000 * 5 / 9
    diffusivity = 1.18e-6
    measured_gradient = (5 / 9) / (50 * 0.3048)
    age = excess**2 / (np.pi * diffusivity * measured_gradient**2)
    gradient = halfspace_heat_flux(age, diffusivity, 1.0, surface, surface + excess)
    assert np.isclose(float(gradient), measured_gradient)
    age_myr = convert(age, "s", "year") / 1e6
    assert 90 < age_myr < 105

    ages = convert(np.logspace(6, 10, 200), "year", "s")
    depth = np.linspace(0, 400e3, 201)
    fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4))
    left.loglog(convert(ages, "s", "year") / 1e6, halfspace_heat_flux(ages, diffusivity, 1.0, surface, surface + excess) * 1e3)
    left.axhline(measured_gradient * 1e3, color="k", ls="--", label="measured gradient")
    left.axvline(age_myr, color="tab:red", label=f"{age_myr:.0f} million years")
    left.set(xlabel="age [million years]", ylabel="surface gradient [K/km]")
    left.legend()
    right.plot(halfspace_temperature(depth, age, diffusivity, surface, surface + excess), depth / 1e3)
    right.invert_yaxis()
    right.set(xlabel="temperature [K]", ylabel="depth [km]", title="Kelvin's geotherm")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.335 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_03_kelvin_cooling_earth.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/plate_tectonics/plot_03_kelvin_cooling_earth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_kelvin_cooling_earth.ipynb <plot_03_kelvin_cooling_earth.ipynb>`

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

      :download:`Download Python source code: plot_03_kelvin_cooling_earth.py <plot_03_kelvin_cooling_earth.py>`

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

      :download:`Download zipped: plot_03_kelvin_cooling_earth.zip <plot_03_kelvin_cooling_earth.zip>`


.. only:: html

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

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