.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/climate/plot_08_keeling_curve.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_climate_plot_08_keeling_curve.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_climate_plot_08_keeling_curve.py:


Keeling's curve (1958)
======================

Charles David Keeling began continuous measurements of carbon dioxide at
Mauna Loa in 1958. Within two years the record showed a seasonal cycle from
the breathing of northern forests and a steady rise. Here the rise is
synthetic: emissions grow by 2% a year and each pulse decays in a single
reservoir with a 50-year time scale. For steady exponential growth, the
fraction of emitted carbon left in the air tends to ``g tau / (1 + g tau)``,
here one half.

.. GENERATED FROM PYTHON SOURCE LINES 13-39



.. image-sg:: /api/gallery/climate/images/sphx_glr_plot_08_keeling_curve_001.png
   :alt: A synthetic Keeling curve, airborne fraction 0.50
   :srcset: /api/gallery/climate/images/sphx_glr_plot_08_keeling_curve_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.climate import carbon_airborne_fraction, carbon_decay
    from earthsciencekit.units import convert

    growth, tau = 0.02, 50.0  # per year, years
    years = np.arange(1750, 2020, 1 / 12)
    dt = 1 / 12
    emissions = 10e12 * np.exp(growth * (years - 2020))  # kg C per year
    age = years[:, None] - years[None, :]
    weight = carbon_decay(emissions[None, :] * dt, convert(tau, "year", "s"), convert(np.clip(age, 0, None), "year", "s"))
    excess = np.where(age >= 0, weight, 0).sum(axis=1)
    exact = 10e12 * (np.exp(growth * (years - 2020)) - np.exp(growth * (1750 - 2020) - (years - 1750) / tau)) / (growth + 1 / tau)
    np.testing.assert_allclose(excess[120:], exact[120:], rtol=0.02)
    fraction = carbon_airborne_fraction(excess[-1], emissions.sum() * dt)
    assert np.isclose(fraction, growth * tau / (1 + growth * tau), atol=0.02)

    ppm = 280 + excess / 2.12e12 + 3 * np.sin(2 * np.pi * (years - 0.3))
    record = years >= 1958
    fig, ax = plt.subplots()
    ax.plot(years[record], ppm[record], lw=0.8)
    ax.set(xlabel="year", ylabel="CO2 [ppm]", title=f"A synthetic Keeling curve, airborne fraction {fraction:.2f}")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.281 seconds)


.. _sphx_glr_download_api_gallery_climate_plot_08_keeling_curve.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/climate/plot_08_keeling_curve.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_08_keeling_curve.ipynb <plot_08_keeling_curve.ipynb>`

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

      :download:`Download Python source code: plot_08_keeling_curve.py <plot_08_keeling_curve.py>`

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

      :download:`Download zipped: plot_08_keeling_curve.zip <plot_08_keeling_curve.zip>`


.. only:: html

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

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