.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/climate/plot_15_gregory_forcing_feedback_regression.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_15_gregory_forcing_feedback_regression.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_15_gregory_forcing_feedback_regression.py:


Gregory's forcing-feedback regression (2004)
============================================

Jonathan Gregory and colleagues proposed a way to read forcing and feedback
from a single run in which CO2 is quadrupled abruptly. Each year the net
top-of-atmosphere imbalance ``N = F - lambda T`` is plotted against the
warming. The intercept is the forcing, the slope is minus the feedback, and the
line crosses zero at the equilibrium warming, without running to equilibrium.
Here the run is a one-box model with seeded annual noise added to the
imbalance.

.. GENERATED FROM PYTHON SOURCE LINES 13-39



.. image-sg:: /api/gallery/climate/images/sphx_glr_plot_15_gregory_forcing_feedback_regression_001.png
   :alt: Abrupt 4×CO2: 3.4 K per doubling
   :srcset: /api/gallery/climate/images/sphx_glr_plot_15_gregory_forcing_feedback_regression_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.climate import equilibrium_warming, gregory_regression, simulate_one_box
    from earthsciencekit.units import convert

    forcing, restoring, capacity = 7.4, 1.1, 3e8
    years = np.arange(0, 151)
    warming = simulate_one_box(forcing, restoring, capacity, convert(years, "year", "s")).values[:, 0]
    imbalance = forcing - restoring * warming
    np.testing.assert_allclose(gregory_regression(warming, imbalance), [forcing, restoring])
    noisy = imbalance + np.random.default_rng(2004).normal(0, 0.4, years.size)
    fitted_forcing, fitted_restoring = gregory_regression(warming[1:], noisy[1:])
    assert np.isclose(fitted_forcing, forcing, rtol=0.1) and np.isclose(fitted_restoring, restoring, rtol=0.1)
    sensitivity = equilibrium_warming(fitted_forcing / 2, fitted_restoring)

    line = np.linspace(0, fitted_forcing / fitted_restoring, 2)
    fig, ax = plt.subplots()
    ax.scatter(warming[1:], noisy[1:], c=years[1:], s=10, cmap="viridis", label="annual means")
    ax.plot(line, fitted_forcing - fitted_restoring * line, "k", label=f"fit: F = {fitted_forcing:.1f} W/m², λ = {fitted_restoring:.2f}")
    ax.axhline(0, color="0.5", lw=0.8)
    ax.set(xlabel="warming [K]", ylabel="TOA imbalance [W/m²]", title=f"Abrupt 4×CO2: {sensitivity:.1f} K per doubling")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.090 seconds)


.. _sphx_glr_download_api_gallery_climate_plot_15_gregory_forcing_feedback_regression.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_15_gregory_forcing_feedback_regression.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_15_gregory_forcing_feedback_regression.ipynb <plot_15_gregory_forcing_feedback_regression.ipynb>`

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

      :download:`Download Python source code: plot_15_gregory_forcing_feedback_regression.py <plot_15_gregory_forcing_feedback_regression.py>`

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

      :download:`Download zipped: plot_15_gregory_forcing_feedback_regression.zip <plot_15_gregory_forcing_feedback_regression.zip>`


.. only:: html

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

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