:orphan:

.. include:: /_generated/nav/climate.rst

Climate examples
================

One executed example per breakthrough in :doc:`/history/climate_breakthroughs`,
in chronological order, each with an asserted check of the result it shows.
Download the Python source or notebook from each page. :doc:`/guides/climate` records units and
limits; all examples use deterministic synthetic inputs and require no downloads.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Joseph Fourier argued that the Earth would be much colder if it simply radiated away the sunlight it absorbs, and that the atmosphere must hold heat in. A planet in radiative balance emits what it absorbs, which for the present albedo of about 0.3 gives an effective temperature near 255 K. The measured mean surface temperature of about 288 K is 33 K warmer; that gap is the greenhouse effect.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_01_fourier_greenhouse_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_01_fourier_greenhouse`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Fourier's greenhouse (1824)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Eunice Foote set glass cylinders of different gases in sunlight and found that the one filled with carbon dioxide grew hottest and stayed hot longest. She suggested that more of it in the air would warm the Earth. The simplest model of that effect is one atmospheric layer, transparent to sunlight, that absorbs a fraction of the infrared from the ground and re-emits it both up and down. A fully absorbing layer warms the surface by a factor of 20.25.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_02_foote_heated_co2_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_02_foote_heated_co2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Foote's heated carbon dioxide (1856)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Josef Stefan noticed that John Tyndall&#x27;s measurements of a glowing platinum wire fit a simple law. The wire radiated 11.7 times more at 1200 °C than at 525 °C, and the ratio of the absolute temperatures to the fourth power is 11.6. Boltzmann derived the law from thermodynamics in 1884. It gives the outgoing longwave radiation of every planet.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_03_stefan_t4_law_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_03_stefan_t4_law`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Stefan's fourth-power law (1879)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Svante Arrhenius calculated by hand how the surface temperature would change if the carbon dioxide in the air were multiplied or divided. He found that the warming grows with the logarithm of the concentration, so every doubling adds the same amount; his estimate was 5 to 6 °C per doubling. With a logarithmic forcing and a linear feedback, each doubling here adds 3 K.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_04_arrhenius_co2_sensitivity_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_04_arrhenius_co2_sensitivity`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arrhenius's sensitivity to CO2 (1896)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Milutin Milanković computed the sunlight each latitude receives through the year and how it changes as the tilt and orbit of the Earth vary. He proposed that ice ages begin when high northern summers receive little sunlight. The daily mean at the top of the atmosphere depends on latitude, the Sun&#x27;s declination and the Earth-Sun distance. Whatever the season, the global mean is a quarter of the solar constant.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_05_milankovic_orbital_insolation_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_05_milankovic_orbital_insolation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Milanković's orbital insolation (1920)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Guy Stewart Callendar compiled temperature records from about 200 stations, found that the world had warmed since the late 19th century, and attributed the warming to carbon dioxide from burning fuel. His estimate of about 2 °C per doubling was larger than the radiative response alone. Planck&#x27;s restoring coefficient 4 sigma T3 gives only about 1 K per doubling, so feedbacks such as water vapour must amplify it.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_06_callendar_measured_warming_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_06_callendar_measured_warming`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Callendar's measured warming (1938)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Roger Revelle and Hans Suess showed that seawater resists taking up carbon dioxide. Because of carbonate chemistry, a 10% rise in the CO2 pressure of the air is balanced by only about a 1% rise in the dissolved carbon of the surface ocean. This ratio, about 10, is the buffer (Revelle) factor. In equilibrium the share of added carbon left in the air is 1 / (1 + M_o / (R M_a)) for atmospheric and oceanic inventories M_a and M_o, so the ocean holds far less of it than a simple partition by inventory would suggest. Inventories here are round illustrative values.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_07_revelle_suess_buffer_factor_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_07_revelle_suess_buffer_factor`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Revelle and Suess's buffer factor (1957)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="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.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_08_keeling_curve_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_08_keeling_curve`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Keeling's curve (1958)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Syukuro Manabe and Richard Wetherald computed the temperature profile of a single atmospheric column in which radiation and convection balance. Where radiative equilibrium alone would be unstable, convection holds the temperature at a fixed lapse rate. With relative humidity held fixed, doubling CO2 warmed the surface by about 2.3 K. In this simplest version, the troposphere passes through the effective temperature at the emission height, and more CO2 lifts that height. The surface then warms by the lapse rate times the lift. The model keeps the stratosphere at a fixed skin temperature, so it misses the stratospheric cooling that Manabe and Wetherald also found.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_09_manabe_wetherald_radiative_convective_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_09_manabe_wetherald_radiative_convective`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Manabe and Wetherald's radiative-convective equilibrium (1967)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mikhail Budyko and William Sellers independently built energy-balance models in which ice reflects more sunlight than ocean or land. Colder climates grow more ice and absorb less, which cools them further. Both found that a drop of a few percent in sunlight could freeze the whole planet, and that a frozen Earth would stay frozen until the Sun grew far brighter: a hysteresis loop. Inverting the energy balance gives the solar constant that holds each temperature, which traces every equilibrium at once.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_10_budyko_sellers_ice_albedo_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_10_budyko_sellers_ice_albedo`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Budyko and Sellers's ice-albedo feedback (1969)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Klaus Hasselmann showed that slow climate variability needs no slow cause. The ocean integrates fast, random weather forcing, just as a heavy particle integrates molecular kicks in Brownian motion. The result is red noise: a spectrum flat below the frequency lambda / (2 pi C) and falling as frequency squared above it. Here a seeded white-noise forcing drives a 50 m mixed layer, sampled every month for 4000 years.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_11_hasselmann_stochastic_climate_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_11_hasselmann_stochastic_climate`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hasselmann's stochastic climate (1976)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A panel of the US National Academy of Sciences chaired by Jule Charney reviewed the climate models of the day. It concluded that doubling CO2 would warm the Earth by 3 K, probably between 1.5 and 4.5 K. It also warned that ocean heat capacity would delay the warming by decades. In a one-box model the delay is the time scale C / lambda, so a more sensitive climate (a smaller lambda) also responds more slowly.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_12_charney_report_sensitivity_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_12_charney_report_sensitivity`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Charney report's sensitivity range (1979)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="James Hansen and colleagues projected the warming from rising CO2 with a one-dimensional model whose ocean mixed layer stores heat. They showed that the depth of ocean in contact with the surface sets how fast the warming appears. Until equilibrium, part of the forcing goes into the ocean rather than back to space. The heat stored at any time equals the integrated imbalance between forcing and the radiative restoring.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_13_hansen_ocean_heat_uptake_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_13_hansen_ocean_heat_uptake`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hansen's ocean heat uptake (1981)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gunnar Myhre and colleagues fitted simple expressions to line-by-line radiative calculations for the well-mixed greenhouse gases. CO2 forcing is logarithmic, 5.35 ln(C / C0), because its strongest bands are saturated. Methane and nitrous oxide grow with the square root of concentration, less a term for the band near 7.7 μm that they share. The IPCC adopted the formulas in 2001; from 1750 to 1998 they give about 1.46, 0.48 and 0.15 W/m² for the three gases.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_14_myhre_forcing_formulas_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_14_myhre_forcing_formulas`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Myhre's forcing formulas (1998)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="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.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_15_gregory_forcing_feedback_regression_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_15_gregory_forcing_feedback_regression`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gregory's forcing-feedback regression (2004)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="By 2005, ocean temperature profiles going back to the 1950s gave the first global estimates of thermosteric sea-level rise. Antonov, Levitus and Boyer found about 0.33 mm per year from warming of the upper 700 m over 1955-2003. With satellite altimetry and glacier mass balance, this made it possible to close the budget: the observed rise should be the sum of warming water and added meltwater. About 362 Gt of water raises the global ocean by 1 mm. The numbers below are illustrative.">

.. only:: html

  .. image:: /api/gallery/climate/images/thumb/sphx_glr_plot_16_sea_level_budget_thumb.png
    :alt:

  :doc:`/api/gallery/climate/plot_16_sea_level_budget`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Thermal expansion and ice melt in the sea-level budget (2005)</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/climate/plot_01_fourier_greenhouse
   /api/gallery/climate/plot_02_foote_heated_co2
   /api/gallery/climate/plot_03_stefan_t4_law
   /api/gallery/climate/plot_04_arrhenius_co2_sensitivity
   /api/gallery/climate/plot_05_milankovic_orbital_insolation
   /api/gallery/climate/plot_06_callendar_measured_warming
   /api/gallery/climate/plot_07_revelle_suess_buffer_factor
   /api/gallery/climate/plot_08_keeling_curve
   /api/gallery/climate/plot_09_manabe_wetherald_radiative_convective
   /api/gallery/climate/plot_10_budyko_sellers_ice_albedo
   /api/gallery/climate/plot_11_hasselmann_stochastic_climate
   /api/gallery/climate/plot_12_charney_report_sensitivity
   /api/gallery/climate/plot_13_hansen_ocean_heat_uptake
   /api/gallery/climate/plot_14_myhre_forcing_formulas
   /api/gallery/climate/plot_15_gregory_forcing_feedback_regression
   /api/gallery/climate/plot_16_sea_level_budget


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: climate_python.zip </api/gallery/climate/climate_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: climate_jupyter.zip </api/gallery/climate/climate_jupyter.zip>`


.. only:: html

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

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