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Why the Forcing from Carbon Dioxide Scales as the Logarithm of Its Concentration

David M. RompsaDepartment of Earth and Planetary Science, University of California, Berkeley, California
bClimate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California

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Jacob T. SeeleycDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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Jacob P. EdmandKoBold Metals, Berkeley, California

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Abstract

The radiative forcing from carbon dioxide is approximately logarithmic in its concentration, producing about 4 W m−2 of global-mean forcing for each doubling. Although these are basic facts of climate science, competing explanations for them have been given in the literature. Here, the reasons for the logarithmic forcing of carbon dioxide are explored in detail and a simplified model for the forcing is constructed. An essential component is the particular distribution of absorption coefficients within the 15-μm band of carbon dioxide. An alternative explanation, which does not depend on the spectrum of carbon dioxide but instead hinges on the tropospheric lapse rate, is shown to be neither necessary nor sufficient to explain the logarithmic forcing of carbon dioxide and to be generally inapplicable to well-mixed greenhouse gases in Earth’s atmosphere.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

The first two authors contributed equally to this work.

Corresponding author: David M. Romps, romps@berkeley.edu

Abstract

The radiative forcing from carbon dioxide is approximately logarithmic in its concentration, producing about 4 W m−2 of global-mean forcing for each doubling. Although these are basic facts of climate science, competing explanations for them have been given in the literature. Here, the reasons for the logarithmic forcing of carbon dioxide are explored in detail and a simplified model for the forcing is constructed. An essential component is the particular distribution of absorption coefficients within the 15-μm band of carbon dioxide. An alternative explanation, which does not depend on the spectrum of carbon dioxide but instead hinges on the tropospheric lapse rate, is shown to be neither necessary nor sufficient to explain the logarithmic forcing of carbon dioxide and to be generally inapplicable to well-mixed greenhouse gases in Earth’s atmosphere.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

The first two authors contributed equally to this work.

Corresponding author: David M. Romps, romps@berkeley.edu
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