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

Abstract

The radiative forcing from carbon dioxide is approximately logarithmic in its concentration, producing about 4 W m22 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-mm 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.