Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

Abstract

We model the wavelength-dependent absorption of atmospheric gases by assuming constant massabsorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analyticallysolved by a discrete ordinate method. The general solution is analyzed for a water vapor saturatedatmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stableequilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing fromprevious radiative’convective models, we find that the amount of carbon dioxide strongly modifiesthe value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption ofradiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect ofcarbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runawaygreenhouse state than thin carbon dioxide ones.