The Role of Relative Humidity in Radiative–Convective Equilibrium

Abstract

Abstract The following conditions are derived for the existence of a radiation limit of tropospheric origin in a nongray atmosphere, extending the work on a gray atmosphere by Nakajima et al.: 1) the atmosphere must become sufficiently optically thick, and 2) the temperature must become only a function of optical depth at each frequency, independent of surface temperature. The first condition is satisfied at high temperatures even in a window region as long as there is weak but nonzero absorption, because the optical depth of the entire atmosphere roughly scales as saturation vapor pressure. At high temperatures, the pseudoadiabatic temperature structure asymptotes to the saturation vapor pressure curve, satisfying the second condition at each frequency. A rapidly decreasing vertical gradient of water vapor mixing ratio allows temperature to asymptote faster in optical depth coordinates than in pressure coordinates. Analyses using a radiative–convective model show that interactive relative humidity can give rise to a different kind of runaway greenhouse effect and multiple equilibria, if the strength of relative humidity feedback exceeds a critical value. The results suggest that this mechanism may be able to explain the runaway greenhouse effect found by Rennó et al. and radiative–convective multiple equilibria by Rennó. The framework employed in this study will serve as a diagnostic tool for further research on the runaway greenhouse effect and radiative–convective multiple equilibria.