Atmospheric Radiative Equilibria Part Ii: Bimodal Solutions for Atmospheric Optical Properties Revised Version

A simple theoretical model of atmospheric radiative equilibrium is solved analytically to help understand the energetics of maintaining Earth's tropical and subtropical climate. The model climate is constrained by energy balance between shortwave (SW) and longwave (LW) radiative uxes. Given a complete set of SW and LW optical properties in each atmospheric layer, the model yields a unique equilibrium-temperature pro le. On the contrary, if the atmospheric temperature pro le and SW properties are prescribed, the model yields essentially two distinct LW transmissivity pro les. This bimodality is due to a nonlinear competition between the ascending and descending energy uxes, as well as to their local conversion to sensible heat in the atmosphere. Idealized slab models that are often used to describe the greenhouse e ect are shown to be a special case of our model when this nonlinearity is suppressed. In this special case, only one solution for LW transmissivity is possible. Our model's bimodality in LW transmissivity for given SW uxes and temperature pro le may help explain certain features of Earth's climate: at low latitudes the temperature pro les are fairly homogeneous, while the humidity pro les exhibit a bimodal distribution { one mode is associated with regions of moistand-ascending, the other with dry-and-subsiding air. The model's analytical results show good agreement with the European Centre for Medium-Range Weather Forecasts' reanalysis data. Sensitivity analysis of the temperature pro le with respect to LW transmissivity changes leads to an assessment of the low-latitude climate's sensitivity to the \runaway greenhouse" e ect.