Atmospheric radiative equilibria. Part II: Bimodal solutions for atmospheric optical properties

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 fluxes. Given a complete set of SW and LW optical properties in each atmospheric layer, the model yields a unique equilibrium-temperature profile. In contrast, if the atmospheric temperature profile and SW properties are prescribed, the model yields essentially two distinct LW transmissivity profiles. This bimodality is due to a nonlinear competition between the ascending and descending energy fluxes, as well as to their local conversion to sensible heat in the atmosphere. Idealized slab models that are often used to describe the greenhouse effect are shown to be a special case of our model when this nonlinearity is supressed. In this special case only one solution for LW transmissivity is possible. Our model's bimodality in LW transimissivity for given SW fluxes and temperature profile may help explain certain features of Earth's climate: at low latitudes the temperature profiles are fairly homogenous, while the humidity profiles exhibit a bimodal distribution; one mode is associated with regions of moist-and-ascending, the other with dry-and-subsiding air. The model's analytical results show good agreement with the European Centre for Medium- Range Weather Forecast's reanalysis data. Sensitivity analysis of the temperature profile with respect to LW transimissivity changes leads to an assessment of the low-latitude climate's sensivity to the "runaways greenhouse" effect.