Estimates for Infrared Transfer in Finite Clouds

Abstract

Upper and lower bounds are computed for the infrared radiance within a cloud of finite size. The bounds are established by an iterative procedure, analogous to the iterative solution of the radiative transfer equation, except that at every iteration the angular integration in the scattering term of the radiative transfer equation is restricted to a fixed conical region. The estimates are not restricted to clouds of any particular shape, temperature distribution, or radiance field incident upon the cloud. The absorption approximation, in which the albedo is set to zero and scattering is neglected, is shown to lie between the upper and lower bounds. As an illustration, estimates are derived for a cubic cloud (Deirmendjian's C1, 10 ?m) to obtain cheeks on numerical solutions of the radiative transfer equation (RTE) computed by various authors. For the cubic cloud, it is observed that the absorption approximation is in reasonable agreement with the results of a Monte-Carlo simulation.