Simple Approximations for Calculations of Absorption in Clouds

Abstract

Scaling principles can be used to transform problems of radiative transfer in media that scatter anisotropically to equivalent isotropic problems with exact solutions. By using such scaling principles together with geometric optics to relate the albedo for single scattering to drop radius and bulk absorption coefficient, very simple relationships can be obtained to calculate absorption of solar radiation by optically thick clouds. The results predict a dependence of absorption on the square root of cloud drop radius and thereby a dependence on air mass and pollution. Although these formulas are approximate, they are probably as good as the exact theory to within the limits of experimental accuracy, and they have the virtue of being exceedingly simple while retaining in their derivation the physics underlying the dependences that they indicate.