Scattering of Visible Radiation by Finite Clouds

Abstract

A theoretical model of the scattering of shortwave radiation is applied to clouds finite in horizontal extent. The resulting irradiance patterns are then compared with calculations for horizontally semi-infinite clouds. This analysis shows, that the irradiance fields are dramatically dependent upon energy passing through the vertical sides of the finite sized clouds. Directional reflectance of individual cubic clouds is shown to be approximately 25% less than for semi-infinite clouds of optical depths ranging from 20 to 80. Directional reflectance from the top of cubic clouds for small solar zenith angle continues to increase at large optical depths (?70) while the infinite cloud becomes nearly asymptotic at this point. It is shown that for a solar zenith angle of 60°, the directional reflectance for a 2/10 sky cover of cubic clouds is 0.29 while for 2/10 coverage of semi-infinite cloud the directional reflectance is 0.185. Implications of differences between the cubic cloud results and the semi-infinite cloud case are discussed. These implications include: the effect on calculated planetary albedo; a possible explanation for reported correlations of cloud brightness, cloud height and precipitation; and effects on the surface energy budget.