Reflected Solar Flux for Horizontally Inhomogeneous Atmospheres

Abstract

Reflected fluxes are investigated for a spatially heterogeneous medium. Multidimensional radiative transfer equations for a collimated source are solved as a standard eigenvalue problem (discrete-ordinate method) by using a Fourier series decomposition of the radiation field. The essential features of the method are described including the limitations of the method. Numerical computations for a medium of a spatial structure of radiative properties, which is specified by a Gaussian or a cosine function, show that spatial heterogeneity makes the atmosphere less reflective. The decrease in reflectivity depends on the nature of the spatial heterogeneity and is qualitatively explained by an approximation using a linear weighting of the radiative properties of plane-parallel clouds; the nonlinear relationship between a plane-parallel albedo and optical thickness leads to a lower reflectivity for a heterogeneous atmosphere than that for a plane-parallel medium of an equivalent domain-averaged optical thickness. The approximation, however, underestimates the reflectivity, which suggests that there are some intrinsic effects of the heterogeneous medium. Various numerical calculations show that the intrinsic effects are well characterized by considering the similar effects to the cloud-cloud interaction and the enhanced illumination applied for broken cloud fields. An increase in the intrinsic effect leads to the albedo for an inhomogeneous atmosphere approaching the plane-parallel albedo of an equivalent domain-averaged optical thickness.