An approximation to multiple scattering in the earth's atmosphere Almucantar radiance formulation

An empirical expression is derived to account for the molecular multiple scattering contribution to the almucantar radiance field. Formulas for the correction factors which incorporate the effects of multiple scattering and nonzero ground albedo are also given. The use and accuracy of the multiple-scattering approximation in direct problems of radiative transfer associated with almucantar radiance are discussed and illustrated by examples. It is shown that in almost all instances, inclusion of the molecular multiple-scattering contribution reduces the errors obtained with the single-scattering approximation by a factor of at least 2.