Numerical technique for solving the radiative transfer equation for a spherical shell atmosphere

Abstract

A method for numerically solving the equation of radiative transfer in a spherical shell atmosphere is presented. The method uses a conical boundary and a Gauss-Seidel iteration scheme to solve for all orders of scattering along a single radial line in the atmosphere. Tests of the model indicate an accuracy better than 1% for most Earth-atmosphere situations. Results from this model are compared with flat-atmosphere model results for a scattering-only atmosphere. These comparisons indicate that excluding spherical effects for solar zenith angles greater than 85° leads to errors larger than 5% at optical depths as small as 0.10.