The picard iterative approximation to the solution of the integral equation of radiative transfer—part II. Three-dimensional geometry

Abstract The present paper presents the Picard Iterative (PI) algorithm for the solution of the 3-D radiative transfer equation (RTE). The method is based on the integral equation form of the RTE. Results presented demonstrate that the PI technique provides a high degree of accuracy, converges in a small number of iterations, accommodates inhomogeneous cloud optical parameters, and naturally incorporates a wide variety of boundary conditions. In particular, periodic boundary conditions facilitate the computation of cloud field radiance patterns involving a repeated array of cells containing one or more clouds. The use of the δ-function approximation significantly reduces the computer memory requirements and associated run times for scattering phase functions which are moderately to highly peaked. Results are obtained and compared with the Discrete Ordinate 1-D homogeneous slab.