DIRECT SOLUTION OF THE SPHERICAL HARMONICS APPROXIMATION TO THE RADIATIVE TRANSFER EQUATION FOR AN ARBITRARY SOLAR ELEVATION - 1. THEORY.

Abstract

The spherical harmonics approximation to the transfer equation for an azimuth-dependent component of intensity of scattered radiation is reduced by finite differences to a block algebraic system of particularly simple structure. This algebraic system can be solved numerically for homogeneous or nonhomogeneous models of a plane-parallel atmosphere, using the finite-differences analog of the simple-shooting technique based on initial-value problems of the multiple-shooting technique for the solution of two-point boundary-value problems.