Solution of Radiative Transfer Problems Using the Invariant Sn Method

Abstract

The discrete ordinate difference equations of radiative transfer for a slab in the form presented by Carlson and by Lathrop & Carlson can be written in a form consistent with principles of invariance. It is shown that this permits solution of the equations, without the need for iteration in scattering problems, by a method which converges in the limit to that of Rybicki & Usher. The new method is economical to use, both in respect of storage and of computing time, and may be preferable to that of Rybicki & Usher in problems with anisotropic phase functions. The mathematical structure of the equations and its implications are briefly discussed. Specimen numerical results are provided for diffuse reflection from an isotropically scattering homogeneous slab and compared with results published by other investigators.