The Delta-Four-Stream Approximation for Radiative Flux Transfer

Abstract

We present an approximate technique for solving the radiative transfer problem for fluxes reflected, transmitted, and absorbed by a homogeneous scattering layer. The technique is a straightforward “delta-function” modification of a solution to the transfer equation in closed form via the discrete-ordinates method with four streams. By the use of four streams, significant improvement in accuracy is obtained for anisotropic phase functions over that obtained by similarly employed two-stream approximations with delta-functions. However, the computational effort is increased only slightly. We present equations for the general case of a layer underlaid by a reflecting Lambert surface. Graphical comparisons are given of fractional error resulting from the use or this method with that resulting from the use of typical four-stream and delta-two-stream (or delta-Eddington) techniques.