Radiative Transfer through Media with Uncertain or Variable Parameters

Abstract

While it is now possible to compute the optical transmission, reflection and absorption of a homogeneous horizontal layer of known parameters to great accuracy, the input parameters (optical depth, scattering phase function and single-scattering albedo) are in general neither precisely known nor exactly constant over a layer. In this paper several simple representations of the distributions of input parameters are used to compute the mean values and standard deviations of layer transmission, reflection and absorption. The effects of variability in input parameters depend on the mean-layer properties; under certain conditions this variability induces errors on the order of 5% in the derived optical properties. This magnitude is comparable to the differences between those obtained by the Eddington, delta-Eddington, and discrete ordinate four-steam approximations, and a more precise 20-stream doubling method.