Angular distribution of the Stokes vector in a plane-parallel, vertically inhomogeneous medium in the vector discrete ordinate radiative transfer (VDISORT) model

Abstract

A method is developed to calculate analytically the Stokes vector at arbitrary angles and optical depths from a given vector discrete ordinate solution. The derived expressions are analytic solutions to the radiative transfer equation for the full 4-vector (polarized) radiative transfer problem. These analytic solutions satisfy the boundary and across-layer continuity conditions in a vertically inhomogeneous slab consisting of multiple plane-parallel layers. The scheme is tested for Rayleigh scattering, scattering by spherical particles, and scattering by nonspherical particles. In all three test cases, this method proves to be superior to a spline interpolation that has previously been used in connection with the vector discrete ordinate method, both in terms of accuracy and in terms of computational speed. In contrast to the spline, the analytic method presented here has no difficulties with extrapolations. It is interesting to note that the analytic expressions developed here actually improve the discrete ordinate results, when a numerical imprecision at some of the quadrature points.