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

A method is developed to calculate analytically the Stokes vector at arbitr ary angles and optical depths from a given Vector discrete ordinate solutio n. The derived expressions are analytic solutions to the radiative transfer equation for the full 4-vector (polarized) radiative transfer problem. The se analytic solutions satisfy the boundary and across-layer continuity cond itions in a vertically inhomogeneous slab consisting of multiple plane-para llel layers. The scheme is tested for Rayleigh scattering, scattering by sp herical particles, and scattering by nonspherical particles. In all three t est cases, this method proves to be superior to a spline interpolation that has previously been used in connection with the vector discrete ordinate m ethod, both in terms of accuracy and in terms of computational speed. In co ntrast to the spline, the analytic method presented here has no difficultie s with extrapolations. It is interesting to note that the analytic expressi ons developed here actually improve the discrete ordinate results, when a n umerical imprecision at some of the quadrature points. (C) 2000 Elsevier Sc ience Ltd. All rights reserved.