Solution of vector radiative transfer problem using small-angle modification of spherical harmonics method

Polarization properties of the scattered radiation contain important information about the scattering media which cannot be retrieved from the analysis of the total intensity only. That is why modern remote sensing systems either measure the polarization itself (Glory, Polder, Parasol) or consider the effect of polarization in the signal (GOSAT, MODIS). We are considering the vector radiative transfer (VRT) problem with arbitrary anisotropy of scattering. The solution is represented as a sum of anisotropic and regular components. The first component contains direct beam and the most anisotropic part of the solution which is evaluated in the small angle modification of the spherical harmonics method (MSH). The MSH formulation provides an analytical description of the anisotropic part of the solution at forward scattering yielding a very fast and accurate code. The small angle modification is formulated in the along-the-direct-beam frame of reference where the MSH solution is azimuthally smooth. The approximate nature of the small angle modification (MSH) is compensated in the regular part of the VRT equation with modified source function and boundary conditions. The regular part is smooth and is computed using the discrete ordinates method. The fast code for polarized radiative transfer modeling in a single layer is available in The MathWorks Matlab® environment. At present, we are working on generalization of the described algorithm for a multilayered atmosphere with non-Lambertian reflectance and on re-coding it in C/C++.