3D Radiative Transfer in Weakly Inhomogeneous Medium. Part II: Discrete Ordinate Method and Effective Algorithm for Its Inversion

Abstract

The forward discrete ordinate method (DOM) has been reformulated to include effects of a weak inhomogeneity of a medium. The modification is based on an expansion of the direct beam source term. This treatment of the source term is similar to the gradient correction (GC) method, presented in the first part of the paper for the diffusion approximation. The same requirement on the scales of variations applies to the current method: length of horizontal variations of optical properties of the medium should be large in comparison to the mean radiative transport length. The modification has another important advantage in that it permits obtaining particular solutions for both infrared and direct beam radiative transfer in one computational step. An effective algorithm for solving inverse radiative transfer problems has been developed following the above reformulation. This algorithm modifies the DOM using Newton?s iterative scheme in order to find a solution of the inverse problem. The algorithm convergence rate is very high. Typically, two to three iterations are enough in order to obtain a solution with sufficiently high accuracy. The algorithm can be applied to the plane-parallel radiative transfer as well as to the GC method. The combination of the GC approach and the effective inverse algorithm creates an extremely useful and efficient tool for extraction of cloud fields from satellite imagery. It allows the algorithm to use radiance data with multiple views of the same pixel as an input and produce correct output even for large solar zenith or satellite view angles, when an independent pixel approximation fails.