Green’s function method for the radiative transfer problem I Homogeneous non-Lambertian surface

Abstract

An application of the Green's function method to the one-dimensional radiative transfer problem with a non-Lambertian surface is described. This method separates atmospheric radiative transport from the lower boundary condition and allows expressing a solution analytically for an arbitrary surface reflectance. In the physical sense, the Green's function represents bidirectional atmospheric transmission for the unitary radiance source located at the bottom of the atmosphere. The boundary-value problem for the Green's function is adjoint to the problem for atmospheric path radiance, and therefore it can be solved by use of existing numerical methods by reversal of the direction of light propagation. From an analysis of an exact operator solution and extensive numerical study, we found two accelerating parameterizations for computing the surface-reflected radiance. The first one is a maximum-eigenvalue method that is comparable in accuracy with rigorous radiative transfer codes in calculations with realistic land-cover types. It requires a total of the first three orders of the surface-reflected radiance. The second one is based on the Lambertian approximation of multiple reflections. Designed for operational applications, it is much faster: Already the first-order reflected radiance ensures an average accuracy of better than 1%.