Green's function method for the radiative transfer problem. I. Homogeneousnon-Lambertian surface

An application of the Green's function method to the one-dimensional radiat ive transfer problem with a non-Lambertian surface is described. This metho d separates atmospheric radiative transport from the lower boundary conditi on and allows expressing a solution analytically for an arbitrary surface r eflectance. In the physical sense, the Green's function represents bidirect ional atmospheric transmission for the unitary radiance source located at t he bottom of the atmosphere. The boundary-value problem for the Green's fun ction is adjoint to the problem for atmospheric path radiance, and therefor e 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 solut ion and extensive numerical study, we found two accelerating parameterizati ons for computing the surface-reflected radiance. The first one is a maximu m-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 s econd one is based on the Lambertian approximation of multiple reflections. Designed for operational applications, it is much faster: Already the firs t-order reflected radiance ensures an average accuracy of better than 1%. ( C) 2001 Optical Society of America.