Calculation of the angular radiance distribution for a coupled atmosphere and canopy

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically be an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. This algorithm enables one to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary conditon can be easily incorporated into the iteration procedure. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented is also well suited for analyzing the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near-infrared regions