Modeling Radiative Transfer in Heterogeneous 3-D Vegetation Canopies

T h e DART (discrete anisotropic radiative transfer) model simulates radiative transfer in heterogeneous 3-D scenes that may comprise different landscape features; i.e., leaves, grass, trunks, water, soil. The scene is divided into a rectangular cell matrix, i.e., building block for simulating larger scenes. Cells are parallelipipedic. Their optical properties are represented by individual scattering phase functions that are directly input into the model or are computed with optical and structural characteristics of elements within the cell. Radiation scattering and propagation are simulated with the exact kernel and discrete ordinate approaches; any set of discrete direction can be selected. In addition to topography and hot spot, leaf specular and first-order polarization mechanisms are modeled. Two major iterative steps are distinguished: 1) Cell illumination with direct sun radiation: Within cell multiple scattering is accurately simulated. 2) Interception and scattering of previously scattered radiation: Atmospheric radiation, possibly anisotropic, is input at this stage. Multiple scattering is stored as spherical harmonics expansions, for reducing computer memory constraints. The model iterates on step 2, for all cells, and stops with the energetic equilibrium. Two simple accelerating techniques can be used: 1) Gauss Seidel method, i.e., simulation of scattering with radiation already scattered at the iteration stage, and (2) decrease of the spherical harmonics expansion order with the iteration order. Moreover, convergence towards the energetic equilibrium is accelerated with an exponential fitting technique. This model predicts the bidirectional reflectance distribution function of 3-19 canopies. Radiation components associated with leaf volume and surface mechanisms are distin-