A hybrid geometric-optical radiative-transfer model for directional reflectance of discontinuous vegetation canopies

At the scale of a small volume in which leaves can be regarded as being homogeneously distributed, some recently developed RT (radiative transfer) theories can accurately model directional reflectance of plant canopies by using such descriptors as leaf scattering characteristics, leaf size, etc. However, at the scale of a stand, GO (geometric optical) models catch the basic features of discontinuous canopies under sunlight, i.e., the foliage is clustered into crowns and the crowns cast shadows. Hence in practice up to now, simple pure GO models are the only models applicable to natural discrete crown canopies. However, pure GO models require signatures of sunlit and shaded crown surface and background as known parameters under a given situation or to be determined in situ. This has been proven a major restricting factor in applications and model inversion. The authors present a hybrid GO-RT approach to model the radiation climate in a discontinuous canopy. A key element in this approach is a gap probability (P_gap) model which the authors developed earlier. P_gap between crowns, on one hand, can be obtained through a pure GO model which reflects the structure at the stand scale. On the other hand, P_gap within the crown is closely related to the process that radiation collides and is scattered by foliage. Hence P_gap becomes a natural link between the two kinds of models at their corresponding scales. Vertical distribution of sunlit clown surface is first obtained by GO method. Then the within-crown pathlength distributions and associated single scattering source distributions at different heights are obtained. Successive orders of scattering are handled with a formulation more similar to radiative theories, with considering the openness distribution of discontinuous canopies