A simple anisotropic reflectance model for homogeneous multilayer canopies

This article deals with the representation of the canopy bidirectional reflectance factor (BRF) with a model that is simple, for inversion purposes, and computationally cheap. The objective was to derive the analytical expressions of radiative transfer in covers that may comprise strongly anisotropic vegetation layers and/or bottom interface. This is carried out through the introduction of an additional upward directional flux that originates from the anisotropic components of the cover, in a widely used and reliable three-flux model, that is, the SAIL (scattering by arbitrarily inclined leaves) model. It results in a multi-layered four-flux model with a fast computer code. Parameters (i.e., rsm and rdm) that characterize the anisotropic behavior of canopy layers are computed with the same input parameters as the SAIL model. Moreover, at least one additional parameter is used for characterizing the anisotropic behavior of the bottom interface, that is, soil surface. Depending on the LAI (leaf angle index) and LAD (leaf angle distribution) of the upper layer and on the degree of anisotropy of the underlying layers, differences between BRFs that are derived from the four-flux model and from the SAIL model can be large. This stresses the necessity of the introduction of an upward directional flux in presence of covers with strongly anisotropic characteristics.