Extension of virtual flux decomposition model to the case of two vegetation layers: FDM-2

As an approximation, the forest could be assumed a discrete media composed of three main components: trees, understory vegetation and soil background. To describe the reflectance of such a canopy in the optical wavelength domain, it is necessary to develop a radiative transfer model which considers two vegetation layers (understory and trees). In this article, we propose a new model, FDM-2, an extension of the flux decomposition model (FDM), to take into account such a canopy architecture. Like FDM, FDM-2 models the diffuse flux anisotropy and takes into account the hot spot effect as well as conserves energy. The hot spot which corresponds to an increase of the probability of photon escape after first collision close to the backscattering direction is modeled as a decrease of “the effective vegetation density” encountered by the diffuse flux (E+1) and the radiance both created by first order scattering of the direct sun radiation. Compared to the turbid case (for which our model is equivalent to SAIL++ and therefore accurately conserving energy), such a density variation redistributes energy but does not affect the budget. Energy remains well conserved in the discrete case as well. To solve the RT problem, FDM-2 separates E+1 from the high order diffuse flux. As E+1 corresponding effective density is not constant function of the altitude (when traveling along the canopy) therefore it is decomposed into sub-fluxes of constant densities. The sub-flux RT problems are linear and simply solved based on SAIL++ formalism. The global RT solution is obtained summing the contribution of the sub-fluxes. Simulation tests confirm that FDM-2 conserves energy (i.e., radiative budget closes to zero in the purist corner case with an error due to the discretization less than 0.5%). Compared to the Rayspread model (among the best 3-D models of the RAMI Exercise third phase), our model provides similar performance. ► We model radiative transfer in canopy composed by two vegetation layers and soil. ► The model is an extension of FDM for two vegetation layers.► The hot spot is taken into account and energy is conserved. ► FDM-2 is based on the effective vegetation density approach to conserve energy.► Simulation results are similar to the best 3-D models of RAMI exercise.