Vegetation radiative transfer modeling based on virtual flux decomposition

Many physically based approaches for modeling the scattering properties of vegetation (i.e. methods based on radiative transfer models, RTM) suffer from significant shortcomings. In particular, the energy conservation problem has remained unsolved for a long time. This is particularly evident when introducing finite size scattering elements (leaves or shoots) into equations originally describing a turbid medium. This phenomenon, called the hot spot effect, is treated in classical RTM by increasing the reflectance value at the first collision of incident photons. To overcome this shortcoming, we propose in this paper a new model called the flux decomposition model (FDM) and based on the Kallel et al. approach (AddingSD) which propose a formulation showing that the hot spot could be viewed as an increase of the posterior gap probability. The formalism is based on a decrease of the vegetation density and is called 'the effective vegetation density'. Thus, inspired from this idea, in our study, energy conservation is achieved using the same effective density to estimate the upward diffuse flux provided by the first collision of the solar irradiance (E+1) as well as the diffuse fluxes created by E+1 scattering. Finally, to solve the RT equations, E+1 is divided into virtual subfluxes having simple expressions, allowing the division of the problem into a finite number of subproblems, each one corresponding to a given subflux easily solved based on SAIL++ formalism. Simulation tests show that the proposed model conserves energy with good accuracy. Compared to 3-D models in the ROMC/RAMI three database, our model performs similarly. Finally, compared to AddingSD, the running time is drastically reduced from about 15 min to a few milliseconds.