Canopy Bidirectional Reflectance Calculation based on adding method and SAIL formalism

The SAIL model (proposed by Verhoef) is largely used in the remote sensing community to calculate the canopy bidirectional reflectance distribution function. The simulation results appear acceptable compared to observations especially for not very dense planophile vegetation. However, for erectophile dense crops (e.g. corn) the simulations appear less accurate. This inadequacy is due to the assumption that the multiple scattered are isotropically distributed. The SAIL parameters are interpretable at the level of elementary layer components. Now, the adding method (initially proposed by Van de Hulst) provides a good framework to model the radiative transfer inside a vegetation layer, but its parameter estimation lies on very simple geometric modeling of the canopy. In this paper, we propose an adaptation of the Adding method using the SAIL model canopy representation. Such an approach allows both to overcome the isotropy assumption and to take into account the multi hot spot effect. It also allows to check the energy conservation in both turbid and discrete case.