Canopy bidirectional reflectance calculation based on Adding method and SAIL formalism: AddingS/AddingSD

he 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 fluxes 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 first propose an adaptation of the Adding method using the SAIL model canopy representation in the turbid case: it is called AddingS model. Such an approach allows to overcome the isotropy assumption. Second, AddingS is extended to the Discrete case: defining the AddingSDmodel. It allows to take into account the multi hot spot effect. Moreover, the AddingS and AddingSD models allow to check the energy conservation in respectively turbid and discrete cases. Finally, in order to keep reasonable time performance, a fast computation method was developed