Canopy BRDF differentiation on LAI based on Monte Carlo Ray Tracing

Abstract

Radiative transfer models (RTM) enable the simulation of remote sensing observations and can therefore be useful for sensitivity analyses and model inversions, for example to determine the biophysical properties of vegetation. For this purpose, the calculation of observation derivatives is crucial. In this study, we propose to differentiate vegetation RTM based on Monte Carlo Ray tracing, PolVRT, as a function of the leaf area index (LAI). The variation of LAI is done considering the average leaf area ($u$). The difference between simulations corresponding to two areas close to each other ($u$ and $u^{\prime }$) is used to calculate the derivative as the limit when $u^{\prime }$ approaches $u$. We propose in this work to adjust traced paths for $u$ to simulate ($u^{\prime }$), but such paths are weighted to correct their bias. This weighting is based on the technique of Importance Sampling. It increases the weighting of likely paths and conversely decreases it of unlikely ones. We have made a correction for the hot spot effect, since there is a strong dependency between the incident and backscattered paths. Our approach performances are verified using some discrete ROMC scene parameters and compared with the standard finite difference technique.