Parameterization and correction of hotspot parameters of Ross-Li kernel driven models on POLDER dataset

Abstract

The semi-empirical kernel-driven linear bidirectional reflectance distribution function (BRDF) model is important and has been widely used in the remote sensing community. The hotspot signature is an important characteristic of the BRDF shapes and is commonly quantified by two degrees of freedom: the hotspot height and width near the hotspot direction. This research aimed to correct the hotspot effect of the Ross-Li BRDF model for potential users by correcting the Ross and Li kernels with an exponential function of two hotspot parameters (C1/C2). This method has been developed in previous studies, but it was comprehensively applied to other kernel functions in the current study. Given the gap between leaves in the canopy, we corrected the overlap function of GO kernel with hotspot function. We analyzed the two hotspot parameters for the Ross-Li model by using the entire archive of POLDER BRDF database. First, we used six combinations of Ross and Li kernels to fit a typical single POLDER data for a specific analysis. We also analyzed the sensitivity of C1/C2 for these model combinations using the single POLDER pixel. Second, we used the entire POLDER dataset and acquired the optimum values of the hotspot parameters by using the root mean square error (RMSE) method. Finally, we analyzed the sensibility of the hotspot parameter in each model using 2D contour plots that distinctly show the variations in RMSEs as functions of C1 and C2. (1) The proposed hotspot parameterization method could be used to various combination models of Ross and Li kernels. The model with such a hotspot correction method improved the fitting ability of the hotspot signature better than the original model. (2) The optimum values of two hotspot parameters were significantly different between models, especially for the two geometric optical kernels, namely, LiSparseRChen (LSRC) and LiDenseRChen (LDRC). The value of C1 parameters in the LDRC models was generally smaller than that in the LSRC models. The possible reason could be that the LDRC kernel function modeled the hotspot effect on the canopy scale accurately, such that the role of the hotspot parameters (especially for C1) was secondary in this situation. (3) In general, the value of the C1 parameter in a single model was more sensitive to the variation in hotspot effect than the C2 parameter. This study comprehensively corrects the hotspot effect of the Ross-Li model for various applications for potential users who pay attention to the hotspot signatures of their applications. This study is also valuable for domestic multi-angle satellites in accurately reconstructing future hotspot signatures from multi-angle observations.