Evaluation of Linear Kernel-Driven BRDF Models over Snow-Free Rugged Terrain.

Semi-empirical kernel-driven models have been widely used to characterize anisotropic reflectance due to their simple form and physically meaningful approximation. Recently, several kernel-driven models have been coupled with topographic effects to improve the fitting of bidirectional reflectance over rugged terrains. However, extensive evaluations of the various models' performances are required before their subsequent application in remote sensing. Three typical kernel-driven BRDF models over snow-free rugged terrains such as the RTLSR, TCKD, and the KDST-adjusted TCKD (KDST-TCKD) were investigated in this paper using simulated and observed BRFs. Against simulated data, the fitting error (NIR/Red RMSE) of the RTLSR gradually increases from 0.0358/0.0342 to 0.0471/0.0516 with mean slopes (alpha) increases from 9.13 degrees to 33.40 degrees. However, the TCKD and KDST-TCKD models perform an overall better fitting accuracy: the fitting errors of TCKD gradually decreased from 0.0366/0.0337 to 0.0252/0.0292, and the best fit from the KDST-TCDK model with NIR/Red RMSE decreased from 0.0192/0.0269 to 0.0169/0.0180. When compared to the sandbox data (alpha from 8.4 degrees to 30.36 degrees), the NIR/Red RMSE of the RTLSR model ranges from 0.0147/0.0085 to 0.0346/0.0165, for the TCKD model from 0.0144/0.0086 to 0.0298/0.0154, and for the KDST-TCKD model from 0.0137/0.0082 to 0.0234/0.0149. Using MODIS data, the TCKD and KDST-TCKD models show more significant improvements compared to the RTLSR model in rugged terrains. Their RMSE differences are within 0.003 over a relatively flat terrain (alpha < 10 degrees). When alpha is large (20 degrees-30 degrees and >30 degrees), the RMSE of the TCKD model has a decrease of around 0.01 compared to that of the RTLSR; for KDST-TCKD, it is approximately 0.02, and can even reach 0.0334 in the savannas. Therefore, the TCKD and KDST-TCKD models have an overall better performance than the RTLSR model in rugged terrains, especially in the case of large mean slopes. Among them, the KDST-TCKD model performs the best due to its consideration of topographic effects, geotropic growth, and component spectra.