SGOT: A Simplified Geometric-Optical Model for Crown Scene Components Modeling over Rugged Terrain

Topography affects the fraction of scene components of the canopy and background, resulting in the observed reflectance distortion. Modeling the canopy reflectance over rugged terrain needs to account for topographic effects. For this purpose, the existing models greatly increased the mathematical complexity while improving description of terrain and crown structure, which dramatically decreased the computational efficiency so as to limit their universal application. In this study, we developed a simplified geometric-optical model (SGOT) for simulating the scene components over rugged terrain. The geotropism of tree growth was considered to make SGOT physically sound. The internal structure of crown was simplified to make SGOT mathematically simpler. Scene component observations derived from Persistence of Vision Ray-tracer (POV-Ray) on surfaces with different normal directions and simulations were made using Geometric-Optical and Mutual Shadowing Coupled with Topography Model (GOMST) and Geometric-Optical for Sloping Terrains Model GOST; models were combined to test the SGOT model. In addition, topographic factors and crown density effect on the scene components modeling were analyzed. The results indicated that SGOT has good accuracy (R² for the areal proportions of sunlit crown (Kc), sunlit background (Kg), shaded crown (Kt), and shaded background (Kz) are 0.853, 0.857, 0.914, and 0.838, respectively) compared with POV-Ray simulation, and performs better than GOMST, especially in scenes with high crown density. Moreover, SGOT outperformed the compared models in computational efficiency (4% faster than GOMST and 29.5% faster than GOST). Finally, the simulations of the scene components distribution in different topographic factors and crown density were further discussed. SGOT and GOST can both capture scene component variations caused by terrain better than GOMST, but comparatively, SGOT provides a more efficient tool to simulate the crown scene components because of its physical soundness and mathematical simplicity, and consequently, it will facilitate the modeling of canopy reflectance over mountainous regions.