GOST: A Geometric-Optical Model for Sloping Terrains

GOST is a geometric-optical (GO) model for sloping terrains developed in this study based on the four-scale GO model, which simulates the bidirectional reflectance distribution function (BRDF) of forest canopies on flat surfaces. The four-scale GO model considers four scales of canopy architecture: tree groups, tree crowns, branches, and shoots. In order to make this model suitable for sloping terrains, the mathematical description for the projection of tree crowns on the ground has been modified to consider the fact that trees grow vertically rather than perpendicularly to sloping grounds. The simulated canopy gap fraction and the area ratios of the four scene components (sunlit foliage, sunlit background, shaded foliage, and shaded background) by GOST compare well with those simulated by 3-D virtual canopy computer modeling techniques for a hypothetical forest. GOST simulations show that the differences in area ratios of the four scene components between flat and sloping terrains can reach up to 50%-60% in the principal plane and about 30% in the perpendicular plane. Two case studies are conducted to compare modeled canopy reflectance with observations. One comparison is made against Landsat-5 Thematic Mapper (TM) reflectance, demonstrating the ability of GOST to model canopy reflectance variations with slope and aspect of the terrain. Another comparison is made against MODIS surface reflectance, showing that GOST with topographic consideration outperforms that without topographic consideration. These comparisons confirm the ability of GOST to model canopy reflectance on sloping terrains over a large range of view angles.