Application of a Hypergeometric Model in Simulating Canopy Gap Fraction and BRF for Forest Plantations on Sloping Terrains

The influence of tree distribution and slope on canopy gap fraction (GF) and bidirectional reflectance factor (BRF) is shown here to be non-negligible. Trees are often assumed to be randomly distributed in natural forests due to random distribution of natural resources, but this assumption is not valid for forest plantations. A geometric optical model for forest plantations (GOFP) is a geometric optical model for forest plantations on horizontal surfaces based on the theory of exclusion distance among crowns. Sloping terrains change the exclusion distance among crowns, and inevitably affect the canopy GF and BRF. In this article, GOFP with a hypergeometric model (distances among trees are considered) on horizontal surfaces is modified as GOFP-T to simulate BRF for forest plantations on sloping terrains under two scenarios: (horizontal distances among crowns remain unchanged with slope) and (sloping distances among crowns remain unchanged with slope). Two three-dimensional (3-D) radiative transfer models (DART and LESS) and field measurements are used to evaluate and validate GOFP-T simulations. The results show that 1) the canopy GF, four component area ratios, and canopy BRF simulated by GOFP-T show high consistency with results from the two 3-D model: root-mean-square errors in GF, sunlit foliage, and sunlit ground are less than 0.02, 0.06, and 0.03, respectively; 2) forest coverage and canopy reflectance in GOFP-T are compared well with point cloud results from an airboard LiDAR system and Landsat 8 OLI surface reflectance products, respectively, indicating that GOFP-T has ability in simulating canopy reflectance for forest plantations on sloping terrains. GOFP-T with the hypergeometric model in this article is the first simple model to simulate canopy GF and BRF for forest plantations on sloping terrains.