GSV-SRTS: A Heterogeneous Landscape Soil-Canopy Reflectance Model Over Sloping Terrain with an Extended GSV and Stochastic Radiative Transfer Theory

Abstract. Accurately modelling radiation interactions within canopy layers and soil backgrounds is crucial for biophysical variables retrieval across regional or global scales. However, terrain relief can introduce significant uncertainties into forward radiative transfer modeling. Despite the development of numerous canopy reflectance models for sloping terrain, the heterogeneous characteristics of soil-canopy objects have often been overlooked, leading to distortions in the bidirectional reflectance distribution in small-scale landscapes. In this study, we present a canopy reflectance model suitable for heterogeneous structures on sloping terrain. By extending the stochastic radiative transfer theory from flat terrain to sloping terrain and integrating the soil General Spectral Vector, the GSV-SRTS model was introduced. This enables accurate prediction of soil-canopy radiative transfer within subpixel 3-D heterogeneous mountain landscapes. The proposed GSV-SRTS model was evaluated against the Discrete Anisotropic Radiative Transfer (DART) model, compared with typical mountain canopy reflectance models, and validated against remote sensing observations at varying spatial resolutions. The results showed that the GSV-SRTS model achieves good accuracy in the comparisons with DART (R² = 0.9136 (0.9052) and root-mean-square errors (RMSE) = 0.0246 (0.0216) in the red (NIR (Near-Infrared)) band) and performs well in real mountainous areas, particularly with high spatial resolution remote sensing observations (R² = 0.9078 (0.9143) and RMSE = 0.0201 (0.0212)). Furthermore, the GSV-SRTS model effectively captures the impacts of canopy structure and terrain factors on bidirectional reflectance. This underscores the GSV-SRTS model as a reliable physical tool for simulating radiation regimes over sloping terrain, with the potential to enhance the accuracy of biophysical variable retrieval from remote sensing observations.