HBiM2: A multi-angle hyperspectral soil radiative transfer model for simulating the reflectance of dry and wet soils

A soil radiative transfer model (RTM) capable of simultaneously characterizing the spectral and directional reflectance of soil is essential for the accurate retrieval of soil-related parameters. However, most existing soil RTMs exhibit inherent limitations in jointly simulating spectral-directional behavior. For instance, the Hapke model primarily focuses on directional reflectance and lacks an explicit spectral formulation, while the MARMIT-2 model is designed for spectral modeling but does not explicitly account for directional effects. These limitations restrict the applicability of current models under complex surface conditions, particularly in the presence of variations in soil moisture and texture. To address these issues, we propose an unified soil RTM framework capable of modeling soil reflectance across both dry and wet conditions. Firstly, we develop the dry soil model (i.e., Hapke-BSM, HB) by coupling the Hapke model and dry soil components of the brightness-shape-moisture (BSM) model. Then, we propose a wet soil model (i.e., Hapke-BSM-improved MARMIT-2, HBiM2), which integrates the HB model with an improved multilayer RTM of soil reflectance (MARMIT) model framework that explicitly accounts for directional effects. Finally, the proposed soil models are validated using various datasets covering 10 soil textures, 14 particle sizes, multiple moisture levels, and a wide range of observational geometries over the 0.4–2.4 μm spectral range. The HB model demonstrates high accuracy across diverse conditions (R2 > 0.98, RMSE <0.02), while the HBiM2 model exhibits consistently robust performance under varying moisture and angular conditions (R2 > 0.95, RMSE <0.02). These results indicate strong agreement between simulated and measured reflectance under controlled conditions, supporting the proposed HBiM2 model framework, in which the HB component effectively characterizes dry soil reflectance.