Solar Zenith Angle Correction of Nadir-View Canopy Reflectance: A Simple Physics-Guided Semi-Empirical Method Based on Spectral Invariant Theory

Correcting the solar angle effect on the canopy bidirectional reflectance factor (BRF) is essential for quantitative remote sensing but remains challenging due to the limited solar–view geometries of satellite observations and the complex radiative transfer process. This study develops a semi-empirical, physics-guided model—referred to as the p-S model—to correct nadir-view canopy BRF across arbitrary solar zenith angles (SZAs) using a single reference observation. Grounded in spectral invariant theory (p-theory), the model expresses canopy BRF in a concise analytical ratio form and, for the first time, introduces a hotspot factor to describe the enhanced backscattering effect when solar and viewing directions coincide. The p-S model was validated using homogeneous, row-structured, and RAdiation transfer Model Intercomparison (RAMI) forest canopies simulated by the Discrete Anisotropic Radiative Transfer (DART) model, as well as real Landsat 8 observations. Across the red and near-infrared (NIR) bands, the p-S model accurately reproduced BRF patterns with root mean square errors (RMSEs) ( < 0.008 in red and 0.0142 in NIR bands). By providing representative parameter sets (a, b, c, and LAI) for major vegetation types, the p-S model offers a practical framework for solar angle correction of canopy BRF across diverse ecosystems, while application to Landsat 8 imagery successfully reproduced diurnal trends in canopy BRF and the normalized difference vegetation index (NDVI). The p-S model offers an efficient and physically consistent framework for canopy BRF correction under varying SZAs.