APPLE-GO: Modeling high-spatial resolution forest canopy reflectance with effect of Adjacent Pixels using Path Length Extended Geometric Optical theory

Forests are the key component of terrestrial ecosystems, playing a vital role in the global carbon and water cycles as well as in climate change. Satellite remote sensing imagery has the advantage of quantitatively monitoring and assessing the health status of forest canopies at large scales. With the improvement in spatial resolution of satellite sensors, it has become feasible to conduct quantitative research at high spatial resolutions (< 10 m). However, classic physical models that are based on simplified assumptions and only account for the radiative transfer process within the target pixel face challenges in supporting quantitative analysis at high-resolution scales, as high-resolution pixels are subject to significant radiative influences from adjacent pixels. In this study, we propose a high-spatial resolution forest canopy reflectance model, APPLE-GO, which comprehensively considers the shading effect and cross-radiation caused by adjacent pixels. The two-dimensional path length distribution (2-PLD) method is used to calculate the area fractions of each component, while shading factors are introduced to quantitatively calculate the reductions in the area fractions of sunlit components due to adjacent pixels. Multiple scattering energy is calculated based on the spectral invariant theory and the eight-neighborhood convolution algorithm. The bi-directional reflectance factor (BRF) calculated by the APPLE-GO model was evaluated against the three-dimensional (3D) radiative transfer model LESS, yielding RMSEs/RRMSEs of 0.008/10.2 % and 0.054/15.9 % in the red and near-infrared (NIR) bands, respectively. The model was also validated with satellite observations, showing RMSEs below 0.01 (RRMSE <27 %) for larch forests and under 0.017 (RRMSE <35 %) for mixed forests in the visible bands. These results demonstrate that the proposed model can accurately calculate the BRF in the nadir viewing direction, highlighting its potential for extracting vegetation parameters from high-resolution remotely sensed imagery.