A model based on spectral invariant theory for correcting topographic effects on vegetation canopy reflectance

Topography alters both the incident radiation and radiative transfer (RT) processes within the canopy, leading to changes in the canopy bidirectional reflectance factor (BRF). Most traditional semi-physical terrain correction (TC) methods for vegetation canopy BRFs rely on simplifying physically-based analytical RT models. However, these analytical RT models are not comprehensively parameterized for all RT computations, leading to the neglect of crucial processes, such as multiple scattering processes during the derivation of semi-physical TC methods. The spectral invariants theory (p-theory) offers an efficient approach to model canopy BRFs by simplifying RT computations. We extended p-theory to sloping terrain, considering the variation of the terrain-induced incident radiation and RT processes, and developed a canopy BRF TC model, termed the p-C method. The p-C method applies not only to spectral bands with lower multiple scattering within the canopy (e.g., visible bands) but also to near-infrared (NIR) bands, where multiple scattering effects may be more pronounced than in the visible bands within the canopy. We used the three-dimensional RT model DART (Discrete Anisotropic Radiative Transfer) to simulate BRFs of homogeneous, realistic canopies of the RAMI (RAdiation transfer Model Intercomparison) experiment, and BRF images with real DEM (Digital Elevation Model) to evaluate the p-C method and to compare it with traditional empirical and semi-physical TC methods (CC, SCS, SCS+C, DS, PLC-S, and SE). The p-C method reduced the RMSE (root mean square error) by 67 %, 64 %, 64 %, 85 %, 83 %, and 54 % respectively over these methods. Furthermore, when applied to Landsat 8 OLI remote sensing BRF images, the p-C method effectively eliminated terrain texture, as confirmed by visual interpretation and the linear regression between the corrected BRF images and the local solar incidence angle. Currently, the p-C method only considers illuminated slopes, and corrections for shaded slopes need to be studied in the future.