Theoretical Evaluation of Anisotropic Reflectance Correction Approaches for Addressing Multi-Scale Topographic Effects on the Radiation-Transfer Cascade in Mountain Environments

Research involving anisotropic-reflectance correction (ARC) of multispectral imagery to account for topographic effects has been ongoing for approximately 40 years. A large body of research has focused on evaluating empirical ARC methods, resulting in inconsistent results. Consequently, our research objective was to evaluate commonly used ARC methods using first-order radiation-transfer modeling to simulate ASTER multispectral imagery over Nanga Parbat, Himalaya. Specifically, we accounted for orbital dynamics, atmospheric absorption and scattering, direct- and diffuse-skylight irradiance, land cover structure, and surface biophysical variations to evaluate their effectiveness in reducing multi-scale topographic effects. Our results clearly reveal that the empirical methods we evaluated could not reasonably account for multi-scale topographic effects at Nanga Parbat. The magnitude of reflectance and the correlation structure of biophysical properties were not preserved in the topographically-corrected multispectral imagery. The CCOR and SCS+C methods were able to remove topographic effects, given the Lambertian assumption, although atmospheric correction was required, and we did not account for other primary and secondary topographic effects that are thought to significantly influence spectral variation in imagery acquired over mountains. Evaluation of structural-similarity index images revealed spatially variable results that are wavelength dependent. Collectively, our simulation and evaluation procedures strongly suggest that empirical ARC methods have significant limitations for addressing anisotropic reflectance caused by multi-scale topographic effects. Results indicate that atmospheric correction is essential, and most methods failed to adequately produce the appropriate magnitude and spatial variation of surface reflectance in corrected imagery. Results were also wavelength dependent, as topographic effects influence radiation-transfer components differently in different regions of the electromagnetic spectrum. Our results explain inconsistencies described in the literature, and indicate that numerical modeling efforts are required to better account for multi-scale topographic effects in various radiation-transfer components.