Modeling the top-of-atmosphere radiance of alpine snow with topographic effects explicitly solved

Optical remote sensing of snow is challenged by the complex radiative transfer mechanism in alpine environments. The representation of topographic effects in interpreting satellite imagery of snow is still limited to inadequate analytical modelization. Here we develop a framework that explicitly solves multiple terrain reflections and generates the top-of-atmosphere (TOA) radiance of alpine snow by the modified four-stream radiative transfer theory. This framework comprises an atmosphere module, a terrain module and a surface spectra module relying on the approximate asymptotic radiative transfer (ART) model. In the terrain module, the iterative solution to multiple terrain reflections is facilitated with a viewshed calculating algorithm which identifies adjacent slopes and related geometric angles to derive terrain-reflected irradiance. The modeled TOA radiance is compared with Landsat-8/9 OLI, Sentinel-2A/B MSI and Terra MODIS radiance imagery. Experiments of several snow-covered mountainous regions in the Pamir area reveal that the TOA radiance modeling results agree well with satellite observations with reported $R^2$ $\ge 0.86$, though subject to the uncertainties due to complex topography and seasonality. The modeled terrain-reflected irradiance is verified with the ray-tracing software called LargE-Scale Remote Sensing Data and Image Simulation Framework (LESS), and reliable modeling performance is confirmed as $R^2$ values are $\ge 0.90$. This model framework allows for better interpreting the apparent spectra of alpine snow through the physically-based linkage with snow’s intrinsic properties and environmental conditions.