Uncertainty quantification of surface reflectance for satellite hyperspectral remote sensing

In hyperspectral remote sensing, the accuracy of surface reflectance has become as a critical factor influencing quantitative applications. However, there remains a lack of comprehensive analysis concerning the factors contributing to surface reflectance uncertainty and the methodologies for their quantification, particularly in the context of complex terrains. Based on a radiative transfer model with atmospheric terrain coupling, the paper proposes a method for quantifying uncertainty by combining the law of propagation of uncertainty (LPU) with the Monte Carlo method (MCM). The impacts of radiometric calibration accuracy, terrain, and atmospheric parameter accuracy are evaluated. We incorporate model parameter uncertainties, along with their associated probability distributions, as inputs for uncertainty analysis. Throughout the surface reflectance inversion process, for procedures with analytical transfer functions, uncertainty propagates through the model using LPU. When analytical transfer functions are unavailable, the Monte Carlo method is employed, ultimately providing reflectance uncertainty on a per-pixel, per-band basis. A case study in the Guanting Reservoir test area in Hebei, China is conducted. Through uncertainty analysis and systematic evaluation, it is found that the uncertainty of at-sensor radiance and the uncertainty of direct solar irradiance are the two major sources of reflectance uncertainty. After 700 nm, the at-sensor radiance uncertainty stabilizes at 20%, while the direct solar irradiance contributes 80%. The results indicate that improving reflectance accuracy requires not only enhancing the calibration precision but also improving the matching accuracy between topographic factors and at-sensor radiance.