Uncertainty quantification for a global imaging spectroscopy surface composition investigation

Abstract Airborne and orbital imaging spectroscopy can facilitate the quantification of chemical and physical attributes of surface materials through analysis of spectral signatures. Prior to analysis, estimates of surface reflectance must be inferred from radiance measurements in a process known as atmospheric correction, which compensates for the distortion of the electromagnetic signal by the atmosphere. Inaccuracies in the correction process can alter characteristic spectral signatures, leading to subsequent mischaracterization of surface properties. Global observations pose new challenges for mapping surface composition, as varied atmospheric conditions and surface biomes challenge traditional atmospheric correction methods. Recent work adopted an optimal estimation (OE) approach for retrieving surface reflectance from observed radiance measurements, providing the reflectance estimates with a posterior probability. This work incorporates these input probabilities to improve the accuracy of surface feature measurements. We demonstrate this using a generic feature-fitting method that is applicable to a wide range of Earth surface studies including geology, ecosystem studies, hydrology and urban studies. Specifically, we use a probabilistic framework based on generalized Tikhonov-regularized least squares, a rigorous formulation for appropriate weighting of features by their observation uncertainty and leveraging of prior knowledge of material abundance for improving estimation accuracy. We demonstrate the validity of this procedure and quantify the increase in model performance by simulating expected accuracies in the reflectance estimation. To evaluate global uncertainties in mineral estimation, we simulate observations representative of the expected global range of atmospheric water vapor and aerosol levels, and characterize the sensitivity of our procedure to those quantities.