Error covariance structure caused by uncertainties in atmospheric correction for optical sensors

In satellite remote sensing of land surface Essential Climate Variables (ECVs) using optical sensors, an atmospheric correction step is typically required to convert top-of-atmosphere (TOA) bi-directional reflectances into top-of-canopy (TOC) bi-directional reflectances. We analyse the error covariance structure of TOC reflectances that arises specifically from uncertainties in atmospheric correction. Using SMAC as the atmospheric correction model and Automatic Differentiation (AD) for efficient Jacobian computation, we quantify these error covariances across different scenarios. Our results show that uncertainties in the atmospheric state introduce non-negligible correlations of both signs between different satellite bands. Since these correlations are often overlooked, explicitly accounting for them could improve the accuracy of land surface ECV retrievals.