A Monte Carlo Propagation of the Full Variance-Covariance of GRACE-Like Level-2 Data With Applications in Hydrological Data Assimilation and Sea-Level Budget Studies

Understanding mass (re-)distribution within the Earth system, and addressing global challenges such as the impact of climate change on water resources requires global time-variable terrestrial water storage (TWS) estimates along with reasonable uncertainty fields. The Gravity Recovery and Climate Experiment (GRACE) and GRACE-FO satellite missions provide time-variable gravity fields with full variance-covariance information. A rigorous uncertainty propagation of these errors to TWS uncertainties is mathematically challenging and computationally inefficient. We propose a Monte Carlo Full Variance-Covariance (MCFVC) error propagation approach to precisely compute TWS uncertainties. We also establish theoretical criteria to predict the actual convergence and accuracy of MCFVC, showing a convergence after 10,000 realizations with the relative error of 2.8% for variance and 4.7% for covariance at the confidence level of 95%. This can be achieved in few seconds using a single CPU to compute the uncertainties of each 1° resolution globally gridded TWS field. A validation against the rigorous error propagation method indicates relative differences of less than 0.8%. A global uncertainty assessment shows that neglecting the covariance of gravity coefficients can considerably bias the TWS uncertainties, that is, up to 60%, in some basins like Eyre. Flexibility of MCFVC allows the quantification of filtering impacts on the uncertainty of TWS fields, for example, up to 35% in the Tocantins River Basin. An empirical model is provided to reproduce GRACE-like TWS uncertainty fields for hydrological studies. Finally, experiments of GRACE(-FO) data assimilation for hydrological applications and sea-level budget estimation are presented that indicate the importance of accounting for the full covariance information in these studies.