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 - Fan Yang; Ehsan Forootan; Shuhao Liu; Maike Schumacher (Water Resources Research)
Abstract 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.