Estimating signal loss in regularized GRACE gravity field solutions

Gravity field solutions produced using data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are subject to errors that increase as a function of increasing spatial resolution. Two commonly used techniques to improve the signal-to-noise ratio in the gravity field solutions are post-processing, via spectral filters, and regularization, which occurs within the least-squares inversion process used to create the solutions. One advantage of post-processing methods is the ability to easily estimate the signal loss resulting from the application of the spectral filter by applying the filter to synthetic gravity field coefficients derived from models of mass variation. This is a critical step in the construction of an accurate error budget. Estimating the amount of signal loss due to regularization, however, requires the execution of the full gravity field determination process to create synthetic instrument data; this leads to a significant cost in computation and expertise relative to post-processing techniques, and inhibits the rapid development of optimal regularization weighting schemes. Thus, while a number of studies have quantified the effects of spectral filtering, signal modification in regularized GRACE gravity field solutions has not yet been estimated. In this study, we examine the effect of one regularization method. First, we demonstrate that regularization can in fact be performed as a post-processing step if the solution covariance matrix is available. Regularization then is applied as a post-processing step to unconstrained solutions from the Center for Space Research (CSR), using weights reported by the Centre National d'Etudes Spatiales/Groupe de Recherches de geodesie spatiale (CNES/GRGS). After regularization, the power spectra of the CSR solutions agree well with those of the CNES/GRGS solutions. Finally, regularization is performed on synthetic gravity field solutions derived from a land surface model, revealing that in some locations significant signal loss can result from regularization. This signal loss is similar in magnitude to estimated signal loss in post-filtered solutions. End-users of GRACE data can use this method to improve the error budgets of GRACE time-series, or to restore the power lost through regularization using a scaling technique.