Optimization of GRACE-based mass anomaly estimates using the first-order Tikhonov regularization, with application to the Greenland Ice Sheet

It is common to convert GRACE-based level-2 data product (spherical harmonic coefficients) into mass anomalies at the Earths surface using spherical harmonic synthesis. We claim that it is more appropriate to use for that purpose a least-squares adjustment (which can be understood in this context as a variant of mascon approach). Among other, this allows one to take into account the stochastic model of errors in the spherical harmonic coefficients, as well as a various physical constraints, such as geometry of coastal lines, geometry of deserts, etc. The latter constraints can be implemented, e.g., by introducing a spatially-varying first-order Tikhonov regularization. We apply such an approach to make a state-of-the-art estimate of Greenland Ice Sheet (GrIS) mass losses. First, a numerical study is carried out to optimize the spatially-varying regularization and demonstrate the performance of the developed approach. We show, among other, that the optimal regularization parameters strongly depend on the region and the spatial scale of interest. For instance, a substantially different regularization is recommended for the best global estimates of mass anomalies, for the best estimates of mass anomalies with Greenland only (pointwise), and for the best estimates of total mass anomalies per GrIS drainage system. This suggests that an optimal estimate of mass anomalies produced by a regularized least-squares adjustment tailored for a particular application is, in general, superior to an off-the-shelf mascon-type data product. Second, the mass trends in 20022023 per drainage system and over entire Greenland are estimated from actual GRACE/GRACE-FO level-2 data products. We show, among other, that the average rate of total mass loss in Greenland in the considered time interval is of the order of 270 Gt/yr. Furthermore, we analyze the factors that affect the estimated trends and quantify the uncertainties of the obtained estimates.