Estimation of mass variations within Greenland by an inversion of GRACE/GFO spherical harmonic coefficients into a global set of mascon-type mass anomalies

Satellite gravimetry is one of the primary tools to monitor mass variations of ice sheets. In this study, we apply data from GRACE and GRACE Follow-on (GFO) missions to quantify ice mass variations per Drainage Basin (DB) of the Greenland Ice Sheet (GrIS). To that end, we invert monthly sets of GRACE/GFO-based sets of spherical harmonic coefficients into mascon-type mass anomalies defined on a global equiangular grid. To suppress noise in the obtained estimates, a first-order Tikhonov regularization is applied. Regularization parameters are defined separately for ocean and land areas to ensure a much higher smoothness of mass anomalies over the ocean, as compared to the land. Such an approach offers a number of advantages, as compared to an estimation of mascon-type mass anomalies within a limited region only: (i) there is no need in low-degree coefficients that cannot be provided by GRACE/GFO missions with a sufficient accuracy (such as degree-1, C_2,0, and C_3,0 coefficients); (ii) it is not necessary to incorporate a correction for a leakage of hydrological and ice-related signals into Greenland from surrounding areas, since those signals are co-estimated; (iii) error propagation is straightforward.

In our study, we use as input the monthly ITSG-Grace2018 solutions produced at Graz Technical University (Austria). The resulting mass anomalies are estimated on a global 1^o × 0.4^o grid. Ultimately, they are integrated to yield the total mass anomaly per DB (the GrIS being split into six DBs).To enable the data inversion in spite of a large number of unknown parameters, we exploit the pre-conditioned conjugate gradient method. Two different regularization parameters are used within the study area: (i) a relatively small parameter for the Greenland’s coastal area and the periphery of the GrIS and (ii) a much larger regularization parameter for the inner part of the GrIS. To find the optimal values of the regularization parameters, we make use of a numerical study. We simulate a realistic signal and noise for one particular month (namely, Jan. 2019). Then, we select the regularization parameters that result in the smallest RMS differences between the estimated and the “true” mass anomalies per DB. Those parameters ensure a sufficient suppression of random noise in the mass anomaly estimates, while avoiding a substantial signal leakage between the DBs. The optimal values of the regularization parameters are applied to process all the available GRACE/GFO monthly solutions in the time interval from Apr. 2002 to Dec. 2021. This allows us to produce a time-series of mass anomalies for each of the six DBs under consideration, as well as for the territory of Greenland as a whole. The obtained results were submitted to the IMBIE-3 inter-comparison project.