Precise estimation of regional mass trends in Greenland using a global regularized inversion of level-2 data from GRACE/GFO satellite missions

The Greenland Ice Sheet (GrIS) has been a major single contributor to global sea level rise in recent decades, so that making accurate projections of its future behavior is a highly relevant task both for scientific community and for the human society in general. To that end, the mechanisms behind the observed ice mass changes must be understood in detail. This implies a need in accurate models of all those mechanisms, which requires, in turn, a sufficiently high accuracy of independent mass change estimates for validation and calibration purposes. For instance, the relative uncertainty of the Regional Atmospheric Climate Model RACMO describing the Surface Mass Balance (SMB) of the GrIS is of the order of 10%. Uncertainty of independent information must be at least comparable. This pose a challenge for all the groups involved into the estimation of GrIS mass variations from GRACE and GRACE Follow-On (GFO) data, since the accuracy of existing estimates typically does not match this requirement (especially in the context of individual drainage systems). Moreover, it is still not uncommon to refrain from an accurate assessment of the uncertainties of the obtained mass change estimates at all.

We propose to make an accurate estimation of regional mass changes in Greenland by an inversion of  GRACE/GFO-based level-2 data product (spherical harmonic coefficients) into a global set of mass anomalies using a regularized least-squares adjustment. We apply such an approach to estimate regional mass trends in the time interval Apr.2002–Aug.2023, both per Greenland’s Drainage System (DS) and for Greenland as a whole. First, a numerical study is carried out to optimize parameters of  the adopted spatially-varying 1^st-order Tikhonov regularization, as well as to quantify the error budget of the estimated regional mass trends. We show, among other, that random noise in input data plays only a minor role in the considered case, as compared to signal leakage and uncertainties of Glacial Isostatic Adjustment (GIA) modelling. Second, we apply the optimized regularization scheme to the level-2 data product from the Institute of Geodesy at Graz University of Technology (ITSG), having chosen the variant complete to the maximum degree 120. The regional mass losses per DS are found to vary between 18 Gt/yr (northeast DS) and 79 Gt/yr (southeast DS). The rate of the total mass loss in Greenland is estimated as 267.5 Gt/yr. The total errors of the obtained estimates are of the order of 4 and 10 Gt/yr for individual DSs and for entire Greenland, respectively. Finally, we demonstrate that it is important to take into account the Earth’s oblateness in the course of a regional mass change estimation, since the errors introduced by a spherical Earth approximation can be comparable to the total errors of the obtained estimates.