Joint inversion of GNSS and GRACE data for ice mass loads in Greenland

Rapid melting of the Greenland Ice Sheet (GrIS) in response to global warming has been a major contributor to global sea level rise in the last 20 years. The ability of the Gravity Recovery and Climate Experiment (GRACE) to estimate GrIS mass changes is limited by its coarse (∼330 × 330 km²) spatial resolution. The Greenland Geodetic Network (GNET) senses the solid Earth's elastic responses to changing ice mass loads, as well as glacial isostatic adjustment (GIA). The GNET stations are sensitive to local ice mass changes at the scale of tens of kilometers, but have poor spatial coverage compared to GRACE, since all bedrock Global Navigation Satellite System (GNSS) stations are located near the margins of the GrIS. GRACE gravity observations and GNSS measurements of crustal displacement provide complementary constraints on GrIS mass changes. Here, we exploit this complementarity, by developing a joint inversion method that combines the norms of gradients and makes judicious use of the l-curve to estimate GrIS mass changes at 0.25°- grids. We modify the Laplacian operator, commonly used in previous studies, to make it suitable for the irregular inversion area and to avoid unrealistic inversion results at the land-sea boundary in Greenland. We have adopted a new weight allocation strategy to ensure that GRACE and GNSS data make similar contributions to the joint inversion results, avoiding the loss of information contained in GNSS due to the difference in spatial coverage between the two types of data. The joint inversion results are compared to satellite altimetry-derived GrIS mass changes and two GNET verification sites not involved in the inversion. This joint inversion method most strongly improves the spatial resolution of ice mass change estimates in low-altitude areas of Greenland. We recovered the melting signal of the GrIS leaking into the non-ice-covered land, and joint inversion indicates during January 2008 to December 2020 an ice mass trend (-254.0 Gt/yr) which is slightly slower than that inferred using GRACE mascon methods (-261.3 Gt/yr), but the annual amplitude of ice mass change (152.6 Gt) is significantly higher than GRACE (135.0 Gt). We identified areas with significant changes in ice mass that were not resolved by GRACE, and found (not surprisingly) that mass fluctuations were greater at outlet glacier locations than in adjacent areas of the ice sheet. Ice mass changes inferred from vertical land motion are sensitive to GIA corrections, and the difference in the rate of ice mass loss evaluated using different GIA models can reach around 20 Gt/yr, similar to GRACE-inferred mass estimates. This study successfully applies inverting GNSS and GRACE data for ice mass change at the edge of Greenland.