Summary Previous work has demonstrated a significant correlation between the pattern of sea level change computed from an altimeter-based inference of Greenland ice mass flux from 1993-2019 and sea surface height (SSH) observations adjacent to the island. However, a key question is unanswered in this detection; namely, what constraints on ice mass flux do the SSH observations provide? To address this issue, we perform a series of inversions of the available SSH data offshore Greenland. Our results indicate that such inversions are highly non-unique. However, we also demonstrate that robust inferences can be obtained by incorporating reasonable a-priori constraints, in our case limiting the ice model to a small set of discs associated with the major drainage basins of the ice sheet that are proximal to the SSH observations. Our inversions in this case yield estimates of average ice mass loss in the range 0.62-0.70 mm/yr in units of equivalent global mean sea level change over the period 1993-2019, when the observations are corrected for the signal of dynamic sea level change. This inference agrees with independent ice altimeter-based estimates of Greenland ice sheet mass flux rates, showing broadly consistent relative ice mass loss rates across southern Greenland basins. Our analysis is the first to directly invert SSH observations for ice mass changes and we conclude that the consideration of such data, particularly in combination with other data sets (e.g., GRACE gravity, ice altimeter measurements, GNSS observations) has the potential to improve constraints on ice sheet mass changes in a warming world.
Coulson et al. (2026) studied this question.