On the robustness of predictions of sea level fingerprints

The rapid melting of the Earth\textquoterights ice reservoirs will produce geographically distinct patterns of sea level change that have come to be known as sea level fingerprints. A basic, gravitationally self-consistent theory for computing these patterns appeared in the 1970s; however, recent, highly discrepant fingerprint calculations have led to suggestions that the algorithms and/or theoretical implementation adopted in many previous predictions is not robust. We present a suite of numerical predictions, including benchmark comparisons with analytic results, that counter this argument and demonstrate the accuracy of most published predictions. Moreover, we show that small differences apparent in calculations published by some groups can be accounted for by subtle differences in the underlying physics. The paper concludes with two sensitivity analyses: (1) we present the first-ever calculation of sea level fingerprints on earth models with 3-D variations in elastic structure and density, and conclude that this added complexity has a negligible effect on the predictions; (2) we compare fingerprints of polar ice sheet mass flux computed under the (very common) assumption of a uniform melt distribution to fingerprints calculated using melt geometries constrained by analysing recent trends in GRACE gravity data. Predictions in the near field of the ice sheets are sensitive to the assumed melt geometry; however, this sensitivity also extends to the far field, particularly in the case of Antarctic mass changes, because of the strong dependence of the rotational feedback signal on the melt geometry. We conclude that inferences of ice sheet mass flux based on modern sea level constraints should consider these more realistic melt geometries.