Should coastal planners have concern over where land ice is melting?

There is a general consensus among Earth scientists that melting of land ice greatly contributes to sea-level rise (SLR) and that future warming will exacerbate the risks posed to human civilization. As land ice is lost to the oceans, both the Earth's gravitational and rotational potentials are perturbed, resulting in strong spatial patterns in SLR, termed sea-level fingerprints. We lack robust forecasting models for future ice changes, which diminishes our ability to use these fingerprints to accurately predict local sea-level (LSL) changes. We exploit an advanced mathematical property of adjoint systems and determine the exact gradient of sea-level fingerprints with respect to local variations in the ice thickness of all of the world's ice drainage systems. By exhaustively mapping these fingerprint gradients, we form a new diagnosis tool, henceforth referred to as gradient fingerprint mapping (GFM), that readily allows for improved assessments of future coastal inundation or emergence. We demonstrate that for Antarctica and Greenland, changes in the predictions of inundation at major port cities depend on the location of the drainage system. For example, in London, GFM shows LSL that is significantly affected by changes on the western part of the Greenland Ice Sheet (GrIS), whereas in New York, LSL change predictions are greatly sensitive to changes in the northeastern portions of the GrIS. We apply GFM to 293 major port cities to allow coastal planners to readily calculate LSL change as more reliable predictions of cryospheric mass changes become available.