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

Abstract

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.

Fig. 1. Sensitivity of SLR to worldwide variations in ice thickness.

(A) Gradient −dS_NY/dH (in 10⁻³ μm/m per km²) of sea level in New York (S_NY) with respect to ice thickness (H) changes in glaciated areas. The gradient units reflect a measure of SLR change (in μm) per unit of ice thickness change (in m) per area unit of ice (in km²), which is equivalent to SLR change (in mm) per unit change in ice mass (in GT). Signs rendered for dS/dH result in positive sensitivities of SLR to negative thickness changes (that is, shrinking ice sheets and glaciers resulting in positive GMSL rise). (B) GRACE-inferred ice thickness change (in cm/year) for Antarctica during January 2003–December 2015, demonstrating strong spatial variability. (C) Gradient −dS_Sydney/dH (in μm/m per km²) of sea level in Sydney (S_Sydney) with respect to ice thickness (H) changes in Antarctica. (D) LSL contribution −dS_Sydney/dH*ΔH (in μm/km² per year) for each km² area of Antarctica to LSL in Sydney. The sum of this quantity over the entire ice sheet quantifies the contribution of the entire AIS to LSL in Sydney. Coastlines are plotted in black.

Fig. 2. Sensitivity of SLR along U.S./Canadian coastlines to GrIS thickness variations.

Gradient −dS/dH (in 10⁻³ μm/m per km²) at U.S. and Canadian coastal cities. Maps 1 to 9 correspond, respectively, to gradients computed for each of the named ports numbered clockwise from Halifax. −dS/dH is computed using the ISSM-AD (23) gradient solver. The forward SLR run used to support the derivation of –dS/dH is shown in the center Earth map (in mm/year). It is computed using the ISSM-SESAW (29) solver with model inputs (ice thickness change) inferred from GRACE for the period 2003–2016. This forward model therefore captures the response to thickness changes in all of the main glaciated areas of the world (including, among others, Alaskan and Canadian Arctic Glaciers, Himalayan Glaciers, Patagonia Glaciers, and the Greenland and Antarctica Ice Sheets) (28), hence representing a truly global “ice” fingerprint.

Fig. 3. GMSL ratios for select coastline cities across Europe applied to GrIS.

GMSL ratios (in %) for coastal cities across Europe (from −100 to 100%). The ratios are defined as gradients of local SLR with respect to changes in ice thickness, −dS/dH, normalized by the equivalent GMSL gradient –dS_GMSL/dH, where S_GMSL is the GMSL signal induced by an equivalent change in ice thickness. These ratios measure the departure from GMSL contributed by local ice thickness changes in Greenland. They can be used to multiply against observed/predicted ice thickness changes to quantify any non-GMSL effects at any coastal city of the world.

Fig. 4. Projected contribution of GrIS to SLR in New York and London based on the SeaRISE experiments.

Two hundred–year projection of the contribution (in μm/km²) of local areas in Greenland to SLR in New York (first column), London (second column), and any geographical location that experiences only the GMSL variation (third column) using two models of ice thickness change from the SeaRISE (15) experiments: Simulation Code for Polythermal Ice Sheets (SICOPOLIS) and University of Maine Ice Sheet Model (UMISM). The units reflect a measure of SLR change (in μm) per area unit (in km²) of the GrIS. It is equal to the gradient fingerprint multiplied by the GrIS thickness change, or dS/dH|_local*ΔH, where dS/dH|_local is the gradient fingerprint for the local port city and ΔH is the projected ice thickness change for the GrIS. This localized contribution can be summed up over the entire GrIS to compute SLR for London, for example, ${\text{SLR}}_{\text{London}}={\displaystyle {\int }_{\text{GrIS}}}\frac{\mathit{d}\mathit{S}}{\mathit{d}\mathit{H}}{|}_{\text{London}}*\mathrm{\Delta }\mathit{H}*\mathit{d}\mathit{A}$. For reference, we provide total SLR computed for London, New York, and the GMSL scenario. Note that in these two SeaRISE GrIS projections, both London and New York have LSL changes that are reduced over the GMSL rise that will affect far-field cities.