Greenland ice sheet climate disequilibrium and committed sea-level rise

The study addresses how much sea-level rise is already committed by the Greenland ice sheet due to its current disequilibrium with climate. Since the 1980s, Greenland’s mass budget deficit emerged from increases in surface meltwater run-off and tidewater ice discharge. Predicting Greenland’s response remains difficult because ice sheet models struggle with process representation and realistic coupling to land, atmosphere, and ocean boundaries. To overcome these limitations, the authors quantify Greenland’s committed area and volume changes needed to bring the ice sheet into equilibrium with recent climate, asking: given the observed imbalance, what minimum sea-level rise is already locked in, irrespective of future climate evolution?

Previous work highlights rapid increases in Greenland run-off under Arctic warming and substantial contemporary mass loss, but model-based projections are challenged by uncertainties in coupling and key processes. Volume–area scaling theory has been used to estimate lower bounds on committed mass loss for mountain glaciers and ice caps. The authors extend this theoretical framework to the Greenland ice sheet by summing over many subregions to reduce errors, noting that while a non-linear scaling exponent (~1.25) is theoretically appropriate, it can render inversions ill-posed for single, large ice masses. Recent studies also document increasing interannual climate variability over Greenland and the role of atmospheric circulation modes (e.g., NAO) in driving extreme melt years, factors that are not fully captured by global climate models.

The approach quantifies Greenland’s geometrical disequilibrium with recent climate using the accumulation area ratio (AAR) derived from satellite optical imagery and links it to mass balance via regression. Key elements: 1) Data inputs: multi-year inventories of (a) tidewater glacier discharge (D); (b) SMB (precipitation minus sublimation minus run-off) from two regional climate models—MAR v3.10 and RACMO2.3p2—statistically downscaled to 1 km; and (c) AAR from NASA MODIS MOD10A1 daily albedo (2000–2019), using a bare-ice albedo threshold of 0.565 ± 0.109 based on PROMICE observations. The Greenland ice mask is from BedMachine v3. 2) Sectoral framework: Greenland’s contiguous ice sheet and peripheral ice caps (>30 km²) are partitioned into 473 flow sectors (after Mouginot et al.), enabling sector-wise AAR, SMB, and discharge computations and use of the law of large numbers to reduce scaling errors when aggregating. 3) AAR–mass balance regression: For each grouping, the equilibrium AAR (AAR_eq) is obtained by regressing annual AAR against mass balance, defining the AAR at which mass balance equals zero. The disequilibrium metric α = AAR/AAR_eq quantifies the fractional area change needed to equilibrate the ice geometry to the imposed climate. 4) Effective ablation area for tidewater sectors: Because calving truncates ablation areas, an effective ablation area correction is applied so that tidewater sectors have an equilibrium AAR_eq consistent with land-terminating sectors (AAR_eq = 0.780 ± 0.02), increasing tidewater imbalance assessments by 25 ± 4% on average. 5) Area–volume scaling: Volume change is derived from ΔV = (α^γ − 1) V with a conservative linear exponent γ = 1 to provide a mathematically sound lower bound and to accommodate flow interactions between adjacent sectors; using γ = 1.25 would raise volumes by ~20% but introduces ill-posedness for a single large mass. Committed area change is ΔA = A(α − 1). Eustatic SLR is ΔV/β with β = 362 Gt mm⁻¹. 6) Climate scenarios: Three perpetual reference climates are applied: Recent (mean 2000–2019), High-melt (2012, NAO −1.6), and Low-melt (2018, NAO +1.5). 7) Error propagation and ensemble: A 54-member ensemble (3 × 3 × 2 × 3) samples uncertainties in (i) tidewater AAR_eq adjustment (0.76–0.80), (ii) albedo threshold (±0.109, halved in propagation), (iii) SMB model choice (MAR vs RACMO), and (iv) discharge D (±10%). Sectoral results are aggregated; uncertainties are reported as single standard deviations. 8) Validation: Annual mass balances (2003–2019) are compared against GRACE/GRACE-FO gravimetry, showing equivalence on average (−272 ± 45 vs −270 ± 86 Gt yr⁻¹; correlation 0.640, P = 0.005). 9) Notes: Small glaciers <30 km² (≈1% area) are accounted for via mean specific imbalance (−446 ± 309 kg m⁻² yr⁻¹), adding 3.4 ± 2.7 mm SLE under recent climate. The method yields committed losses but does not constrain timescales.

- Committed SLR under recent climate: Applying the 2000–2019 average climate in perpetuity yields a committed retreat of 59 ± 15 × 10³ km² (3.3 ± ~0.8–0.9% area/volume loss), equivalent to 110 ± 27 × 10³ km³ of ice and 274 ± 68 mm of eustatic SLR. Greenland’s glacierized area considered is 1,783,090 km². - High- and low-melt end-members: Perpetual high-melt conditions like 2012 commit 169 ± 29 × 10³ km² (10 ± 2%) area loss, 314 ± 54 × 10³ km³ volume loss, and 782 ± 135 mm SLR. Perpetual low-melt 2018 conditions imply a temporary mass budget surplus corresponding to −168 ± 63 mm SLR (drawdown). - Mass budget components (2000–2019 averages): Total precipitation P = 745 Gt yr⁻¹ (trend ΔP = −18 ± 56 Gt yr⁻¹); Solid ice discharge D = 473 Gt yr⁻¹ (ΔD = 5 ± 9 Gt yr⁻¹); Run-off R = 413 Gt yr⁻¹ (ΔR = 95 ± 90 Gt yr⁻¹); SMB = 286 Gt yr⁻¹ (ΔSMB = −118 ± 106 Gt yr⁻¹). SMB variability is dominated by run-off (corr(SMB,R) = −0.855, 1−P > 0.999); corr(SMB,P) = 0.528 (1−P > 0.983). - Regional patterns: Western Greenland exhibits roughly fourfold higher imbalance than eastern sectors under recent climate. SW sector shows strongest sensitivity: under 2012 perpetual climate it commits 186 ± 30 mm SLR; under 2018 it shows a 22 ± 13 mm drawdown. NW sector commits 79 ± 12 mm SLR under recent climate, rising to 169 ± 28 mm under 2012 and near-equilibrium under 2018. SE sector contributes only ~4% of recent imbalance despite high discharge but rises to 67 ± 8 mm under 2012 and is near-equilibrium under 2018. CE region is near equilibrium under recent climate, but under 2012 commits 90 ± 17 mm SLR and under 2018 yields a 44 ± 8 mm drawdown. NE sector commits 24 ± 9 mm (recent) and 65 ± 8 mm (2012). - Sectoral contrasts: Although land-terminating sectors comprise ~25% of area, they account for ~41% of the recent imbalance, underscoring the dominant role of surface ablation. - Sensitivity to circulation extremes: The extreme NAO-driven years 2012 (negative NAO) and 2018 (positive NAO) bracket Greenland’s response between strong committed loss and near-equilibrium, highlighting increased climate variability and sensitivity to atmospheric circulation.

By quantifying the lower-bound committed mass loss inherent in Greenland’s current geometry under recent climate, the study directly addresses how much sea-level rise is already locked in, independent of future emissions pathways. The results indicate a minimum commitment of 274 ± 68 mm eustatic SLR from Greenland alone, with potential to exceed 780 mm under sustained high-melt conditions analogous to 2012. These findings align with structured expert judgment for Greenland’s SLR contribution by 2100 and with expectations for meter-scale SLR under strong warming scenarios, while emphasizing Greenland’s high sensitivity to interannual extremes in atmospheric circulation not fully captured by global models. The analysis complements process-based transient models by providing an observation-grounded, theory-based lower bound on committed loss; however, it does not specify response timescales. The dominance of run-off variability and the disproportionate contribution from land-terminating sectors further emphasize the primacy of surface processes, while marine-terminating sectors remain vulnerable to dynamic and ocean-forced changes not included in the geometric disequilibrium calculation.

The study provides a conservative, observation-constrained lower bound on Greenland’s committed sea-level contribution due to its disequilibrium with recent climate: at least 274 ± 68 mm eustatic SLR, irrespective of twenty-first-century climate trajectories. Under sustained high-melt conditions akin to 2012, the commitment rises to 782 ± 135 mm. The method integrates satellite-derived AAR, SMB, and tidewater discharge across 473 sectors and applies linearized area–volume scaling to ensure a robust lower bound while minimizing inversion errors. The results underscore Greenland’s acute sensitivity to atmospheric circulation extremes and increasing interannual variability. Future work should: (1) couple this disequilibrium framework with process-based models to constrain response timescales; (2) better integrate realistic atmosphere–ocean–ice forcings and amplifying feedbacks; (3) quantify potential additional losses from evolving ice dynamics and ocean forcing; and (4) improve representation of extremes and variability in climate projections relevant to Greenland’s mass balance.

- No timescale: The approach estimates committed losses but does not constrain how quickly they will unfold. - Conservative lower bound: Using a linear scaling exponent (γ = 1) underestimates volume changes by ~20% relative to γ ≈ 1.25, providing a lower bound but not a central estimate. - Dynamic and oceanic processes: Potential future changes in ice discharge driven by fjord/ocean circulation, submarine melting, calving dynamics, and subglacial conditions are not included if they are not attributable to geometric adjustment. - Spatial resolution and coverage: Ice areas <30 km² are not directly resolved in MODIS-based AAR; a closure correction is applied using mean specific imbalance, adding uncertainty. - Model dependence: SMB fields come from two RCMs (MAR, RACMO) and are downscaled; uncertainties are propagated but residual model structural differences remain. - AAR retrievals: Dependence on albedo thresholding and effective ablation area correction for tidewater sectors introduces methodological assumptions, albeit explored in ensemble uncertainty.