Overshooting the critical threshold for the Greenland ice sheet

The Greenland ice sheet (GrIS) has contributed over 20% of observed global sea-level rise (SLR) since 2002 and is expected to be a major contributor to future SLR. Theory, modelling, and palaeoclimate evidence indicate the GrIS has multiple stable states with critical thresholds in global mean temperature (GMT), beyond which positive feedbacks can drive self-sustained ice loss and hysteresis. Warming-induced freshwater input from Greenland also threatens to weaken the Atlantic Meridional Overturning Circulation (AMOC), with broad climatic consequences. Observations show accelerating meltwater runoff and precursor signals of critical transitions. Given uncertainties in meeting near-term temperature targets and the possibility of temporary overshoots followed by later cooling via CO2 removal, the study aims to quantify how the magnitude and duration of temperature overshoots and subsequent convergence temperatures affect GrIS stability, SLR contributions, and the potential for avoiding or reversing transitions to reduced-ice or ice-free states.

Previous work demonstrates GrIS multistability and critical thresholds, with potential transitions leading to several metres of SLR (e.g., Robinson et al. 2012; Pattyn et al. 2018; Gregory et al. 2004, 2020; Aschwanden et al. 2019). Since 2002, GrIS contributed >20% to observed SLR (Rietbroek et al. 2016). Exceeding 1.5 °C could trigger multiple tipping points (Armstrong McKay et al. 2022). Observations indicate nonlinear increases in Greenland runoff (Trusel et al. 2018) and early-warning signals of a tipping point (Boers & Rypdal 2021). Overshoot scenarios are relevant given challenges in limiting end-century warming below 1.5–2 °C (Rogelj et al. 2015; Raftery et al. 2017; Tong et al. 2019), with potential later CO2 removal (Azar et al. 2013; Ritchie et al. 2021). Feedbacks affecting GrIS include melt-elevation and albedo feedbacks (Levermann & Winkelmann 2016; Zeitz et al. 2021) and possible negative atmospheric feedbacks via increased accumulation (Barletta et al. 2018). AMOC changes can modulate Greenland climate (Jackson et al. 2015; Caesar et al. 2018; Boers 2021). The study builds on and compares to multi-model projections (ISMIP6: Goelzer et al. 2020; Seroussi et al. 2020; Edwards et al. 2021) and explores long-term commitments and hysteresis (Van Breedam et al. 2020; Noël et al. 2021; Höning et al. 2023).

Two independent ice-sheet modelling frameworks are employed: (1) PISM driven by a diurnal Energy Balance Model for surface mass balance (PISM-dEBM), capturing surface albedo feedbacks; and (2) the ice-sheet model Yelmo coupled to the Regional Energy-Moisture Balance Orographic model (Yelmo-REMBO), which includes a dynamic, simplified atmosphere and snowpack energy balance. Both models have been validated for past, present, and future ice-sheet evolution. Forcing: A prescribed change in regional summer (JJA) surface temperature relative to present day is applied, with a 1.61 scaling factor between regional winter and summer temperatures to obtain the seasonal cycle. Regional anomalies are linearly mapped to GMT anomalies above preindustrial levels using an Arctic amplification scaling (details in Methods: Climate forcing). Experimental design: (A) Short-term overshoots. From AD 2000 to 2100, apply a linear increase in JJA temperature to a peak ΔT_max,JJA. From 2100 to 2200, linearly cool to a convergence temperature ΔT_conv,JJA ranging from 0 to 4.0 °C above present (corresponding approximately to 0.5–3.9 °C GMT above preindustrial). After 2200, keep temperature constant and simulate for an additional 100 kyr to determine long-term equilibria or trends. (B) Long-term overshoots. After the same warming to 2100, vary the convergence time Δt_c to reach ΔT_conv,JJA (0–4.0 °C), with Δt_c spanning from 100 years to several millennia (up to 10,000 years), then hold constant and integrate for 100 kyr. Diagnostics: Total GrIS ice volume, minimum and equilibrium volumes, and equivalent SLR contributions are computed. Stability diagrams are constructed across grids of ΔT_max,JJA, ΔT_conv,JJA, and Δt_c. Sensitivity to equilibrium behavior and potential non-convergence is assessed via late-time trends (90–100 kyr). Spatial patterns of retreat and intermediate states are analyzed, including southwestern and northern GrIS sensitivity. Models are run at horizontal resolutions of about 16–20 km due to computational constraints given the large ensemble size.

• Threshold for abrupt total GrIS loss: 1.7–2.3 °C GMT above preindustrial. Specifically, ~2.3 °C with PISM-dEBM and ~1.7 °C with Yelmo-REMBO. - Without mitigation (post-2100 temperatures held constant): PISM-dEBM shows >20% ice-volume loss for ΔT_JJA > 1.0 °C and >80% loss for ΔT_JJA > 2.2 °C; Yelmo-REMBO indicates complete melt for ΔT_JJA > 1.4 °C. At ΔT_JJA = 7.0 °C, GrIS is lost in <5 kyr in both models. - Short-term overshoots (cooling 2100–2200): Converging to ≤1.5 °C GMT above preindustrial (ΔT_conv,JJA ≈ 1.3 °C) by 2200 yields a stable ice sheet with <1 m long-term SLR in both models, though interim SLR can slightly exceed 1 m in PISM-dEBM. Above ΔT_conv,JJA > 2.2 °C (PISM-dEBM) and >1.4 °C (Yelmo-REMBO), the GrIS is lost regardless of the peak in 2100. Equilibrium state depends mainly on convergence temperature, not the overshoot peak. - Long-term overshoots: Maximum SLR depends strongly on overshoot magnitude, convergence temperature, and convergence time. For Δt_c = 1,000 years, maximum SLR is similar to equilibrium SLR for 100-year convergence except at very high overshoots (>6 °C JJA). Even with ΔT_conv,JJA = 0 °C, high overshoots produce >1 m maximum SLR. For Δt_c = 10,000 years and ΔT_conv,JJA = 0 °C, overshoots ΔT_max,JJA > 2.5 °C yield >1 m maximum SLR; overshoots >6.0 °C lead to at least 5 m (PISM-dEBM) and 7 m (Yelmo-REMBO) maximum SLR before recovery. - Recovery potential: With ΔT_conv,JJA = 0 °C, both models ultimately return close to present-day volumes. For short overshoots (≤1,000 years), maximum SLR is <~1.25 m with recovery; for ≥5,000 years, complete temporary loss can occur before regrowth (7 m SLR), occurring at Δt_c = 5,000 years in Yelmo-REMBO and at 10,000 years in PISM-dEBM. - Hysteresis and irreversibility: For higher convergence temperatures, practical irreversibility emerges. PISM-dEBM approaches intermediate equilibrium states up to ~25% volume loss at ΔT_conv,JJA = 2.2 °C. Yelmo-REMBO shows that for long convergence times (>5,000 years) and high overshoots, regrowth may be prevented even below the critical threshold, implying an irreversibility range ~0.5 °C below the threshold after complete loss. - Safe operating spaces: Keeping convergence time <1,000 years and ΔT_conv,JJA ≈ 0 °C (≈0.5 °C GMT above preindustrial) limits maximum SLR to <2 m for all overshoot temperatures in both models. Overshoots below the threshold show weak dependence on convergence time. - Spatial sensitivity: Southwestern Greenland is most sensitive, retreating first, followed by northern retreat. PISM-dEBM exhibits intermediate stable states and decamillennial fluctuations near ΔT_JJA ≈ 2.2 °C, partly due to interplay of bedrock uplift and melt-elevation feedback.

The two modelling approaches, despite differing complexity and feedback representations, yield consistent qualitative behavior in thresholds, safe spaces, and timescale dependencies. PISM-dEBM explicitly captures surface albedo feedback in the SMB scheme but lacks atmospheric dynamical coupling, whereas Yelmo-REMBO includes a simplified dynamic atmosphere that captures both albedo-related warming and some negative feedbacks via precipitation changes along retreating margins. The existence of intermediate states and oscillations in PISM-dEBM, driven by interactions of glacial isostatic adjustment and melt-elevation feedback, facilitates reversibility before crossing the final threshold; Yelmo-REMBO lacks such stable intermediate states, indicating model dependence in detailed trajectories. The study highlights that post-overshoot outcomes are governed primarily by convergence temperatures and cooling timescales due to the ice sheet’s slow response. Uncertainties in Arctic amplification and long-term climate–ocean circulation changes (e.g., AMOC weakening) could narrow or widen the safe space, with competing effects via temperature and precipitation over Greenland. Even when an irreversible transition is avoided, temporary overshoots can cause peak SLR of several metres for millennia, implying long-lasting coastal impacts and potential AMOC perturbations from freshwater fluxes. The thresholds derived align with prior literature, reinforcing the importance of limiting GMT increase below ~1.5–2.5 °C and, if overshoots occur, ensuring rapid temperature reduction over centuries.

Using two independent ice-sheet models, the study constrains critical GMT thresholds for abrupt GrIS loss to ~1.7–2.3 °C above preindustrial and quantifies how overshoot magnitude, convergence temperature, and cooling timescale control GrIS stability and SLR. It identifies safe operating spaces where rapid post-2100 cooling to ≤~1.5 °C GMT prevents irreversible transitions and limits long-term SLR, while emphasizing that even temporary overshoots can produce multi-metre peak SLR. Southwestern Greenland dominates early retreat and the extent of intermediate states. Future research should: (1) conduct coordinated model intercomparisons under overshoot protocols to refine threshold estimates; (2) employ fully coupled Earth system models with interactive ice sheets to capture atmosphere–ocean–ice feedbacks and AMOC impacts; (3) explore higher spatial resolution and improved SMB physics; and (4) reduce uncertainties in Arctic amplification and long-term climate dynamics to better delineate safe spaces.

• Model structure differences lead to quantitative discrepancies: PISM-dEBM shows intermediate stable states and oscillations; Yelmo-REMBO transitions more abruptly and can exhibit irreversibility near the threshold. - Atmospheric coupling is simplified or absent: PISM-dEBM lacks dynamic atmospheric feedbacks; Yelmo-REMBO includes a simple atmosphere but not a fully coupled GCM, potentially omitting key circulation and cloud–precipitation feedbacks. - Resolution constraints (≈16–20 km) may underresolve small-scale processes; chosen due to computational demands of large ensembles. - Uncertainty in Arctic amplification magnitude and future regional climate over Greenland affects mapping from regional JJA anomalies to GMT and the size of safe spaces. - Long-term climate, ocean, and AMOC changes beyond 2100 are uncertain and not fully represented, potentially altering precipitation and temperature over Greenland. - Some simulations do not reach steady state even after 100 kyr, indicating slow equilibration and potential sensitivity to long-term Earth deformation and feedback timescales.