The long–term sea–level commitment from Antarctica

. The evolution of the Antarctic Ice Sheet is of vital importance given the coastal and societal implications of ice loss, with a potential to raise sea level by up to 58 m if melted entirely. However, future ice–sheet trajectories remain highly uncertain. One of the main sources of uncertainty is related to nonlinear processes and feedbacks of the ice sheet with the Earth System on different timescales. Due to these feedbacks and the ice–sheet inertia, ice loss may already be triggered in the next decades and then unfolds delayed on multi–centennial to millennial timescales. This committed Antarctic sea– 5 level contribution is not reflected in typical sea–level projections based on mass balance changes of Antarctica, which often cover decadal–to–centennial timescales. Here, using two ice–sheet models, we systematically assess the multi–millennial sea– level commitment from Antarctica in response to warming projected over the next centuries under low– and high–emission pathways. This allows bringing together the time horizon of stakeholder planning with the much longer response times of the Antarctic Ice Sheet. 10 Our results show that warming levels representative of the lower–emission pathway SSP1-2.6 may already result in an Antarctic mass loss of up to 6 m sea–level equivalent on multi–millennial timescales. This committed mass loss is due to a strong grounding–line retreat in the Amundsen Sea Embayment as well as a potential drainage from the Ross Ice Shelf catchment and onset of ice loss in Wilkes subglacial


Introduction
The future sea-level contribution from the Antarctic Ice Sheet, which stores enough ice to raise sea level by up to 58 m (Fretwell et al., 2013), is of vital importance for coastal communities ranging from small islands to the world's mega-cities, ecosystems and the global economy (Clark et al., 2016).In addition, the Antarctic Ice Sheet is subject to several positive (and negative) feedback mechanisms determining its longterm stability (Fyke et al., 2018;Garbe et al., 2020).For example, accelerated ice loss may be triggered once the self-reinforcing surface melt-elevation feedback (Levermann and Winkelmann, 2016;Oerlemans, 1981) kicks in.With the lowering of the icesheet surface due to melting, it is exposed to higher air temperatures owing to the atmospheric lapse rate.Surface melting is, in turn, enhanced, promoting persistent ice loss upon crossing a critical threshold.Furthermore, the marine parts of the ice sheet, e.g., in West Antarctica or the Aurora and Wilkes subglacial basins in East Antarctica, are found to be susceptible to self-sustained, potentially irreversible grounding-line retreat (Garbe et al., 2020;Rosier et al., 2021;Mengel and Levermann, 2014;Feldmann et al., 2014).The rapid grounding-line retreat is often associated with a self-amplifying feedback in which the increased ice flow across the grounding line caused by an initial retreat fosters further retreat.In a theoretical flowline setup, it was shown that, due to the ice flux being a nonlinear function of the ice thickness, grounding lines of ice sheets grounded below sea level on a retrograde, inland sloping bed are unstable (Marine Ice Sheet Instability; Weertman, 1974;Schoof, 2007).More complex stability conditions arise in three dimensions when accounting for additional processes such as, e.g., buttressing (Gudmundsson et al., 2012;Haseloff and Sergienko, 2018;Pegler, 2018), calving and submarine melting (Haseloff and Sergienko, 2022) or the presence of feedbacks between the ice sheet and its environment (Sergienko, 2022).Ice loss may be dampened, on the other hand, by negative feedbacks such as introduced by e.g., the isostatic rebound of the solid Earth underlying the ice sheet to ice mass changes, which could potentially stabilize West Antarctic grounding lines (Coulon et al., 2021;Barletta et al., 2018).
Depending on the interplay of these feedbacks, persistent mass loss may be triggered once critical forcings or tipping points (Lenton et al., 2008;Armstrong McKay et al., 2022), for instance in temperature, are crossed.The Antarctic Ice Sheet was therefore classified as a tipping element of the climate system (Lenton et al., 2008;Armstrong McKay et al., 2022).Due to the inertia in the system and the related delay in the ice-sheet response under realistic forcing, the ice sheet's trajectory likely deviates from the ice-sheet equilibrium response to warming (Garbe et al., 2020;Rosier et al., 2021).While consequences of self-sustained ice loss potentially triggered in the next decades may play out and become visible over millennial timescales (Reese et al., 2023) (characterized as a slow onset of tipping; Ritchie et al., 2021), tipping may be sped up by forcing beyond the critical threshold.For the Greenland Ice Sheet, it was shown that the timescales of ice-sheet decline strongly depend on how far its critical temperature threshold is exceeded (Robinson et al., 2012).
Previous assessments of the long-term contribution to sea-level rise from the Antarctic Ice Sheet have been primarily restricted to a single ice-sheet model and have rarely explored intra-and inter-model uncertainties as well as uncertainties in climate forcing (Golledge et al., 2015;Clark et al., 2016): They suggest that the grounding lines in the Amundsen Sea Embayment may at present already be undergoing or may be committed to a self-amplified retreat under sustained presentday climate conditions until a new stable geometric configuration is reached (Reese et al., 2023;Joughin et al., 2014;Favier et al., 2014;Seroussi et al., 2017;Arthern and Williams, 2017;Golledge et al., 2019Golledge et al., , 2021)).The potential for pronounced grounding-line recession in marine-based portions of West Antarctica and the Wilkes subglacial basin in East Antarctica until the end of the millennium (Golledge et al., 2015;Clark et al., 2016;Winkelmann et al., 2015;Bulthuis et al., 2019;Chambers et al., 2022;Coulon et al., 2023) was illustrated for higher-emission scenarios, giving rise to an Antarctic mass loss of multiple https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.meters of sea-level equivalent.On multi-millennial timescales, the loss of the portion of the ice sheet grounded above sea level in East Antarctica may be locked in for strong atmospheric warming, which would eventually commit the Antarctic Ice Sheet to contribute several tens of meter to global mean sea-level rise (Clark et al., 2016;Winkelmann et al., 2015).
Here we systematically study the long-term multi-millennial evolution of the Antarctic Ice Sheet in response to a wide range of possible future climate trajectories and thereby quantify its sea-level commitment for stabilized climate at different points in time over the course of the next centuries taking into account uncertainties in climatic boundary conditions and ice-sheet processes, by means of two different ice-sheet models: PISM (Bueler and Brown, 2009;Winkelmann et al., 2011) and Kori-ULB (previously called f.ETISh; Pattyn, 2017).The remainder of this paper is structured as follows: In the following Sect. 2 we describe the methods for performing sea-level projections on multi-millennial timescales.Results are presented in Sect. 3 and discussed in Sect. 4 with a focus on different sources of uncertainties, arising from the divergence of future climate trajectories as well as structural uncertainties, distinct initialisations and certain processes and their parameterisations in ice-sheet models.

PISM
The Parallel Ice Sheet Model (PISM; Bueler and Brown, 2009;Winkelmann et al., 2011) is an open-source, thermo-mechanicallycoupled ice sheet/stream/shelf model.In hybrid mode, the shallow-ice approximation (SIA) and shallow-shelf approximation (SSA) are solved and superimposed, giving rise to different dynamic regimes from the slow-flowing ice in the ice-sheet interior to the faster-flowing streams and ice shelves.We here use a modified version of PISM release v1.0 (Garbe et al., 2020).
In particular, centered differences of the ice thickness across the grounding line are calculated to derive the surface gradient, which have been shown to improve the representation of the driving stress at the grounding line (Reese et al., 2023).We use a rectangular grid of 16 km horizontal resolution and a vertical grid structure with the highest resolution at the base of the ice sheet and shelves.
Basal shear stress τ b and shallow-shelf approximation basal sliding velocities u b are related in a general power law of the form with the threshold velocity u th = 100 m yr −1 and the sliding exponent q.The yield stress τ c is determined by the Mohr-Coulomb failure criterion (Cuffey and Paterson, 2010) as including the till friction angle ϕ and the effective pressure N till .The till friction angle is parameterized as piecewise linear with bed elevation (Martin et al., 2011) where the values for the constants N 0 , e 0 and C c are chosen following Bueler and van Pelt (2015).The amount of water from basal melt in the till layer W till with a maximum of W max = 2 m evolves according to the non-conserving 'null' hydrology model (as described in Bueler and van Pelt, 2015) with a decay rate C of water in the till.The grounding-line position is simulated at a subgrid scale evolving freely without imposing additional flux conditions.Basal resistance is linearly interpolated on a sub-grid scale around the grounding line (Feldmann et al., 2014), while sub-shelf melt in partially floating cells is not applied in the experiments presented here.We apply eigencalving, which linearly relates the calving rate to the spreading rate tensor with a proportionality factor of K = 1x10 17 m s (Levermann et al., 2012).Additionally, thin ice below 50 m is removed at the calving front (thickness calving) and a maximum extent for ice shelves is defined (Garbe et al., 2020;Albrecht et al., 2020).Our simulations include the effect of the viscous and elastic response of the bedrock to changes in ice load, following Lingle and Clark (1985) and Bueler et al. (2007), with an upper mantle viscosity η = 1x10 21 Pa s and density ρ = 3300 kg m −3 as well as a flexural rigidity of the lithosphere of 5x10 24 N m.

Kori-ULB
The Kori-ULB ice flow model, which is the follow-up of the f.ETISh model (Pattyn, 2017), is a vertically-integrated, thermomechanically-coupled hybrid ice-sheet/ice-shelf model, and incorporates relevant features for studying the evolution of the Antarctic Ice Sheet such as the mass balance-elevation feedback, basal sliding, sub-shelf melting, calving, and bedrock deformation.The ice flow is governed by a combination of the shallow-ice (SIA) and shallow-shelf (SSA) approximations for grounded ice and by the shallow-shelf approximation for floating ice shelves (Bueler and Brown, 2009;Winkelmann et al., 2011).Simulations of the multi-millennial Antarctic sea-level contribution presented here were performed with Kori-ULB version 0.91 at a horizontal resolution of 16 km.
Basal sliding is parameterized using a Weertman sliding law, i.e., where τ b and v b are the basal shear stress and the basal velocity, respectively, and with a basal sliding exponent m = 3.The values of the basal sliding coefficient A b are inferred following the nudging method of Pollard and DeConto (2012b) and Bernales et al. (2017).
At the grounding line, a flux condition (related to the ice thickness at the grounding line; Schoof, 2007) is imposed as in Pollard and DeConto (2012a) and Pollard and DeConto (2020) to account for grounding-line migration.This implementation can reproduce the steady-state behavior of the grounding line and its migration (Schoof, 2007) also at coarse resolution (Pattyn et al., 2013).Using this flux condition, the marine ice-sheet behavior in Antarctica was simulated by large-scale ice-sheet models (Pollard and DeConto, 2012a;DeConto and Pollard, 2016;Pattyn, 2017;Sun et al., 2020) buttressed conditions as in high-resolution models (Pollard and DeConto, 2020).Calving at the ice front depends on the parameterized combined penetration depths of surface and basal crevasses relative to the total ice thickness.Similar to Pollard et al. (2015) and DeConto and Pollard (2016), the parameterisation of the crevasse penetration depths involves the divergence of the ice velocity, the accumulated strain, and the ice thickness.Bedrock adjustment in response to changes in ice and ocean load is taken into account by means of the commonly used Elastic Lithosphere-Relaxed Asthenosphere (ELRA) model, where the solid-Earth system is represented by a relaxing viscous asthenosphere below a thin elastic lithosphere plate (Le Meur and Huybrechts, 1996;Coulon et al., 2021).A spatially uniform relaxation time of 3000 years and a flexural rigidity of the lithosphere of 10 25 N m is chosen in the simulations presented here.

Assessing Antarctic sea-level commitment
We aim to determine the long-term multi-millennial sea-level contribution from the Antarctic Ice Sheet and thereby its sealevel commitment using the ice-sheet models PISM and Kori-ULB (compare Sect. 2.1).After initializing the models to obtain initial Antarctic Ice Sheet configurations and running historical simulations (described in more detail in the following Sect.2.2.2 and 2.2.3, and illustrated in Figure 1), we assess the response of the Antarctic Ice Sheet to changes in the oceanic and atmospheric boundary conditions derived from state-of-the-art climate model projections available from the sixth phase of the Coupled Model Intercomparison Project (CMIP6) under the Shared Socioeconomic Pathways SSP1-2.6 and SSP5-8.5 (thereby covering a wide range from lower-to higher-emission scenarios).As we are interested in the long-term response, we focus on a set of CMIP6 General Circulation Models (GCMs) that provide forcing until the year 2300.Thereby, we obtain the transient realized sea-level contribution of the Antarctic Ice Sheet at given points in time (for instance, in the year 2100, filled dots in Figure 1).We then quantify the long-term committed sea-level contribution by stabilizing forcing conditions of the climate trajectories at regular intervals in time ('branching off' in the years 2050, 2100, 2150, 2200, 2250 and 2300) and letting the ice sheet evolve over several millennia (until year 7000) under fixed climatic boundary conditions characteristic for the respective branchoff year (Fig. 1, open dots).Climate conditions of the distinct branchoff years are determined as the mean over the previous ten years before the branchoff.

initialisation
Both ice sheet models are initialized using constant climatic boundary conditions representing the year 1950 (Fig. 1).More specifically, 'historic' climatic boundary conditions for the year 1950 are constructed using the historic changes in ocean and atmosphere with respect to the reference period from 1995 to 2014 from the Norwegian Earth System Model (NorESM1-M; Bentsen et al., 2013).The oceanic and atmospheric anomalies are averaged over the period 1945-1955 and subsequently added to present-day atmospheric temperatures and precipitation as well as observed present-day ocean temperatures and salinities.To build initial ice-sheet representations with PISM, a spin-up approach is applied for each of the atmospheric climatologies individually.Uncertainties in ice-sheet model parameters are taken into account by running an ensemble of spin-up simulations and choosing the initial state which fits well to observations of present-day ice thickness, ice velocities and grounding-line position.More specifically, starting from Bedmap2 ice thickness and topography (Fretwell et al., 2013), PISM is run for 600 000 years with constant geometry to obtain a thermodynamic equilibrium.Applying the constant historic boundary conditions associated with the year 1950, an ensemble of simulations with varying model parameters (guided by recent PISM ensembles; Reese et al., 2023;Albrecht et al., 2020) is run for several thousand years.Here, we include the SIA enhancement factor (E SIA ∈ 1.5, 2; varied around the reference value of Albrecht et al., 2020) and parameters related to basal sliding, namely the pseudo-plastic sliding exponent (q ∈ 0.25, 0.5, 0.75, within the range investigated by Albrecht et al., 2020;Lowry et al., 2021), the till effective overburden fraction (δ ∈ 1.5, 2.0, 2.5; Bueler and van Pelt, 2015) and the decay rate of till water content (C ∈ 7, 10 mm yr −1 , equivalent to the range explored by Albrecht et al., 2020).After 5000 years of simulation, the ensemble members are assessed with a scoring method following Albrecht et al. (2020) and Reese et al. (2020).The scoring method is based on the mean-square-error mismatch of grounded and floating ice area, ice thickness, grounding-line location and surface velocity compared to present-day observations (Fretwell et al., 2013;Rignot et al., 2011).Each indicator is evaluated for the entire Antarctic domain as well as for the Amundsen, Filchner-Ronne and Ross regions individually.The five best-scoring ensemble members in terms of the continental as well as the basin-scale indicators are continued until reaching 50 000 years of simulation, and experiments are performed with the ice-sheet configuration performing well in the scoring after 50 000 years.
For Kori-ULB, ice-sheet initial conditions and basal sliding coefficients are obtained in an inverse simulation following Pollard and DeConto (2012b) for each of the 'historic' atmospheric climatologies associated with the year 1950 (as described above).In this inverse procedure, the difference to the observed ice thickness (Bedmachine; Morlighem et al., 2020) is minimized by iteratively adjusting the basal sliding coefficients under grounded ice and sub-shelf melt rates under floating ice (Bernales et al., 2017).The resulting sub-shelf melt rates may therefore be interpreted as balance sub-shelf melt rates and are independent of the oceanic boundary conditions (forcing), while the ice-sheet states are in steady-state with the initial atmospheric climatologies.Applying constant historic ocean and atmospheric boundary conditions associated with the year 1950, a short relaxation is run for 10 years after the model initialisation and before the historical simulation.This limits an initial shock that may results from the transition from the balance sub-shelf melt rates derived during the transient spin-up to the imposed sub-shelf melt parameterisation scheme.The two initial ice-sheet states resulting from the nudging spin-ups are therefore in quasi-equilibrium.They compare well to the observed ice dynamics, ice geometry, and grounding-line position (compare Fig. S1), and are within the range of the ISMIP6 models (Seroussi et al., 2019).Starting from the initial ice-sheet configurations and climate conditions of the year 1950 described above, we run historical simulations for the time period from 1950 to 2015 (Fig. 1).Changes in oceanic and atmospheric conditions are derived from NorESM1-M, as recommended within ISMIP6 (Barthel et al., 2020;Nowicki et al., 2020).The corresponding ice-sheet response (as determined by PISM and Kori-ULB) over the historical period is shown in Figure S2.The atmospheric and oceanic forcing conditions until the year 2300, which are applied to the ice-sheet models for studying the future evolution of the Antarctic Ice Sheet, rely on a subset of state-of-the-art GCM projections available within CMIP6 (MRI-ESM2-0, UKESM1-0-LL, CESM2-WACCM, and IPSL-CM6A-LR).We apply climate forcing under both the Shared Socioeconomic Pathways SSP5-8.5 and SSP1-2.6.The selection of CMIP6 GCMs was guided by the limited availability of extended climate projections until 2300 within ScenarioMIP (O'Neill et al., 2016), while the climate sensitivity of the available GMCs (Meehl et al., 2020) and their performance in comparison with observations (e.g., Beadling et al., 2020;Purich and England, 2021;Bracegirdle et al., 2020) were considered as secondary criteria.
Following Nowicki et al. (2020), spatially-varying atmospheric (near-surface air temperature) as well as oceanic (salinity and temperature) anomalies with respect to the 1995-2014 mean climatology are directly derived from NorESM1-M over the historical period as well as from projections of the selected CMIP6 GCMs until the year 2300.Note that, for precipitation, ratios (instead of anomalies) with respect to the 1995-2014 mean precipitation are determined to avoid 'negative' absolute precipitation (e.g., Goosse et al., 2010, Equation 30).The respective anomalies are added to the present-day climatologies for the atmosphere (MAR, RACMO) and the ocean (Schmidtko et al., 2014).Thus, the resulting forcing matches present-day conditions in the 1995-2014 reference period (as in Reese et al., 2023).For the oceanic properties, yearly averaged forcing is applied to the ice-sheet models.Missing values for the oceanic forcing on the continental shelf (arising due to the coarse resolution of CMIP6 GCMs) and in currently ice-covered regions are filled following Kreuzer et al. (2021), i.e., by averaging over all existing values in neighbouring cells.In contrast, monthly forcing is used at the interface of the ice sheet to the atmosphere (as in Golledge et al., 2019).
Surface melt and runoff are determined from monthly atmospheric temperature and precipitation (i.e., accounting for the seasonal cycle) using a positive-degree-day (PDD) scheme (Reeh, 1991).The amount of PDD follows the approach presented in Calov and Greve (2005), with a default value for the standard deviation of σ = 5 °C and σ = 4 °C for PISM and Kori-ULB, respectively.Snow accumulation rates are derived from precipitation via an atmospheric temperature threshold with a linear transition between snow and rain.In Kori-ULB, natural variability is considered when determining snow accumulation rates (similar to the calculation of the amount of positive-degree-days) using a standard deviation of σ = 3.5 °C.Melt coefficients of 3 mm w.e. per PDD for snow and 8 mm w.e. per PDD for ice are used in both ice-sheet models after a comparison to MAR estimates until the year 2100 (Kittel et al., 2021;Coulon et al., 2023).A constant fraction of surface melt refreezes in PISM (Reeh, 1991), while Kori-ULB applies a simple thermodynamic parameterisation of the refreezing process (Huybrechts and De Wolde, 1999;Coulon et al., 2023).Computing surface melt and runoff in a PDD approach follows Garbe et al. ( 2020 static ice-sheet geometry neglecting, for example, the surface melt-elevation feedback (Kittel et al., 2021).
To account for the surface melt-elevation feedback, the near-surface air temperature is corrected for changes in ice-sheet surface elevation.More specifically, air temperatures T forcing provided to the ice-sheet models are shifted linearly with a change in surface elevation ∆h as following the atmospheric lapse rate Γ of 8°C / km.
Sub-shelf melt rates are computed by using the Potsdam Ice-shelf Cavity mOdel (PICO; Reese et al., 2018).PICO calculates sub-shelf melt rates from far-field salinities and temperatures and parameterizes the overturning circulation in ice-shelf cavities.Ocean properties derived from CMIP6 GCMs are linearly interpolated to the continental shelf depth (Kreuzer et al., 2021) to be applicable to PICO.The overturning strength parameter C = 3x10 6 m 6 s −1 kg −1 and the turbulent heat exchange coefficient γ * T = 7x10 −5 m s −1 (with correction of ocean properties of Schmidtko et al. (2014) to match observed present-day melt rates from Adusumilli et al. (2020)) are used for PISM experiments, as they have been found to fit melt sensitivities well (Reese et al., 2023).For Kori-ULB experiments, the overturning strength and the turbulent heat exchange coefficient are chosen as C = 1x10 6 m 6 s −1 kg −1 and γ T = 4x10 −5 m s −1 , respectively.

Results
We here present the transient response of the Antarctic Ice Sheet to a range of possible future climate trajectories until the year 2300 (Sect.3.1) along with the associated committed ice-sheet evolution on multi-millennial timescales (Sect.3.2).
The dependency of the committed sea-level contribution on the environmental conditions in Antarctica sustained over several thousands of years after their stabilization at different points in time during the next centuries is assessed in Sect.3.3.

Transient ice-sheet response until 2300
Following the lower-emission pathway SSP1-2.6 results in a sea-level change ranging from -5.0 cm to +8.0 cm by the end of this century and from -0.2 m to +0.5 m in 2300 (Fig. 2a; Tab. 1).Therein, Kori-ULB projects a positive sea-level contribution for this lower-emission scenario (dashed lines), while PISM projects a sea-level drop (solid lines).The overall sign of icesheet mass changes contributing to a change in sea-level depends on the balance between the dynamic response to sub-shelf melting and ice-shelf thinning and the surface mass balance.We find that the integrated surface mass balance remains positive for both ice-sheet models until 2300 under SSP1-2.6 (Fig. S3a).However, the response in dynamic discharge contributing to a sea-level increase on centennial timescales is higher in Kori-ULB (with ice-sheet thinning in the Amundsen Sea Embayment Under climate trajectories following the SSP5-8.5 emission pathway, the Antarctic ice loss varies between -6.0 cm and +6.0 cm sea-level equivalent by the end of this century, increasing to +0.7 -+3.1 m by 2300 (Fig. 2b; Tab. 1).The initial sealevel drop by 2100 is again found in simulations from PISM and can be attributed to increasing snowfall with warming, which dominates the ice-sheet mass balance until the end of this century.Simulations by Kori-ULB show an earlier grounding-line retreat in the Amundsen Sea Embayment, outweighing the initial increase in the integrated surface mass balance and resulting in a positive sea-level contribution already during the 21st century.Beyond 2100 and over the course of the following two centuries, the grounding line in the Amundsen Sea Embayment may retreat substantially (Fig. 3b, realized) depending on the sensitivity of the initial state to the imposed ocean warming (being strongest under IPSL-CM6A-LR and UKESM1-0-LL; Fig. S8-S11 show the individual ice-sheet response determined by both ice-sheet models to the different centennial climate trajectories).At the same time, the integrated surface mass balance starts to decrease and may even turn negative for strong atmospheric warming (Fig. S3b).The major ice shelves including the Ross Ice Shelf as well as the Filchner-Ronne Ice Shelf thin, in particular near the grounding line, and are (in PISM only) even lost sequentially by 2150 and 2300, respectively (Fig. 3b, realized; Fig. S10-S11).As a consequence of reduced buttressing, the grounding line in the Siple Coast region starts to show retreat.
Overall, the global mean sea-level contribution due to mass balance changes of the Antarctic Ice Sheet projected by PISM and Kori-ULB on centennial timescales (Fig. 2a and b; Tab. 1) is within the range of recent estimates: by the end of this century, estimates by the Ice Sheet Model Intercomparison Project ISMIP6 range from -9 cm to +30 cm under higher-emission pathways and from -1.4 cm to +15.5 cm under lower-emission pathways (Seroussi et al., 2020;Payne et al., 2021).The forced response of the Antarctic Ice Sheet until 2300 is in line with the results of both Golledge et al. (2015) and Chambers et al. (2022) and is consistent with the range of -0.3 m -+3.2 m sea-level equivalent given as estimate for the Antarctic sea-level contribution in the latest IPCC assessment (Fox-Kemper et al., 2021).

Long-term committed ice-sheet evolution over the next millennia
Oceanic and atmospheric warming projected for the upcoming centuries may trigger changes in the dynamics and geometry of the Antarctic Ice Sheet that are not realized on the same timescales (as the forcing), but unfold thereafter over the course of the following millennia, due to ice-sheet inertia and nonlinear feedbacks.After determining the transient realized sea-level response over the next centuries (Sect.3.1), we investigate this long-term committed evolution of the Antarctic Ice Sheet by keeping environmental conditions constant at different points in time and letting the ice sheet evolve over several millennia (see Sect. 2.2.1).
Our simulations confirm that sea level may keep rising for centuries to millennia to come even if warming is kept at a constant level (Fig. 2c and d, consistent with, e.g., Winkelmann et al., 2015;Van Breedam et al., 2020).The delayed response of the Antarctic Ice Sheet on millennial timescales gives rise to a substantial gap between the transient realized (described in the previous Sect.3.1) and the long-term committed Antarctic sea-level contribution, being more than the 100 ( 10 We find a sharp increase in the Antarctic sea-level contribution over the next millennium, irrespective of the emission scenario.When following the lower-emission pathway SSP1-2.6, the ice-sheet response levels off after a peak in the rate of Antarctic ice loss within this millennium or at latest by the beginning of the following millennium.It then stabilizes at qualitatively different stages of ice-sheet decline (Fig. 2c and e).In some cases, abrupt changes in the Antarctic sea-level contribution occur delayed (compared to other trajectories under the lower-emission pathway) in PISM, with a lag of multiple millennia to the onset of the perturbation in ice-sheet boundary conditions.These ice-sheet trajectories, however, eventually converge to the same magnitude of sea-level contribution on multi-millennial timescales.In our simulations under SSP1-2.6,we do not find a strong dependency of the long-term ice-sheet configuration reached in year 7000 on the point in time after which climatic boundary conditions are kept constant (Fig. 2e; Fig. 3a, committed).When sustaining the warming level potentially reached until year 2050, global mean sea-level may increase by +0.4 m to +3.8 m on the long-term (Fig. 2e; Tab. 1).
For climatic boundary conditions representative of the end of this century and thereafter, Antarctic mass changes range between -0.2 m and +6.3 m of sea-level equivalent, which unfolds over the next millennia (Fig. 2e; Tab. 1).The applied GCM forcing determines the magnitude of the committed Antarctic sea-level contribution under SSP1-2.6 at a given (branchoff) point in time (Fig. 2e).For both ice-sheet models, stronger ocean warming in the Wilkes basin projected by UKESM1-0-LL and IPSL-CM6A-LR compared to the other GCMs may promote grounding-line retreat in this region (compare Fig. S12-S15), giving rise to the upper limit of long-term ice loss found under the lower-emission pathway (Fig. 2e).The magnitude of mass loss is further modulated by the consequences of a potential collapse of the Ross Ice Shelf as well as the extent of grounding-line recession in the Amundsen Sea Embayment.In PISM, a substantial portion of the marine ice-sheet in West Antarctica is lost by year 7000 under most considered climate trajectories (compare Fig. S14-S15), determining (in combination with a potential grounding-line retreat in the Wilkes basin) the upper range of Antarctic sea-level commitment under SSP1-2.6 in our ensemble of simulations (Fig. 2e).While the Ross Ice Shelf collapses under SSP1-2.6 in PISM, Filchner-Ronne Ice Shelf remains intact in most of these simulations (except for CESM2-WACCM).In Kori-ULB, grounding-line retreat is limited to Pine Island and Thwaites Glacier while both large ice shelves are preserved (with a slight grounding-line advance for Ross Ice Shelf, compare Fig. S12-S13).This limits the long-term sea-level change from Antarctica to approximately +3.0 m in Kori-ULB (in combination with a retreating grounding line in Wilkes basin under UKESM1-0-LL and IPSL-CM6A-LR; Fig. 2e).
Under the SSP5-8.5 emission scenario, the potential magnitude as well as the range of the long-term Antarctic sea-level response substantially increase with the point in time at which ocean and atmospheric warming is stabilized (Fig. 2f).Under the sustained warming levels potentially reached during the next decades (that is, by 2050) under this high-warming climate trajectory, long-term mass losses are projected to arise from marine regions in West Antarctica (Fig. 3b, committed), leading to +0.5 m -+3.7 m of global mean sea-level rise (comparable to changes under SSP1-2.6;Tab. 1).In addition, the grounding line at the Siple Coast may retreat inland with a thinning of Ross Ice Shelf (or even a collapse, Fig. 3b, committed), as suggested in simulations by PISM.In response to changes in climatic boundary conditions projected for the end of this century, we find the committed sea-level contribution to be substantially larger (Fig. 2f): Marine parts of the West Antarctic Ice Sheet show a significant retreat (in some cases the West Antarctic Ice Sheet even collapses entirely), accompanied by a strong inland retreat of the grounding line in the East Antarctic Wilkes basin on the long term (depending on the climate forcing, Fig. 3b, committed; Fig. S16-S19).Compared to ice-sheet changes triggered within the next decades, this can lead to more than a doubling of the long-term mass loss ranging between +1.2 m and +8.5 m sea-level equivalent (by year 7000, Fig. 2f; Tab. 1).The mass loss until year 3000 amounts to +1.0 m -+4.9 m sea-level equivalent (compare Tab. 1), consistent with Chambers et al. (2022).For warming levels that are reached under SSP5-8.5 for any of the branchoff points after 2100, mass loss from Antarctica may continue well beyond the end of this millennium, with high rates of the Antarctic contribution to sea-level rise until the end of our simulations in year 7000 (Fig. 2d).This is due to additional and persistent ice loss in the Aurora, Wilkes and Recovery subglacial basins (Fig. 3b, committed).We also find a substantial ice thickness decrease in inner parts of East Antarctica grounded above sea level that is triggered under sustained high levels of warming and possibly exacerbated by the melt-elevation feedback (Fig. 3b, committed).In such cases, the long-term contribution of the Antarctic Ice Sheet to global mean sea-level rise may be as high as +40.8 m for sustained warming levels representative for the year 2300 (in the year 7000; with ice loss of +5.9 m -+31.7 m and +3.3 m -+13.8 m sea-level equivalent by the year 5000 and 3000, respectively, compare Tab. 1).Our upper range of long-term mass loss committed under constant climatic boundary conditions reached by the year 2300 is thus higher than previous estimates (under Representative Concentration Pathway RCP8.5, Golledge et al., 2015;Bulthuis et al., 2019), likely caused by higher magnitudes of imposed warming in the selected GCMs employed here.
In summary, comparing the long-term ice loss under both emission pathways, we find that the committed Antarctic sea-level contribution at a given point in time diverges beyond the end of this century (Fig. 2f, comparing projected multi-millennial ice loss under SSP5-8.5 to SSP1-2.6 indicated by light grey box).That is, the emission pathways become increasingly relevant for the long-term mass loss from Antarctica after 2100.At the same time, even the lower-emission scenario poses a considerable Table 1.Mean, minimum and maximum value of the combined realized and committed ice loss (in meters sea-level equivalent) as determined by the ice-sheet models PISM and Kori-ULB under emission pathways SSP1-2.6 and SSP5-8.5.Ice loss is given for different points in time where climatic boundary conditions are stabilized.For a given point in time, upper rows represent SSP1-2.6 and lower rows correspond to SSP5-8.5.

Realized
Committed

Threshold behavior in response to changing climatic boundary conditions
The Antarctic Ice Sheet has been shown to exhibit a nonlinear response to warming and hysteresis behavior in quasi-equilibrium on multi-millennial timescales.These ice-sheet states complement the quasi-equilibrium response of the Antarctic Ice Sheet (obtained by Garbe et al., 2020) as they record the long-term response to faster warming as projected under the different SSP scenarios.Figure 4 shows the committed sea-level contribution of the Antarctic Ice Sheet (in the year 7000) for a given regional (Antarctic-averaged) atmospheric warming level, thereby overcoming the dependency of ice loss on the diverging climate trajectories (Sect.3.2).
For regional warming levels of up to 4°C, as reached by 2300 under SSP1-2.6 and by 2050 under SSP5-8.5,we find a committed collapse of the Amundsen Sea basin, in some cases even a partial collapse of the West Antarctic Ice Sheet, resulting in a long-term Antarctic mass loss of up to 6.0 m sea-level equivalent over multi-millennial timescales (Fig. 4a and b, I and II).With both ice-sheet models, our experiments show a strong grounding-line retreat in the Amundsen Sea Embayment for this temperature range (Fig. 4c and d, I and Fig. 5d and g), consistent with previous work (Garbe et al., 2020).This may be accompanied by a connection from Pine Island Glacier to Ronne Ice Shelf, giving rise to ice loss from this region (Fig. 4c and   d, I and Fig. 5a).While Ross Ice Shelf is maintained in simulations with Kori-ULB, it is lost in most simulations with PISM (compare Fig. 4c and d, I).The collapse of Ross Ice Shelf is accompanied by the drainage of the corresponding catchment area (Fig. 4c, I and Fig. 5e and h), except for regional atmospheric warming below 1°C (projected by MRI-ESM2-0 under SSP1-2.6 until year 2050 only) which is comparable with the ice-sheet equilibrium response determined by means of PISM in Garbe et al. (2020).While 2% of the initial ice mass in Antarctica contributing to global mean sea-level rise is lost in Kori-ULB (raising global mean sea-level by up to approximately +2.0 m), a slightly higher fraction of 6% (equivalent to a global mean sea-level change between +3.0 m and +4.0 m) is found in simulations with PISM (Fig. 4b), due to the discharge of larger parts of the West Antarctic Ice Sheet as opposed to an advance of the grounding line in the Siple Coast area in Kori-ULB (compare Fig. 4c and d, I).The uncertainty in the initial ice-sheet configurations of each model results in differences on the order of decimeters in sea-level contribution in this warming range and is thus less significant than the inter-model spread.Overall, there is a good agreement also in the patterns of mass loss for the different initial configurations.Some of our simulations (across both ice-sheet models) also show an onset of grounding-line retreat in Wilkes basin in this range of atmospheric warming, shifting the upper bound of ice loss up to +6.0 m sea-level equivalent and widening the intra-model spread (Fig. 4b-d, I and Fig. 5i).This region contributes up to +1.5 m to the long-term sea-level change, which may occur for a mean ocean-temperature change exceeding +0.5°C -+1°C in this basin (depending on the ice-sheet model, with earlier onset of retreat in Kori-ULB; Fig. 5i).The loss of ice grounded below sea level in this particular (Wilkes) basin is triggered for slightly lower ocean warming than in Garbe et al. (2020) and Golledge et al. (2015), but is located within the range of idealized experiments by Mengel and Levermann (2014).
The long-term response of the marine basins may further depend on the ratio of atmospheric to oceanic warming: Despite exposing the ice sheet to higher atmospheric warming levels as derived from CESM2-WACCM under the lower-emission pathway, the grounding line in Wilkes subglacial basin does not experience retreat under these forcing conditions (due to weaker ocean forcing compared to UKESM1-0-LL, Fig. 4c, II and  II), which further raises with enhanced warming (Fig. 5c).Such a retreat of the basins connected to Filchner-Ronne Ice Shelf occurs in Kori-ULB only at slightly higher warming levels (see below, Fig. 4d).
Antarctic atmospheric warming levels of +5°C to +7°C are projected by the end of this century when following the higher-emission pathway (Fig. 4  Exceeding an atmospheric warming of +8°C in Antarctica gives rise to a further increase in the fraction of ice that is lost on multi-millennial timescales from 15 % up to 40 % at +14°C (Fig. 4 IV).Enhanced long-term mass loss with stronger Antarctic warming is found in particular for Filchner-Ronne, Recovery and Wilkes subglacial basins (Fig. 5a-c, i).In addition, some of our experiments suggest the onset of ice drainage from the East Antarctic Aurora basin (Fig. 5f; in accordance with Golledge et al., 2015), associated with a substantially increasing contribution to sea-level rise from this basin (for RACMO initial state, Fig. S19) in this warming range.The ice stored in the Aurora basin is lost completely in both ice-sheet models for even higher atmospheric warming levels (see below and Fig. 4V).While the general dependency of ice loss from the Aurora region on the atmospheric forcing in our simulations is in agreement with Golledge et al. (2017), stronger warming of the atmosphere is required here for triggering the retreat.For sustained regional atmospheric warming above +15°C (projected by CESM2-WACCM after year 2200), we find that large parts of the marine basins in Antarctica are lost and ice grounded above sea level in East Antarctica starts to decline substantially on multi-millennial timescales (Fig. 4V).Over the next millennia, this gives rise to an ice loss equivalent to a sea-level change of up to +40.8 m.It cannot be ruled out that Antarctica could become ice-free under the given climate conditions, consistent with Garbe et al. (2020) and Winkelmann et al. (2015), given the continued increase of the Antarctic sea-level contribution at the end of our simulations (Fig. 2d).Overall, the sea-level commitment increases nonlinearly with increasing atmospheric temperature change in Antarctica (Fig. 4a), with a spread in mass loss at a given warming level due to differences in parameter choices (here arising as part of the initialisation) and structural (model) uncertainty.In other words, the ice-sheet sensitivity to warming varies with the initial Antarctic ice-sheet configuration and its characteristics.While we can identify distinct clusters of qualitatively different icesheet behavior on the continental-scale with changing atmospheric warming (Fig. 4), critical thresholds in climatic boundary conditions inducing persistent ice loss are masked in the continent-wide committed sea-level contribution and can be located on a basin-scale (Fig. 5).The importance of structural differences between the ice-sheet models, their initialisation and related parameter choices for Antarctic sea-level commitment and respective critical temperature thresholds is discussed in Sect.4.1.In this paper, we determine the multi-millennial sea-level contribution from mass balance changes of the Antarctic Ice Sheet under a range of possible climate trajectories for both low-and high-emission pathways.In particular, we quantify the longterm Antarctic sea-level commitment when stabilising climatic boundary conditions at different points in time.That is, the atmospheric and oceanic changes potentially established during the upcoming centuries are sustained for several thousands of years, and we explore their long-term impacts on the Antarctic Ice Sheet.Experiments were carried out systematically for stabilized climate at different points in time over the course of the next centuries and in a consistent way with the stand-alone ice-sheet models PISM and Kori-ULB accounting for some inter-and intra-model uncertainty.
Our experiments illustrate a substantial gap between the realized and committed sea-level change from the Antarctic Ice Sheet.While the projected Antarctic mass change by the end of this century may raise global mean sea-level by a few centimeters (or could potentially result in a sea-level drop, spanning a range from -0.1 m to +0.1 m sea-level equivalent), the Antarctic Ice Sheet may be committed to a strong grounding-line retreat in the Amundsen Sea Embayment up to a collapse of the West Antarctic Ice Sheet for sustained climate conditions at levels projected to be reached during this century (that is, branching off in the years 2050 or 2100, depending on the GCM) even under the lower-emission pathway.Mass loss from the marine Wilkes subglacial basin in East Antarctica may unfold on multi-millennial timescales for warm ocean conditions projected by some GCMs as early as the second half of this century under the lower-emission scenario.Stabilizing climate conditions later in time (for instance in the year 2300) and following the higher-emission pathway SSP5-8.5 may additionally trigger a substantial decline of the terrestrial East Antarctic Ice Sheet, resulting in long-term mass losses of up to +40.8 m sea-level equivalent.
Determining the committed evolution of the Antarctic Ice Sheet triggered by the warming projected for the next centuries extends previous studies of the long-term ice-sheet response (especially in the Amundsen Sea sector) under sustained presentday conditions.For example, Reese et al. (2023) and Golledge et al. (2019) suggest a committed (potentially irreversible) grounding-line retreat in West Antarctica under present-day conditions on centennial timescales in response to atmospheric and oceanic changes over the past decades.We also add to the assessment of the long-term Antarctic sea-level commitment to future warming by the end of this century (Chambers et al., 2022;Lowry et al., 2021) and by 2300 (Golledge et al., 2015;Bulthuis et al., 2019;Coulon et al., 2023)

Uncertainties in Antarctic sea-level commitment
The committed Antarctic sea-level contribution is subject to uncertainties related to the substantial spread of warming projected by the selected GCMs for a given point in time (climate forcing uncertainty, Sect.3.2).Critical temperature thresholds giving rise to self-sustained ice loss further vary in our experiments as a result of inter-and intra-model uncertainties (Sect.3.3).
These uncertainties may be induced by differences in the model structure and the parameterisation of certain processes (e.g., Seroussi et al., 2020), initialisation procedures (e.g., Seroussi et al., 2019;A dalgeirsdóttir et al., 2014) as well as parameter choices (e.g., Bulthuis et al., 2019;Nias et al., 2016;Coulon et al., 2023).The role of these different sources of uncertainties for the multi-millennial Antarctic sea-level response presented in this work is discussed in the following.

Uncertainty due to climate forcing
The climate forcing from the four GCMs employed here results in a wide spread of the realized and especially committed sea-level contribution from Antarctica, making it one of the most important sources of uncertainty.
For low to intermediate warming levels covered by the lower-emission pathway SSP1-2.6, the uncertainty introduced by the climate forcing at a given point in time is comparable to the uncertainty caused by inter-model differences (compare Fig. 2e), except for the response to CESM2-WACCM under SSP1-2.6.Here, PISM shows an onset of ice discharge from the Recovery basin after Filchner-Ronne Ice Shelf is lost (Fig. S14-15), while corresponding ice loss is triggered for stronger changes in climatic boundary conditions in Kori-ULB (compare Fig. S12-S13 for SSP1-2.6 to Fig. S16-S17 for SSP5-8.5).This gives rise to a larger difference in the Antarctic sea-level contribution determined by both ice-sheet models.
We find that the growing spread of the committed Antarctic sea-level contribution under the higher-emission scenario SSP5-8.5 for stabilizing the ice-sheet boundary conditions later in time can (to a large part) be attributed to the divergence of the climate trajectories projected by the four GCMs.They are characterized by different warming rates and climate sensitivities, resulting in a substantial climate forcing uncertainty at a specific point in time: While for MRI-ESM2-0 a comparably low equilibrium climate sensitivity was determined (3.2°C, below the multimodel mean of 3.7°C; Meehl et al., 2020), the equilibrium climate sensitivities of UKESM1-0-LL (5.3°C), CESM2-WACCM (4.8°C) and IPSL-CM6A-LR (4.6°C) are at the upper end of the range of climate sensitivities reported for CMIP6.CESM2-WACCM also shows a significantly stronger regional atmospheric warming under SSP5-8.5 beyond 2150 than the other GCMs (Tab.S1).This translates into a growing uncertainty in projected long-term Antarctic ice loss under SSP5-8.5 with a substantially higher committed sea-level contribution from Antarctica for the same year under CESM2-WACCM compared to the other applied CMIP6 GCMs.For example, the committed Antarctic sea-level contribution determined by Kori-ULB and PISM under CESM2-WACCM ranges between 24.3 m and 40.8 m (when assuming a stabilization of climatic conditions representative for the year 2300).In contrast, we find an Antarctic Uncertainty arising from intra-and inter-model differences On multi-millennial timescales, both ice-sheet models show a good agreement in the pattern of mass loss and the resulting sea-level contribution from Antarctica for strong atmospheric warming (above 15°C of regional atmospheric temperature change), where the ice-sheet's decline (predominantly of its terrestrial parts grounded above sea level) is driven by atmospheric changes rather than ocean warming.The onset of grounding-line retreat in Antarctic marine basins is located at different low to intermediate warming levels due to inter-model differences.Both ice-sheet models agree on an early retreat of grounding lines of Pine Island and Thwaites Glacier in the Amundsen Sea Embayment, consistent with previous findings that the groundinglines may at present already be undergoing a self-sustained retreat or that this retreat has been locked in due to changes in the climatic boundary conditions over the past decades (Favier et al., 2014;Golledge et al., 2019;Reese et al., 2023).Ice loss from the catchment draining Ross Ice Shelf and a (partial) collapse of the West Antarctic Ice Sheet is triggered, however, for lower warming in PISM than in Kori-ULB, resulting in a multi-meter spread of the long-term committed sea-level contribution for Antarctic-averaged atmospheric warming up to 4°C (Fig. 4).This grounded ice-sheet response is accompanied by a different response of the major ice shelves in both ice-sheet models.Sequential collapse of the Ross and Filchner-Ronne Ice Shelf is projected by PISM for the change in oceanic and atmospheric conditions projected under SSP1-2.6,while both shelves are preserved in Kori-ULB under this lower-emission pathway and in some cases even under the higher-emission pathway SSP5-8.5.Ice-sheet sensitivities of the marine Wilkes and Recovery subglacial basins in East Antarctica to changes in atmospheric and oceanic boundary conditions also vary depending on the ice-sheet model configuration, such that persistent ice loss is triggered for different magnitudes of warming.
This inter-model discrepancy may be the result of several factors related to the characteristics of both ice-sheet models: The grounding line in the Siple Coast area is relatively sensitive to changes in climatic boundary conditions in PISM, being located upstream of the observed grounding line at present-day (compare Fig. S1; as often observed in a model initialisation in a spin-up approach, e.g., Reese et al., 2023) and showing thinning in Ross Ice Shelf over the historical period (compare Fig. S2; also when determining the historical ice-sheet evolution on higher horizontal resolution using PISM,e.g., Reese et al., 2020Reese et al., , 2023)).The grounding-line advance in the Siple Coast found in Kori-ULB under SSP1-2.6 may result from a drift of the initialisation procedure, which could be due to an underestimation of the sub-shelf melt rates obtained from PICO compared to the balance melt rates derived during the nudging procedure (Sect.2.2.2).Finally, some ice shelves are sustained longer in Kori-ULB, which could be due to the different calving schemes employed in the ice-sheet models (Levermann et al., 2012;Pollard et al., 2015;DeConto and Pollard, 2016).
Our simulations are performed on a comparably coarse horizontal resolution of 16 km, allowing for a large number of experiments as presented here, which is needed to cover the wide range of uncertainties.The migration of the grounding line in PISM is captured reasonably well, even on such a coarse resolution, with a sub-grid interpolation scheme (Feldmann et al., 2014), which allows to reproduce glacial cycles of the Antarctic Ice Sheet (Albrecht et al., 2020).Garbe et al. (2020) showed resolving grounding-line dynamics at a coarse resolution is addressed by imposing a flux condition (Pollard andDeConto, 2012a, 2020), which results in a good agreement with high-resolution models.
Characteristics of the initial states give rise to an intra-model spread in the projected multi-millennial sea-level contribution for a given warming level.In our experiments, we rely on two different present-day atmospheric climatologies (Kittel et al., 2021;Van Wessem et al., 2018) that are involved in building the respective initial ice-sheet configurations (Sect.2.2.2).
While a recent intercomparison concluded that Antarctic climate is represented reasonably well compared to observations in state-of-the-art RCMs, disagreement with respect to precipitation and atmospheric temperatures between the RCMs still exists for some areas (Mottram et al., 2021).For enhanced atmospheric warming, the difference between the initial states of Kori-ULB constructed with the atmospheric climatologies derived from MAR and RACMO increases in terms of sea-level contribution.For warming covered by the lower-emission pathway SSP1-2.6, the difference on the order of decimeters of sealevel equivalent (Fig. S20) is due to varying ice-sheet sensitivities of both initial states in the Wilkes suglacial basin and the Siple Coast (Fig. S12-S13).The gap in mass loss amounts to multiple meters of sea-level equivalent for an Antarctic-averaged atmospheric warming above 15°C (compare Fig. S20).Most of the marine-based portions of Antarctica are lost already before reaching this warming range, such that this difference arises from a stronger decline of ice grounded above sea level for the atmospheric climatology derived from MAR than from RACMO, potentially caused by enhanced surface melting with the former.The initial states built in a spin-up approach with PISM differ in their dynamical response due to the distinct parameter combinations favoured by the scoring in the initial-state ensembles for the distinct atmospheric climatologies (Reese et al., 2023;Albrecht et al., 2020, see Sect. 2.2.2).Overall, we find that mass loss is higher for the RACMO initial state with a lower pseudo-plastic sliding exponent q = 0.5 (compared to q = 0.75 as an outcome of the initialisation given the MAR atmospheric climatology, comparable with Lowry et al., 2021).This is the case both during the historical period and for a large range of the covered projected atmospheric temperature changes (Fig. S20).For a regional atmospheric warming of up to about 4°C the difference in sea-level contribution between the PISM initial states is generally on the order of decimeters.Given an initialisation with the atmospheric climatology derived from RACMO, the ice sheet is more sensitive to changes in its climatic boundary conditions in the Recovery and Aurora basin (occurring for Antarctic-averaged atmospheric temperature changes above approximately +8°C), with a global mean sea-level change being up to +9.0 m higher compared to the MAR initial state.
The response of both present-day representations of Antarctica to strong regional warming above +15°C (where the decline of remaining terrestrial parts in East Antarctica dominates) agrees well.Here, a slightly more pronounced mass loss is found for the ice-sheet initialisation involving the MAR atmospheric climatology (with higher atmospheric temperatures enhancing surface melt and runoff of the remaining ice grounded above sea level).
While taking into account distinct Antarctic ice-sheet representations as a result of an initial-state ensemble covering relevant model parameters, some sources of intra-model uncertainties cannot be further explored here due to computational constraints in favor of sampling a wide range of possible future climates.One of these is the uncertainty related to the subshelf melt parameterisation: To determine sub-shelf melt, PICO (Reese et al., 2018) with a fixed combination of the overturning parameter and the effective turbulent heat exchange coefficient parameter is chosen out of a diverse set of available sub-shelf melt parameterisations (recently compared in Burgard et al., 2022).rates averaged over Antarctic ice shelves related to the vertical overturning circulation in ice-shelf cavities and to resemble the typical pattern of strongest melt near the grounding line (Reese et al., 2018(Reese et al., , 2023)).However, smoother spatial fields of basal melt in PICO compared to observations (Reese et al., 2018) and determining melt as linearly related to temperature (Reese et al., 2018;Burgard et al., 2022) may eventually impact long-term ice dynamics.In a next step, the long-term ice-sheet response when including larger parts of the parameter space covered in the initial-state ensemble and beyond could be explored, allowing to quantify how parametric uncertainty translates into multi-millennial Antarctic sea-level commitment.

Boundary conditions
Following recent efforts in projecting the Antarctic sea-level contribution on different timescales ranging from the next decades until 2100 to several millennia (Seroussi et al., 2020;Payne et al., 2021;Golledge et al., 2019Golledge et al., , 2015)), we base the imposed changes in climatic conditions in Antarctica on state-of-the-art GCMs from the Coupled Model Intercomparison Project CMIP6.Biases in the chosen GCMs and a poor representation of conditions at the ice-sheet margins due to their coarse resolution (Beadling et al., 2020;Bracegirdle et al., 2020;Purich and England, 2021) may influence the simulated mass changes of the Antarctic Ice Sheet presented here.First of all, this is relevant for interpreting the simulated historic evolution of the ice sheet because it captures the response to the changes in atmospheric and oceanic conditions over the past decades simulated by one selected GCM (NorESM1-M; Barthel et al., 2020;Bentsen et al., 2013) only.Including the historic ice-sheet trajectory was shown to be essential for Antarctic sea-level projections by 2100 (Reese et al., 2020).Potential biases in the historic ice-sheet evolution (due to biases in the forcing, but likewise in the ice-sheet models itself) may also play a role for the multi-millennial ice-sheet response presented here.The GCMs available to provide future changes in boundary conditions until 2300 are characterized by a large range of climate sensitivities with a high upper bound (Meehl et al., 2020), which has been suggested to not be in accordance with paleoclimate evidence (Zhu et al., 2021).It introduces large uncertainties in the Antarctic sea-level commitment for fixing climatic boundary conditions at the same point in time (as discussed above).
Consequently, the derived future climate trajectories and respective projected multi-millennial Antarctic ice loss should only be related to emissions with care and can rather be seen as a potential range of climate futures for Antarctica.
For determining the long-term Antarctic sea-level commitment, we assume constant climate conditions on multi-millennial timescales.Keeping climatic boundary conditions constant on multi-millennial timescales allows us to assess the long-term ice-sheet stability and committed sea-level contribution under an idealized combination of atmospheric and oceanic changes with respect to present-day.This approach has been invoked previously (e.g., Golledge et al., 2015), but comes with certain assumptions: For instance, a continued ocean response to changing CO 2 conditions and atmospheric warming (Li et al., 2013) may result in an altered ratio of atmospheric and oceanic changes beyond the point in time where a stabilization of climatic boundary conditions is assumed here.In addition, observed interannual and decadal variability (Paolo et al., 2018;Jenkins et al., 2018) et al., 2020;Robel et al., 2019).
Finally, climate trajectories distinct from climate stabilization scenarios may impact the Antarctic Ice Sheet response in the near and far future.This includes increasingly discussed (temperature) overshoot pathways showing a reversal of climate conditions after exceeding a warming of, e.g., 1.5°C (Tokarska et al., 2019).The corresponding response of the Antarctic Ice Sheet is, however, not well constrained.In particular, the timescale difference between the ice sheet's response and the potentially high rates of future warming may allow for trajectories deviating from the equilibrium response of the ice sheet.
That is, large-scale ice-sheet changes described here may potentially be reversible despite having crossed a critical threshold upon reverting temperatures to present-day or pre-industrial climate conditions in a 'safe' overshoot (Ritchie et al., 2021).Our experiments form the basis for assessing the response of the Antarctic Ice Sheet to a reversal of climatic boundary conditions and relevant timescales.It will allow us to characterize the (ir-)reversibility of the Antarctic mass loss presented here.
Missing feedback mechanisms relevant for long-term Antarctic mass loss Several positive and negative feedbacks (Fyke et al., 2018) between the Antarctic Ice Sheet and the Earth system are missing in stand-alone ice-sheet model projections such as the ones presented here, but may be relevant for the long-term stability of the Antarctic Ice Sheet.Including the missing feedbacks in future fully-coupled assessments of the Antarctic sea-level commitment could change the timing and rates of (abrupt) mass loss determined in our experiments, either by dampening or by accelerating Antarctic ice loss.However, such fully-coupled Earth system models including the ice sheets, which are capable of simulating the multi-millennial response as needed for this study, are not yet available.We here include some of the relevant feedbacks using parametrisations: Atmospheric temperature imposed to the Antarctic Ice Sheet is modified in our experiments using the atmospheric lapse rate to account for the impact of a changing ice-surface elevation.This also feeds into the surface melt determined by the positive-degree-day approach, depicting the surface melt-elevation feedback (Levermann and Winkelmann, 2016).The potentially strong decline of ice volume under warming projected for higher-emission pathways may, however, additionally result in changes of the atmospheric circulation and respective precipitation patterns (compare e.g., Merz et al., 2014, for Greenland), which are not covered in our experiments.By applying the positive-degree-day approach to determine the future ice-sheet surface melt, we do not account for the self-amplifying melt-albedo feedback (Jakobs et al., 2019(Jakobs et al., , 2021)).While polar-oriented regional climate models cannot provide boundary conditions (or dynamically interact with ice sheets) on multi-millennial timescales considered here as of yet, approaches of intermediate complexity such as the recently introduced (simple) diurnal Energy Balance Model (Garbe et al., 2023;Zeitz et al., 2021) may allow to include the potentially accelerating effect of changes in albedo on projected ice loss through enhanced surface melting (Garbe et al., 2023) in the future.In addition, freshwater fluxes from mass balance changes of the Antarctic Ice Sheet into the surrounding ocean have been suggested to result in atmospheric cooling in the Southern Hemisphere competing with a potential enhancement of ice loss by the end of the century in a positive feedback due to subsurface ocean warming (Golledge et al., 2019).This selfamplifying feedback could have played a role in abrupt ice discharge events during the last deglaciation (Weber et al., 2014).
It remains to be explored how such ice-ocean feedbacks could play out on multi-millennial timescales in Antarctica's future.West and East Antarctica are not considered: By assuming uniform solid-Earth properties, ocean-driven ice loss from marine basins in East Antarctica may be underestimated on millennial timescales (Coulon et al., 2021), such that our estimates of committed East Antarctic mass loss may be seen as conservative.On the other hand, taking into account characteristic rheological properties of the solid Earth in West Antarctica could promote rapid bedrock uplift, thereby delaying ice-sheet changes.
While various sources of uncertainties remain to be explored for quantifying the long-term Antarctic sea-level commitment, our analysis shows (across distinct ice-sheet models) that the long-term multi-millennial impacts on the Antarctic Ice Sheet of warming projected for a given point in time are profound when compared to the sea-level change realized at this point in time.
Our findings thus stress the importance of complementing typical decadal-to-centennial projections of the future evolution of the Antarctic Ice Sheet by the respective committed Antarctic sea-level contribution for long-term decision making.
in our simulations with a lower value of 24°for topography below -700 m and an upper https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.value of 30°for topography above 500 m (following Reese et al., 2023).The effective pressure N till in PISM is a function of the overburden pressure P 0 and the fraction of the effective water thickness in the till layer s = W till /W max : , with similar results under https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.

Figure 1 .
Figure 1.Schematic of the experimental design (a): Idealized and simplified stability diagram of the Antarctic Ice Sheet as possible tipping element, which illustrates some underlying factors potentially contributing to a gap between the transient realized and long-term committed ice-sheet response (in terms of sea-level contribution).(b): Schematic summary of the experimental design used for assessing the longterm committed contribution from the Antarctic Ice Sheet to sea-level rise with the ice-sheet models PISM and Kori-ULB.Starting with the initialisation of the ice-sheet models to build ice-sheet representations in 1950, historical simulations are run until 2015 (present-day).Using potential future climate trajectories based on CMIP6, the transient realized Antarctic sea-level change is projected until the year 2300.Additional simulations branching off at regular intervals in time determine the sea-level commitment under stabilized climatic boundary conditions sustained over several millennia.
https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.2.2.3 Forcing and boundary conditions over the historical period and until 2300 ) and DeConto et al. (2021), likewise studying the future Antarctic response to changing environmental conditions and the ice-sheet https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.stability on multi-millennial timescales.Applying the surface mass balance determined by RCMs, which are in turn forced by climate projections of GCMs, would be an alternative approach for projecting Antarctic sea-level change.However, surface mass balance estimates from RCMs are not yet available beyond the end of this century and may be biased by the use of a https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.extending inland, Fig. S4-S5) than in PISM (see Fig. S6-S7 for comparison), explaining the diverging sea-level contribution under SSP1-2.6 until 2300.
)-fold of the https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.sea-level change projected by the year 2100 (2300) (compare Figure 2a -d; Tab. 1).This commitment gap (Winkelmann et al., in review) depends on the specific climate trajectory and the warming levels that are reached at the respective (branchoff) point in time.
Fig. S16-S19 show the individual long-term ice-sheet response determined by both ice-sheet models to sustained warming levels reached by 2050 in the GCMs.Major portions of the catchment region of Thwaites and Pine Island Glaciers are drained in both ice-sheet models.https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.

Figure 2 .Figure 3 .
Figure 2. Projected ice loss from Antarctica on centennial to multi-millennial timescales (in meters sea-level equivalent) in response to changing climate conditions as projected by four different GCMs (given by the colour) under emission pathways SSP1-2.6 (upper row) and SSP5-8.5 (lower row), simulated by the ice-sheet models PISM (solid) and Kori-ULB (dashed).(a) and (b): Transient sea-level response from Antarctica until year 2300.(c) and (d): Multi-millennial Antarctic sea-level response until year 7000 to warming reached at different points in time throughout the next centuries.(e) and (f): Committed Antarctic sea-level contribution in the year 7000.Different atmospheric climatologies involved in the ice-sheet initialisation are indicated by the shape of the marker.Open and filled markers correspond to the long-term sea-level change determined by PISM and Kori-ULB, respectively.For comparison of the committed sea-level rise under both emission pathways, the range of long-term Antarctic ice loss by 7000 under SSP1-2.6 is indicated by the light grey box in (f).

390(
that is, when temperatures change much slower than typical rates of change of an ice sheet;Garbe et al., 2020).In the following, we explore the relationship between climate boundary conditions potentially reached throughout the next centuries and sustained for several thousands of years and the configurations that the Antarctic Ice Sheet evolves to under these conditions https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.
Fig. 5i) in PISM experiments.While showing some limited grounding-line retreat in the Wilkes subglacial basin, the sea-level contribution of approximately 1.0 m determined by Kori-ULB is lower due to limited grounding-line retreat and subsequent ice loss in the basins draining Ross Ice Shelf as well as https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.less pronounced thinning in Recovery basin (compared to PISM; Fig.4d, II).Exceeding the regional atmospheric warming of 2.5°C projected by CESM2-WACCM under SSP1-2.6 also induces the long-term loss of Filchner-Ronne Ice Shelf in addition to Ross Ice Shelf in PISM experiments (comparable to the long-term response found inGolledge et al. (2015) after following emission pathway RCP4.5 with warming of about 2.2°C), which is accompanied by a retreat of the grounding line in Robin subglacial basin (Fig.4b and c, II).Ice streams that drain the Recovery basin start showing a contribution to the long-term sea-level change (of about 5.0 m of sea-level equivalent in total for 2.5 °C to 4.0°C of Antarctic-averaged warming) (Fig.4c, Fig.5e and h).That is, we find a complete collapse of the West Antarctic Ice Sheet in both ice-sheet models for an Antarcticaveraged atmospheric warming above +4°C.The inter-model spread in mass loss is explained by a stronger thinning of ice draining into the eastern Weddell Sea region in PISM in combination with a more pronounced thickening in the inner parts of East Antarctica in Kori-ULB within this warming range (compare Fig.S16-S17 for Kori-ULB with Fig.S18-S19 for PISM when sustaining warming projected for year 2100).

470Figure 4 .Figure 5 .
Figure 4. Committed sea-level contribution from the Antarctic Ice Sheet.(a) and (b): Long-term ice loss from the Antarctic Ice Sheet (in meters sea-level equivalent) for year 7000 in response to Antarctic-averaged atmospheric temperature change (compared to 1995-2014).The change in climatic boundary conditions is sustained for several millennia.(b) is a zoom into (a) for a lower atmospheric temperature change.(c) and (d): Fractions of experiments that show grounding-line retreat in year 7000 in PISM and Kori-ULB, respectively.The fraction is determined for all experiments that are assigned to the distinct clusters I-V.
by exploring the multi-millennial consequences of stabilizing climatic boundary conditions at different points in time over the course of the next centuries, in a consistent way for two ice-sheet models.From a dynamical systems perspective, the long-term stability of the Antarctic Ice Sheet under present and potential future rates of warming (being much faster than typical rates of change in an ice sheet) is studied.This complements the quasi-equilibrium ice-sheet response to warming presented byGarbe et al. (2020) and, thereby, bridges the gap to the transient realized sea-level change from Antarctica (e.g., by the end of this century as inSeroussi et al., 2020).https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.
is neglected in the imposed constant climate conditions for simplicity, which has been shown to potentially result https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License. in a lower long-term ice-sheet volume (compared to a stable climate; Mikkelsen et al., 2018) up to ice-sheet retreat (Christian https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.Finally, while bedrock adjustment to changes in ice load is included in our experiments, opposing Earth structures between https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.modelling groups (whose models are listed in Table S1 of this paper) for producing and making their model output available.This work has been performed in the context of the FutureLab on Earth Resilience in the Anthropocene at the Potsdam Institute for Climate Impact Research.https://doi.org/10.5194/tc-2023-156Preprint.Discussion started: 9 October 2023 c Author(s) 2023.CC BY 4.0 License.
in year 3000 Committed in year 5000 Committed in year 7000