More than half of Earth’s freshwater resources are held by the Antarctic Ice Sheet, which thus represents by far the largest potential source for global sea-level rise under future warming conditions1. Its long-term stability determines the fate of our coastal cities and cultural heritage. Feedbacks between ice, atmosphere, ocean, and the solid Earth give rise to potential nonlinearities in its response to temperature changes. So far, we are lacking a comprehensive stability analysis of the Antarctic Ice Sheet for different amounts of global warming. Here we show that the Antarctic Ice Sheet exhibits a multitude of temperature thresholds beyond which ice loss is irreversible. Consistent with palaeodata2 we find, using the Parallel Ice Sheet Model3,4,5, that at global warming levels around 2 degrees Celsius above pre-industrial levels, West Antarctica is committed to long-term partial collapse owing to the marine ice-sheet instability. Between 6 and 9 degrees of warming above pre-industrial levels, the loss of more than 70 per cent of the present-day ice volume is triggered, mainly caused by the surface elevation feedback. At more than 10 degrees of warming above pre-industrial levels, Antarctica is committed to become virtually ice-free. The ice sheet’s temperature sensitivity is 1.3 metres of sea-level equivalent per degree of warming up to 2 degrees above pre-industrial levels, almost doubling to 2.4 metres per degree of warming between 2 and 6 degrees and increasing to about 10 metres per degree of warming between 6 and 9 degrees. Each of these thresholds gives rise to hysteresis behaviour: that is, the currently observed ice-sheet configuration is not regained even if temperatures are reversed to present-day levels. In particular, the West Antarctic Ice Sheet does not regrow to its modern extent until temperatures are at least one degree Celsius lower than pre-industrial levels. Our results show that if the Paris Agreement is not met, Antarctica’s long-term sea-level contribution will dramatically increase and exceed that of all other sources.
This is a preview of subscription content
Subscription info for Chinese customers
We have a dedicated website for our Chinese customers. Please go to naturechina.com to subscribe to this journal.
Get time limited or full article access on ReadCube.
All prices are NET prices.
All data used for this study are publicly available. Antarctic surface mass balance data from RACMO2.3p2 were downloaded from https://www.projects.science.uu.nl/iceclimate/publications/data/2018/index.php#vwessem2018_tc. Antarctic bedrock topography and ice thickness data are from the Bedmap2 compilation, available at https://secure.antarctica.ac.uk/data/bedmap2/. The Schmidtko ocean temperature and salinity dataset can be retrieved at https://www.geomar.de/en/staff/fb1/po/sschmidtko/southern-ocean/. The datasets generated and analysed during this study are available from the corresponding author upon reasonable request.
Fretwell, P. et al. Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. Cryosphere 7, 375–393 (2013).
Turney, C. S. M. et al. Early Last Interglacial ocean warming drove substantial ice mass loss from Antarctica. Proc. Natl Acad. Sci. USA 117, 3996–4006 (2020).
Bueler, E. & Brown, J. Shallow shelf approximation as a ‘sliding law’ in a thermomechanically coupled ice sheet model. J. Geophys. Res. 114, F03008 (2009).
Winkelmann, R. et al. The Potsdam Parallel Ice Sheet Model (PISM-PIK)—Part 1: Model description. Cryosphere 5, 715–726 (2011).
PISM, a Parallel Ice Sheet Model: User’s Manual http://pism-docs.org/ (2017).
The IMBIE Team. Mass balance of the Antarctic Ice Sheet from 1992 to 2017. Nature 558, 219–222 (2018).
Rignot, E. et al. Four decades of Antarctic Ice Sheet mass balance from 1979–2017. Proc. Natl Acad. Sci. USA 116, 1095–1103 (2019).
Intergovernmental Panel on Climate Change (IPCC) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2013).
Frieler, K. et al. Consistent evidence of increasing Antarctic accumulation with warming. Nat. Clim. Chang. 5, 348–352 (2015).
Winkelmann, R., Levermann, A., Martin, M. A. & Frieler, K. Increased future ice discharge from Antarctica owing to higher snowfall. Nature 492, 239–242 (2012).
Weertman, J. Stability of ice-age ice sheets. J. Geophys. Res. 66, 3783–3792 (1961).
Oerlemans, J. Some basic experiments with a vertically-integrated ice-sheet model. Tellus 33, 1–11 (1981).
Huybrechts, P. et al. Response of the Greenland and Antarctic ice sheets to multi-millennial greenhouse warming in the Earth system model of intermediate complexity LOVECLIM. Surv. Geophys. 32, 397–416 (2011).
Levermann, A. & Winkelmann, R. A simple equation for the melt elevation feedback of ice sheets. Cryosphere 10, 1799–1807 (2016).
Clarke, G. K. C., Nitsan, U. & Paterson, W. S. B. Strain heating and creep instability in glaciers and ice sheets. Rev. Geophys. 15, 235–247 (1977).
Weertman, J. Stability of the junction of an ice sheet and an ice shelf. J. Glaciol. 13, 3–11 (1974).
Mercer, J. H. West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster. Nature 271, 321–325 (1978).
Gudmundsson, G. H., Krug, J., Durand, G., Favier, L. & Gagliardini, O. The stability of grounding lines on retrograde slopes. Cryosphere 6, 1497–1505 (2012).
Gomez, N., Pollard, D. & Holland, D. Sea-level feedback lowers projections of future Antarctic Ice-Sheet mass loss. Nat. Commun. 6, 8798 (2015).
Fyke, J., Sergienko, O., Löfverström, M., Price, S. F. & Lenaerts, J. T. M. An overview of interactions and feedbacks between ice sheets and the Earth system. Rev. Geophys. 56, 361–408 (2018).
Golledge, N. R. et al. The multi-millennial Antarctic commitment to future sea-level rise. Nature 526, 421–425 (2015).
Winkelmann, R., Levermann, A., Ridgwell, A. & Caldeira, K. Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet. Sci. Adv. 1, e1500589 (2015).
Robinson, A., Calov, R. & Ganopolski, A. Multistability and critical thresholds of the Greenland ice sheet. Nat. Clim. Chang. 2, 429–432 (2012).
Huybrechts, P. Formation and disintegration of the Antarctic ice sheet. Ann. Glaciol. 20, 336–340 (1994).
DeConto, R. M. & Pollard, D. Contribution of Antarctica to past and future sea-level rise. Nature 531, 591–597 (2016).
Sutter, J., Gierz, P., Grosfeld, K., Thoma, M. & Lohmann, G. Ocean temperature thresholds for Last Interglacial West Antarctic Ice Sheet collapse. Geophys. Res. Lett. 43, 2675–2682 (2016).
Golledge, N. R., Levy, R. H., McKay, R. M. & Naish, T. R. East Antarctic ice sheet most vulnerable to Weddell Sea warming. Geophys. Res. Lett. 44, 2343–2351 (2017).
Pattyn, F. et al. The Greenland and Antarctic ice sheets under 1.5 °C global warming. Nat. Clim. Chang. 8, 1053–1061 (2018).
Pollard, D. & DeConto, R. M. Modelling West Antarctic ice sheet growth and collapse through the past five million years. Nature 458, 329–332 (2009).
Alley, R. B. et al. Oceanic forcing of ice-sheet retreat: West Antarctica and more. Annu. Rev. Earth Planet. Sci. 43, 207–231 (2015).
Dutton, A. et al. Sea-level rise due to polar ice-sheet mass loss during past warm periods. Science 349, aaa4019 (2015).
Pollard, D. & DeConto, R. M. Hysteresis in Cenozoic Antarctic ice-sheet variations. Glob. Planet. Change 45, 9–21 (2005).
Gasson, E. G. W., DeConto, R. M., Pollard, D. & Levy, R. Dynamic Antarctic ice sheet during the early to mid-Miocene. Proc. Natl Acad. Sci. USA 113, 3459–3464 (2016).
Liu, Z. et al. Global cooling during the Eocene-Oligocene climate transition. Science 323, 1187–1190 (2009).
Hansen, J., Sato, M., Russell, G. & Kharecha, P. Climate sensitivity, sea level and atmospheric carbon dioxide. Phil. Trans. R. Soc. A 371, 20120294 (2013).
Rahmstorf, S. & England, M. H. Influence of Southern Hemisphere winds on North Atlantic Deep Water flow. J. Phys. Oceanogr. 27, 2040–2054 (1997).
Albrecht, T., Winkelmann, R. & Levermann, A. Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM)—Part 1: Boundary conditions and climatic forcing. Cryosphere 14, 599–632 (2020).
Schmidtko, S., Heywood, K. J., Thompson, A. F. & Aoki, S. Multidecadal warming of Antarctic waters. Science 346, 1227–1231 (2014).
Mouginot, J., Rignot, E. & Scheuchl, B. Sustained increase in ice discharge from the Amundsen Sea Embayment, West Antarctica, from 1973 to 2013. Geophys. Res. Lett. 41, 1576–1584 (2014).
Rignot, E., Mouginot, J., Morlighem, M., Seroussi, H. & Scheuchl, B. Widespread, rapid grounding line retreat of Pine Island, Thwaites, Smith, and Kohler glaciers, West Antarctica, from 1992 to 2011. Geophys. Res. Lett. 41, 3502–3509 (2014).
Favier, L. et al. Retreat of Pine Island Glacier controlled by marine ice-sheet instability. Nat. Clim. Chang. 4, 117–121 (2014).
Joughin, I., Smith, B. E. & Medley, B. Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science 344, 735–738 (2014).
Naish, T. R. et al. Obliquity-paced Pliocene West Antarctic ice sheet oscillations. Nature 458, 322–328 (2009).
Levermann, A. et al. The multimillennial sea-level commitment of global warming. Proc. Natl Acad. Sci. USA 110, 13745–13750 (2013).
Mengel, M. & Levermann, A. Ice plug prevents irreversible discharge from East Antarctica. Nat. Clim. Chang. 4, 451–455 (2014).
Golledge, N. R. et al. Antarctic climate and ice-sheet configuration during the early Pliocene interglacial at 4.23 Ma. Clim. Past 13, 959–975 (2017).
Golledge, N. R. et al. Global environmental consequences of twenty-first-century ice-sheet melt. Nature 566, 65–72 (2019).
Bassis, J. N. & Walker, C. C. Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice. Proc. R. Soc. A 468, 913–931 (2012).
Edwards, T. L. et al. Revisiting Antarctic ice loss due to marine ice-cliff instability. Nature 566, 58–64 (2019).
Meredith, M. et al. Polar regions. In IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (eds Pörtner, H.-O. et al.) https://www.ipcc.ch/srocc/chapter/chapter-3-2/ (in the press).
Schellnhuber, H. J., Rahmstorf, S. & Winkelmann, R. Why the right climate target was agreed in Paris. Nat. Clim. Chang. 6, 649–653 (2016).
Lenton, T. M. et al. Climate tipping points—too risky to bet against. Nature 575, 592–595 (2019).
Lliboutry, L. A. & Duval, P. Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies. Ann. Geophys. 3, 207–224 (1985).
Feldmann, J., Albrecht, T., Khroulev, C., Pattyn, F. & Levermann, A. Resolution-dependent performance of grounding line motion in a shallow model compared with a full-Stokes model according to the MISMIP3d intercomparison. J. Glaciol. 60, 353–360 (2014).
Schoof, C. & Hindmarsh, R. C. A. Thin-film flows with wall slip: an asymptotic analysis of higher order glacier flow models. Q. J. Mech. Appl. Math. 63, 73–114 (2010).
Cuffey, K. M. & Paterson, W. S. B. The Physics of Glaciers 4th edn (Elsevier, Academic Press, 2010).
Bueler, E. & van Pelt, W. Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model version 0.6. Geosci. Model Dev. 8, 1613–1635 (2015).
Lingle, C. S. & Clark, J. A. A numerical model of interactions between a marine ice-sheet and the solid Earth: application to a West Antarctic ice stream. J. Geophys. Res. Oceans 90, 1100–1114 (1985).
Bueler, E., Lingle, C. S. & Brown, J. Fast computation of a viscoelastic deformable Earth model for ice-sheet simulations. Ann. Glaciol. 46, 97–105 (2007).
Dee, D. P. et al. The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137, 553–597 (2011).
van Wessem, J. M. et al. Modelling the climate and surface mass balance of polar ice sheets using RACMO2—Part 2: Antarctica (1979–2016). Cryosphere 12, 1479–1498 (2018).
Reese, R., Albrecht, T., Mengel, M., Asay-Davis, X. & Winkelmann, R. Antarctic sub-shelf melt rates via PICO. Cryosphere 12, 1969–1985 (2018).
Olbers, D. & Hellmer, H. A box model of circulation and melting in ice shelf caverns. Ocean Dyn. 60, 141–153 (2010).
Levermann, A. et al. Kinematic first-order calving law implies potential for abrupt ice-shelf retreat. Cryosphere 6, 273–286 (2012).
Albrecht, T., Martin, M. A., Haseloff, M., Winkelmann, R. & Levermann, A. Parameterization for subgrid-scale motion of ice-shelf calving fronts. Cryosphere 5, 35–44 (2011).
Cuffey, K. M. et al. Deglacial temperature history of West Antarctica. Proc. Natl Acad. Sci. USA 113, 14249–14254 (2016).
Seroussi, H. et al. initMIP-Antarctica: an ice sheet model initialization experiment of ISMIP6. Cryosphere 13, 1441–1471 (2019).
Li, C., von Storch, J.-S. & Marotzke, J. Deep-ocean heat uptake and equilibrium climate response. Clim. Dyn. 40, 1071–1086 (2013).
Rignot, E., Mouginot, J. & Scheuchl, B. Ice flow of the Antarctic Ice Sheet. Science 333, 1427–1430 (2011).
J.G., J.F.D. and R.W. were supported by the Leibniz Association project DominoES. T.A. and R.W. are supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the priority program “Antarctic Research with comparative investigations in Arctic ice areas” by grants WI4556/2-1 and WI4556/4-1, and within the framework of the PalMod project (FKZ: 01LP1925D) supported by the German Federal Ministry of Education and Research (BMBF) as a Research for Sustainability initiative (FONA). J.F.D. is grateful for financial support by the Stordalen Foundation via the Planetary Boundary Research Network (PB.net), the Earth League’s EarthDoc programme, and the European Research Council Advanced Grant project ERA (Earth Resilience in the Anthropocene; grant ERC-2016-ADG-743080). This research was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement number 820575 (TiPACCs). The development of PISM is supported by NASA grant NNX17AG65G and NSF grants PLR-1603799 and PLR-1644277. We further acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research (BMBF) and the Land Brandenburg for supporting this project by providing resources on the high-performance computer system at the Potsdam Institute for Climate Impact Research. We thank M. Mengel for providing the Antarctic equilibrium used as a basis for the simulations.
The authors declare no competing interests.
Peer review information Nature thanks Nicholas R Golledge and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
a, Observed ice surface elevation (Bedmap2, ref. 1), regridded to 16 km. Grounding lines are shown in white; surface-height contours are given every 250 m. b, Modelled ice surface elevation of the reference state serving as initial configuration for the hysteresis experiments. Grounding lines are shown in white; surface-height contours are given every 250 m. c, Modelled minus observed (Bedmap2) ice surface elevation. d, Scatter plot for comparison of modelled and observed ice thickness for each grid cell. Red identity line illustrates where modelled ice thickness would perfectly match the observations. RMSE, root-mean-square error.
a, Observed ice surface velocities69, regridded to 16 km. b, Modelled ice surface velocities of reference state. c, Model minus observed ice surface velocity. d, Scatter plot of model versus observed ice surface velocity. The red line is the identity line.
Equilibrium ice thickness difference of the regrown ice-sheet configuration (at pre-industrial temperatures, that is, 0 °C GMT anomaly) minus the reference ice-sheet thickness. Red lines denote the reference grounding-line locations; blue lines show their respective locations after regrowth. Areas of the ice sheet which do not regrow to their original extents are highlighted in orange. Surface-height contour lines of the regrown ice sheet are given at 200-m intervals.
a, Sea-level relevant ice volume for a global warming rate of 1 °C per 10,000 years above pre-industrial conditions. The blue curve is the same as the blue curve in Fig. 2; the grey shadings show the model sensitivity by encompassing the total range of individual model responses with respect to the variation of critical model parameters, as detailed below. b–g, Same as a, but showing the respective simulations for the tested model parameters (thin blue lines) in comparison to the reference simulation (thick blue line): b, ice-shelf removal mechanism (PD, present-day); c, viscosity of the upper mantle in the Earth-deformation model; d, decay rate of the subglacial meltwater in the till layer; e, unitless exponent in the ‘pseudo-plastic’ sliding law; f, unitless flow enhancement factor for the SSA velocities4; and g, horizontal model grid resolution.
This figure continues Fig. 4; the equilibrium ice-sheet surface elevation is shown in metres for different warming levels (7 °C, 8 °C, 9 °C and 10 °C GMT anomaly above pre-industrial level), comparing the retreat (upper panels) and regrowth (lower panels) branch of the hysteresis curve. Ice surface-height contours are delineated at 1,000-m intervals. Grounding-line locations of the reference state are shown in red; ice shelves are marked in light blue. The absolute sea-level relevant ice-volume anomaly compared to the reference state (in m SLE), that is, the committed sea-level rise, is given for each panel. Blue shadings illustrate the bedrock depth in metres below the present-day sea level; brown shadings illustrate the bedrock elevation in metres above the present-day sea level (a.s.l.). ASB, Aurora subglacial basin; WSB, Wilkes subglacial basin.
Antarctic ice mass fluxes showing (in gigatonnes per year) the contributions of different atmospheric and oceanic processes to the total ice mass changes over the entire range of GMT anomalies along the lower hysteresis branch derived from the quasi-static reference simulation. Positive flux values denote mass gains, negative values denote mass losses. The sea-level relevant ice-sheet volume (in m SLE) is indicated by the dashed grey line with respect to the right-hand axis.
Ice-sheet retreat along the upper branch of the hysteresis. Shown is the quasi-static evolution of the ice-sheet surface elevation in metres for a global warming rate of 1 °C per 10,000 years above pre-industrial conditions (grey shading; contour lines at 500 m intervals), sub-shelf melt rates in metres per year (purple–orange shading) as well as bedrock topography below (blue shading) and above (brown shading) present-day sea level (m a.s.l. = metres above sea level). EAIS = East Antarctic Ice Sheet, WAIS = West Antarctic Ice Sheet, IS = ice shelf, FRIS = Filchner–Ronne Ice Shelf. Lower panel shows the ice volume change (blue curve, in metres sea-level equivalent, m SLE) as well as total Antarctic ice mass balance fluxes (purple curve, in gigatonnes per year).
Ice-sheet regrowth along the lower branch of the hysteresis. Shown is the quasi-static evolution of the ice-sheet surface elevation in metres for a global cooling rate of −1 °C per 10,000 years starting from ice-free conditions (grey shading; contour lines at 500 m intervals), sub-shelf melt rates in metres per year (purple–orange shading) as well as bedrock topography below (blue shading) and above (brown shading) present-day sea level (m a.s.l. = metres above sea level). EAIS = East Antarctic Ice Sheet, WAIS = West Antarctic Ice Sheet, IS = ice shelf, FRIS = Filchner–Ronne Ice Shelf. Lower panel shows the ice volume change (blue curve, in metres sea-level equivalent, m SLE) as well as total Antarctic ice mass balance fluxes (purple curve, in gigatonnes per year).
About this article
Cite this article
Garbe, J., Albrecht, T., Levermann, A. et al. The hysteresis of the Antarctic Ice Sheet. Nature 585, 538–544 (2020). https://doi.org/10.1038/s41586-020-2727-5
Nature Climate Change (2022)
Nature Geoscience (2022)
Nature Reviews Earth & Environment (2022)
Nature Climate Change (2022)
The influence of emissions scenarios on future Antarctic ice loss is unlikely to emerge this century
Communications Earth & Environment (2021)