The hysteresis of the Antarctic Ice Sheet

Abstract

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.

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Fig. 1: Antarctic ice velocities and surrounding ocean temperatures.
Fig. 2: Hysteresis of the Antarctic Ice Sheet.
Fig. 3: Ice-sheet volume differences between retreat and regrowth.
Fig. 4: Long-term ice loss for different warming levels.
Fig. 5: Ocean-driven versus atmosphere-driven ice loss.

Data availability

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.

Code availability

PISM is freely available as open-source code from https://github.com/pism/pism. The code version used in this study is available at https://doi.org/10.5281/zenodo.3956431. PISM input data are pre-processed using https://github.com/pism/pism-ais with original data citations.

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Acknowledgements

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.

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R.W. conceived the study. All authors designed the research and contributed to the analysis. J.G. carried out the model simulations. J.G. and R.W. wrote the manuscript with contributions from all co-authors.

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Correspondence to Ricarda Winkelmann.

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Extended data figures and tables

Extended Data Fig. 1 Comparison of modelled and observed ice geometry.

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.

Extended Data Fig. 2 Comparison of modelled and observed ice velocities.

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.

Extended Data Fig. 3 Regrown Antarctica.

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.

Extended Data Fig. 4 Hysteresis sensitivity to model parameter variations.

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. bg, 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.

Extended Data Fig. 5 Long-term ice loss for different warming levels.

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.

Extended Data Fig. 6 Ocean-driven versus atmosphere-driven ice loss (regrowth branch).

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.

Supplementary information

Video 1

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).

Video 2

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).

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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

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