Ice-sheet mass balance and climate change

Journal name:
Nature
Volume:
498,
Pages:
51–59
Date published:
DOI:
doi:10.1038/nature12238
Received
Accepted
Published online

Since the 2007 Intergovernmental Panel on Climate Change Fourth Assessment Report, new observations of ice-sheet mass balance and improved computer simulations of ice-sheet response to continuing climate change have been published. Whereas Greenland is losing ice mass at an increasing pace, current Antarctic ice loss is likely to be less than some recently published estimates. It remains unclear whether East Antarctica has been gaining or losing ice mass over the past 20 years, and uncertainties in ice-mass change for West Antarctica and the Antarctic Peninsula remain large. We discuss the past six years of progress and examine the key problems that remain.

At a glance

Figures

  1. Summary of estimates of rates of ice mass change for Antarctica and Greenland.
    Figure 1: Summary of estimates of rates of ice mass change for Antarctica and Greenland.

    In the studies published before 2012 (ref. 2, a) and in 2012 (b), each estimate of a temporally averaged rate of mass change is represented by a box whose width indicates the time period studied, and whose height indicates the error estimate. Single-epoch (snapshot) estimates of mass balance are represented by vertical error bars when error estimates are available, and are otherwise represented by asterisks. Line colour indicates mass assessment technique (see key); line type indicates data source. 2012 studies in b comprise IMBIE combined estimates2 (solid lines), and estimates by Sasgen and others16, 20 and King and others11 (dashed lines), Zwally and others19 (dot-dashed lines), Harig and Simons89 and Ewert and others90 (dotted lines).

  2. Comparison of projected global, Antarctic and Greenland surface air temperature and snowfall anomalies to 2100.
    Figure 2: Comparison of projected global, Antarctic and Greenland surface air temperature and snowfall anomalies to 2100.

    a, Anomaly of global mean 2m air temperature (T2m) simulated by 30 GCMs from the CMIP5 data base. Values are with respect to 1970–99 for the RCP 4.5 (blue) and RCP 8.5 (red) scenarios. We refer to ref. 91 for more details about the Representative Concentration Pathways (RCP) scenarios. The evolving ensemble means are plotted as thick lines, with vertical bars representing ±1s.d. for each decade. A 10-year running mean was used to smooth the curves. b, Same as a but for Antarctica. The land/sea mask from each GCM is used to delimit Antarctica. c, Same as a but for T2m over GIS. The T2m anomaly is taken over the area covering Greenland (60–85°N and 20–70°W) and where surface elevation is higher than 1,000m above sea level. d, Same as b but for precipitation. Anomalies are given in per cent with respect to the mean precipitation for 1970–99. e, Same as c but for precipitation.

  3. Illustration of a marine ice sheet and its interaction with the ocean.
    Figure 3: Illustration of a marine ice sheet and its interaction with the ocean.

    a, Warm modified Circumpolar Deep Water (mCDW) leads to melting at the grounding line, leading to ice-shelf thinning, grounding-line retreat, and initial thinning. b, Marine ice-sheet instability occurs when, in the absence of buttressing, the grounding line retreats on an upward-sloping (in the direction of the flow) bedrock (unstable): ice flux increases with thickness at the grounding line, leading to an increased outflux to the ocean and enhanced thinning that may be compensated by further grounding-line retreat, until a new downward-sloping bed (pinning point) is reached (stable). Thinning of ice sheet and shelf can also be caused by surface melt and increased calving.

References

  1. Solomon, S., et al., eds. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2007)
  2. Shepherd, A. et al. A reconciled estimate of ice sheet mass balance. Science 338, 11831189 (2012).
    Gives an overall view of remote sensing of ice-sheet mass balance and arrives at a nearly reconciled estimate of the contribution of the ice sheets to sea-level rise.
  3. Davis, C. H. & Li, Y. H. McConnell, J. R., Frey, M. M. & Hanna, E. Snowfall-driven growth in East Antarctic ice sheet mitigates recent sea-level rise. Science 308, 18981901 (2005)
  4. Zwally, H. J. et al. Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992–2002. J. Glaciol. 51, 509527 (2005)
  5. Zwally, H. J. et al. Greenland ice sheet mass balance: distribution of increased mass loss with climate warming. J. Glaciol. 57, 88102 (2011)
  6. Velicogna, I. Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE. Geophys. Res. Lett. 36, L19503 (2009)
  7. Rignot, E. & Kanagaratnam, P. Changes in the velocity structure of the Greenland ice sheet. Science 311, 986990 (2006)
  8. Rignot, E., Velicogna, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys. Res. Lett. 38, L05503 (2011)
  9. Ettema, J. et al. Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling. Geophys. Res. Lett. 36, L12501 (2009)
  10. Lenaerts, J. T. M., van den Broeke, M. R., van de Berg, W. J., van Meijgaard, E. & Munneke, P. K. A new, high-resolution surface mass balance map of Antarctica (1979–2010) based on regional atmospheric climate modeling. Geophys. Res. Lett. 39, L04501 (2012)
  11. King, M. A. et al. Lower satellite-gravimetry estimates of Antarctic sea-level contribution. Nature 491, 586589 (2012)
  12. Whitehouse, P. L., Bentley, M. J. & Le Brocq, A. M. A deglacial model for Antarctica: geological constraints and glaciological modelling as a basis for a new model of Antarctic glacial isostatic adjustment. Quat. Sci. Rev. 32, 124 (2012)
  13. Ivins, E. R. et al. Antarctic contribution to sea-level rise observed by GRACE with improved GIA correction. J. Geophys. Res.. http://dx.doi.org/10.1002/jgrb.50208 (in the press)
  14. Thomas, I. D. et al. Widespread low rates of Antarctic glacial isostatic adjustment revealed by GPS observations. Geophys. Res. Lett. 38, L22302 (2011)
  15. Whitehouse, P. L., Bentley, M. J., Milne, G. A., King, M. A. & Thomas, I. D. A new glacial isostatic adjustment model for Antarctica: calibrated and tested using observations of relative sea-level change and present-day uplift rates. Geophys. J. Int. 190, 14641482 (2012).
    Demonstrates that new GIA models for Antarctica, which have been central to reconciling mass-balance estimates, greatly improve the fit between modelled and observed (GPS) uplift rates.
  16. Sasgen, I. et al. Antarctic ice-mass balance 2002 to 2011: regional re-analysis of GRACE satellite gravimetry measurements with improved estimate of glacial-isostatic adjustment. Cryosphere Discuss. 6, 37033732 (2012)
  17. Horwath, M., Legresy, B., Remy, F., Blarel, F. & Lemoine, J. M. Consistent patterns of Antarctic ice sheet interannual variations from ENVISAT radar altimetry and GRACE satellite gravimetry. Geophys. J. Int. 189, 863876 (2012)
  18. Zwally, H. J. & Giovinetto, M. B. Overview and assessment of Antarctic ice-sheet mass balance estimates: 1992–2009. Surv. Geophys. 32, 351376 (2011)
  19. Zwally, H. J. et al. Mass balance of Antarctic ice sheet 1992 to 2008 from ERS and ICESat: gains exceed losses. ISMASS 2012 Workshop (2012); available at http://www.climate-cryosphere.org/en/events/2012/ISMASS/AntarcticIceSheet.html
  20. Sasgen, I. et al. Timing and origin of recent regional ice-mass loss in Greenland. Earth Planet. Sci. Lett. 333-334, 293303 (2012)
  21. Ritz, C., Rommelaere, V. & Dumas, C. Modeling the evolution of Antarctic ice sheet over the last 420 000 years: implications for altitude changes in the Vostok region. J. Geophys. Res. 106, 3194331964 (2001)
  22. Schoof, C. Ice sheet grounding line dynamics: steady states, stability, and hysteresis. J. Geophys. Res. 112, F03S28 (2007)
  23. Pollard, D. & Deconto, R. M. Modelling West Antarctic ice sheet growth and collapse through the past five million years. Nature 458, 329332 (2009)
  24. Bueler, E. & Brown, J. Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model. J. Geophys. Res. 114, F03008 (2009)
  25. Pattyn, F. A new three-dimensional higher-order thermomechanical ice sheet model: basic sensitivity, ice stream development and ice flow across subglacial lakes. J. Geophys. Res. 108 (B8). 2382 (2003)
  26. Blatter, H. Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients. J. Glaciol. 41, 333344 (1995)
  27. Gillet-Chaulet, F. et al. Greenland Ice Sheet contribution to sea-level rise from a new-generation ice-sheet model. Cryosphere 6, 15611576 (2012).
    Represents the first complete implementation of full Stokes in dynamical ice-sheet models.
  28. Larour, E., Seroussi, H., Morlighem, M. & Rignot, E. Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM). J. Geophys. Res. 117, F01022 (2012)
  29. Cornford, S. L. et al. Adaptive mesh, finite volume modeling of marine ice sheets. J. Comput. Phys. 232, 529549 (2013).
    A complete and correct implementation of 3D grounding line dynamics applied to Pine Island glacier for a loss of ice shelf buttressing, uniquely showing large grounding-line retreat.
  30. Moon, T. & Joughin, I. Smith, B. & Howat, I. 21st-century evolution of Greenland outlet glacier velocities. Science 336, 576578 (2012)
  31. Gogineni, P. CReSIS Data Products. http://data.cresis.ku.edu/ (2012)
  32. Arthern, R. J. & Gudmundsson, G. H. Initialization of ice-sheet forecasts viewed as an inverse Robin problem. J. Glaciol. 56, 527533 (2010)
  33. Scambos, T. A., Bohlander, J. A., Shuman, C. A. & Skvarca, P. Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica. Geophys. Res. Lett. 31, L18402 (2004)
  34. Rignot, E. et al. Recent ice loss from the Fleming and other glaciers, Wordie Bay, West Antarctic Peninsula. Geophys. Res. Lett. 32, L07502 (2005)
  35. Jacobs, S. S., Jenkins, A., Giulivi, C. F. & Dutrieux, P. Stronger ocean circulation and increased melting under Pine Island Glacier ice shelf. Nature Geosci. 4, 519523 (2011)
  36. MacAyeal, D. R. Scambos, T. A., Hulbe, C. L. & Fahnestock, M. A. Catastrophic ice-shelf break-up by an ice-shelf-fragment-capsize mechanism. J. Glaciol. 49, 2236 (2003)
  37. Joughin, I., Smith, B. E. & Holland, D. M. Sensitivity of 21st century sea level to ocean-induced thinning of Pine Island Glacier, Antarctica. Geophys. Res. Lett. 37, L20502 (2010)
  38. Rignot, E. et al. Recent Antarctic ice mass loss from radar interferometry and regional climate modelling. Nature Geosci. 1, 106110 (2008)
  39. Pattyn, F. et al. Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison. J. Glaciol (in the press).
    A community inter-comparison exercise that shows the capabilities of current ice-sheet models for robustly simulating grounding-line migration, which is key for predicting marine ice-sheet behaviour.
  40. Greischar, L. L. & Bentley, C. R. Isostatic equilibrium grounding line between the West Antarctic inland ice-sheet and the Ross ice shelf. Nature 283, 651654 (1980)
  41. Gomez, N., Mitrovica, J. X., Huybers, P. & Clark, P. U. Sea level as a stabilizing factor for marine-ice-sheet grounding lines. Nature Geosci. 3, 850853 (2010)
  42. Gomez, N., Pollard, D., Mitrovica, J. X., Huybers, P. & Clark, P. U. Evolution of a coupled marine ice sheet-sea level model. J. Geophys. Res. 117, F01013 (2012)
  43. Das, S. B. et al. Fracture propagation to the base of the Greenland ice sheet during supraglacial lake drainage. Science 320, 778781 (2008)
  44. Schoof, C. Ice sheet acceleration driven by melt supply variability. Nature 468, 803806 (2010).
    Shows the important role of the ice sheet–ice shelf transition zone in controlling marine ice-sheet dynamics (in particular, stability/instability).
  45. Sundal, A. et al. Melt-induced speed-up of Greenland ice sheet offset by efficient subglacial drainage. Nature 469, 521524 (2011)
  46. Bartholomew, I. et al. Short-term variability in Greenland Ice Sheet motion forced by time-varying meltwater drainage: implications for the relationship between subglacial drainage system behavior and ice velocity. J. Geophys. Res. 117, F03002 (2012)
  47. Amundson, J. & Truffer, M. A unifying framework for iceberg-calving models. J. Glaciol. 56, 822830 (2010)
  48. Hindmarsh, R. C. A. An observationally validated theory of viscous flow dynamics at the ice-shelf calving front. J. Glaciol. 58, 375387 (2012)
  49. Bassis, J. N. The statistical physics of iceberg calving and the emergence of universal calving laws. J. Glaciol. 57, 316 (2011)
  50. Levermann, A. et al. Kinematic first-order calving law implies potential for abrupt ice-shelf retreat. Cryosphere 6, 273286 (2012)
  51. Benn, D. I., Warren, C. R. & Mottram, R. H. Calving processes and the dynamics of calving glaciers. Earth Sci. Rev. 82, 143179 (2007)
  52. Nick, F. M., Vieli, A., Howat, I. M. & Joughin, I. Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus. Nature Geosci. 2, 110114 (2009)
  53. Goelzer, H. et al. Millennial total sea-level commitments projected with the Earth system model of intermediate complexity LOVECLIM. Environ. Res. Lett. 7, 045401 (2012)
  54. Nghiem, S. V. et al. The extreme melt across the Greenland ice sheet in 2012. Geophys. Res. Lett. 39, L20502 (2012).
    Key paper documenting this large-scale Greenland melt event that was unprecedented in the modern satellite record.
  55. Screen, J. A., Deser, C. & Simmonds, I. Local and remote controls on observed Arctic warming. Geophys. Res. Lett. 39, L10709 (2011).
    Provides strong observational and model evidence of symptoms and causes of the recent amplified Arctic warming.
  56. Yoshimori, M. & Abe-Ouchi, A. Sources of spread in multimodel projections of the Greenland ice sheet surface mass balance. J. Clim. 25, 11571175 (2012)
  57. Harper, N., Humphrey, N. F., Pfeffer, W. T., Brown, J. & Fettweis, X. Greenland ice-sheet contribution to sea-level rise buffered by meltwater storage in firn. Nature 491, 240243 (2012)
  58. Fettweis, X. et al. Estimating Greenland ice sheet surface mass balance contribution to future sea level rise using the regional atmospheric climate model MAR. Cryosphere 7, 469489 (2013)
  59. Price, S. F., Payne, A. J., Howat, I. M. & Smith, B. E. Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade. Proc. Natl Acad. Sci. USA 108, 89788983 (2011)
  60. Nick, F. M. et al. Future sea-level rise from Greenland’s main outlet glaciers in a warming climate. Nature 497, 235238 (2013)
  61. Goelzer, H. et al. Sensitivity of Greenland ice sheet projections to model formulations. J. Glaciol. (in the press)
  62. Bindschadler, R. A. et al. Ice sheet model sensitivities to environmental forcing and their use in projecting future sea level (the SeaRISE project). J. Glaciol. 59, 195224 (2013)
  63. Arneborg, L., Wåhlin, A. K., Björk, G., Liljebladh, B. & Orsi, A. H. Persistent inflow of warm water onto the central Amundsen shelf. Nature Geosci. 5, 876880 (2012)
  64. Bengtsson, L., Koumoutsaris, S. & Hodges, K. Large-scale surface mass balance of ice sheets from a comprehensive atmospheric model. Surv. Geophys. 32, 459474 (2011)
  65. Winkelmann, R., Levermann, A., Martin, M. A. & Frieler, K. Increased future ice discharge from Antarctica owing to higher snowfall. Nature 492, 239242 (2012)
  66. Little, C., Oppenheimer, M. & Urban, N. M. Upper bounds on twenty-first-century Antarctic ice loss assessed using a probabilistic framework. Nature Clim. Change http://dx.doi.org/10.1038/nclimate1845 (published online, 17 March 2013)
  67. Church, J. A. et al. Revisiting the Earth's sea-level and energy budgets from 1961 to 2008. Geophys. Res. Lett. 38, L18601 (2011).
    A good and recent (though the numbers are already outdated in many cases) review of all contributions to SLR.
  68. Hock, R., de Woul, M., Radić, V. & Dyurgerov, M. Mountain glaciers and ice caps around Antarctica make a large sea-level rise contribution. Geophys. Res. Lett. 36, L07501 (2009)
  69. Dyurgerov, M. B. Reanalysis of glacier changes: from the IGY to the IPY, 1960–2008. Data Glaciol. Studies 108, 5116 (2010)
  70. Cogley, J. G. Geodetic and direct mass-balance measurements: comparison and joint analysis. Ann. Glaciol. 50, 96100 (2009)
  71. Jacob, T., Wahr, J., Pfeffer, W. T. & Swenson, S. Recent contributions of glaciers and ice caps to sea level rise. Nature 482, 514518 (2012)
  72. Cogley, J. G. in The Future of the World’s Climate 2nd edn (eds Henderson-Sellers, A. & McGuffie, K.) 197222 (Elsevier, 2012)
  73. Arendt, A. et al. Randolph Glacier Inventory: A Dataset of Global Glacier Outlines Version 2.0 (GLIMS Technical Report, Global Land Ice Measurements from Space, Boulder, 2012); available at http://www.glims.org/RGI/
  74. Gardner, A. S. et al. A reconciled estimate of glacier contributions to sea level rise: 2003 to 2009. Science 340, 852857 (2013).
    Presents a consensus estimate of the contributions of glaciers and ice caps to sea-level rise that reconciles the disparate estimates previously available from the different techniques.
  75. Meehl, G. A. et al. Relative outcomes of climate change mitigation related to global temperature versus sea level rise. Nature Clim. Change 2, 576580 (2012)
  76. Gouretski, V. & Koltermann, K. P. How much is the ocean really warming? Geophys. Res. Lett. 34, L01610 (2007)
  77. Domingues, C. M. et al. Improved estimates of upper-ocean warming and multi-decadal sea-level rise. Nature 453, 10901093 (2008)
  78. von Schuckmann, K. & Le Traon, P.-Y. How well can we derive global ocean indicators from Argo data? Ocean Sci. Discuss 8, 9991024 (2011)
  79. Leuliette, E. W. & Willis, J. K. Balancing the sea level budget. Oceanography (Wash. DC) 24, 122129 (2011)
  80. Roemmich, D. & Gilson, J. The global ocean imprint of ENSO. Geophys. Res. Lett. 38, L13606 (2011)
  81. Wada, Y. et al. Past and future contribution of global groundwater depletion to sea-level rise. Geophys. Res. Lett. 39, L09402 (2012)
  82. Pokhrel, Y. N. et al. Model estimates of sea-level change due to anthropogenic impacts on terrestrial water storage. Nature Geosci. 5, 389392 (2012)
  83. Konikow, L. F. Overestimated water storage. Nature Geosci. 6, 34 (2012)
  84. Remy, F., Flament, T., Blarel, F. & Benveniste, J. Radar altimetry measurements over Antarctic ice sheet: a focus on antenna polarization and change in backscatter problems. Adv. Space Res. 50, 9981006 (2012)
  85. Nicholls, R. J. et al. Sea-level rise and its possible impacts given a ‘beyond 4°C world’ in the twenty-first century. Proc. R. Soc. Lond. A 369, 161181 (2011)
  86. Joughin, I., Smith, B., Howat, I., Scambos, T. & Moon, T. Greenland flow variability from ice-sheet-wide velocity mapping. J. Glaciol. 56, 415430 (2010)
  87. Purkey, S. G. & Johnson, G. C. Warming of global abyssal and deep Southern Ocean waters between the 1990s and 2000s: contributions to global heat and sea level rise budgets. J. Clim. 23, 63366351 (2010)
  88. Levitus, S. et al. World ocean heat content and thermosteric sea level change (0–2000m), 1955–2010. Geophys. Res. Lett. 39, L10603 (2012)
  89. Harig, C. & Simons, F. J. Mapping Greenland’s mass loss in space and time. Proc. Natl Acad. Sci. USA 109, 1993419937 (2012)
  90. Ewert, H., Groh, A. & Dietrich, R. Volume and mass changes of the Greenland ice sheet inferred from ICESat and GRACE. J. Geodyn. 59–60, 111123 (2012)
  91. Moss, R. H. et al. The next generation of scenarios for climate change research and assessment. Nature 463, 747756 (2010)
  92. Farrell, W. E. & Clark, J. A. On postglacial sea level. Geophys. J. R. Astron. Soc. 46, 647667 (1976)
  93. Kendall, R. A., Mitrovica, J. X. & Milne, G. A. On post-glacial sea level — II. Numerical formulation and comparative results on spherically symmetric models. Geophys. J. Int. 161, 679706 (2005)
  94. Wahr, J., Wingham, D. & Bentley, C. A method of combining ICESat and GRACE satellite data to constrain Antarctic mass balance. J. Geophys. Res. 105, 1627916294 (2000)
  95. Simpson, M. J. R., Wake, L., Milne, G. A. & Huybrechts, P. The influence of decadal- to millennial-scale ice mass changes on present-day vertical land motion in Greenland: Implications for the interpretation of GPS observations. J. Geophys. Res. 116, B02406 (2011)
  96. Dietrich, R. et al. Rapid crustal uplift in Patagonia due to enhanced ice loss. Earth Planet. Sci. Lett. 289, 2229 (2010)
  97. Sato, T. et al. Reevaluation of the viscoelastic and elastic responses to the past and present-day ice changes in Southeast Alaska. Tectonophysics 511, 7988 (2011)
  98. Morelli, A. & Danesi, S. Seismological imaging of the Antarctic continental lithosphere: a review. Global Planet. Change 42, 155165 (2004)
  99. Tarasov, L., Dyke, A. S., Neal, R. M. & Peltier, W. R. A data-calibrated distribution of deglacial chronologies for the North American ice complex from glaciological modeling. Earth Planet. Sci. Lett. 315–316, 3040 (2012)
  100. Gudmundsson, G. H. et al. The stability of grounding lines on retrograde slopes. Cryosphere 6, 14971505 (2012)

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Author information

Affiliations

  1. Department of Geography, University of Sheffield, Sheffield S10 2TN, UK

    • Edward Hanna
  2. Departamento de Matemática Aplicada a las Tecnologías de la Información, Universidad Politécnica de Madrid, 28040 Madrid, Spain

    • Francisco J. Navarro
  3. Laboratoire de Glaciologie, Université Libre de Bruxelles, B-1050 Brussels, Belgium

    • Frank Pattyn
  4. Antarctic Climate and Ecosystems Cooperative Research Centre, University of Tasmania, Aspendale, Victoria 3195, Australia

    • Catia M. Domingues
  5. Department of Geography, University of Liège, 4000 Liège, Belgium

    • Xavier Fettweis
  6. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109-8099, USA

    • Erik R. Ivins
  7. Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK

    • Robert J. Nicholls
  8. Laboratoire de Glaciologie et Géophysique de l’Environnement, UJF – Grenoble 1/CNRS, 38402 Saint-Martin d’Heres, France

    • Catherine Ritz
  9. Polar Science Center, Applied Physics Laboratory, University of Washington, Seattle, Washington 98105, USA

    • Ben Smith
  10. Department of Earth and Planetary Sciences, University of California, Santa Cruz, California 95064, USA

    • Slawek Tulaczyk
  11. Department of Geography, Durham University, Durham DH1 3LE, UK

    • Pippa L. Whitehouse
  12. NASA Goddard Space Flight Center, Cryospheric Sciences Laboratory, Greenbelt, Maryland 20771, USA

    • H. Jay Zwally

Contributions

E.H. coordinated the study, E.H., F.J.N. and F.P. led the writing, and all authors contributed to the writing and discussion of ideas.

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The authors declare no competing financial interests.

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