Climate Dynamics

, Volume 41, Issue 5–6, pp 1365–1384 | Cite as

A continuous simulation of global ice volume over the past 1 million years with 3-D ice-sheet models

  • B. de BoerEmail author
  • R. S. W. van de Wal
  • L. J. Lourens
  • R. Bintanja
  • T. J. Reerink


Sea-level records show large glacial-interglacial changes over the past million years, which on these time scales are related to changes of ice volume on land. During the Pleistocene, sea-level changes induced by ice volume are largely caused by the waxing and waning of the large ice sheets in the Northern Hemisphere. However, the individual contributions of ice in the Northern and Southern Hemisphere are poorly constrained. In this study, for the first time a fully coupled system of four 3-D ice-sheet models is used, simulating glaciations on Eurasia, North America, Greenland and Antarctica. The ice-sheet models use a combination of the shallow ice and shelf approximations to determine sheet, shelf and sliding velocities. The framework consists of an inverse forward modelling approach to derive a self-consistent record of temperature and ice volume from deep-sea benthic δ18O data over the past 1 million years, a proxy for ice volume and temperature. It is shown that for both eustatic sea level and sea water δ18O changes, the Eurasian and North American ice sheets are responsible for the largest part of the variability. The combined contribution of the Antarctic and Greenland ice sheets is about 10 % for sea level and about 20 % for sea water δ18O during glacial maxima. However, changes in interglacials are mainly caused by melt of the Greenland and Antarctic ice sheets, with an average time lag of 4 kyr between melt and temperature. Furthermore, we have tested the separate response to changes in temperature and sea level for each ice sheet, indicating that ice volume can be significantly influenced by changes in eustatic sea level alone. Hence, showing the importance of a simultaneous simulation of all four ice sheets. This paper describes the first complete simulation of global ice-volume variations over the late Pleistocene with the possibility to model changes above and below present-day ice volume, constrained by observations of benthic δ18O proxy data.


Pleistocene Oxygen isotopes Ice sheet Glacial cycles 



For the use of the PMIP2 GCM model output, we acknowledge the international modelling groups for providing their data for analysis, the Laboratoire des Sciences du Climat et de l’Environnement (LSCE) for collecting and archiving the model data. The analyses were performed using version 01-07-2010 of the database. Part of the computations were performed on the Lisa Compute Cluster, we thank SARA Computing and Networking Services for their support. David Pollard is thanked for providing Antarctic ice volume data over the past 5 Myr. We would like to thank two anonymous reviewers for valuable comments on the manuscript.


  1. Bamber JL, Layberry RL, Gogineni SP (2001) A new ice thickness and bed data set for the Greenland ice sheet 1. Measurements, data reduction, and errors. J Geophys Res 106. doi: 10.1029/2001JD900054
  2. Becker JJ, Sandwell DT, Smith WHF, Braud J, Binder B, Depner J, Fabre D, Factor J, Ingalls S, Kim SH, Ladner R, Marks K, Nelson S, Pharaoh A, Trimmer R, Von Rosenberg J, Wallace G, Weatherall P (2009) Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Marine Geodesy 32(4):355–371CrossRefGoogle Scholar
  3. Beckmann A, Goosse H (2003) A parameterization of ice shelf-ocean interaction for climate models. Ocean Model 5(2):157–170CrossRefGoogle Scholar
  4. Bintanja R, Oerlemans J (1996) The effect of reduced ocean overturning on the climate of the last glacial maximum. Clim Dyn 12:523–533CrossRefGoogle Scholar
  5. Bintanja R, Van de Wal RSW (2008) North American ice-sheet dynamics and the onset of 100,000-year glacial cycles. Nature 454:869–872CrossRefGoogle Scholar
  6. Bintanja R, Van de Wal RSW, Oerlemans J (2002) Global ice volume variations through the last glacial cycle simulated by a 3-D ice-dynamical model. Quat Int 95–96:19–23Google Scholar
  7. Bintanja R, Van de Wal RSW, Oerlemans J (2005a) Modelled atmospheric temperatures and global sea level over the past million years. Nature 437:125–128CrossRefGoogle Scholar
  8. Bintanja R, Van de Wal RSW, Oerlemans J (2005b) A new method to estimate ice age temperatures. Clim Dyn 24:197–211CrossRefGoogle Scholar
  9. Braconnot P, Otto-Bliesner B, Harrison S, Joussaume S, Peterchmitt JY, Abe-Ouchi A, Crucifix M, Driesschaert E, Fichefet T, Hewitt CD, Kageyama M, Kitoh A, Laîné A, Loutre MF, Marti O, Merkel U, Ramstein G, Valdes P, Weber SL, Yu Y, Zhao Y (2007) Results of PMIP2 coupled simulations of the Mid-Holocene and Last Glacial Maximum—Part 1: experiments and large-scale features. Clim Past 3(2):261–277CrossRefGoogle Scholar
  10. Bueler E, Brown J (2009) Shallow shelf approximation as a ”sliding law” in a thermomechanically coupled ice sheet model. J Geophys Res 114. doi: 10.1029/2008JF001179
  11. Chappell J, Shackleton NJ (1986) Oxygen isotopes and sea level. Nature 324:137–140CrossRefGoogle Scholar
  12. Clarke GKC (2005) Subglacial processes. Ann Rev Earth Planet Sc 33:247–276CrossRefGoogle Scholar
  13. Cuffey KM (2000) Methodology for use of isotopic climate forcings in ice sheet models. Geophys Res Lett 27(19):3065–3068CrossRefGoogle Scholar
  14. De Boer B (2012) A reconstruction of ice volume, temperature and atmospheric CO2 over the past 40 million years. PhD thesis, Utrecht UniversityGoogle Scholar
  15. De Boer B, van de Wal RSW, Bintanja R, Lourens L, Tuenter E (2010) Cenozoic global ice-volume and temperature simulations with 1-D ice-sheet models forced by benthic \(\delta^{18}O_i\) records. Ann Glaciol 51(55):23–33Google Scholar
  16. De Boer B, van de Wal RSW, Lourens LJ, Bintanja R (2012) Transient nature of the Earth’s climate and the implications for the interpretation of benthic \(\delta^{18}\)O records. Palaeogeogr Palaeoclimatol Palaeoecol 335–336:4–11CrossRefGoogle Scholar
  17. DeConto RM, Pollard D (2003) A coupled climate-ice sheet modeling approach to the early Cenozoic history of the Antarctic ice sheet. Palaeogeogr Palaeoclimatol Palaeoecol 198:39–42CrossRefGoogle Scholar
  18. Docquier D, Perichon L, Pattyn F (2011) Representing grounding line dynamics in numerical ice sheet models: recent advances and outlook. Surv Geophys 32:417–435CrossRefGoogle Scholar
  19. Duplessy JC, Labeyrie L, Waelbroeck C (2002) Constraints on the ocean oxygen isotopic enrichment between the Last Glacial Maximum and the Holocene: Paleoceanographic implications. Quat Sci Rev 21:315–330CrossRefGoogle Scholar
  20. Ehlers J, Gibbard PL (2007) The extent and chronology of Cenozoic global glaciation. Quat Int 164–165:6–20CrossRefGoogle Scholar
  21. Epica Community Members (2006) One-to-one coupling of glacial climate variability in Greenland and Antarctica. Nature 444:195–198CrossRefGoogle Scholar
  22. Ettema J, van den Broeke MR, van Meijgaard E, van de Berg WJ, Bamber JL, Box JE, Bales RC (2009) Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling. Geophys Res Lett 36. doi: 10.1029/2009GL038110
  23. Fitzgerald PW, Bamber JL, Ridley JK, Rougier JC (2012) Exploration of parametric uncertainty in a surface mass balance model applied to the Greenland ice sheet. J Geophys Res 117(F1). doi: 10.1029/2011JF002067
  24. Fyke JG, Weaver AJ, Pollard D, Eby M, Carter L, Mackintosh A (2011) A new coupled ice sheet/climate model: description and sensitivity to model physics under Eemian, Last Glacial Maximum, late Holocene and modern climate conditions. Geosci Model Dev 4:117–136CrossRefGoogle Scholar
  25. Giovinetto M, Zwally H (1997) Areal distribution of the oxygen-isotope ratio in Antarctica: an assessment based on multivariate models. Ann Glaciol 25:153–158Google Scholar
  26. Gladstone RM, Payne AJ, Cornford SL (2010) Parameterising the grounding line in flow-line ice sheet models. The Cryosphere 4(4):605–619CrossRefGoogle Scholar
  27. Hutter L (1983) Theoretical glaciology. D. Reidel, DordrechtCrossRefGoogle Scholar
  28. Huybrechts P (1990) A 3-D model for the Antarctic ice sheet: a sensitivity study on the glacial-interglacial contrast. Clim Dyn 5(2):79–92Google Scholar
  29. Huybrechts P (1992) The Antarctic ice sheet and environmental change: a three-dimensional modelling study. PhD thesis, Geografisch Instituut, Vrije Universiteit BrusselGoogle Scholar
  30. Huybrechts P (2002) Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles. Quat Sci Rev 21:203–231CrossRefGoogle Scholar
  31. Huybrechts P, de Wolde J (1999) The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming. J Clim 12(8):2169–2188CrossRefGoogle Scholar
  32. Janssens I, Huybrechts P (2000) The treatment of meltwater retention in mass-balance parameterizations of the Greenland ice sheet. Ann Glaciol 31:133–140CrossRefGoogle Scholar
  33. Jakobsson M, Nilsson J, O’Regan M, Backman J, Löwemark L, Dowdeswell JA, Mayer L, Polyak L, Colleoni F, Anderson LG, Björk G, Darby D, Eriksson B, Hanslik D, Hell B, Marcussen C, Sellén E, Wallin Å (2010) An Arctic Ocean ice shelf during MIS 6 constrained by new geophysical and geological data. Quat Sci Rev 29(25–26):3505–3517CrossRefGoogle Scholar
  34. Laskar J, Robutel P, Joutel F, Gastineau M, Correia ACM, Levrard B (2004) A long-term numerical solution for the insolation quantaties of the Earth. Astron Astroph 428:261–285CrossRefGoogle Scholar
  35. Le Brocq AM, Payne AJ, Vieli A (2010) An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1). Earth Syst Sci Data 2(2):247–260CrossRefGoogle Scholar
  36. Le Meur E, Huybrechts P (1996) A comparision of different ways of dealing with isostacy: examples from modelling the Antarctic ice sheet during the last glacial cycle. Ann Glaciol 23:309–317Google Scholar
  37. Lenaerts JTM, van den Broeke MR, van de Berg WJ, van Meijgaard E, Kuipers Munneke P (2012) A new, high-resolution surface mass balance map of Antarctica (1979–2010) based on regional atmospheric climate modeling. Geophys Res Lett 39(4). doi: 10.1029/2011GL050713
  38. Lhomme N, Clarke GKC (2005) Global budget of water isotopes inferred from polar ice sheets. Geophys Res Lett 32. doi: 10.1029/2005GL023774
  39. Liakka J, Nilsson J, Löfverström M (2012) Interactions between stationary waves and ice sheets: linear versus nonlinear atmospheric response. Clim Dyn 38:1249–1262CrossRefGoogle Scholar
  40. Lisiecki L, Raymo M (2005) A Pliocene-Pleistocene stack of 57 globally distributed benthic \(\delta^{18}\hbox{O}\) records. Paleoceanography 20. doi: 10.1029/2004PA001071
  41. Martin MA, Winkelmann R, Haseloff M, Albrecht T, Bueler E, Khroulev C, Levermann A (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK)–Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet. The Cryosphere 5(3):727–740CrossRefGoogle Scholar
  42. Morland LW (1987) Unconfined ice-shelf flow. In: de Veen CJV, Oerlemans J (eds) Dynamics of the West Antarctic Ice Sheet. D. Reidel, Dordrecht, pp 99–116CrossRefGoogle Scholar
  43. Moucha R, Forte AM, Mitrovica JX, Rowley DB, Quéré S, Simmons NA, Grand SP (2008) Dynamic topography and long-term sea-level variations: there is no such thing as a stable continental platform. Earth Planet Sci Lett 271:101–108CrossRefGoogle Scholar
  44. Müller RD, Sdrolias M, Gaine C, Steinberger B, Heine C (2008) Long-term sea-level fluctuations driven by ocean basin dynamics. Science 319:1357–1362CrossRefGoogle Scholar
  45. Olaizola M, van de Wal RSW, Helsen MM, de Boer B (2011) Present-day mass changes for the Greenland ice sheet and their interaction with bedrock adjustment. Cryosphere Discuss 5(6):3455–3477CrossRefGoogle Scholar
  46. Peltier WR (2004) Global glacial isostasy and the surface of the ice-age earth: the ICE-5G (VM2) model and GRACE. Annu Rev Earth Planet Sci 32:111–149CrossRefGoogle Scholar
  47. Pollard D, DeConto RM (2007) A coupled ice-sheet/ice-shelf/sediment model applied to a marine-margin flowline: forced and unforced variations, chap 2. Blackwell Publishing, New York, Spec. Publ. 39, International Association of Sedimentologists, pp 37–52Google Scholar
  48. Pollard D, DeConto RM (2009) Modelling West Antarctic ice sheet growth and collapse throught the past five million years. Nature 458:329–332CrossRefGoogle Scholar
  49. Reerink TJ, Kliphuis MA, Van de Wal RSW (2010) Mapping technique of climate fields between gcm’s and ice models. Geosci Model Dev 3(1):13–41CrossRefGoogle Scholar
  50. Rignot E, Velicogna I, van den Broeke MR, Monaghan A, Lenaerts J (2011) Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys Res Lett 38(5). doi: 10.1029/2011GL046583
  51. Robinson A, Calov R, Ganopolski A (2010) An efficient regional energy-moisture balance model for simulation of the Greenland Ice Sheet response to climate change. The Cryosphere 4(2):129–144CrossRefGoogle Scholar
  52. Robinson A, Calov R, Ganopolski A (2011) Greenland ice sheet model parameters constrained using simulations of the Eemian Interglacial. Clim Past 7(2):381–396CrossRefGoogle Scholar
  53. Roe GH (2002) Modeling precipitation over ice sheets: an assessment using Greenland. J Glaciol 48(160):70–80CrossRefGoogle Scholar
  54. Roe GH, Lindzen RS (2001) The mutual interaction between continental-scale ice sheets and atmospheric stationary waves. J Clim 14(7):1450–1465CrossRefGoogle Scholar
  55. Rohling EJ, Grant K, Bolshaw M, Roberts AP, Siddall M, Hemleben C, Kucera M (2009) Antarctic temperature and global sea level closely coupled over the past five glacial cycles. Nature Geosci 2:500–504CrossRefGoogle Scholar
  56. Schoof C (2010) Coulomb friction and other sliding laws in a higher-order glacier flow model. Math Models Methods Appl Sci 20(1):157–189CrossRefGoogle Scholar
  57. Schrag DP, Adkins JF, McIntyre K, Alexander JL, Hodell DA, Charles CD, McManus JF (2002) The oxygen isotopic composition of seawater during the Last Glacial Maximum. Quat Sci Rev 21:331–342CrossRefGoogle Scholar
  58. Seddik H, Greve R, Zwinger T, Gillet-Chaulet F, Gagliardini O (2012) Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/ice. J Glaciol 58(209):427–440CrossRefGoogle Scholar
  59. Sima A, Paul A, Schulz M, Oerlemans J (2006) Modeling the oxygen-isotopic composition of the North American Ice Sheet and its effect on the isotopic composition of the ocean during the last glacial cycle. Geophys Res Lett 33(15). doi: 10.1029/2006GL026923
  60. Thompson WG, Goldstein SL (2006) A radiometric calibration of the SPECMAP timescale. Quat Sci Rev 25(23–24):3207–3215CrossRefGoogle Scholar
  61. Uppala SM et al (2005) The ERA-40 re-analysis. Q J Roy Meteor Soc 131:2961–3012CrossRefGoogle Scholar
  62. van de Berg, WJ, van den Broeke, M, Ettema J, van Meijgaard E, Kaspar F (2011) Significant contribution of insolation to Eemian melting of the Greenland ice sheet. Nature Geosci 10(4):679–683CrossRefGoogle Scholar
  63. Van den Berg J, Van de Wal RSW, Oerlemans J (2008) A mass balance model for the Eurasian Ice Sheet for the last 120,000 years. Glob Plan Change 61:194–208CrossRefGoogle Scholar
  64. van den Berg J, van de Wal RSW, Milne GA, Oerlemans J (2008) Effect of isostasy on dynamical ice sheet modeling: a case study for Eurasia. J Geophys Res 113(B5). doi: 10.1029/2007JB004994
  65. Van der Veen CJ (1999) Fundamentals of glacier dynamics. A.A. Balkema Publishers, RotterdamGoogle Scholar
  66. Van de Wal RSW (1999) The importance of thermodynamics for modeling the volume of the Greenland ice sheet. J Geophys Res 104:3887–3898CrossRefGoogle Scholar
  67. Weertman J (1957) On the sliding of glaciers. J Glaciol 3:33–38Google Scholar
  68. Winkelmann R, Martin MA, Haseloff M, Albrecht T, Bueler E, Khroulev C, Levermann A (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK)—part 1: Model description. The Cryosphere 5(3):715–726CrossRefGoogle Scholar
  69. Zwally HJ, Giovinetto MB (1997) Areal distribution of the oxygen-isotope ratio in Greenland. Ann Glaciol 25:208–213Google Scholar
  70. Zweck C, Huybrechts P (2005) Modeling of the northern hemisphere ice sheets during the last glacial cycle and glaciological sensitivity. J Geophys Res 110. doi: 10.1029/2004JD005489

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • B. de Boer
    • 1
    Email author
  • R. S. W. van de Wal
    • 1
  • L. J. Lourens
    • 2
  • R. Bintanja
    • 3
  • T. J. Reerink
    • 1
  1. 1.Institute for Marine and Atmospheric research UtrechtUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Earth Siences, Faculty of GeosciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.Royal Netherlands Meteorological Institute (KNMI)De BiltThe Netherlands

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