We use cookies to improve your experience with our site. | More info.

Nature | Letter

日本語要約

Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume

Journal name:
Nature
Volume:
500,
Pages:
190–193
Date published:
DOI:
doi:10.1038/nature12374
Received
Accepted
Published online

The growth and reduction of Northern Hemisphere ice sheets over the past million years is dominated by an approximately 100,000-year periodicity and a sawtooth pattern1, 2 (gradual growth and fast termination). Milankovitch theory proposes that summer insolation at high northern latitudes drives the glacial cycles3, and statistical tests have demonstrated that the glacial cycles are indeed linked to eccentricity, obliquity and precession cycles4, 5. Yet insolation alone cannot explain the strong 100,000-year cycle, suggesting that internal climatic feedbacks may also be at work4, 5, 6, 7. Earlier conceptual models, for example, showed that glacial terminations are associated with the build-up of Northern Hemisphere ‘excess ice’5, 8, 9, 10, but the physical mechanisms underpinning the 100,000-year cycle remain unclear. Here we show, using comprehensive climate and ice-sheet models, that insolation and internal feedbacks between the climate, the ice sheets and the lithosphere–asthenosphere system explain the 100,000-year periodicity. The responses of equilibrium states of ice sheets to summer insolation show hysteresis11, 12, 13, with the shape and position of the hysteresis loop playing a key part in determining the periodicities of glacial cycles. The hysteresis loop of the North American ice sheet is such that after inception of the ice sheet, its mass balance remains mostly positive through several precession cycles, whose amplitudes decrease towards an eccentricity minimum. The larger the ice sheet grows and extends towards lower latitudes, the smaller is the insolation required to make the mass balance negative. Therefore, once a large ice sheet is established, a moderate increase in insolation is sufficient to trigger a negative mass balance, leading to an almost complete retreat of the ice sheet within several thousand years. This fast retreat is governed mainly by rapid ablation due to the lowered surface elevation resulting from delayed isostatic rebound14, 15, 16, which is the lithosphere–asthenosphere response. Carbon dioxide is involved, but is not determinative, in the evolution of the 100,000-year glacial cycles.

View full text

Subject terms:

At a glance

Figures

View all figures
  1. Time series of forcing and responses of Northern Hemisphere ice sheets.
    Figure 1: Time series of forcing and responses of Northern Hemisphere ice sheets.

    Left, time series of the past 400 kyr; right, corresponding spectra. a, Mean extra-atmospheric insolation at latitude 65° N on 21 June of each year, which closely corresponds to the summer solstice. b, Atmospheric CO2 from Vostok ice core on a revised timescale (ref. 23 and references therein). c, δ18O from benthic foraminifera as a proxy for sea level and deep ocean temperature30. d, Modelled sea-level equivalent (SLE) of ice-volume changes relative to present with variations in atmospheric CO2 content and insolation (standard case). e, Same as d but with a constant CO2 concentration of 220 p.p.m. f, Same as e but with instant isostatic rebound. g, Same as d but with different constant CO2 concentrations (blue, 160 p.p.m.; black, 220 p.p.m.; red, 260 p.p.m.) for the North American ice sheet. h, Same as g but for the Eurasian ice sheet. The spectra (right) show the amplitudes (calculated by the Multi-Taper Spectral Analysis Methods (MTM); using Analy Series; http://www.lsce.ipsl.fr/logiciels/index.php) in the corresponding frequencies of the time series (left). The coloured dots indicate peaks with more than 95% significance for the corresponding coloured curves.

  2. Hysteresis of equilibrium states and transient evolution of the Northern Hemisphere ice sheets.
    Figure 2: Hysteresis of equilibrium states and transient evolution of the Northern Hemisphere ice sheets.

    a, Maps showing the equilibrium shapes and surface mass balances of ice sheets when the climatic anomalies relative to present conditions are respectively (left to right) −2, −1, 0 and 1 K (summer temperature) and when the model runs start from large initial ice sheets. Colours indicate the surface mass balance in metres per year. Note the large ablation areas and ablation rates (negative mass balance) that appear in the warm low latitudes. b, Modelled equilibrium and transient ice volumes as functions of the summer temperature anomaly for the North American (left) and Eurasian (right) ice sheets: red dots denote the large-volume equilibrium states if the model runs start from large initial ice sheets; blue dots show the small-volume equilibrium states for small initial ice sheets. The blue areas indicate a positive total mass balance of the ice sheet; red areas indicate a negative total mass balance. The black dots mark the evolution of the transient ice volume every 2 kyr for the last glacial cycle starting 122 kyr bp. The small numbers on the black trajectories show the corresponding time in kiloyears. The horizontal scales below the figures show the relation between the temperature anomaly (Methods) and the corresponding insolation at latitude 65° N on 21 June for two given constant atmospheric CO2 concentrations (220 p.p.m. and 280 p.p.m.). c, Same as b but data shown as time series for the past two glacial cycles.

  3. Role of eccentricity, obliquity and precession in the 100-kyr cycle.
    Figure 3: Role of eccentricity, obliquity and precession in the 100-kyr cycle.

    Time series of the model experiments with one of eccentricity, obliquity or precession fixed for a constant atmospheric CO2 concentration of 220 p.p.m. a, Insolation forcing (insolation at latitude 65° N on 21 June) with variations in eccentricity, obliquity and precession (black lines); with obliquity fixed at 23.5° (red lines); with eccentricity fixed at 0.02 (blue lines); and with perihelion passage fixed at the spring equinox and no precession (green lines). b, Corresponding spectra of insolation change in a (as in Fig. 1a). c, Calculated ice-volume change, expressed as sea-level equivalent (colours same as in a). d, Corresponding spectra of calculated ice-volume change in c (as in Fig. 1d).

Videos

  1. Simulated ice sheet change for the last 400 kyr with the IcIES-MIROC model
    Video 1: Simulated ice sheet change for the last 400 kyr with the IcIES-MIROC model
    This animation shows an oblique view of the model Northern Hemisphere ice sheets (standard case shown in Fig. 1d) computed every 1000 years during the last 400 kyr, together with the evolution of the ice volume. The 100 kyr glacial cycles and the fast terminations at the end of each glacial cycle are the prominently visible patterns.

References

  1. Clark, P. U. et al. The Last Glacial Maximum. Science 325, 710–714 (2009)
  2. Hays, J. D., Imbrie, J. & Shackleton, N. J. Variations in Earth’s orbit - pacemaker of ice ages. Science 194, 1121–1132 (1976)
  3. Milankovitch, M. Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitproblem (R. Serbian Acad., 1941)
  4. Lisiecki, L. E. Links between eccentricity forcing and the 100,000-year glacial cycle. Nature Geosci. 3, 349–352 (2010)
  5. Huybers, P. Combined obliquity and precession pacing of late Pleistocene deglaciations. Nature 480, 229–232 (2011)
  6. Saltzman, B., Hansen, A. R. & Maasch, K. A. The late Quaternary glaciations as the response of a three-component feedback system to Earth-orbital forcing. J. Atmos. Sci. 41, 3380–3389 (1984)
  7. Tziperman, E., Raymo, M. E., Huybers, P. & Wunsch, C. Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing. Paleoceanography 21, PA4206 (2006)
  8. Raymo, M. E. The timing of major climate terminations. Paleoceanography 12, 577–585 (1997)
  9. Paillard, D. The timing of Pleistocene glaciations from a simple multiple-state climate model. Nature 391, 378–381 (1998)
  10. Parrenin, F. & Paillard, D. Amplitude and phase of glacial cycles from a conceptual model. Earth Planet. Sci. Lett. 214, 243–250 (2003)
  11. Abe-Ouchi, A. & Blatter, H. On the initiation of ice sheets. Ann. Glaciol. 18, 203–207 (1993)
  12. Calov, R. & Ganopolski, A. Multistability and hysteresis in the climate-cryosphere system under orbital forcing. Geophys. Res. Lett. 32, L21717 (2005)
  13. Pollard, D. & DeConto, R. M. Hysteresis in Cenozoic Antarctic ice-sheet variations. Global Planet. Change 45, 9–21 (2005)
  14. Oerlemans, J. Model experiments on the 100,000-yr glacial cycle. Nature 287, 430–432 (1980)
  15. Pollard, D. A simple ice-sheet model yields realistic 100 kyr glacial cycles. Nature 296, 334–338 (1982)
  16. Deblonde, G., Peltier, W. R. & Hyde, W. T. Simulations of continental ice sheet growth over the last glacial-interglacial cycle: experiments with a one level seasonal energy balance model including seasonal ice albedo feedback. Palaeogeogr. Palaeoclimatol. Palaeoecol. 98, 37–55 (1992)
  17. Shackleton, N. J. The 100,000-year ice-age cycle identified and found to lag temperature, carbon dioxide, and orbital eccentricity. Science 289, 1897–1902 (2000)
  18. Paillard, D. & Parrenin, F. The Antarctic ice sheet and the triggering of deglaciations. Earth Planet. Sci. Lett. 227, 263–271 (2004)
  19. Peltier, W. R. & Marshall, S. Coupled energy-balance ice-sheet model simulations of the glacial cycle: a possible connection between terminations and terrigenous dust. J. Geophys. Res. 100, 14269–14289 (1995)
  20. Ganopolski, A. & Calov, R. The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles. Clim. Past 7, 1415–1425 (2011)
  21. Gregoire, L. J., Payne, A. J. & Valdes, P. J. Deglacial rapid sea level rises caused by ice-sheet saddle collapses. Nature 487, 219–222 (2012)
  22. Abe-Ouchi, A., Segawa, T. & Saito, F. Climatic conditions for modelling the Northern Hemisphere ice sheets throughout the ice age cycle. Clim. Past 3, 423–438 (2007)
  23. Kawamura, K. et al. Northern Hemisphere forcing of climatic cycles in Antarctica over the past 360,000 years. Nature 448, 912–916 (2007)
  24. Berger, A., Loutre, M. F. & Gallee, H. Sensitivity of the LLN climate model to the astronomical and CO2 forcings over the last 200 ky. Clim. Dyn. 14, 615–629 (1998)
  25. Kurahashi-Nakamura, T., Abe-Ouchi, A. & Yamanaka, Y. Effects of physical changes in the ocean on the atmospheric pCO2: glacial-interglacial cycles. Clim. Dyn. 35, 713–719 (2009)
  26. Ganopolski, A. & Roche, D. M. On the nature of lead-lag relationships during glacial-interglacial climate transitions. Quat. Sci. Rev. 28, 3361–3378 (2009)
  27. He, F. et al. Northern Hemisphere forcing of Southern Hemisphere climate during the last deglaciation. Nature 494, 81–85 (2013)
  28. Claussen, M., Fohlmeister, J., Ganopolski, A. & Brovkin, V. Vegetation dynamics amplifies precessional forcing. Geophys. Res. Lett. 33, L09709 (2006)
  29. Marshall, S. J. & Clark, P. U. Basal temperature evolution of North American ice sheets and implications for the 100-kyr cycle. Geophys. Res. Lett. 29, 2214 (2002)
  30. Lisiecki, L. E. & Raymo, M. E. A. Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records. Paleoceanography 20, PA1003 (2005)
  31. Pollard, D. A retrospective look at coupled ice sheet-climate modeling. Clim. Change 100, 173–194 (2010)
  32. Braconnot, P. et al. Evaluation of climate models using palaeoclimatic data. Nature Clim. Change 2, 417–424 (2012)
  33. Reeh, N. Parameterization of melt rate and surface temperature on the Greenland ice sheet. Polarforschung 59, 113–128 (1991)
  34. Berger, A. L. Long-term variations of daily insolation and quaternary climatic changes. J. Atmos. Sci. 35, 53–74 (1978)
  35. Petit, J. R. et al. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399, 429–436 (1999)
  36. Calov, R., Ganopolski, A., Petoukhov, V., Claussen, M. & Greve, R. Large-scale instabilities of the Laurentide ice sheet simulated in a fully coupled climate-system model. Geophys. Res. Lett. 29, 2216 (2002)
  37. Laske, G. & Masters, G. A global digital map of sediment thickness. Eos Trans. AGU 78, F483 (1997)
  38. Pollard, D. in Milankovitch and Climate: Understanding the Response to Astronomical Forcing Pt 2 (eds Berger, A., Imbrie, J., Hays, H., Kukla, G. & Saltzman, B.) 541–564 (Reidel, 1984)
  39. Pollard, D. & DeConto, R. M. Modelling West Antarctic ice sheet growth and collapse through the past five million years. Nature 458, 329–332 (2009)
  40. Okuno, J. & Nakada, M. Effects of water load on geophysical signals due to glacial rebound and implications for mantle viscosity. Earth Planets Space 53, 1121–1135 (2001)
  41. Okada, Y. Interaction between Northern Hemisphere Ice Sheet and Solid Earth Throughout the Ice Age Cycle [in Japanese]. MSc thesis, Univ. Tokyo. (2008)
  42. Crucifix, M., Loutre, M. F., Lambeck, K. & Berger, A. Effect of isostatic rebound on modelled ice volume variations during the last 200 kyr. Earth Planet. Sci. Lett. 184, 623–633 (2001)

Download references

Author information

Affiliations

  1. Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa 277-8568, Japan

    • Ayako Abe-Ouchi,
    • Jun’ichi Okuno &
    • Heinz Blatter

  2. Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan

    • Ayako Abe-Ouchi,
    • Fuyuki Saito,
    • Jun’ichi Okuno &
    • Kunio Takahashi

  3. National Institute of Polar Research, Tachikawa, Tokyo 190-8518, Japan

    • Ayako Abe-Ouchi,
    • Kenji Kawamura &
    • Jun’ichi Okuno

  4. Institute of Biogeosciences, Japan Agency for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan

    • Kenji Kawamura

  5. Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York 10964, USA

    • Maureen E. Raymo

  6. Institute for Atmospheric and Climate Science, ETH Zurich, CH-8092 Zurich, Switzerland

    • Heinz Blatter

Contributions

A.A.-O. designed the research and experiments, and wrote the manuscript with F.S., K.K., M.E.R. and H.B. A.A.-O. and F.S. developed the numerical model, performed the experiments and analysed the results with K.T., K.K. and H.B. K.K. provided the ice-core data, and J.O. provided the Earth model for glacial isostatic rebound. All authors discussed the results and provided inputs on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

Video

  1. Video 1: Simulated ice sheet change for the last 400 kyr with the IcIES-MIROC model (2,893 KB, Download)
    This animation shows an oblique view of the model Northern Hemisphere ice sheets (standard case shown in Fig. 1d) computed every 1000 years during the last 400 kyr, together with the evolution of the ice volume. The 100 kyr glacial cycles and the fast terminations at the end of each glacial cycle are the prominently visible patterns.

PDF files

  1. Supplementary Information (1.4 MB)

    This file contains Supplementary Text, Supplementary Figures 1-6 and Supplementary References.

Comments

  1. Report this comment #64119

    Richard Whaley said:

    Isostatic Rebound will not lower the Ice Surface

    It was thought that the Ice Ages were caused by small changes in sunlight from the Earth's orbit. Abe-Ouchi et al have shown by simulating these orbital changes over 400k years that there is no observable 100k year period - the Ice Age period over the last million years. They search for mechanisms in computer models, particularly the effect of delayed isostatic rebound of the ground surface downwards from the weight of ice (Ref 1). However they have not taken into account the Ice Age cycles in the parameters they model. These result in any lowering of the ground surface being made up by snow over the Poles - which will not fall in height causing melting as Abe-Ouchi et al propose. The triggering of the rapid withdrawal of the ice still requires an explanation.

    It is generally recognised that Ice Ages require a continent over a Pole (Ref 2). This means the main driver is snow at the S Pole, flowing out as a glacier from its last minimum, and the period is mainly set by the time it takes for this outflow to reach a latitude where melting equals the rate of outflow. Within this process there are a number of cycles: the Height of the Ice as the snow builds up around the Pole from the last minimum, which controls the Rate of Outflow of the Ice, which in turn controls the Advance of the whole Cap (Ref 3 figs 2 ? 4).

    The three parameters above all change from the near Ice Age minimum at present. The spreading of the S Pole Cap reflects more sunlight, so the Earth cools.

    What is not understood is why the Ice suddenly retreats from its maximum in just 10k years. Abe-Ouchi et al propose that this may be largely due to isostatic rebound (downwards) which they build into their models. It is known the weight of the ice sheet causes the ground surface to sink - but there are delays of thousands of years. The rise is still occurring from the last Ice maximum. They propose that the delayed sinking of 1/3 height of the ice sheet causes the sheet's surface to fall near Ice Age maximum to an altitude where it melts.

    We need to consider those cycles in Italics above. Isostatic rebound will not cause melting near the Pole, nor will it exist at the edges of the Caps where melting occurs. We need to compare the annual rise in Height of the Ice near the maximum extent of the Ice (near year 100k in Fig 2 Ref 3) with 1/3 the rise in Height of the Ice around year 85k (estimate of fall in ground surface near year 100k). It is not apparent there will be any lowering of the Ice Surface - lowering of the ground surface being made up by the annual snow fall - which anyway will be near maximum in the Ice Age cycle. Further, Rate of Outflow of Ice is much higher at 100k than at 85k - so at mid latitudes between the Pole and edge of the Cap any fall in the ground surface will also have the high outflow of the ice flowing into any depression. It cannot be said a lowering of the ice surface has any part to play in triggering the sudden withdrawal of the ice. Richard Whaley, Norh East Hants Historical & Archaeological Society. richard@whaley.me.uk

    References

    1. A. Abe-Ouchi et al, "Insolation driven 100,000 year glacial cycles and hysteresis of ice sheets", Nature 8 August 2013, 500, No.7461, p190 (The paper commented on)

    2. BBC Radio 4 In Our Time, 14 February 2013, British Broadcasting Corporation

    3. R Whaley, "Ice Ages: Geothermal energy is the driver", North East Hants Hist & Arch Soc e News 10, "www.nehhas.org.uk/ice.htm": http://www.nehhas.org.uk/ice.htm

Subscribe to comments

Additional data