A simple rule to determine which insolation cycles lead to interglacials

Abstract

The pacing of glacial–interglacial cycles during the Quaternary period (the past 2.6 million years) is attributed to astronomically driven changes in high-latitude insolation. However, it has not been clear how astronomical forcing translates into the observed sequence of interglacials. Here we show that before one million years ago interglacials occurred when the energy related to summer insolation exceeded a simple threshold, about every 41,000 years. Over the past one million years, fewer of these insolation peaks resulted in deglaciation (that is, more insolation peaks were ‘skipped’), implying that the energy threshold for deglaciation had risen, which led to longer glacials. However, as a glacial lengthens, the energy needed for deglaciation decreases. A statistical model that combines these observations correctly predicts every complete deglaciation of the past million years and shows that the sequence of interglacials that has occurred is one of a small set of possibilities. The model accounts for the dominance of obliquity-paced glacial–interglacial cycles early in the Quaternary and for the change in their frequency about one million years ago. We propose that the appearance of larger ice sheets over the past million years was a consequence of an increase in the deglaciation threshold and in the number of skipped insolation peaks.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Occurrence of interglacials over the past 800,000 years.
Figure 2: Interglacials, continued interglacials and interstadials in relation to caloric summer half-year insolation over the past 2.6 Myr.
Figure 3: Caloric summer half-year insolation peaks over the past 2.6 Myr.
Figure 4: Caloric summer half-year insolation peaks against time since the onset of the previous interglacial over the past 1 Myr.
Figure 5: Effective energy at each insolation peak during the past 2.6 Myr.
Figure 6: Simulations of the most probable sequences of interglacials over the past 1 Myr.

References

  1. 1

    Milankovic´, M. Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem (Royal Serbian Academy, 1941)

  2. 2

    Hays, J. D., Imbrie, J. & Shackleton, N. J. Variations in the Earth’s orbit: pacemaker of the ice ages. Science 194, 1121–1132 (1976)

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  3. 3

    Cheng, H. et al. The Asian monsoon over the past 640,000 years and ice age terminations. Nature 534, 640–646 (2016)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Tzedakis, P. C. et al. Can we predict the duration of an interglacial? Clim. Past 8, 1473–1485 (2012)

    Article  Google Scholar 

  5. 5

    Imbrie, J. et al. On the structure and origin of major glaciation cycles. 2. The 100,000-year cycle. Paleoceanography 8, 699–735 (1993)

    ADS  Article  Google Scholar 

  6. 6

    Saltzman, B. & Maasch, K. A. A first-order global model of late Cenozoic climate. Trans. R. Soc. Edinb. Earth Sci. 81, 315–325 (1990)

    Article  Google Scholar 

  7. 7

    Paillard, D. The timing of Pleistocene glaciations from a simple multiple-state climate model. Nature 391, 378–381 (1998)

    ADS  Article  Google Scholar 

  8. 8

    Berger, A., Li, X. S. & Loutre, M. F. Modelling Northern Hemisphere ice-volume over the last 3 Ma. Quat. Sci. Rev. 18, 1–11 (1999)

    ADS  Article  Google Scholar 

  9. 9

    Paillard, D. & Parrenin, F. The Antarctic ice-sheet and the triggering of deglaciations. Earth Planet. Sci. Lett. 227, 263–271 (2004)

    ADS  CAS  Article  Google Scholar 

  10. 10

    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)

    ADS  Article  Google Scholar 

  11. 11

    Huybers, P. Glacial variability over the last two million years: an extended depth-derived age model, continuous obliquity pacing, and the Pleistocene progression. Quat. Sci. Rev. 26, 37–55 (2007)

    ADS  Article  Google Scholar 

  12. 12

    Huybers, P. Combined obliquity and precession pacing of late Pleistocene deglaciations. Nature 480, 229–232 (2011)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Ganopolski, A. & Calov, R. The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles. Clim. Past 7, 1415–1425 (2011)

    Article  Google Scholar 

  14. 14

    Imbrie, I. Z., Imbrie-Moore, A. & Lisiecki, L. E. A phase-space model for Pleistocene ice volume. Earth Planet. Sci. Lett. 307, 94–102 (2011)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Parrenin, F. & Paillard, D. Terminations VI and VIII (~530 and ~720 kyr BP) tell us the importance of obliquity and precession in the triggering of deglaciations. Clim. Past 8, 2031–2037 (2012)

    Article  Google Scholar 

  16. 16

    Ashwin, P. & Ditlevsen, P. The middle Pleistocene transition as a generic bifurcation on a slow manifold. Clim. Dyn. 45, 2683–2695 (2015)

    Article  Google Scholar 

  17. 17

    Shackleton, N. Oxygen isotope analyses and Pleistocene temperatures re-assessed. Nature 215, 15–17 (1967)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Shackleton, N. J. & Opdyke, N. D. Oxygen isotope and palaeomagnetic stratigraphy of equatorial Pacific core V28–238: oxygen isotope temperatures and ice volumes on a 105 and 106 year scale. Quat. Res. 3, 39–55 (1973)

    CAS  Article  Google Scholar 

  19. 19

    Past Interglacial Working Group of PAGES. Interglacials of the last 800,000 years. Rev. Geophys. 54, 162–219 (2016)

  20. 20

    Lisiecki, L. E. & Raymo, M. E. A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records. Paleoceanography 20, PA1003 (2005)

  21. 21

    Huybers, P. Early Pleistocene glacial cycles and the integrated summer insolation forcing. Science 313, 508–511 (2006)

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  22. 22

    Bounceur, N., Crucifix, M. & Wilkinson, R. D. Global sensitivity analysis of the climate–vegetation system to astronomical forcing: an emulator-based approach. Earth Syst. Dynam. 6, 205–224 (2015)

    ADS  Article  Google Scholar 

  23. 23

    Raymo, M. E. & Nisancioglu, K. The 41 kyr world: Milankovitch’s other unsolved mystery. Paleoceanography 18, PA2011 (2003)

  24. 24

    Shackleton, N. J., Berger, A. & Peltier, W. R. An alternative astronomical calibration of the lower Pleistocene timescale based on ODP Site 677. Trans. R. Soc. Edinb. Earth Sci. 81, 251–261 (1990)

    Article  Google Scholar 

  25. 25

    Raymo, M. E. The timing of major climate terminations. Paleoceanography 12, 577–585 (1997)

    ADS  Article  Google Scholar 

  26. 26

    Lang, N. & Wolff, E. W. Interglacial and glacial variability from the last 800 ka in marine, ice and terrestrial archives. Clim. Past 7, 361–380 (2011)

    Article  Google Scholar 

  27. 27

    MacAyeal, D. R. A catastrophe model of the paleoclimate. J. Glaciol. 24, 245–257 (1979)

    ADS  Article  Google Scholar 

  28. 28

    Birchfield, G. E., Weertman, J. & Lunde, A. T. A paleoclimate model of Northern Hemisphere ice sheets. Quat. Res. 15, 126–142 (1981)

    Article  Google Scholar 

  29. 29

    Pollard, D. A coupled climate-ice-sheet model applied to the Quaternary ice ages. J. Geophys. Res. Oceans 88, 7705–7718 (1983)

    ADS  Article  Google Scholar 

  30. 30

    Abe-Ouchi, A. et al. Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume. Nature 500, 190–193 (2013)

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  31. 31

    Bouttes, N. et al. Impact of oceanic processes on the carbon cycle during the last termination. Clim. Past 8, 149–170 (2012)

    Article  Google Scholar 

  32. 32

    Hodell, D. A. & Channell, J. T. Mode transitions in Northern Hemisphere glaciation: co-evolution of millennial and orbital variability in Quaternary climate. Clim. Past 12, 1805–1828 (2016)

    Article  Google Scholar 

  33. 33

    Lawrence, K. T., Sosdian, S., White, H. E. & Rosenthal, Y. North Atlantic climate evolution through the Plio-Pleistocene climate transitions. Earth Planet. Sci. Lett. 300, 329–342 (2010)

    ADS  CAS  Article  Google Scholar 

  34. 34

    Naafs, B. D. A. et al. Strengthening of North American dust sources during the late Pliocene (2.7 Ma). Earth Planet. Sci. Lett. 317–318, 8–19 (2012)

    ADS  Article  Google Scholar 

  35. 35

    Hodell, D. A. & Venz-Curtis, K. A. Late Neogene history of deepwater ventilation in the Southern Ocean. Geochem. Geophys. Geosyst. 7, Q09001 (2006)

    Article  Google Scholar 

  36. 36

    Lisiecki, L. E. Atlantic overturning responses to obliquity and precession over the last 3 Myr. Paleoceanography 29, 71–86 (2014)

    ADS  Article  Google Scholar 

  37. 37

    Shackleton, N. J. & Opdyke, N. D. Oxygen-isotope and paleomagnetic stratigraphy of Pacific core V28–239: late Pliocene to latest Pleistocene. Geol. Soc. Am. 145, 449–464 (1976)

    CAS  Google Scholar 

  38. 38

    Pisias, N. G. & Moore, T. C., Jr. The evolution of Pleistocene climate: a time series approach. Earth Planet. Sci. Lett. 52, 450–458 (1981)

    ADS  Article  Google Scholar 

  39. 39

    Ruddiman, W. F., Raymo, M. & McIntyre, A. Matuyama 41,000-year cycles: North Atlantic Ocean and Northern Hemisphere ice sheets. Earth Planet. Sci. Lett. 80, 117–129 (1986)

    ADS  CAS  Article  Google Scholar 

  40. 40

    Maasch, K. A. Statistical detection of the mid-Pleistocene transition. Clim. Dyn. 2, 133–143 (1988)

    Article  Google Scholar 

  41. 41

    Clark, P. U. et al. The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2 . Quat. Sci. Rev. 25, 3150–3184 (2006)

    ADS  Article  Google Scholar 

  42. 42

    Martínez-Garcia, A. et al. Southern Ocean dust–climate coupling over the past four million years. Nature 476, 312–315 (2011)

    ADS  Article  Google Scholar 

  43. 43

    McClymont, E., Sosdian, S. M., Rosell-Melé, A. & Rosenthal, Y. Pleistocene sea-surface temperature evolution: early cooling, delayed glacial intensification, and implications for the mid-Pleistocene climate transition. Earth Sci. Rev. 123, 173–193 (2013)

    ADS  CAS  Article  Google Scholar 

  44. 44

    Head, M. J. & Gibbard, P. L. Early–Middle Pleistocene transitions: linking terrestrial and marine realms. Quat. Int. 389, 7–46 (2015)

    Article  Google Scholar 

  45. 45

    Elderfield, H. et al. Evolution of ocean temperature and ice volume through the mid-Pleistocene climate transition. Science 337, 704–709 (2012)

    ADS  CAS  Article  Google Scholar 

  46. 46

    Ehlers, J., Gibbard, P. L. & Hughes, P. D. (eds) Quaternary Glaciations – Extent and Chronology. A Closer Look (Developments in Quaternary Sciences Vol. 15, Elsevier, 2011)

  47. 47

    Maslin, M. A. & Brierley, C. M. The role of orbital forcing in the Early Middle Pleistocene Transition. Quat. Int. 389, 47–55 (2015)

    Article  Google Scholar 

  48. 48

    Berger, W. H. & Jansen, E. in The Polar Oceans and Their Role in Shaping the Global Environment (eds Johannessen, O. M. et al.) 295–311 (Geophysical Monograph Series Vol. 84, American Geophysical Union, 1994)

    Google Scholar 

  49. 49

    Tziperman, E. & Gildor, H. On the mid-Pleistocene transition to 100-kyr glacial cycles and the asymmetry between glaciation and deglaciation times. Paleoceanography 18, 1001 (2003)

    ADS  Article  Google Scholar 

  50. 50

    Laskar, J. et al. A long-term numerical solution for the insolation quantities of the Earth. Astron. Astrophys. 428, 261–285 (2004)

    ADS  Article  Google Scholar 

  51. 51

    Shackleton, N. J. & Pisias, N. G. in The Carbon Cycle and Atmospheric CO2: Natural Variations Archean to Present (eds Sundquist, E. T & Broecker, W. S. ) 303–317 (Geophysical Monograph Series Vol. 32, American Geophysical Union, 1985)

    Google Scholar 

  52. 52

    Ninkovich, D. & Shackleton, N. J. Distribution, stratigraphic position and age of ash layer “L”, in the Panama Basin region. Earth Planet. Sci. Lett. 27, 20–34 (1975)

    ADS  Article  Google Scholar 

  53. 53

    Shackleton, N. J., Hall, M. A. & Pate, D. Pliocene stable isotope stratigraphy of Site 846. In Proc. Ocean Drilling Program, Scientific Results Vol. 138 (eds Pisias, N. G. et al.) 337–355 (Ocean Drilling Program, 1995)

    Google Scholar 

  54. 54

    Crucifix, M. Palinsol: insolation for palaeoclimate studies, R package version 0.93, https://bitbucket.org/mcrucifix/insol (2016)

  55. 55

    Chen, M.-H., Ibrahim, J. G. & Kim, S. Properties and implementation of Jeffreys’s prior in binomial regression models. J. Am. Stat. Assoc. 103, 1659–1664 (2008)

    MathSciNet  CAS  Article  PubMed  PubMed Central  Google Scholar 

  56. 56

    Robert, C. P. & Wraith, D. Computational methods for Bayesian model choice. AIP Conf. Proc. 1193, 251–262 (2009)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank D. A. Hodell, S. J. Crowhurst, M. A. Maslin, L. C. Skinner, L. Cannings and members of the PAGES Working Groups on Past Interglacials (PIGS) and Quaternary Interglacials (QUIGS) for discussions. P.C.T. acknowledges funding from a Leverhulme Trust Research Project Grant (RPG-2014-417). M.C. and T.M. acknowledge support from the Belgian Policy Office under contract BR/121/A2/STOCHCLIM. E.W.W. is funded under a Royal Society Research Professorship and M.C. is a senior research scientist with the Belgian National Fund of Scientific Research. This is a contribution to PAGES QUIGS.

Author information

Affiliations

Authors

Contributions

P.C.T. led the study and the writing of the paper with contributions from E.W.W., M.C. and T.M. M.C. and T.M. developed the methodology and performed the statistical analyses. E.W.W. led the development of the interglacial taxonomy. All authors contributed equally to the ideas in this paper.

Corresponding author

Correspondence to P. C. Tzedakis.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks D. Paillard and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Definition of interglacial onsets in LR04 and S05.

a, LR04 1,300–2,600 kyr bp (original record in black, detrended record in red). The linear trend over the period 1,500–2,600 kyr bp is removed in the detrended record (Methods). An interglacial onset is identified when the detrended value of δ18O falls below the lower threshold of 3.68‰ (upper dashed line) after once being above the higher threshold of 3.92‰ (lower dashed line) (Methods). b, LR04 record 0–1,300 kyr bp. c, S05 record 1,300–2,600 kyr bp (original record in black, detrended record in red). The linear trend over the period 1,500–2,600 kyr bp is removed in the detrended record (Methods). An interglacial onset is identified when the detrended value of δ18O falls below the lower threshold of 3.88‰ (upper dashed line) after once being above the higher threshold of 4.12‰ (lower dashed line) (Methods). d, S05 record 0–1,300 kyr bp. In all panels, the light blue circles indicate the first data point after the interglacial onset.

Extended Data Figure 2 Examples of classification of caloric summer insolation peaks based on the detrended LR04 record.

Shown are cases for which (i) the detrended δ18O′ is near a threshold, (ii) the insolation peak is classified as a continued interglacial, or (iii) the classification result is different between the LR04 and S05 records. Each panel shows changes in detrended δ18O′ (‰) of the LR04 record as a function of age (kyr bp). The timing of caloric summer insolation peaks is indicated by a vertical line at the centre of each panel. For each insolation peak, we seek an obvious minimum in the detrended δ18O′ that falls either just before, or within 10 kyr after, the insolation peak. An insolation peak is associated with an interglacial if the detrended δ18O′ minimum is below 3.68‰ (upper dashed line). The insolation peak associated with an interglacial is then classified as an interglacial onset if there is a detrended δ18O′ value higher than 3.92‰ (lower dashed line) between the current interglacial state and the previous interglacial state. Otherwise, it is classified as a continued interglacial. An insolation peak is associated with an interstadial if the obvious minimum in detrended δ18O′ does not pass the lower threshold of 3.68‰. See Supplementary Table 1 for details. Red, black and light blue labels indicate interglacial onsets, continued interglacials and interstadials, respectively. The labels above each panel correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 3 Examples of classification of caloric summer insolation peaks based on the detrended S05 record.

Shown are cases for which (i) the detrended δ18O′ is near a threshold, (ii) the insolation peak is classified as a continued interglacial, or (iii) the classification result is different between the LR04 and S05 records. Each panel shows changes in detrended δ18O′ (‰) of the S05 record as a function of age (kyr bp). The timing of caloric summer insolation peaks is indicated by a vertical line at the centre of each panel. For each insolation peak, we seek an obvious minimum in the detrended δ18O′ that falls either just before, or within 10 kyr after, the insolation peak. An insolation peak is associated with an interglacial if the detrended δ18O′ minimum is below 3.88‰ (upper dashed line). The insolation peak associated with an interglacial is then classified as an interglacial onset if there is a detrended δ18O′ value higher than 4.12‰ (lower dashed line) between the current interglacial state and the previous interglacial state. Otherwise, it is classified as a continued interglacial. An insolation peak is associated with an interstadial if the obvious minimum in detrended δ18O′ does not pass the lower threshold of 3.88‰. See Supplementary Table 1 for details. Red, black and light blue labels indicate interglacial onsets, continued interglacials and interstadials, respectively. The labels above each panel correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 4 Illustration of estimating times since previous deglaciation in the interval MIS 7e–5e.

Elapsed time is calculated as the interval from the caloric summer insolation peak nearest to the onset of an interglacial to an ensuing insolation peak, on the assumption that each peak could potentially have led to a complete deglaciation. The orange line shows the LR04 benthic δ18Ο stack20. The black line is the caloric summer half-year insolation at 65° N. The vertical dashed lines indicate the ages of insolation peaks nearest to the onsets of an interglacial. Elapsed times are indicated by double-headed arrows. The labels correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 5 Caloric summer half-year insolation peaks against time since the previous onset of an interglacial.

a, 1–1.5 Myr bp. b, 1.5–2.6 Myr bp. In b, the diagonal line separates insolation peaks associated with interglacial onsets (red circles) from those associated with continued interglacials (black diamonds) and interstadials (light blue triangles). The diagonal line is derived as the 50th percentile of having an interglacial onset in the statistical model calibrated over the past 2.6 Myr (Methods); the grey strip for 1.5–2.6 Myr bp indicates the 25th–75th percentiles. The slope of the diagonal line is 0.0021 ± 0.0001 GJ m−2 kyr−1. The labels on the data correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 6 Interglacials, continued interglacials and interstadials in relation to summer solstice mean daily insolation at 65° N over the past 2.6 Myr.

a, 1,980–2,660 kyr bp. b, 1,320–2,000 kyr bp. c, 660–1,340 kyr bp. d, 0–680 kyr bp. (Note age overlap between panels.) The orange line shows the LR04 benthic δ18Ο stack20. The black line is the summer solstice mean daily insolation at 65° N, calculated from the orbital solution of ref. 50 (Methods). Periods of above-average obliquity are shaded in grey. On the insolation curve, each peak is coded according to the classification in Supplementary Table 2: red circles, insolation maxima nearest to the onset of interglacials; black diamonds, continued interglacials; light blue triangles, interstadials; open symbols indicate uncertainty in the assignments. The vertical black lines represent the onset of interglacials, determined as the point at which the benthic isotope record crosses a threshold (Methods). Either MIS or ages of insolation peaks (kyr bp) are shown at the top of each panel for the onset of interglacials, or at the bottom of each panel for continued interglacials and interstadials.

Extended Data Figure 7 65° N summer solstice mean daily insolation peaks over the past 2.6 Myr.

Each insolation peak is plotted according to the classification as the onset of an interglacial (red circle), a continued interglacial (black diamond) or an interstadial (light blue triangle), as in Supplementary Table 2; open symbols correspond to uncertain assignments. The labels on the data correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 8 65° N summer solstice mean daily insolation peaks against time since the onset of the previous interglacial.

a, 0–1 Myr bp. The diagonal line represents a possible threshold (567.5 − 0.575 × (elapsed time)) that separates insolation peaks associated with the interglacial onsets (red circles) from peaks associated with interstadials (light blue triangles) and a continued interglacial (black diamond), with fewest failures (MIS 11c and 979 kyr bp). b, 1.5–2.6 Myr bp. Inset, 1–1.5 Myr bp. The labels on the data correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 9 Effective energy at each summer solstice mean daily insolation peak over the past 2.6 Myr.

The effective energy is defined in equation (1), with a discount rate of 0.575 W m−2 kyr−1 estimated from Extended Data Fig. 8a. Each insolation peak is plotted according to the classification as the onset of an interglacial (red circles), a continued interglacial (black diamonds) or an interstadial (light blue triangles), as in Supplementary Table 2; open symbols correspond to uncertain assignments. The horizontal dashed line is a possible threshold for a complete deglaciation (567.5 W m−2 over the past 1 Myr), which separates insolation peaks associated with interglacial onsets (red circles) from the others, with one false negative (MIS 11c) and one false positive (979 kyr bp). The labels on the data correspond to either MIS or ages of insolation peaks (kyr bp).

Extended Data Figure 10 Estimation of the timing of the Early Pleistocene ramp in the deglaciation threshold.

Histogram obtained by Monte Carlo sampling of the posterior distributions (25,000 samples) of the parameters of the logistic regression model for the onset of interglacials, using a ramp function as described in Methods. Shown is the timing of the onset versus the end of the ramp function, as displayed in Fig. 5.

Supplementary information

Supplementary Tables

This file contains Supplementary Tables 1 and 2. (XLSX 21 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tzedakis, P., Crucifix, M., Mitsui, T. et al. A simple rule to determine which insolation cycles lead to interglacials. Nature 542, 427–432 (2017). https://doi.org/10.1038/nature21364

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.