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A simple rule to determine which insolation cycles lead to interglacials

Nature volume 542, pages 427–432 (2017)Cite this article

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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.

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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.

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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.

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Authors and Affiliations

  1. Department of Geography, Environmental Change Research Centre, University College London, London, UK

    P. C. Tzedakis

  2. Université catholique de Louvain, Earth and Life Institute, Georges Lemaître Centre for Earth and Climate Research, Louvain-la-Neuve, Belgium

    M. Crucifix & T. Mitsui

  3. Department of Earth Sciences, University of Cambridge, Cambridge, UK

    E. W. Wolff

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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.

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Correspondence to P. C. Tzedakis.

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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.

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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

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