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Influence of external forcings on abrupt millennial-scale climate changes: a statistical modelling study

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Abstract

The last glacial period was punctuated by a series of abrupt climate shifts, the so-called Dansgaard–Oeschger (DO) events. The frequency of DO events varied in time, supposedly because of changes in background climate conditions. Here, the influence of external forcings on DO events is investigated with statistical modelling. We assume two types of simple stochastic dynamical systems models (double-well potential-type and oscillator-type), forced by the northern hemisphere summer insolation change and/or the global ice volume change. The model parameters are estimated by using the maximum likelihood method with the NGRIP \(\hbox {Ca}^{2+}\) record. The stochastic oscillator model with at least the ice volume forcing reproduces well the sample autocorrelation function of the record and the frequency changes of warming transitions in the last glacial period across MISs 2, 3, and 4. The model performance is improved with the additional insolation forcing. The BIC scores also suggest that the ice volume forcing is relatively more important than the insolation forcing, though the strength of evidence depends on the model assumption. Finally, we simulate the average number of warming transitions in the past four glacial periods, assuming the model can be extended beyond the last glacial, and compare the result with an Iberian margin sea-surface temperature (SST) record (Martrat et al. in Science 317(5837): 502–507, 2007). The simulation result supports the previous observation that abrupt millennial-scale climate changes in the penultimate glacial (MIS 6) are less frequent than in the last glacial (MISs 2–4). On the other hand, it suggests that the number of abrupt millennial-scale climate changes in older glacial periods (MISs 6, 8, and 10) might be larger than inferred from the SST record.

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Notes

  1. The thresholds are set to \(y=\pm 0.4\) to be able to count the lowest interstadial event with \(y\sim 0.5\) (GI-4 in Rasmussen et al. (2014)) and the highest stadial event with \(y\sim -0.7\) (GS-22 in the same). These thresholds yield total 26 warming transitions during 11–100 ka BP. Similar criteria are used in (Alley et al. 2001; Ditlevsen et al. 2005).

  2. Schulz et al. (2002) assume that the North Atlantic THC is controlled by the freshwater flux anomaly (runoff from ice sheets) in proportion to the ice volume itself, referring to Marshall and Clarke (1999). However, in other studies, the freshwater flux is related to the loss of the ice volume (Knutti et al. 2004; Jackson et al. 2010).

  3. The 20-year average NGRIP \(\hbox {Ca}^{2+}\) record provided in Seierstad et al. (2014) has 26 missing values during 11–100 ka BP, which represent 0.6 % of the 4451 data points. We just interpolate them linearly for simplicity.

  4. The average period between successive warming transitions under stochastic noise is not determined by the eigenfrequency of the equilibrium point for the deterministic case. For the case of model A with \(F_\text{ext}=0\), the former period is \(\sim\)1700 years but the latter period is \(\sim\)1000 years.

  5. For instance, the time intervals between two subsequent data points are \(\sim\)170 year on average (with maximum 650 year) during the past 100 ka BP, but they are \(\sim\)480 year on average (with maximum 1640 year) during 100–400 ka BP.

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Acknowledgments

We thank P. Ditlevsen, H. Goosse, M. Van Ginderachter, D. Kondrashov, and E. W. Wolff for helpful comments and suggestions. This work is supported by the Belgian Federal Science Policy Office under contract BR/12/A2/STOCHCLIM. MC is research scientist with the Belgian National Fund of Scientific Research.

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  1. Earth and Life Institute, Georges Lemaître Centre for Earth and Climate Research, Université catholique de Louvain, BE-1348, Louvain-la-Neuve, Belgium

    Takahito Mitsui & Michel Crucifix

  2. Belgian National Fund of Scientific Research, Rue d’Egmont, 5, BE-1000, Brussels, Belgium

    Michel Crucifix

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Mitsui, T., Crucifix, M. Influence of external forcings on abrupt millennial-scale climate changes: a statistical modelling study. Clim Dyn 48, 2729–2749 (2017). https://doi.org/10.1007/s00382-016-3235-z

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