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On the Stochastic Nature of the Rapid Climate Shifts during the Last Ice Age

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  • 1 Centre for Ice and Climate, The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
  • | 2 Department of Mechanical Engineering, Technical University of Denmark, Lyngby, Denmark
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Abstract

The rapid climate shifts observed in the glacial climate are analyzed. The transitions into the warm interstadial states, the onsets, are easily identifiable in the record. The distribution of waiting times between consecutive onsets is well fitted, assuming that the remaining residence time in each state is independent of the past. This implies that it has a simple no-memory exponential waiting time distribution, but with the mean waiting time depending on the climate state. The mean waiting time from one onset to the next is around 2400 yr. The most likely (maximum likelihood) distribution derived solely from the onset sequence is rather insensitive to the mean waiting time in the warm interstadials in the range of 400–1200 yr. When extending the analysis to include the transitions from the warm interstadials to the cold stadials observed with a larger uncertainty, the distributions in the two states are well fitted to exponential distributions, with mean waiting times of around 800 yr in the warm state and around 1600 yr in the cold state. This observation is an important piece in the climate puzzle, because the fact that the climate is a no-memory process indicates that the transitions are noise induced and the mean residence time in one state indicates how stable that climate state is to perturbations. The possibility of a hidden periodic driver is also investigated. The existence of such a driver cannot be ruled out by the relatively sparse data series (containing only 21 onsets). However, because the record is fitted just as well by the much simpler random model, this should be preferred from the point of view of simplicity.

Corresponding author address: Peter D. Ditlevsen, Centre for Ice and Climate, The Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, Copenhagen DK-2100, Denmark. Email: pditlev@gfy.ku.dk

Abstract

The rapid climate shifts observed in the glacial climate are analyzed. The transitions into the warm interstadial states, the onsets, are easily identifiable in the record. The distribution of waiting times between consecutive onsets is well fitted, assuming that the remaining residence time in each state is independent of the past. This implies that it has a simple no-memory exponential waiting time distribution, but with the mean waiting time depending on the climate state. The mean waiting time from one onset to the next is around 2400 yr. The most likely (maximum likelihood) distribution derived solely from the onset sequence is rather insensitive to the mean waiting time in the warm interstadials in the range of 400–1200 yr. When extending the analysis to include the transitions from the warm interstadials to the cold stadials observed with a larger uncertainty, the distributions in the two states are well fitted to exponential distributions, with mean waiting times of around 800 yr in the warm state and around 1600 yr in the cold state. This observation is an important piece in the climate puzzle, because the fact that the climate is a no-memory process indicates that the transitions are noise induced and the mean residence time in one state indicates how stable that climate state is to perturbations. The possibility of a hidden periodic driver is also investigated. The existence of such a driver cannot be ruled out by the relatively sparse data series (containing only 21 onsets). However, because the record is fitted just as well by the much simpler random model, this should be preferred from the point of view of simplicity.

Corresponding author address: Peter D. Ditlevsen, Centre for Ice and Climate, The Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, Copenhagen DK-2100, Denmark. Email: pditlev@gfy.ku.dk

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