### Abstract

Original language | English |
---|---|

Pages (from-to) | 27-46 |

Number of pages | 20 |

Journal | IMA Journal of Applied Mathematics |

Volume | 76 |

Issue number | 1 |

Early online date | 13 Dec 2010 |

DOIs | |

Publication status | Published - Feb 2011 |

### Fingerprint

### Keywords

- climate tipping
- slow passage through saddle-node bifurcation
- time series analysis

### Cite this

*IMA Journal of Applied Mathematics*,

*76*(1), 27-46. https://doi.org/10.1093/imamat/hxq060

**Climate tipping as a noisy bifurcation : a predictive technique.** / Thompson, John M. T.; Sieber, Jan.

Research output: Contribution to journal › Article

*IMA Journal of Applied Mathematics*, vol. 76, no. 1, pp. 27-46. https://doi.org/10.1093/imamat/hxq060

}

TY - JOUR

T1 - Climate tipping as a noisy bifurcation

T2 - a predictive technique

AU - Thompson, John M. T.

AU - Sieber, Jan

PY - 2011/2

Y1 - 2011/2

N2 - It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case, we present a scheme of analysis that determines the best stochastic fit to the existing data. This provides the evolution rate of the effective control parameter, the variation of the stability coefficient and the path itself and its tipping point. By assessing the actual effective level of noise in the available time series, we are then able to make probability estimates of the time of tipping. This new technique is applied, first, to the output of a computer simulation for the end of greenhouse Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state with ice caps. Second, we use the algorithms to give probabilistic tipping estimates for the end of the most recent glaciation of the Earth using actual geological ice-core data.

AB - It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case, we present a scheme of analysis that determines the best stochastic fit to the existing data. This provides the evolution rate of the effective control parameter, the variation of the stability coefficient and the path itself and its tipping point. By assessing the actual effective level of noise in the available time series, we are then able to make probability estimates of the time of tipping. This new technique is applied, first, to the output of a computer simulation for the end of greenhouse Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state with ice caps. Second, we use the algorithms to give probabilistic tipping estimates for the end of the most recent glaciation of the Earth using actual geological ice-core data.

KW - climate tipping

KW - slow passage through saddle-node bifurcation

KW - time series analysis

U2 - 10.1093/imamat/hxq060

DO - 10.1093/imamat/hxq060

M3 - Article

VL - 76

SP - 27

EP - 46

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 1

ER -