Climate tipping as a noisy bifurcation: a predictive technique

John M. T. Thompson, Jan Sieber

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)27-46
Number of pages20
JournalIMA Journal of Applied Mathematics
Volume76
Issue number1
Early online date13 Dec 2010
DOIs
Publication statusPublished - Feb 2011

Fingerprint

Climate
Ice
Bifurcation
Earth (planet)
Greenhouse
Greenhouses
Estimate
Control Parameter
Time series
Fold
Computer Simulation
Path
Output
Computer simulation
Coefficient
Modeling
Cap

Keywords

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

Cite this

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

In: IMA Journal of Applied Mathematics, Vol. 76, No. 1, 02.2011, p. 27-46.

Research output: Contribution to journalArticle

Thompson, John M. T. ; Sieber, Jan. / Climate tipping as a noisy bifurcation : a predictive technique. In: IMA Journal of Applied Mathematics. 2011 ; Vol. 76, No. 1. pp. 27-46.
@article{0abe62d3373c44f7b07470078413dbc7,
title = "Climate tipping as a noisy bifurcation: a predictive technique",
abstract = "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.",
keywords = "climate tipping, slow passage through saddle-node bifurcation, time series analysis",
author = "Thompson, {John M. T.} and Jan Sieber",
year = "2011",
month = "2",
doi = "10.1093/imamat/hxq060",
language = "English",
volume = "76",
pages = "27--46",
journal = "IMA Journal of Applied Mathematics",
issn = "0272-4960",
publisher = "Oxford University Press",
number = "1",

}

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 -