Climate tipping as a noisy bifurcation: a predictive technique

• Published in: IMA Journal of Applied Mathematics
• Main Authors: Thompson, J.M., Sieber, J.
• Language: unknown
• Published: Oxford University Press for Institute of Mathematics and its Applications 2010
• Subjects: climate tipping; slow passage through saddle-node bifurcation; time-series analysis; ice core
• Online Access: http://hdl.handle.net/10036/3853; https://doi.org/10.1093/imamat/hxq060

This is an electronic version of an article published in IMA Journal of Applied Mathematics, Vol. 76 (1), pp. 27-46. Copyright © 2012 Institute of Mathematics and its Applications Copyright © The Author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 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.