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Climate tipping as a noisy bifurcation: a predictive technique

Presented by: 
M Thompson & J Sieber [Cambridge and Portsmouth Universities]
Wednesday 25th August 2010 - 10:00 to 11:00
INI Seminar Room 1
Session Title: 
Tipping points
In the first half of this contribution (speaker JMTT) we review the bifurcations of dissipative dynamical systems. The co-dimension-one bifurcations, namely those which can be typically encountered under slowly evolving controls, can be classified as safe, explosive or dangerous. Focusing on the dangerous events, which could underlie climate tippings, we examine the precursors (in particular the slowing of transients) and the outcomes which can be indeterminate due to fractal basin boundaries. It is often known, from modelling studies, that a certain mode of climate tipping is governed by an underlying bifurcation. For the case of a so-called fold, a commonly encountered bifurcation (of the oceanic thermohaline circulation, for example), we estimate (speaker JS) how likely it is that the system escapes from its currently stable state due to noise before the tipping point is reached. Our analysis is based on simple normal forms, which makes it potentially useful whenever this type of tipping is identified (or suspected) in either climate models or measurements. Drawing on this, we suggest 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 (parabolic) variation of the stability coefficient, 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. In this vein, we examine, first, 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 archaeological ice-core data.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons