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• Complexity & Statistics: Tipping Points & Crashes

Web page

http://www.rss.org.uk/main.asp?page=1321&event=1186

Categories

Climate, Complex Systems

Submitter

Petrina Butler

https://www.jiscmail.ac.uk/cgi-bin/filearea.cgi?LMGT1=ENVSTAT&a=get&f=/meet_1010.html

There is much interest in the possibility of detecting and predicting critical changes in complex systems. Climate tipping points, earthquakes and financial crashes are three examples. A variety of techniques for tackling these challenges are being developed by physicists, mathematicians and statisticians, but their success is still a matter for debate. This meeting brings together researchers and practitioners from several disciplines to present and discuss their ideas about this important topic, and aims to stimulate further interest and advances in the field.

Parallels between earthquake prediction, financial crash prediction and epileptic seizure predictions DIDIER SORNETTE (ETH Zurich)

Climate tipping as a noisy bifurcation: a predictive technique MICHAEL THOMSON (University of Cambridge/University College London) and JAN SIEBER (University of Portsmouth)

Change point detection using the informational approach with applications in atmospheric sciences CLAUDIE BEAULIEU (Princeton University)

Title TBA VALERIE LIVINA (University of East Anglia)

Markovian predictive, and conceivably causal representations of stochastic processes COSMA SHALIZI (Carnegie Mellon University/Santa Fe Institute)

A Royal Statistical Society meeting sponsored by

Industrial Mathematics Knowledge Transfer Network ktn.innovateuk.org/web/mathsktn

Cambridge Centre for Risk Studies, University of Cambridge Judge Business School www.risk.jbs.cam.ac.uk

Registration

Please use the booking form to register.

Meeting Contact

Chris Ferro, University of Exeter (C.A.T.Ferro@exeter.ac.uk)

Nick Watkins, British Antarctic Survey (nww@bas.ac.uk)

Organising Group

Environmental Statistics Section

ABSTRACTS

DIDIER SORNETTE - Parallels between earthquake prediction, financial crash prediction and epileptic seizures predictions TBA

MICHAEL THOMPSON and JAN SIEBER Climate tipping as a noisy bifurcation: a predictive technique In the first half of this contribution 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 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.

COSMA SHALIZI Markovian, predictive, and conceivably causal representations of stochastic processes Basically any stochastic process can be represented as a random function of a homogeneous, measured-valued Markov process. The Markovian states are minimal sufficient statistics for predicting the future of the original process. This has been independently discovered multiple times since the 1970s, by researchers in probability, dynamical systems, reinforcement learning and time series analysis, under names like "the measure-theoretic prediction process", "epsilon machines", "causal states", "observable operator models", and "predictive state representations". I will describe the mathematical construction and information-theoretic properties of these representations, touch briefly on their reconstruction from data, and finally consider under what conditions they may allow us to form causal models of dynamical processes.

VALERIE LIVINA Applying degenerate fingerprinting in studying climate tipping points Recently, Held and Kleinen employed lag-1 autocorrelation for detection of bifurcation in the modelled collapse of termohaline circulation in CLIMBER2 model [1]. Following their approach, we developed an alternative method based on Detrended Fluctuation Analysis (DFA) to monitor short-term correlations in fluctuations after removal of trends which may affect autocorrelations [2]. In addition, we consider lag-1 autocorrelation after removal of local linear trend. In these three techniques we calculate so-called “propagators”: ACF-propagator, ACF-propagator with trend removal and DFA-propagator. Noticeable trend of propagators towards critical value 1 indicates approaching of bifurcation or transition. Comparing ACF-propagators with and without trend removal allows us to detect the subsets of data affected by simple trends, and the DFA-propagator provides information about possible growing effects of short-term memory that may result in nonstationary behaviour of time series and lead to a bifurcation. Combined together, the techniques help distinguish between transitions and genuine bifurcations and allow us to study climate tipping points.

Ditlevsen and Johnsen [3] analysed autocorrelation and variance of GRIP ice-core data and concluded that Dansgaard-Oeschger (DO) events were noise-induced jumps between system double-well-potential. This kind of abrupt transitions may be unpredictable [4], providing no early warning signal of approaching a tipping point, but in the case of combined increase of autocorrelation and increase of memory effects, the early warning using degenerate fingerprinting is possible. Moreover, in systems with memory (autocorrelation exponent gamma less than 1), monitoring only ACF/DFA-propagators without monitoring variance is sufficient for bifurcation detection.

We apply propagator techniques to various artificial datasets and recorded climatic time series and discuss detected transitions and bifurcations in the context of the main tipping points described in [5].

Held and Kleinen, GRL 2004 Livina and Lenton, GRL 2007 Ditlevsen and Johnsen, GRL 2010 Livina, Ditlevsen and Lenton, submitted Lenton et al, PNAS 2008

CLAUDIE BEAULIEU Change point detection using the informational approach with applications in atmospheric sciences A change point in a time series can be viewed as a time point at which the parameters of a statistical distribution or a statistical model change. Most change point detection techniques were developed to identify the most likely time for a shift and to test whether or not this shift occurred by comparing the model with a shift to a simpler model without a shift. Change points can be observed in a wide variety of fields (e.g. economy, social sciences and climate). Change point methods have been applied to climate time series to detect artificial or natural discontinuities and regime shifts.

Most change point approaches were designed to detect a specific type of shift: a change in the mean, in the variance, in both the mean and the variance or in the parameters of a regression model, but not to discriminate between several types of changes. Furthermore, most change point methods make the hypothesis that the residuals are independent, but the presence of autocorrelation is a common feature of climate time series (especially at short time scales). If not taken into account in the analysis, the presence of positive autocorrelation can lead to the detection of false shifts. Several studies have started to take into account a first order autoregressive model in change point detection. The autocorrelation structure in climate time series can often be explained by the El Nino Southern Oscillation or by climate forcings such as volcanic eruptions and solar irradiance. These covariate effects can be integrated in the model to determine whether change points remain when taking them into account.

In this work, the informational approach is used to discriminate between several types of changes (shifts in the mean, shifts in the variance, shift in the trend, shift in the relation with covariate effects or a combination of these different types of changes) by fitting a hierarchy of models. The autocorrelation structure is identified in each model (not restricted only to a first order autoregressive model) and integrated in the analysis. The usefulness of this approach to detect change points in atmospheric CO2 concentration, in the growth rate of atmospheric CO2 and in the sources and sinks of atmospheric CO2 is demonstrated through applications.