Abstract/Summary

Tipping events in dynamical systems have been studied in many contexts, often modelled by the decay of critical modes, system states which are tending towards bifurcation, characterised by increased return times to stable equilibria. Temporal scaling properties of time series data can be used to detect the presence of a critical mode by estimating the decay rate, and indicators of changes in these properties may therefore be used to provide an early warning signal (EWS) for an impending tipping event. The lag-1 autocorrelation function (ACF(1)) indicator and the detrended fluctuation analysis (DFA) indicator have previously been used in such a way; in this paper we introduce a novel scaling indicator based on the decay rate of the power spectrum (PS). We compare the ACF(1), DFA- and PS-indicators using artificial data; data from a model which includes a bifurcation point; and sea-level pressure data along the paths of 14 tropical cyclones. By using the PS-indicator with such data, we show that the new indicator may be used to provide an EWS in a context where the ACF(1)- and DFA-indicators fail.