Detecting Critical Slowing Down under the influence of continuous-time Red Noise

Abstract

The observational research of tipping elements in the climate system relies largely on time series analysis via so-called Early Warning Signals. An upward trend in the estimated variance or lag-1 autocorrelation of the observable may be a sign for Critical Slowing Down (CSD), a phenomenon exhibited during the destabilization a system’s fixed point. This approach has been employed extensively both for assessing contemporary tipping risks [1] and understanding the dynamics in the advent of past abrupt climate change [2]. However, this inference of destabilization from statistical observations is in general only valid under certain model assumptions with regard to both the deterministic dynamics and the stochastic component (noise). While the assumption of additive white noise is the most canonical approach to representing unresolved dynamics, it has long been understood that certain variabilities in the climate system exhibit correlation and persistence [3]. In this case, trends in the above indicators should no longer be attributed solely to CSD, since they may also be rooted in possibly changing correlation characteristics of the driving noise. While there has been progress in the development of indicators for discrete-time models incorporating correlated noise [4], the task of assessing discrete-time data from continuous-time models has not received as much attention. We present a simple linearly restoring stochastic model with red noise as its driving force and discuss possible avenues of estimating system stability from time series data through the autocorrelation structure and power spectral density of the observable. We quantitatively compare these methods to conventional Early Warning Signals, highlighting the potential pitfalls of the latter in this setting. [1] Boers, N. (2021). Observation-based early-warning signals for a collapse of the Atlantic Meridional Overturning Circulation. Nature Climate Change 11[2] Rypdal, M. (2016). Early-Warning Signals for the Onsets of Greenland Interstadials and the Younger Dryas–Preboreal Transition, Journal of Climate, 29(11)[3] Mann, M.E., Lees, J.M. (1996). Robust estimation of background noise and signal detection in climatic time series. Climatic Change 33[4] Rodal, M., Krumscheid, S., Madan,G. , LaCasce, J.H., and Vercauteren, N. (2022). Dynamical stability indicator based on autoregressive moving-average models: Critical transitions and the Atlantic meridional overturning circulation, Chaos 32