The role of edge states for early-warning of tipping points

TL;DR

This paper explores how unstable edge states can be used to identify early-warning signals of tipping points in high-dimensional systems, with applications demonstrated in climate models and dynamical systems.

Contribution

It introduces a novel approach to detect relevant observables for early-warning signals by analyzing the unstable edge states in complex systems.

Findings

Edge states help identify variables with critical slowing down.

The method is demonstrated on climate model simulations of AMOC collapse.

Edge states provide a predictive tool for tipping points in high-dimensional systems.

Abstract

Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations away from a reference attractor as the TP is approached. But for high-dimensional systems it is not obvious which variables or observables would display the critical dynamics and carry CSD. Many variables may display no CSD, or show changes in variability not related to a TP. It is thus helpful to identify beforehand which observables are relevant for a given TP. Here we propose this may be achieved by knowledge of an unstable edge state that separates the reference from an alternative attractor that remains after the TP. This is because stochastic fluctuations away from the reference attractor are preferentially directed towards the edge state along a most likely path (the instanton). As the TP is approached the edge state and reference attractor typically become closer, and the fluctuations can evolve further along the instanton. This can be exploited to find observables with substantial CSD, which we demonstrate using conceptual dynamical systems models and climate model simulations of a collapse of the Atlantic Meridional Overturning Circulation (AMOC).