An early warning indicator for tipping in a strongly forced system

Classical critical slowing down early warning signals (observing increasing trends in the autocorrelation and variance) have been developed to try and detect when a system is approaching a tipping point, typically represented mathematically by a bifurcation.  However, these signals often fail for strongly forced slow systems. Here we propose a new method that reconstructs the quasi-equilibrium state and therefore produces a robust indication of where the critical threshold may lie in a system.

We show that the variance of this reconstructed quasi-equilibrium state increases exponentially ahead of its critical threshold, at time tcrit, for both strongly forced fast and slow systems. Using both the reconstructed quasi-equilibrium state and the inverse of its variance allows us to diagnose the location of the critical threshold for a strongly forced, slow system which has passed the critical threshold but not yet tipped, and where classical critical slowing down indicators often fail.