Limits of large deviation theory in predicting transition paths of climate tipping events

Abstract

Following Hasselmann’s ansatz, the climate system may be viewed as a multistable dynamical system internally driven by noise. Its long-term evolution will then feature noise-induced critical transitions between the competing attracting states. In the weak-noise limit, large deviation theory allows predicting the transition rate and most probable transition path of these tipping events. However, the limit of zero noise is never obtained in reality. In this work we show that, even for weak finite noise, sample transition paths may disagree with the large deviation prediction – the minimum action path, or instanton – if multiple timescales are at play. We illustrate this behavior in selected box models of the bistable Atlantic Meridional Overturning Circulation (AMOC), where different restoring times of temperature and salinity induce a fast-slow characteristic. While the minimum action path generally crosses the basin boundary at a saddle point, we demonstrate cases in which ensembles of sample transition paths cross far away from the saddle. We discuss the conditions for saddle avoidance and relate this to the flatness of the quasipotential, a central object of large deviation theory. We further probe the vicinity of the weak-noise limit by applying a pathspace method that generates transition samples for arbitrarily weak noise. Our results highlight that predictions by large deviation theory must be treated cautiously in multiscale dynamical systems.