Chaotic Kramers' Law: Hasselmann's Program and AMOC Tipping

TL;DR

This paper extends Kramers' law to bistable systems driven by chaotic dynamics, demonstrating its applicability to climate models like the AMOC and discussing its limitations and implications for understanding climate tipping points.

Contribution

It introduces a chaotic Kramers' law for bistable systems with chaotic forcing, applicable beyond the stochastic limit, and applies it to a climate model of the AMOC.

Findings

Chaotic forcing can induce transitions similar to noise-driven cases.

Chaotic Kramers' law holds even far from the stochastic limit.

Insights into AMOC collapse and recovery dynamics.

Abstract

In bistable dynamical systems driven by Wiener processes, the widely used Kramers' law relates the strength of the noise forcing to the average time it takes to see a noise-induced transition from one attractor to the other. We extend this law to bistable systems forced by fast chaotic dynamics, which we argue is in some cases a more realistic modeling approach than unbounded noise forcing. Transitions similar to the noise-driven case can only occur if the amplitude of the chaotic forcing is large enough. If this is the case, in our numerical example - a reduced-order model of the Atlantic Meridional Overturning Circulation (AMOC) - we observe the chaotic Kramers' law to hold even when the chaotic forcing is far from the stochastic limit. We discuss the limitations of the chaotic Kramers' law, how to address the numerical issues associated with the timescale separation, and give a possible explanation for the dynamics of recently found AMOC collapses and recoveries in complex climate models.