Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

TL;DR

This paper explores different mechanisms of climate tipping points, including bifurcation, noise-induced, and a novel rate-dependent type where rapid changes can cause abrupt shifts without bifurcations or noise.

Contribution

It introduces and demonstrates the concept of rate-dependent tipping (R-tipping) in climate models, expanding understanding beyond traditional bifurcation and noise-induced tipping.

Findings

All three tipping types can occur in simple climate models.

Rapid parameter changes can cause tipping without bifurcations or noise.

Rate-dependent tipping poses risks even in stable climate states.

Abstract

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to "tip" or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.