Coherence resonance and stochastic tipping points in climate dynamics

A crucial aspect currently under debate in climate dynamics is whether abrupt climate transitions (such as the glacial terminations and Dansgaard-Oeschger events on the millennial time scale, the Kuroshio Extension bimodal variability on a decadal time scale, etc.) are the result of a tipping point (TP) being exceeded, in which case precursors may be identified, or if they are rather excited by fast noise dynamics. In this context, a case study based on a low-order double-gyre excitable ocean model shows that the TPs of a deterministic, dissipative dynamical system leading to relaxation oscillations (ROs) may have limited physical meaning if the system is perturbed by noise. In this case the transition to ROs occurs via the coherence resonance (CR) mechanism in a parameter range (in which the system is excitable) preceding the deterministic TP. We thus extend the concept of TP so as to incorporate the effect of noise in a single stochastic parameter, the stochastic TP (STP), which identifies abrupt transitions in the corresponding random dynamical system. STPs are shown to anticipate substantially the deterministic TPs in a significant range of noise parameters. The implications concerning the possibility that early warning signals can be detected from climate time series if CR occurs are finally discussed.