Predictability of tipping points with rate-dependent effects

Due to non-linearities in the dynamics of crucial elements in the climate system, Earth’s safe operating space is limited. Beyond a certain level of a control parameter, such as the atmospheric Greenhouse gas concentration, qualitative regime shifts in one or more sub-systems may take place. Additionally, theoretical studies suggest that abrupt, irreversible change can happen already prior to the crossing of a critical threshold in a control parameter.

In these so-called rate-induced transitions, the effective parameter level to induce tipping depends on the rate of change, or more generally the precise trajectory of the changing control parameter. Here we show rate-induced tipping points of the overturning circulation in a global ocean model. Due to the chaotic dynamics of the system, whether there will be tipping or not depends both on the rate and initial conditions in a very sensitive, non-smooth way. This raises questions about whether the safe operating space is still well-defined, and whether an approach of its boundary can be predicted.

For tipping points associated with slow passages across a bifurcation, generic early-warning signals have been developed for these purposes. Due to the necessarily fast parameter changes involved in rate-induced tipping, early-warning is more challenging. In many cases the tipping involves a saddle escape, which results in a delay of the actual transition and can be exploited for early-warning. Here this is demonstrated in the context of low-dimensional models. While due to the sensitivity of the dynamics around the saddle one might not be able to predict with certainty whether and when the system will tip, the indicators presented here may allow issuing a warning as the system gets close to tipping.