Abrupt climate change as rate-dependent cascading tipping point

Abstract. We propose a conceptual model comprising a cascade of tipping points as a mechanism for past abrupt climate changes. In the model, changes in a control parameter, which could for instance be related to changes in the atmospheric circulation, induce sequential tipping of sea-ice cover and the ocean's meridional overturning circulation. The ocean component, represented by the well-known Stommel box model, is shown to display so-called rate-induced tipping. Here, an abrupt resurgence of the overturning circulation is induced before a bifurcation point is reached due to the fast rate of change of the sea-ice. During the rate-induced transition, the system is attracted by the stable manifold of a saddle. This results in a significant delay of the tipping if the system spends longer periods of time in the vicinity of the saddle before escaping towards the alternative state of a vigorous overturning circulation. The delay opens up the possibility for an early warning of the impending abrupt transition by detecting the change in linear stability. We propose early warning by estimating properties of the Jacobian from the noisy time series, which are shown to be useful as a generic precursor to detect rate-induced tipping.