Abrupt climate change as a rate-dependent cascading tipping point

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. Because of the multi-scale nature of the climate system, this type of tipping cascade may also be a risk concerning future global warming. The relatively short timescales involved make it challenging to detect these tipping points from observations. However, with our conceptual model we find that there can be a significant delay in the tipping because the system is attracted by the stable manifold of a saddle during the rate-induced transition before escaping towards the undesired state. This opens up the possibility for an early warning of the impending abrupt transition via detection of the changing linear stability in the vicinity of the saddle. To do so, we propose estimating the Jacobian from the noisy time series. This is shown to be a useful generic precursor to detect rate-induced tipping.