Evaluating the skill of a geometric early warning for tipping in a rapidly forced nonlinear system

The future behavioural fate of a forced nonlinear system may at times depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the system to a basin boundary of a future behaviour and small changes in the forcing can lead to drastically different behaviours. This sensitivity may be present only for a limited time when the forcing is most rapidly changing and so we investigate a geometric early warning to evaluate whether we are in such a sensitive state. This involves computing an approximation of the R-tipping edge state which is a dynamic state that requires knowledge of the future behaviour of the forcing.  We contrast this with early warnings of bifurcation-induced tipping, where an assumption of slow variation of forcing is needed. We provide an example of early prediction of future state for a 3-box model of the Atlantic Meridional Overturning Circulation (AMOC) with specified rapid forcing and show that the skill compares favourably with a simple threshold approach.