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

Abstract The future behavioural fate of a forced nonlinear system can depend sensitively on how it is forced, and on natural fluctuations within the system. This is especially the case if there is rate-induced tipping, where small changes in the forcing can lead to drastically different eventual behaviours. This sensitivity may be present only for a limited period of time, for example, when the forcing is changing most rapidly. We extend a recently proposed geometric early warning that can measure when a system is in such a sensitive state. We show how to compute the signed distance to an approximate R-tipping threshold, which we refer to as the R-tipping indicator. The R-tipping threshold is a dynamic state that embeds knowledge of the system and future behaviour of the forcing. As an example, we consider early prediction of the final state for a 3-box model of the Atlantic Meridional Overturning Circulation (AMOC) with specified and rapid forcing. For this model, we give a method to approximate the R-tipping indicator and estimate its skill in forecasting the eventual state of the system, even when the forcing is still underway. The skill of the geometric early warning based on the R-tipping indicator compares favourably to thresholds based on state variables or critical slowing down.