Detecting hotspots of atmosphere–vegetation interaction via slowing down – Part 1: A stochastic approach

An analysis of so-called early warning signals (EWS) is proposed to identify the spatial origin of a sudden transition that results from a loss in stability of a current state. EWS, such as rising variance and autocorrelation, can be indicators of an increased relaxation time (slowing down). One particular problem of EWS-based predictions is the requirement of sufficiently long time series. Spatial EWS have been suggested to alleviate this problem by combining different observations from the same time. However, the benefit of EWS has only been shown in idealised systems of predefined spatial extent. In a more general context like a complex climate system model, the critical subsystem that exhibits a loss in stability (hotspot) and the critical mode of the transition may be unknown. In this study we document this problem with a simple stochastic model of atmosphere–vegetation interaction where EWS at individual grid cells are not always detectable before a vegetation collapse as the local loss in stability can be small. However, we suggest that EWS can be applied as a diagnostic tool to find the hotspot of a sudden transition and to distinguish this hotspot from regions experiencing an induced tipping. For this purpose we present a scheme which identifies a hotspot as a certain combination of grid cells which maximise an EWS. The method can provide information on the causality of sudden transitions and may help to improve the knowledge on the susceptibility of climate models and other systems.