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Critical transitions occur when a system undergoes a sudden shift from one state to another. Early warning signals (EWS) are indicators that can be used to potentially anticipate critical transitions in such systems, which may be temporal or spatio-temporal. Temporal systems are those whose state varies over time, whereas spatio-temporal systems also vary over a spatial domain. While temporal EWS can be applied to spatio-temporal systems by averaging over the spatial domain, spatially-informed EWS should, in principle, be able to outperform their temporal counterparts by making use of the additional spatial information. We seek to understand how EWS for spatial systems compare to those used for temporal systems. To facilitate comparison, we explore how EWS performance is measured. We use the strength of EWS trends, quantified using Kendall's τ, as a proxy for performance. Other factors, such as robustness to choices of parameters used for detrending, statistical significance, and agreement with expected EWS behaviour, are considered. This assessment of EWS based on these factors enables an informed comparison and decision regarding which signals to apply to different systems for potential indications of critical transitions. We find that while spatially-informed EWS generally offer improved performance over temporal EWS for the example systems studied, we find the choice is system specific.
Robinson et al. (Mon,) studied this question.