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Catastrophic regime shifts in complex natural systems may be averted throughadvanced detection. Recent work has provided a proof-of-principle that manysystems approaching a catastrophic transition may be identified through thelens of early warning indicators such as rising variance or increased returntimes. Despite widespread appreciation of the difficulties and uncertaintyinvolved in such forecasts, proposed methods hardly ever characterize theirexpected error rates. Without the benefits of replicates, controls, orhindsight, applications of these approaches must quantify how reliabledifferent indicators are in avoiding false alarms, and how sensitive they areto missing subtle warning signs. We propose a model based approach in order toquantify this trade-off between reliability and sensitivity and allowcomparisons between different indicators. We show these error rates can bequite severe for common indicators even under favorable assumptions, and alsoillustrate how a model-based indicator can improve this performance. Wedemonstrate how the performance of an early warning indicator varies indifferent data sets, and suggest that uncertainty quantification become a morecentral part of early warning predictions.

Quantifying Limits to Detection of Early Warning for Critical Transitions