Quantifying resilience and the risk of regime shifts under strong correlated noise [Quantifizierung der Resilienz und des Risikos von Regimeshifts unter dem Einfluss von stark korreliertem Rauschen]

Heßler, Martin; Kamps, Oliver

Zusammenfassung

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations. Significance Statement: Commonly proposed statistical early warning measures are scarcely applicable to realistic problems in which limited data availability, coarse-grained sampling and strong correlated noise are typical. Even under favourable simulation conditions they are difficult to interpret due to their qualitative nature, slight trend changes or too-late-increase for policymakers to avoid undesired consequences. Not only in ecology or climate science the development of a robust quantitative resilience measure would be of great importance to guide decision-making processes. Therefore, we propose a novel quantitative measure of resilience, which is system comparable to some extent and outperforms the common indicators under strong correlated noise. It is easy-to-interpret because of credibility intervals and exhibits trends early enough for decision makers to intervene successfully.