Bayesian analysis of early warning signals using a time-dependent model

Abstract. A tipping point is defined by the IPCC as a critical threshold beyond which a system reorganizes, often abruptly and/or irreversibly. Tipping points can be crossed solely by internal variation in the system or by approaching a bifurcation point where the current state loses stability, which forces the system to move to another stable state. It can be shown that before a bifurcation point is reached there are observable changes in the statistical properties of the state variable. These are known as early warning signals and include increased fluctuation and autocorrelation time. It is currently debated whether or not Dansgaard–Oeschger (DO) events, which are abrupt warmings of the North Atlantic region which occurred during the last glacial period, are preceded by early warning signals. To express the changes in statistical behavior we propose a model based on the well-known first-order autoregressive (AR) process, with modifications to the autocorrelation parameter such that it depends linearly on time. In order to estimate the time evolution of the autocorrelation parameter we adopt a hierarchical Bayesian modeling framework, from which Bayesian analysis can be performed using the methodology of integrated nested Laplace approximations. We then apply the model to segments of the oxygen isotope ratios from the Northern Greenland Ice Core Project record corresponding to 17 DO events. Statistically significant early warning signals are detected for a number of DO events, which suggests that such events could indeed exhibit signs of ongoing destabilization and may have been caused by approaching a bifurcation point. The methodology developed to perform the given early warning analyses can be applied more generally and is publicly available as the R package INLA.ews.