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 and forces the system to move to another stable state. It is currently debated whether or not Dansgaard-Oeschger (DO) events, abrupt warmings occurring during the last glacial period, are noise-induced or caused by the system reaching a bifurcation point. 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 correlation time. To express this behaviour we propose a new model based on the well-known first order autoregressive process (AR), with modifications to the correlation parameter such that it depends linearly on time. In order to estimate the time evolution of the correlation 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. Early warning signals were detected and found statistically significant for a number of DO events, suggesting that such events could indeed be 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.