Bayesian identification of early warning signals for long-range dependent climatic time series

TL;DR

This paper introduces a Bayesian method to detect early warning signals in long-range dependent climatic time series, effectively accounting for noise and trends to improve detection accuracy.

Contribution

It develops a flexible Bayesian framework using fractional Gaussian noise models with time-varying Hurst exponents for better early warning detection in climate data.

Findings

Detected early warning signals in Atlantic multidecadal variability index

Did not find early warnings in Dansgaard-Oeschger paleoclimate records

Demonstrated robustness of the method through extensive simulations

Abstract

Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points. However, these indicators are sensitive to observational noise, long-term mean trends, and long-memory dependence, all of which are prevalent in climatic time series. Such effects can easily obscure genuine signals or generate spurious detections. To address these challenges, we employ a flexible Bayesian framework for modelling time-varying autocorrelation in long-range dependent time series, also accounting for time-varying variance. The approach uses a mixture of two fractional Gaussian noise processes with a time-dependent weight function to represent fractional Gaussian noise with a time-varying Hurst exponent. Inference is performed via integrated nested Laplace approximation, enabling joint estimation of mean trends and handling of irregularly sampled observations. The strengths and limitations of detecting changes in the autocorrelation is investigated in extensive simulations. Applied to real climatic data sets, we find evidence of early warning signals in a reconstructed Atlantic multidecadal variability index, while dismissing such signals for paleoclimate records spanning the Dansgaard-Oeschger events.