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

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.

Figures (9)

• Figure 1: Simulated realization from \ref{['eq:model']} illustrating the weighted sum of two fGns having Hurst exponents $H_1 = 0.6$ (left) and $H_2 = 0.8$ (middle), giving a process with time-varying autocorrelation (right).
• Figure 2: Mapping (solid line) between the Hurst exponent and the weight function found by minimizing the KLD between an fGn and the proposed model component in \ref{['eq:model']} with $H_1 = 0.6$ and $H_2 = 0.8$.
• Figure 3: Upper panels: Posterior mean estimates for the probabilities $\hat{p} = P(H_2-H_1>0\mid \boldsymbol{y})$ for time series generated by \ref{['eq:model']} having length $n=200$ (left), $n = 500$ (middle) and $n = 1000$ (right). The number of simulations for each $n$ is 2000 and the horizontal lines correspond to $\hat{p} = 0.95$. Lower panels: Kendall's $\tau_K$ for local Hurst exponents of the same series, estimated in sliding windows of length $n/4$. The horizontal lines correspond to the $5\%$ upper quantiles of the test statistic $\tau_K$, assuming a null hypothesis of $H_1 = H_2 = 0.75$.
• Figure 4: Estimated ROC for the binary classification problem predicting the sign of $H_2 - H_1$ for time series of length $n=1000$ (black), $n=500$ (blue) and $n = 200$ (red). Classification using the posterior probabilities $\hat{p}$ (left) and $\tau_K$ for sliding window estimates of the Hurst exponent with window length $n/4$ (right).
• Figure 5: The reconstructed AMV given by michel:22 for the period 850 - 1987. The vertical lines denote changepoints in variance and the series analysed correspond to the time period of 1235 - 1931.