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

2026-02-10

AI Summary

Traditional early warning signals in climate time series are often compromised by noise, trends, and long-range dependence, leading to false positives or missed detections. This work proposes a flexible Bayesian framework that models time-varying autocorrelation and variance through a mixture of two fractional Gaussian noise processes, while incorporating a time-varying Hurst exponent to capture dynamic signatures preceding critical transitions. The approach effectively distinguishes genuine early warning signals from spurious ones, accommodates irregularly sampled data, and enables computationally efficient inference via integrated nested Laplace approximation (INLA). When applied to reconstructed indices of Atlantic multidecadal variability, the method successfully identifies significant early warning signals and concurrently rules out false alarms in records of Dansgaard–Oeschger events.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Graphical Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• early warning signals
• long-range dependence
• climatic time series
• critical transitions
• tipping points

Innovation

• Bayesian framework
• long-range dependence
• time-varying Hurst exponent
• fractional Gaussian noise
• early warning signals