Quantitative Comparison of Causal Inference Methods for Climate Tipping Points

Abstract. Causal inference methods present a statistical approach to the analysis and reconstruction of dynamic systems as observed in nature or in experiments. Climate tipping points are likely present in several core components of the Earth system, such as the Greenland ice sheet or the Atlantic Meridional Overturning Circulation (AMOC), and are characterized by an abrupt and irreversible degradation under sustained global temperatures above their corresponding thresholds. Causal inference methods may provide a promising way to study the interactions of climate tipping elements, which are currently highly uncertain due to limitations in model-based approaches. However, the data-driven analysis of climate tipping elements presents several challenges, e.g., with regard to nonlinearity, delayed effects and confoundedness. In this study, we quantify the accuracy of three commonly used multivariate causal inference methods with regard to these challenges and find unique advantages of each method: The Liang–Kleeman Information Flow is preferable in simple settings with limited data availability, the Peter–Clark Momentary Conditional Independence (PCMCI) provides the most control, e.g., to integrate expert knowledge, and the Granger Causality for State Space Models is advantageous for large datasets and delayed interactions. In general, data sampling intervals should be aligned with the interaction delays, and the inclusion of a confounder (like global temperatures) is crucial to deal with the nonlinear response to (climate) forcing. Based on these findings and given their data masking capabilities, we apply the LKIF and PCMCI methods to reanalysis data to detect tipping point interactions between the AMOC and Arctic summer sea ice, which imply a bidirectional stabilizing interaction, in agreement with physical mechanisms. Our results therefore contribute robust evidence to the study of interactions of the AMOC and the cryosphere.