Unraveling ocean-atmosphere coupled variability with causal methods: transfer entropy and information flow

Causal questions are fundamental to scientific pursuit. The study of causality and its applications has followed a nonlinear trajectory, shaped by diverse methodological developments and debates about their interpretations. Here, we unravel the evolution of these approaches, from Judea Pearl’s formal framework of causal inference to methods based on the reduction of informational surprise, multivariate probability, and dynamical systems. Although principled causal inference ideally relies on Pearl’s framework, its application is often unfeasible. Instead, methods grounded in information theory, combined with prior knowledge of the system, are widely used to assist in the causal inference process. Recent advances include nonlinear, higher-order information-theoretic approaches. These methods are increasingly applied in Earth and climate sciences to address questions such as the causes of extreme events and global warming, or to explore the mutual influences between the ocean and atmosphere in driving the climate system. A key unresolved question concerns the nature of this interaction. Does atmospheric weather drive the ocean, does the ocean steer the atmosphere, or does a coupled mode of variability govern the system? In this context, we investigate the reciprocal influences of ocean and atmosphere using a low-order coupled ocean-atmosphere model that includes realistic thermal and mechanical coupling. By applying Transfer Entropy and the Liang-Kleeman Information Flow, we analyze the dynamical directions within the coupled system. We uncover the directed dynamics of information exchange, adding insight on the emergence of low-frequency variability in the atmosphere. These results offer a new perspective on interannual and decadal-scale climate prediction.