Comparing deterministic and stochastic methods to infer causal Earth system interactions

In an era often referred to as 'the Great Acceleration', it is becoming increasingly urgent to identify causal structures in intertwined Earth system processes. This has led to the development of a wide range of causal inference methods that aim to accurately distinguish causal influences from pure correlation. Many of the established tools fall within two methodological families: state-space approaches, which reconstruct deterministic dynamics, and information-theoretic approaches, which are formulated for coupled stochastic processes. Despite their widespread use, clear guidance on the conditions under which these different approaches are appropriate, and on the associated trade-offs, remains fragmented.

Here, we present a systematic comparison of two representatives from these methodologically different backgrounds. We focus on convergent cross mapping, a deterministic approach, and transfer entropy, a stochastic approach. Both are commonly used for identifying and quantifying interactions in the Earth system from time series data. We assess their performance using (i) synthetic coupled systems with a known causal structure and (ii) real-world meteorological data on the Walker circulation, for which there exists an established physical understanding that can be used as a benchmark. Furthermore, we evaluate the impact of typical challenges related to the data (e.g. observation length, noise) and the underlying dynamics (e.g. latent drivers, causal delay) on detection ability and reliability, and test the sensitivity of the results to initial configuration choices.

Through this work, our aim is to provide a practical workflow and a set of recommendations that clarify the strengths, limitations, and potential synergies of these two conceptually distinct approaches. Finally, we outline and discuss potential use cases in current Earth system research.