Inferring causal associations in hydrological systems: A comparison of methods

Abstract Many research issues in hydrological systems are intrinsically causal, aiming to determine whether and how one factor affects another. Although causal inference methods have been applied more or less in hydrology, there still remains a lack of systematic comparison between different methods. Here, four popular methods in the causal inference community, including the cross-correlation function (CCF), convergent cross mapping (CCM), transfer entropy (TE), and a causal network learning algorithm (PCMCI+) were selected, with a detailed explanation of their basic principles and underlying assumptions. Next, the performances of these methods were evaluated in large sample tests and sensitivity analysis using synthetic time series generated by a conceptual hydrological model with two predesigned causal structures. Then, the four methods were applied in two real-world cases to further understand their characteristics. The findings show the superior performance of the PCMCI + method in synthetic cases and a commendable level of interpretability in real cases, thus warranting its broader application in hydrological systems. The limitations of the other three methods, especially in effectively addressing confounding and mediating factors, led to several unreasonable causal links. Furthermore, the emergence of conflicting results among different methods in real-world applications underscores the necessity for a multifaceted understanding based on their particular assumptions and constraints. A comprehensive application of diverse methods according to the specific issue is encouraged for the robustness of conclusions, with their assumptions clearly stated in advance. Overall, our research reveals the potential and limitations of different causal inference methods in comprehension of complex interactions within hydrological systems, serving as a useful guide for their further prosperity in hydrology.