Detecting hydrological connectivity using causal inference from time series: synthetic and real karstic case studies

We investigate the potential of causal inference methods (CIMs) to reveal hydrological connections from time series. Four CIMs are selected from two criteria, linear or nonlinear and bivariate or multivariate. A priori, multivariate, and nonlinear CIMs are best suited for revealing hydrological connections because they fit nonlinear processes and deal with confounding factors such as rainfall, evapotranspiration, or seasonality. The four methods are applied to a synthetic case and a real karstic case study. The synthetic experiment confirms our expectation: unlike the other methods, the multivariate nonlinear framework has a low false-positive rate and allows for ruling out a connection between two disconnected reservoirs forced with similar effective precipitation. However, for the real case study, the multivariate nonlinear method was unstable because of the uneven distribution of missing values affecting the final sample size for the multivariate analyses, forcing us to cope with the results' robustness. Nevertheless, if we recommend a nonlinear multivariate framework to reveal actual hydrological connections, all CIMs bring valuable insights into the system's dynamics, making them a cost-effective and recommendable comparative tool for exploring data. Still, causal inference remains attached to subjective choices, operational constraints, and hypotheses challenging to test. As a result, the robustness of the conclusions that the CIMs can draw always deserves caution, especially with real, imperfect, and limited data. Therefore, alongside research perspectives, we encourage a flexible, informed, and limit-aware use of CIMs without omitting any other approach that aims at the causal understanding of a system.