Causality Inference: A Comparison of Two Methods with Application to North Atlantic Oscillation and Rainfall in Greece

Abstract In various scientific fields, including climate science, earth science, and hydrology, there is great interest in methods of causal inference. Such methods aim to identify relations of cause and effect between potential drivers and responses based on the available data (typically time series). The recently proposed method of Liang–Kleeman information flow rate (LIFR) has potential advantages for large datasets and nonlinear interactions. However, performance comparisons of LIFR with established causal inference methods are lacking. This paper begins to address this gap in the literature by comparing LIFR with the standard method of Wiener–Granger causality (WGC). LIFR is formulated on the basis of entropy exchange between components of an interacting system and can be estimated by means of data-driven measures. WGC, on the other hand, models an ensemble of time series by means of vector autoregressive models. This work first studies the causal relations in a simulated, bivariate Ornstein–Uhlenbeck linear system using both LIFR and WGC. Next, it investigates the presence of a causal link between the North Atlantic Oscillation index and the monthly rainfall amount in two cases: one is based on reanalysis data for two areas of Greece and the other on ground measurements from the island of Crete (Greece). While the analysis of the linear system shows that LIFR and WGC perform similarly and accurately detect the connectivity of the system, the analysis of the interaction between the North Atlantic Oscillation index and rainfall data by both methods reveals surprises.