Quantifying the Strength and Delay of Climatic Interactions: The Ambiguities of Cross Correlation and a Novel Measure Based on Graphical Models

Abstract Lagged cross-correlation and regression analysis are commonly used to gain insights into interaction mechanisms between climatological processes, in particular to assess time delays and to quantify the strength of a mechanism. Exemplified on temperature anomalies in Europe and the tropical Pacific and Atlantic, the authors study lagged correlation and regressions analytically for a simple model system. A strong dependence on the influence of serial dependencies or autocorrelation is demonstrated, which can lead to misleading conclusions about time delays and also obscures a quantification of the interaction mechanism. To overcome these possible artifacts, the authors propose a two-step procedure based on the concept of graphical models recently introduced to climate research. In the first step, graphical models are used to detect the existence of (Granger) causal interactions that determine the time delays of a mechanism. In the second step, a certain partial correlation and a regression measure are introduced that allow one to specifically quantify the strength of an interaction mechanism in a well interpretable way that enables the exclusion of misleading effects of serial correlation as well as more general dependencies. The potential of the approach to quantify interactions between two and more processes is demonstrated by investigating teleconnections of ENSO and the mechanism of the Walker circulation. The article is intended to serve as a guideline to interpret lagged correlations and regressions in the presence of autocorrelation and introduces a powerful approach to analyze time delays and the strength of an interaction mechanism.