Granger PCA: Extracting Granger-causal patterns in climate fields

Statistical causality methods are becoming increasingly widespread in climate teleconnection analysis, but they typically require a prior reduction of high-dimensional, multivariate climate fields. Most common aggregation techniques, such as spatial averaging or Principal Component Analysis (PCA) (largely known as Empirical Orthogonal Functions, EOF, in the climate community) [1], are not designed to preserve causal structure and can mask spatially complex or low-variance causal signals.

We introduce Granger PCA [2], a novel dimensionality reduction method that explicitly extracts components that are influenced by a causal driver. Instead of maximizing variance, Granger PCA identifies spatial patterns whose associated time series are maximally Granger caused by an external variable, such as a large-scale climate mode. This is achieved by optimizing spatial weights to maximize the Granger causality F-statistic and yields a low-dimensional representation that captures the Granger causal information present in the field.

The method is particularly effective in cases where causal effects are spatially heterogeneous, have low variance, or are hidden by strong local autocorrelation. In such cases, variance-based methods can fail even when robust causal influence exists.

We apply Granger PCA to several teleconnection problems, including the influence of the North Atlantic Oscillation on precipitation and the impact of ENSO on vegetation variability. Granger PCA recovers physically interpretable patterns that are not captured by PCA or correlation-based approaches.

In summary, Granger PCA provides a simple and interpretable framework for causally oriented dimensionality reduction and offers a new tool for teleconnection analysis in climate science.

References

• [1] A. Hannachi, I. T. Jolliffe, D. B. Stephenson et al., “Empirical orthogonal functions and related techniques in atmospheric science: A review,” International Journal of Climatology, vol. 27, no. 9, pp. 1119–1152, 2007.
• [2] G. Varando, M.-Á. Fernández-Torres, J. Muñoz-Marí, and G. Camps-Valls, “Learning causal representations with Granger PCA,” in UAI 2022 Workshop on Causal Representation Learning, 2022.