Spatiotemporal Causal Effect Estimation in Complex Dynamical Systems

Causal Inference is essential for identifying and quantifying causal relationships in systems where randomized controlled experiments are infeasible, but the high dimensionality and co-variability structure of spatiotemporal dynamical systems such as the climate system pose special challenges for causal effect estimation. It is standard for climate scientists to reduce the dimension of their data with pre-processing procedures such as regional means and principal component analysis, but taking a regional mean may mask differences in spatial pattern – such as the difference between Eastern Pacific and Central Pacific El Niño events – that may be relevant for causal relationships. Similarly, principal component analysis may obscure true causal relationships because the spatial pattern associated with maximum co-variability may not be the causally relevant information. Instead of using these preprocessing techniques, the basic procedure of time series causal effect estimation can be simply extended to multivariate time series, but this introduces new complications and heightens already existing complications of time series causal effect estimation. Here, we discuss these complications and present practical solutions. Complications for multi-variate as well as univariate time series include: (1) neighboring points in time and space may be very similar if the scale of the spatiotemporal sampling rate is small relative to the characteristic scale of the variance, resulting in unstable estimations, (2) the do-calculus expression for estimating the response to a hard intervention may include calculations with spatiotemporal gradients so strong they would result in instabilities in the system, and finally, (3) it is often not possible to actually perform a hard intervention in dynamical systems, making the interpretation of the causal effect unclear. The first complication may be addressed using L2 regularization, and the second and third complications may be addressed by focusing on soft interventions of reasonable magnitude that approach zero on their spatiotemporal boundaries. A unique complication of multi-variate causal effect estimation is that, when using L2 regularization, the total causal influence of a climate variable will be penalized inverse-proportionally to the number of spatial datapoints. This complication can be addressed by scaling variables so that the total spatiotemporal variance, rather than the component-wise variance, is one. We showcase the power of the technique by quantifying the spatiotemporal causal effect of El Niño-related sea surface temperature variability on atmospheric pressure variability in the North Atlantic in unforced Community Earth System Model simulations. We demonstrate that spatiotemporal causal effect estimation allows us to simultaneously determine the relevant spatial patterns and more accurately quantify a pattern-dependent causal effect between ENSO and NAO that has thus far proven difficult to measure in observational studies.