Systematic identification of causal relations in high-dimensional chaotic systems: application to stratosphere-troposphere coupling

Abstract

Obtaining reliable causal inference is crucial for understanding the climate system. Convergent Cross Mapping (CCM), a recently developed method to infer causal relationships from time series has been shown to be superior to previous methods which are based on linearity assumptions. However, CCM has so far been only tested on low-dimensional or bivariate models, while real-world systems, like the climate system, are high-dimensional and have many more interacting variables. Here, we demonstrate that standard CCM cannot reliably infer causal relations in high-dimensional chaotic systems. However, by using a hierarchy of conceptual models and observational data we show that time-lagged CCM reliably identifies causal relationships in contrast to standard CCM and Pearson correlation. Furthermore, we systematically demonstrate that time-lagged CCM is able to identify long-distance causal interactions. Moreover, we apply time-lagged CCM to detect causal relations in stratosphere-troposphere coupling, and demonstrate the downward causal chain induced by polar vortex activity.