Estimating time-dependent structures in a multi-variate causality for land-atmosphere interactions

Abstract The land surface and atmosphere interaction forms an integral part of the climate system. However, this intricate relationship involves many complicated interactions and feedback effects between multiple variables. As a result, relying solely on traditional linear regression analysis and correlation analysis to distinguish between multi-variate complex ‘driver-response’ relations can be challenging, since they do not have the needed asymmetry to establish causality. The Liang-Kleeman (LK) information flow theory provides a strict non-parametric causality measurement for identifying the causality between any given time series, and its recent extension from bivariate to multi-variate form provides a powerful tool for causal inference in complex multi-variate systems. However, the multi-variate LK information flow also assumes stationarity in time and requires a sufficiently long time series to ensure statistical sufficiency. To remedy this challenge, we rely on the square root Kalman filter to estimate the time-varying form of the multi-variate LK information flow causality. The results from theoretical and real-world applications show that the new algorithm provides a valuable tool for characterizing time-varying causal relationships in land-atmosphere interactions, even when the time series are short and highly correlated.