Estimating Time-Dependent Structures in a Multivariate Causality for Land–Atmosphere Interactions

Abstract

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 multivariate 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 nonparametric causality measurement for identifying the causality between any given time series, and its recent extension from bivariate to multivariate form provides a powerful tool for causal inference in complex multivariate systems. However, the multivariate 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 multivariate 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. Significance Statement Causality in land–atmosphere interactions is generally characterized by seasonal and intraseasonal changes that are usually not captured with commonly used approaches, because most approaches assume the time series are stationary. In this study, we extend the recently proposed multivariate Liang–Kleeman information flow causality (MtvLK) to handle nonstationary systems such as those in land–atmosphere interactions. By considering nonstationarity, we aim to unravel time-varying causal structures that are usually masked out in commonly used methods. Validating the MtvLK with synthetic models showed that the MtvLK is able to obtain the expected causal structures. Furthermore, real-world applications reveal novel findings of the time-varying causal structures between soil moisture, vapor pressure deficit, and the gross primary product.