Benchmarking conditioners in Liang–Kleeman Information Flow: application to land–atmosphere interactions in humid forests

The Liang–Kleeman Information Flow (LKIF) framework has been increasingly used to identify causality in Earth–system dynamics in recent years. Yet, uncertainties remain regarding how the causal graph changes when mediators and confounders (conditioners) are introduced, i.e., divergence between the bivariate and conditioned forms. A controlled synthetic experiment shows that LKIF preserves correct causal directions under hidden confounding, while differences between bivariate and multivariate estimates still occur. We characterize these differences using time-varying LKIF and introduce several quantifiers, including Conditioner Dominance Index, Moderation Gain, Conditioning Pressure, and Convergence Rate, to evaluate the contributions of conditioners. This is illustrated in an application to soil moisture (SM) and vapor pressure deficit (VPD) couplings with vegetation (leaf area index (LAI) and gross primary productivity (GPP)) in humid forest regions of Southeast China and the Amazon Basin, using satellite-derived and reanalysis data over 1981–2018. We find that the influence of SM on LAI remains consistently stable and shows little sensitivity to the selected conditioners, whereas its influence on GPP and that of VPD on vegetation exhibit substantial divergence between bivariate and multivariate estimates. This divergence peaks under compound dry–hot conditions, with VPD and temperature emerging as dominant conditioners. These results demonstrate that bivariate and multivariate LKIF can yield markedly different conclusions across time and space, especially under compound environmental stress. More importantly, even for the same variables in a causal graph, the same conditioners can affect the temporal evolution of the causal relationships very differently at different locations. This highlights how stationary assumptions may oversimplify causal structure by masking relevant temporal transitions, particularly under compound environmental stress.