Benchmarking Conditioners in Liang–Kleeman Information Flow: Application to Land–Atmosphere Interactions

Abstract. 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 (ΔIF) and introduce several quantifiers, including Mediator Dominance Index, Moderation Gain, Confounding 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)). We find that the influence of SM on LAI remains consistently direct and stable, 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 mediators. These results demonstrate that bivariate and multivariate LKIF can yield markedly different conclusions across time and space, especially under compound environmental stress. This highlights the need for multivariate conditioning when assessing vegetation responses.