Zhao, Yiyang, Ma, Enze, Zhou, Zhaoqiang, Zou, Yiguang, Cao, Zhaodan, Cai, Hejiang, Li, Ci, Yan, Yuhan, and Chen, Yan
Soil moisture‐Precipitation (SM‐P) coupling, especially the causality from SM to P (SM → P), is an important and highly debated topic. The causal inference from observational data provides a statistical approach for this issue, where the experimental research is infeasible. Various causal inference methods exist, each assuming distinct underlying systems for the targeted variables: pure stochastic or deterministic dynamic system (DDS), which means that these methods detect different types of causality: separable or non‐separable. Acknowledging the inherent deterministic dynamic nature of SM‐P coupling, this study employs a DDS‐based method: Convergent Cross‐mapping (CCM), to detect their non‐separable causality. Centering around SM‐P coupling, we also detect the causality between SMs in shallow and deeper layers, and the causality between evapotranspiration (ET) and SMs in all layers. Notably, before applying CCM, a preconditional procedure is required: verifying the DDS nature of targeted variables P, SM, and ET. Key findings of this research include: (a) In SM‐P coupling, only SMs in shallow layers but not deeper layers could render causalities toward P, while P renders causalities toward SMs in all layers. (b) The time‐delay of causality from SM1 to P in spring/summer is around 4–6 days, and that from P to SM1 is around 2–4 days. (c) Inside SMs, shallow SMs have obvious causalities downwards to deeper SMs, but deeper SMs seem harder to render causalities upwards to shallow SMs, explaining why they hardly render causalities to P. In summary, this study furnishes an indispensable DDS‐based complement to stochastic‐based methodologies for SM‐P coupling. Plain Language Summary: This study aims to investigate the causal interaction between soil moisture (SM) and precipitation (P), especially the impact from SM toward P, based on their observational data (i.e., time series), as experimental approaches are impractical given their large‐scale complex physical mechanisms. Many methods exist in the realm of causal detection, either assuming a stochastic underlying system or a deterministic dynamic system (DDS) for the targeted variables. In stochastic systems, causal interactions among variables are separable, whereas they are non‐separable in DDSs. Given that SM‐P coupling seems aligning with the description of a DDS, we employ a DDS‐based method: Convergent Cross‐mapping (CCM), to detect the non‐separable causality between SM and P. Specifically, we explore whether causality exists both from SM to P (SM → P, SM in different layers) and from P to SM (P → SM), and if so, what is the causal response time and how long could the causality last. Meanwhile, the causalities among SMs in different layers, and those between SMs and evapotranspiration (ET), are also detected. Through these inquiries, our findings highlight the DDS nature of SM‐P coupling and their non‐separable causality, underscoring the indispensable role of CCM as a complement to previous stochastic‐based studies for SM‐P coupling. Key Points: Soil moisture‐Precipitation (SM‐P) coupling is detected by Convergent Cross‐mapping (CCM) to investigate their non‐separable causalityThe deterministic dynamic system nature of SM‐P coupling is verified, as a precondition for applying CCM to detect their causalityWhile P could causally impact SMs in all layers; in turn, however, only shallow SMs but not deeper SMs could causally impact P [ABSTRACT FROM AUTHOR]