A model to identify causality for geographic patterns

Identifying causal relationships is essential for understanding the mechanisms through which natural and anthropogenic factors interact within Earth systems. However, in spatial cross-sectional data, the absence of temporal ordering poses significant challenges to traditional causal inference methods. This study proposes a novel Geographical Pattern Causality (GPC) model to detect positive, negative, dark causality and its strength between variables in spatial data. Grounded in dynamical systems theory and generalized embedding principles, the method transforms spatial neighbourhoods into lagged sequences, reconstructs the phase space, and compares symbolic trajectories to assess predictability and consistency in pattern changes—thereby inferring both the direction and type of causality. Case studies demonstrated that, compared to correlation analysis and Linear Non-Gaussian Acyclic Model (LiNGAM), the GPC model could reveal latent causal relationships among weakly correlated variables in geographical systems and capture diverse causal patterns. Despite limitations, such as sensitivity to noise and potential biases from proxy variables, the GPC model provides a novel framework for causal inference based on spatial observations, and it advances both the methodological and theoretical development of causality analysis in complex geographical systems.