Multi-link network modeling of water resource systems: identifying critical linkages driving resilience dynamics

Under changing environmental conditions, river basins face increasing water scarcity and heightened ecological vulnerability, posing greater challenges to water security. The resilience of water resource systems is recognized as offering a novel research perspective and analytical approach for addressing water security issues. The resilience of water resource systems is affected by numerous factors with significant cascading effects. Multi-link network approaches quantitatively capture the complex interrelationships among these factors, offering a scientific basis for effective management and improved water security. In this study, the Fenhe River Basin is selected as the study area to construct a multi-link network centered on hydrometeorological, socioeconomic, and engineering regulation links. The PCMCI algorithm is employed to quantify causal strengths among indicators within this complex network across different time lags, revealing the intertwined interactions, dynamic transmission patterns, and complex nonlinear relationships of the system. Based on the principle of multivariate transfer entropy, key links and critical transmission pathways underlying the evolution of water resource system resilience are identified. The role and effect of these key links on system resilience are analyzed, providing a quantitative assessment of their influence on the overall resilience of the water resource system. The results indicated that: (1) Total water resources, the proportion of secondary industry, and domestic water use indicators have the highest causal connection strengths among the links in the multi-link network of the water resources system; (2) The normalized transfer entropy values of hydrometeorological and socioeconomic links were found to be essentially comparable, whereas the engineering regulation link exhibited the highest normalized transfer entropy value for water resource system resilience. This indicates that the engineered regulation link constitutes the key link driving the evolution of water resource system resilience.