Seeking a pathway towards a more sustainable human-water relationship by coupled model - From a perspective of socio-hydrology.

It is essential to systematically consider social, economic, and natural endowments in managing and allocating water resources. However, few studies have comprehensively quantitatively evaluated the allocation of regional water resources from a socio-hydrology perspective and provided recommendations. To explore this research gap, we have constructed a tightly coupled framework that integrates system dynamics models and optimization algorithms to carry out an innovative redistribution of water resources in Shaanxi Province. The system dynamics model simulation results showed that the error was almost always within 10% over the research period, indicating robust simulation capability and laying a solid foundation for subsequent model coupling. The coupled model achieves convergence in approximately 30 generations by formulating the optimization problem with four individual objectives. Optimizing four objectives concurrently results in convergence around the 150th generation. The optimized Pareto solution sets visually demonstrate the trade-offs between different objectives. In the optimized water allocation schedule, the water consumption in Yulin exhibits a change of 1.22 ×10m, reflecting the most significant optimization effects on agricultural and domestic water allocation. The results indicated that the comprehensive Gini coefficient typically ranged between 0.2 and 0.3. Over the period from the year 2010-2021, the Gini coefficient exhibited a declining trend, signifying a positive trajectory in water resource allocation throughout the research period and a high level of fairness. The annual total green WF of grain in Weinan was the highest at 14.26 ×10m, followed by Xianyang at 9.52 ×10m, and the lowest in Tongchuan at 0.54 ×10m. The annual average amount of blue WF of grain is the highest in Hanzhong, at 11.33 ×10m, followed by Weinan at 9.60 ×10m, and the lowest in Tongchuan at 0.14 ×10m. The coupled framework proposed in this study exhibits significant innovation, scalability, and practical efficiency. It can inspire future research and decision-making and holds the potential for application in other regions.