Exploring coupled coordination and synergistic evolution in a multi-dimensional water system of the Yellow River Basin

• First coupled coordination analysis of the water system in the Yellow River Basin. • High-resolution spatial analysis (62 cities) enables precise water management strategies. • Novel game theory-based model integrates multi-metric weighting for robust decision-making. The Yellow River Basin (YRB) in China is a complex, multi-dimensional water system where water resources, water environment, water ecology, and water disaster—collectively referred to as the “Four-Water System (FWS)”—are intricately interconnected. A novel framework that integrates indicator screening, composite weighting, coupling coordination degree (CCD), and synergy analysis systematically assesses the interdependencies of the FWS. This study examines the FWS of 62 prefecture-level cities in the YRB from 2013 to 2022. The most crucial driving factors in each subsystem of the FWS are respectively per capita water resources (with the maximum weight being 0.53), drinking water quality compliance (0.26), soil erosion control (0.39), and reservoir capacity (0.37). In terms of CCD, most cities are in elementary and intermediate coordination, with the Qinghai and Gansu sections (the source area of the basin) showing particularly marked improvements. In terms of synergistic evolution, water resources dominate the FWS in the midstream and downstream regions. Most cities exhibit high synergy scores (>0.8), whereas downstream scores are systematically lower than midstream values. The 2021 extreme rainstorm event in the middle and lower reaches of the YRB posed a significant threat to regional synergy stability. The findings provide quantitative, location-specific insights for optimizing water resources allocation, enhancing water ecological environmental protection, and strengthening flood disaster resilience.