Systemic Risk-Informed Bi-Level Optimization for Resource Trade-Offs in the Water-Energy-Food-Carbon Nexus

Systemic risks across the water-energy-food-carbon (WEFC) nexus threaten the resilience of major river basins under converging climate, economic, and ecological pressures. This paper presents a bi-level optimization and risk-informed assessment framework that integrates multidimensional risk and equity metrics into resource allocation and policy design, with application to the Yellow River Basin (YRB) in China. By simulating five distinct scenarios, including baseline, climate change, sustainable development, economic priority, and technology innovation, the results show that different governance pathways produce sharply divergent outcomes for efficiency, equity, and systemic vulnerability. Technology- and market-driven strategies increase basin-wide economic output (up to 86.7 billion CNY for Nei Mongol Zizhiqu) but widen spatial inequalities (Gini index up to 0.663) and, in some provinces, raise systemic risk exposure (SRCI up to 0.493). Sustainable development pathways substantially reduce equity gaps (Gini 0.426) and rebalance resource allocation yet may elevate water stress or emissions locally. No single scenario achieves simultaneous gains across all objectives, but only risk-informed, adaptive strategies reveal how targeted water rights trading and ecological safeguards can buffer regional vulnerabilities and enhance overall system resilience. Our results provide quantitative evidence that integrating risk and equity into nexus management enables more robust, context-specific responses to compounding shocks in complex socio-environmental systems.