Water–energy nexus risk-informed water resources management model within demand prediction, risk quantification, and system optimization under uncertainty

Graphical abstract illustrating the proposed water-energy nexus risk-informed water resources management framework. The left panel shows water-demand prediction and Copula-based analysis of water and energy availability. The middle panel presents the optimization framework, which integrates uncertainty analysis, water–energy nexus relationships, Copula-based interaction risk analysis, water allocation, energy-intensity targets, carbon-emission control, and copula-based interval stochastic chance-constrained programming. The right panel presents the resulting optimal allocation schemes across different sectors and risk scenarios, including water allocation, energy consumption, and related resource-distribution patterns. Explicitly accounting for water–energy interconnections in resource management enhances water supply sustainability and mitigates energy and environmental burdens. In this study, a water–energy nexus risk-informed water resources management model was developed for regional supply-demand adjustment by integrating neural networks with copula-based interval stochastic chance-constrained programming. The model was implemented in a typical water- and energy-scarce area, the Pearl River Delta urban agglomeration in Guangdong Province. Different water–energy coupling risk scenarios were constructed using copula functions to identify optimal solutions with respect to energy consumption, carbon emissions, and water resource allocation strategies. The results show that, under the modeled planning scenarios, surface water is projected to account for about 85% of the overall water supply, and the supply from energy-intensive alternative sources, particularly reclaimed water and seawater desalination, is projected to increase by 10–16% under water-shortage conditions. Multiple uncertainties in water and energy systems significantly affect operational strategies and water allocation, and a dynamic trade-off between risk tolerance and efficiency goals is the key factor for decision-making. In the context of increasing water–energy stress, this model can handle the uncertainties of water–energy nexus systems and offer the most effective strategy to support informed decision-making.