Multi-Objective Collaborative Optimization Model and Application of the Water-Energy-Food-Carbon Nexus Under Uncertainty: A Case Study of the Heihe Irrigation Area

Against the backdrop of intensified climate change and increasingly prominent imbalances in resource supply and demand, achieving multi-objective collaborative optimization of the Water-Energy-Food-Carbon (WEFC) nexus under uncertain conditions has become a pivotal task for regional sustainable development. Taking the Heihe River Basin, a typical arid inland river basin in northwest China with a complex WEFC nexus, as the research area, this study develops a multi-objective collaborative optimization model for the WEFC nexus, targeting three core goals: maximizing crop irrigation water productivity, minimizing carbon emissions, and enhancing low-carbon agricultural competitiveness. The model embeds constraints of regional water security, food security, land policy, and total water resource availability, introduces the uncertainty parameter τ to quantify fluctuations in available surface water, and adopts the ideal point method to convert the multi-objective problem into a single-objective optimization task by minimizing the Euclidean distance between feasible solutions and the ideal solution, with a case application in the oasis area of the basin’s middle reaches. Results show the model exhibits excellent stability across varying uncertainty levels: crop irrigation water productivity stabilizes around 1.5 kg/m3, low-carbon agricultural competitiveness at approximately 0.1003 kg/yuan, and spatial differences in resource allocation are evident. Linze gains the most water resources (16.47 × 108 m3) due to geographical advantages, while Gaotai obtains the least (6.51 × 108 m3). In terms of planting structure, vegetables dominate the sown area owing to low carbon emissions and high water use efficiency, while wheat planting is relatively limited by climate adaptability and market demand. Carbon sink analysis confirms vegetables as the primary carbon sequestration contributor in Ganzhou and Linze, offering a practical pathway for agricultural carbon reduction. These findings provide tailored theoretical and practical support for balancing food security, efficient resource utilization, low-carbon development, and ecological protection in arid and semi-arid regions, facilitating regional carbon neutrality and sustainable agricultural development.