A copula-based stochastic fractional programming method for optimizing water-food-energy nexus system under uncertainty in the Aral Sea basin

A copula-based stochastic fractional programming (CSFP) method is developed for optimizing water-food-energy nexus (WFEN) system, which can tackle random variables under conflicting objectives and analyze the interrelationship between marginal benefit and system-failure risk. Then, a CSFP-WFEN model is formulated for the Aral Sea basin and multiple scenarios with individual- and joint-probabilistic risks related to water resources, arable land, and hydropower generation are examined. Synthesizing the results under all scenarios, hydropower generation would decrease by 11.9% and crop area would increase by 12.4% by 2035 under severe water scarcity. Agricultural water would decrease with time (from 69.1% in 2021 to 53.9% in 2035), and the share of wheat farmland would increase by 16.4% for food security. Compared with the traditional stochastic fractional programming (SFP) and copula-based stochastic programming (CSP) methods, the marginal benefit from CSFP would be improved 1.7% and water would be saved 9.2%. To support sustainable development of the study basin, some suggestions can be derived from the results: (i) since agriculture is still the largest water user in the future, it is desired to reduce its water consumption through improving irrigation efficiency and adjusting crop planting structure; (ii) effectively reducing Uzbekistan’s water consumption can improve water allocations to other countries and relieve regional conflicts caused by water shortage; (iii) compared to the single management pattern, the integrated optimization of water, food and energy nexus not only has higher efficiency of resources allocation and utilization, but also allows an increased robustness in controlling system-failure risk under joint probabilistic constraints.