A joint-probabilistic programming method for water resources optimal allocation under uncertainty: A case study in the Beiyun River, China

In recent years, the lower reaches of the Beiyun River have suffered from growing water resource shortages due to the reduction of upstream water resource and drying up of the stream channel. More reasonable and scientifically based water allocation plans should be developed and implemented; however, uncertainties exist regarding the determination of water supply availability and spillage of extra water. To assess and manage regional water shortage, the combined effects of multiple water supply sources as well as the joint probability of typical events should be considered. The joint probability of water supply, considering upstream and local water supplies, was estimated through the copula functions. A multi-objective optimization model was then developed and solved by improved genetic algorithms to plan water resources allocation within a multi-source environment containing multiple competitive users. The framework is demonstrated, and represents a range of different water supply scenarios in terms of different probabilities of occurrence and constraint violations. The results showed that water allocation was greatly influenced by uncertainties, especially in upstream-local water supply. In addition, violating water-allocation constraint posed an extra uncertainty. This study facilitates the proposition of adaption allocation plans for uncertain environments, aiming to balance the shortage, economy, and reliability.