Multi-Objective Optimal Allocation of River Basin Water Resources under Full Probability Scenarios Considering Wet–Dry Encounters: A Case Study of Yellow River Basin

Wet–dry encounters between basins and regions have an important impact on the allocation of water resources. This study proposes a multi-objective allocation model for basin water resources under full probability scenarios considering wet–dry encounters (FPS-MOWAM) to solve the problem of basin water resource allocation. In the FPS-MOWAM model, the sub-regions were merged by precipitation correlation analysis. Next, the joint probability distribution of basin runoff and region precipitation was constructed using copula functions. The possible wet–dry encounter scenarios and their probabilities were then acquired. Finally, the multi-objective allocation model of water resources was constructed using the full probability scenario for wet–dry encounters in each region. The FPS-MOWAM is calculated by the NSGA-II algorithm and the optimal water resource allocation scheme was selected using the fuzzy comprehensive evaluation method. Using the Yellow River Basin as an example, the following conclusions were obtained: (1) the Yellow River Basin can be divided into four sub-regions based on precipitation correlations: Qh-Sc (Qinghai, Sichuan), Sg-Nx-Nmg (Gansu, Ningxia, Inner Mongolia), Sxq-Sxj (Shaanxi, Shanxi), and Hn-Sd (Henan, Shandong), (2) the inconsistencies in synchronous–asynchronous encounter probabilities in the Yellow River Basin were significant (the asynchronous probabilities were 0.763), whereas the asynchronous probabilities among the four regions were 0.632, 0.932, and 0.763 under the high, medium, and low flow conditions in the Yellow River Basin respectively, and (3) the allocation of water resources tends to increase with time, allocating the most during dry years. In 2035, the expected economic benefits are between 11,982.7 billion CNY and 12,499.6 billion CNY, while the expected water shortage rate is between 2.02% and 3.43%. In 2050, the expected economic benefits are between 21,291.4 billion CNY and 21,781.3 billion CNY, while the expected water shortage rate is between 1.28% and 6.05%.