Multi-objective optimization for water allocation of the Yellow River basin based on fluid mechanics, emergy theory, and dynamic differential game

Abstract

The ecological restoration of the Yellow River Basin (YRB) requires urgent scientific and rational quantification of comprehensive value of water resources to optimally allocate water resources. Considering the sustainability of ecological environment, the quantifications of sediment transport value and negative sewage value were introduced into the calculation of comprehensive value of water resources in this study. First, Reynolds time-averaged turbulence equations, force analysis and fluid mechanics were adopted in succession to precisely calculate the work on the bedload sediment and the suspended load sediment. Next, the quantification of the value of sediment transport in each river interval was presented based on the emergy theory. Furthermore, to coordinate and optimize the ecological environmental, economic, and social values, a dynamic differential game-based multi-objective optimal water allocation model of the basin was proposed. On this basis, the Lagrangian multiplier method and the Hamiltonian function were exploited to obtain the optimal trading quantity of water in each province and bargain price. The provinces in the YRB were selected as a case study to verify the feasibility and practicality of the proposed model. Results indicate that (1) compared with previous optimal water allocation schemes, the economic value, social value, ecological environmental value, sediment transport value and negative sewage value of the YRB in this study in 2019 are ¥2.57✕1011, ¥3.27✕1011, ¥2.74✕1011, ¥6.27✕1010, and ¥3.30✕1010, respectively, which is more balanced and sustainable in each field; (2) this model significantly increases the ecological environmental value (EEV) of YRB in 2019 from ¥2.21✕1011 to ¥2.74✕1011—which takes into consideration the sediment transport value (STV) and negative sewage value, and thus the method in this study pays more attention to water ecological sustainability; (3) the model significantly improved the comprehensive value of water resources in the YRB to ¥785.2169✕108 if T=1 month and ¥4471.0611✕108 if T=0.5 year in 2019. Therefore, instead of pursuing economic value unilaterally, this study can coordinate and optimize the ecological environmental, economic, and social values (SV) to improve the strategic trade-offs in efforts towards basin water sustainability.