Sustainable Management and Environmental Protection for Basin Water Allocation: Differential Game-based Multiobjective Programming

Abstract

It is important to manage water resources under emergy theory and its implementation mechanism for water dispatching considering both economic development and environmental needs. To balance compromise resources consumption, economic development and environment protection, a multi-objective dynamic differential game is proposed in this study to determine the optimal tax rate (OTR), optimal trading quantity of water (OTQW) in each province, and the optimal bargain price (OBP). Considering the sustainability of ecological environment, the quantification of negative sewage value and net carbon emission constraints are introduced into the water allocation. To maximize the target revenue functions, minimize the net carbon emission constraints and obtain the sustainable equilibrium solutions in the triple-level game, the costate function, Hamiltonian, and Lagrangian multiplier method are introduced.Then, a water dispatching structure is constructed for error correction between the predicted and actual runoff of the YRB. Taking Yellow River Basin as an example, the validity of the proposed framework and solution method were verified under different hydrological years, 6.5%~9.1% economic benefits higher than other schemes and 4.3%~5.9% net carbon emission lower than other schemes. Compared to previous studies, the standard deviation of economic value, social value, negative ecological environment value in this paper are the least, which indicates that this scheme can better meet the requirements of sustainable 2 development and environmental protection.