Simulation-based inexact chance-constrained nonlinear programming for eutrophication management in the Xiangxi Bay of Three Gorges Reservoir

Although integrated simulation and optimization approaches under stochastic uncertainty have been applied to eutrophication management problems, few studies are reported in eutrophication control planning where multiple formats of uncertainties and nonlinearities are addressed in forms of intervals and probabilistic distributions within an integrated framework. Since the impounding of Three Gorges Reservoir (TGR), China in 2003, the hydraulic conditions and aquatic environment of the Xiangxi Bay (XXB) have changed significantly. The resulting emergence of eutrophication and algal blooms leads to its deteriorated water quality. The XXB becomes an ideal case study area. Thus, a simulation-based inexact chance-constrained nonlinear programming (SICNP) model is developed and applied to eutrophication control planning in the XXB of the TGR under uncertainties. In the SICNP, the wastewater treatment costs for removing total phosphorus (TP) are set as the objective function; effluent discharge standards, stream water quality standards and eutrophication control standards are considered in the constraints; a steady-state simulation model for phosphorus transport and fate is embedded in the environmental standards constraints; the interval programming and chance-constrained approaches are integrated to provide interval decision variables but also the associated risk levels in violating the system constraints. The model results indicate that changes in the violating level (q) will result in different strategy distributions at spatial and temporal scales; the optimal value of cost objective is from [2.74, 13.41] million RMB to [2.25, 13.08] million RMB when q equals from 0.01 to 0.25; the required TP treatment efficiency for the Baisha plant is the most stringent, which is followed by the Xiakou Town and the Zhaojun Town, while the requirement for the Pingyikou cement plant is the least stringent. The model results are useful for making optimal policies on eutrophication control planning and water quality improvement in the XXB.