The optimal agricultural structure and population size within typical watersheds needs to be identified based on the water ecological carrying capacity (WECC). However, real-world systems of water ecological management are complicated as multiple uncertainties exist in the system parameters, which need some effective optimization methods to deal with. This research presents an inexact simulation-based fuzzy credibility-constrained mixed-integer programming (ISFCCMIP) model. Through integrating interval linear programming, fuzzy credibility-constrained programming, mixed-integer programming, global nutrient export from watersheds, and the KirchnereDillon model within a general framework, the developed ISFCCMIP model can effectively deal with the multiple uncertainties in the simulation and optimization processes of water ecological management systems. The developed ISFCCMIP model is applied to a real-world case study in the Xinfengjiang Reservoir Watershed. Results show that the total population that can be carried by the watershed WECC would decrease from [204885, 412367] to [121235, 271280], when the credibility level increases from 0.55 to 0.95. On the contrary, the total agricultural benefit would increase from [3.72, 5.06]
۱۰۸ to [3.75, 5.10]
۱۰۸ $. The total population in the base year far exceeds the watershed WECC. Although the total agricultural benefit in the base year is between the upper and lower bounds of the optimized results, the agricultural structure is not reasonable and needs to be adjusted. Concurrently, multiple results on the optimal agricultural structure and population size are obtained under different credibility levels and in different carrying capacity scenarios. Such results can provide a series of decision alternatives for watershed policy makers to consider the tradeoff between socio-economic development and water ecological protection. The results also assist the sustainable development of the Xinfengjiang Reservoir Watershed. The proposed model is effective for the optimal management of agricultural structure and population size within a reservoir watershed based on the WECC under multiple uncertainties. It also provides a reference for other areas with similar concerns.

Introduction

The aquatic ecosystem plays an important role in the sustainable development of the economy, society, and environment (Englert et al., 2013; He et al., 2018; Li et al., 2016; Reckendorfer et al., 2013). However, with the rapid growth of the social economy in recent years, the aquatic ecosystem has been subjected to intensive and large-scale human activities (ShabanzadehKhoshrody et al., 2016). The total consumption and development intensity of water resources, as well as emission loads of water pollution, have increased, leading to a series of consequences, such as water resource shortages, environment deterioration, and ecological degradation (Jing et al., 2015; Matios and Burney, 2017; Wang et al., 2015; Xu et al., 2017). Such consequences have placed great pressure on aquatic ecosystems and seriously affected the sustainable utilization of their service functions (Ren et al., 2013; Zhang et al., 2017). Therefore, socio-economic activity within a watershed should simultaneously consider water quantity and quality conditions, and these considerations must be based on the water ecological carrying capacity (WECC) (Wang et al., 2014; Zhang et al., 2014). In particular, agricultural industry development and frequent human activities can lead to an increase in water consumption and release of nutrients (e.g., nitrogen and phosphorus, N and P) from watersheds to water bodies downstream, which might further result in insufficient ecological flow and water eutrophication (Rong et al., 2018; Rudnick et al., 2017; Zhang et al., 2015, 2018). It is therefore important to conduct research on the identification of the optimal agricultural structure and population size within typical watersheds based on the WECC. This will help restrain the water ecological deterioration, protect the ecosystem service function, and promote the sustainable development of the socio-economic environment.