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Water scarcity has become a major impediment to economic development, and a scientifically sound water allocation plan is essential to alleviate water scarcity. An opportunity constraint approach is introduced to optimise the uncertainty of the minimum regional development level under five hydrological scenarios, and an interval-fuzzy two-stage chance-constraint model (IFTSC) is constructed to improve the reliability of the model results. The correlation of each stochastic parameter in the IFTSC model with the water allocation results and the economic benefits of the Tingjiang River basin is analysed by the Pearson correlation coefficient method. Simulation results from the IFTSC model show a downward trend in overall water scarcity and an upward trend in overall economic benefits in the Tingjiang River basin. Taking the dry water scenario as an example, the water shortage in the industrial sector decreases by 9.7%, and the overall economic benefits of the Tingjiang River basin increase by 41.58 × 108 CNY. The results of the correlation analysis based on Pearson’s correlation coefficient show that water allocation is strongly positively correlated with variables such as water price and regional minimum development requirements, and economic efficiency is strongly positively correlated with unit scale output value and losses caused by water shortage. This paper provides constructive suggestions and guiding directions for the rational allocation of water resources in the Tingjiang River basin through a detailed analysis of the results and identification of the main stochastic parameters in the water allocation process.

In this work, based on the upper line of water resources utilization and the bottom line of water environmental quality of “Three Lines, Single Project”, a fuzzy optimization method was introduced into the Tingjiang River water resources optimal allocation and eco-compensation mechanism model, which is based on the interval two-stage (ITS) stochastic programming method. In addition, a Tingjiang River water resources allocation and eco-compensation mechanism model based on the interval fuzzy two-stage (IFTS) optimization method was also constructed. The objective functions of both models were to maximize the economic benefits of the Tingjiang River. The available water resources in the basin, the water environmental quality requirements, and regional development requirements were used as constraints, and under the five hydrological scenarios of extreme dryness, dryness, normal flow, abundance, and extreme abundance, the water resources allocation plan of various sectors (industry, municipal, agriculture, and ecology) in the Tingjiang River was optimized, and an eco-compensation mechanism was developed. In this work, the uncertainty of the maximum available water resources in each region and the whole basin was considered. If the maximum available water resources were too high, it would lead to a large waste of water resources, whereas if the maximum available water resources were too low, regional economic development would be limited. Therefore, the above two parameters were set as fuzzy parameters in the optimization model construction in this work. The simulation results from the IFTS model showed that the amount of water available in the river basin directly affects the water usage by various departments, thereby affecting the economic benefits of the river basin and the amount of eco-compensation paid by the downstream areas. The average economic benefit of the Tingjiang River after the optimization of the IFTS model simulation was [3868.51, 5748.99] × 108 CNY, which is an increase of [1.67%, 51.9%] compared to the economic benefit of the basin announced by the government in 2018. Compared to the ITS model, the economic benefit interval of the five hydrological scenarios of extreme dryness, dryness, normal flow, abundance, and extreme abundance was reduced by 28.54%, 44.9%, 31.49%, 40.37%, and 36.43%, respectively, which can improve the economic benefits of the basin and provide more accurate decision-making schemes. In addition, the IFTS simulation showed that the eco-compensation quota paid by downstream Guangdong Province to upstream Fujian Province is [28,116.4, 30,738.6] × 104 CNY, which is a reduction of [8461.404, 110,836] × 104 CNY compared to the 2018 compensation scheme of the government. Compared to the ITS model, the range of eco-compensation values was observed to increase by 9.94%, 54.81%, 15.85%, 50.31%, and 82.90%, respectively, under the five hydrological scenarios, which reduces the burden of ecological expenditure downstream and provides a broader decision-making space for decision-makers and thus enables improved decision-making efficiency. At the same time, after the optimization of the IFTS model, the additional water consumption of the second stage of the Tingjiang River during the extremely dry year decreased by 62.11% compared to the results of the ITS model. The additional water consumption of the industrial sector decreased by 68.39%, the municipal sector decreased by 59.27%, and in the first phase of water resources allocation for 14 districts and counties in the Tingjiang River, industrial and municipal sectors are the main two sectors. After introducing the fuzzy method into the IFTS model, the difference in the water consumption by these two sectors in the basin under different hydrological scenarios can be alleviated, and the waste of water resources caused by too low water allocation or excessive water allocation can be avoided. The national and local (the downstream region) eco-compensation quotas can be indirectly reduced, and the risk of water resources allocation and eco-compensation decision-making in the basin can be effectively reduced.

Being one of the most important sources of water in the Jilin Province in China, the Yinma River Basin (YRB) is facing problems of water scarcity in low economic areas and low utilization in richer areas mainly caused by the irrational allocation of water, excessive pursuit of economic benefits, and neglect of environmental problems. Restricting watershed development involves potential decision-making risks. Some scholars have used the interval two-stage stochastic planning method to adjust water resource allocation in the Drinking Horse River Basin, but the method uses historical statistics for projection and does not take into account the ambiguity and uncertainty in real planning situations. Therefore, this study addresses the problems prevalent in the allocation of water resources in the YRB through optimization using stochastic programming methods, interval and two-stage, and introduces the fuzzy mathematical programming method, with the aim of coordinating the water balance of various water-consuming sectors in the YRB, so as to reconfigure the water allocation. The goal is to solve the existing problems of irrational water allocation, reduce system risks posed by excessive economic development, mitigate water shortages in the water-consuming sectors, and alleviate potential decision-making risks and vague uncertainties associated with the allocation of water resources. Additionally, optimization of the pollution-holding capacity improvement project was carried out. The interval fuzzy two-stage model simulation developed in this study shows that the distribution of water across the different administrative regions can be reduced by up to 30% compared with the original model, effectively reducing the problem of water wastage. Post-optimization, the impact of water shortage in the water resources allocation scheme is alleviated to a significant degree, and there is no water shortage in some areas. At the same time, the eco-environmental sector has gradually taken the leading role in the distribution of water reuse among the different water-consuming sectors. The pollution-holding capacity has been enhanced, and the discharge and river entry chemical oxygen demand (COD) and ammonia nitrogen, two typical pollutants, have been reduced. The membership interval in the interval fuzzy two-stage model reflects the relationship between the possible level of the target value and the risk level. This study provides a guideline for decision makers for balancing the relationship between benefits and risks and proposes a planning scheme that is more conducive to the development of the river basin.

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