Multi-scenario optimization model for operation of inter-basin water transfer-supply systems considering cost–benefit relationships

The shortage of water resources has become a serious obstacle to sustainable economic and social development over the past few decades (Wang et al. 2021; Chen et al. 2023). Water use in many areas is close to exceeding the maximum acceptable water use in the basin, which leaves some administrative areas with serious water management problems (Peng et al. 2017; Wang et al. 2023). Inter-basin water transfer is an effective way to address the uneven distribution of regional water resources. The optimized operation of an inter-basin water transfer system is a widely used approach to achieving optimized regional water resource allocation (Wang et al. 2015; Cirilo et al. 2021; Ye et al. 2023). Improving the efficiency of water use and reducing the cost of water transfer through the joint optimization of multiple water sources is essential (Rosenberg et al. 2008; Xu et al. 2016, 2023). One of the key issues is how to coordinate the allocation of local and diverted water resources in space and time so that the issues of ‘when to supply’ and ‘when to divert’ are addressed at an operational level.

Multiple water source allocation in regional water resource systems has become a hot topic of research over the past few years, especially since the commissioning of water conservation projects such as the South-to-North Water Diversion Project in China. Many scholars have developed mathematical models for this purpose. Initially, optimization strategies were usually proposed to minimize the occurrence of water shortages or to maximize the reliability of water supply (Zeng et al. 2014; Spiliotis et al. 2016; Gu et al. 2017), and it was achieved by regulating the operational rules for water delivery and supply. The optimized allocation of multiple water resources has become increasingly effective over time, particularly in terms of the amount of water transferred. With the development of large-scale construction projects, the cost of water transfers has become an issue that cannot be ignored and multi-objective decision analysis based on the marginal benefits of water transfers and water supply reliability is applied to the allocation of multiple water sources (Wang et al. 2023). Harou et al. (2009) assessed the economic value of water resources based on system analysis and evaluated the linkages between water resource systems and economic activities, leading to an efficient allocation of water resources and the consequent greater social and economic benefits. Chen et al. (2013) investigated the applicability of a two-tier pricing scheme to balance water allocation by using the Stackelberg game model and applied it to the operational management level. The operating model based on maximizing economic efficiency is related to the cost of diverting water. The parameters of the model are difficult to calibrate, as not only construction and operating costs need to be considered, but also the cost of compensation for ecological damage (Matete & Hassan 2005, 2007). Zhang et al. (2017) established a theoretical framework for inter-basin water transfer systems and proposed a corresponding water transfer scheme that takes into account the costs and benefits of water use to some extent. However, the costs of water transfers vary considerably, depending on the composition of the water source, the target audience and the route and distance of the transfer. With the cost of water transfer directly incorporated into the calculation, multi-objective optimization problems for water transfer-supply systems will become more high-dimensional and complex (Zhang et al. 2021; Wang et al. 2022). This study proposes a multi-scenario optimization model for the operation of inter-basin water transfer-supply systems, aiming to provide a feasible approach for developing optimized operation schemes by fully considering the cost–benefit relationships of water transfer. A two-objective optimization model is first established including minimizing the sum of squared water supply deficits and the cost of water transfers. Three water transfer scenarios are developed for different cost–benefit relationships. Based on these scenarios, the established optimization model is further converted into a single-objective optimization model to avoid the direct calculation of complex water transfer costs. The model is finally solved to obtain water transfer schemes and the schemes are evaluated using water supply reliability and a water shortage index. The proposed model is applied to the eastern route of the South-to-North Water Diversion Project in China (ER-SNWDP), demonstrating how the model promotes the efficient usage of multiple water resources in space and time, demonstrating how the model can facilitate the efficient use of multiple water resources in space and time while taking into account the cost–benefit relationships.

The case study was conducted in the ER-SNWDP, located in the center of Jiangsu Province, China. The study area covers 43,143 km², 83% of which is cultivated. The water resources system consists of several water sources including the Hongze Lake, the Luoma Lake and the ER-SNWDP, as well as inflow channels formed by river networks, and links to the Yangtze River, Huaihe River and the Yishusi basin (Liu & Zheng 2002; Du et al. 2016).

As shown in Figure 1, the study area covers the cities of Huaian, Suqian, Xuzhou, Lianyungang and parts of Yangzhou city (Jiangdu, Gaoyou and Baoying county) and Yancheng city (Funing county). Due to the large number of users and for clarity's sake, this paper divides the intake area into three parts and summarizes the water usage for each part. Considering the constraints on the inflow passage of the water supply and the costs of water transfer, the relationship between supply and demand is defined as follows:

• (1)

  The user L (brown area in Figure 1) is supplied with water by the Luoma Lake.

• (2)

  The user P (yellow area in Figure 1) is supplied with water by both the Hongze Lake and the Luoma Lake.

• (3)

  The user H (cyan area in Figure 1) is supplied with water by the Hongze Lake.

In order to determine the optimized operation policy of the inter-basin water transfer-supply system, the following issues have to be addressed:

• (1)

  The cost of using inter-basin water transfers is higher than the cost of local water supplies due to the high construction and operating costs of inter-basin transfer projects. It is therefore important to consider the economics of inter-basin water transfer-supply systems.

• (2)

  The outcome of the water supply from the two sources depends on the synchronicity or non-synchronicity of the inflows between the source and the receiving area, which is determined by the variation in the spatial and temporal distribution of the water supply from the two things.

• (3)

  The annual diversion of water from the Yangtze River is affected by a number of factors, such as the water supply quotas of other provinces and cities such as Shandong and Tianjin, as well as the storage capacity of the water conservancy project infrastructure in the surrounding areas.

To address these issues, we propose a multi-scenario optimized operational model. The impact of economic costs is addressed by setting up operational scenarios for the hydrological project, while synchronicity or non-synchronicity of inflows is dealt with by setting up two lakes with different combinations of inflow patterns.

In order to better reflect the degree of water shortage in the system, we define the integrated water shortage index so that it has the same unit as the water shortage index (SI) in the traditional sense, and is written as ⁠.

The model established for this study should satisfy physical limitations, such as the mass balance equation, the water transfer capacity and the permissible bounds of water storage, as well as other constraint conditions. These constraints are described as follows.

Lastly, all variables are non-negative. In Equations (3)–(8), and are the initial and ending water storage at time period t; and represent the lower and upper bounds of water storage; is the natural inflow to the reservoir; is the controlled inflow from the Luoma Lake to the Hongze Lake; is the controlled inflow from the Hongze Lake to the Luoma Lake; is the controlled inflow from the Yangtze river to the reservoir; is the amount of spill when the storage in the reservoir exceeds the maximum storage; is the water diversion capacity for the donor reservoir and is the water diversion capacity for the Yangtze River.

There are three sources of water supply: local water resources generated by the rainfall-runoff from the catchment area of the two lakes; water transfer from the Hongze Lake to the Luoma Lake and diverted water from the Yangtze River. Local water resources can be distributed via the gravity flow formed by the rainfall-runoff and requires the lowest energy consumption, and hence the lowest economic cost. In the second type, water is pumped and transferred from the Hongze Lake to the Luoma Lake from multiple pumping stations, which requires higher energy consumption and economic cost. Lastly, the long-distance water diversion from the Yangtze River to the Hongze Lake and the Luoma Lake demands the highest energy consumption and economic cost. The supply from these different water sources should be allocated with different priorities according to their cost, which is allowed by the multi-scenario analysis described below.

is the contracted amount of annually diverted water from the Yangtze River, in million m³.

Under the conditions of scenario 1, water scarcity occurs in the water supply system when the exceedance probability of inflow to Hongze Lake is more than 50% and that of the Luoma Lake is more than 40%. The water shortage index increases gradually from 0.05 to 0.60 with the decrease of inflow from the Hongze Lake and the Luoma Lake (an increase in probability indicates a decrease in inflow). The variation rule of the water shortage index under scenario 2 is similar to that of scenario 1. In this case, the rate can be reduced to a certain extent by transferring water from the Hongze Lake to the Luoma Lake especially while the inflow of the Hongze Lake is high relative to that of the Luoma Lake, i.e., if the exceedance probability of inflow to the Luoma Lake varies between 40 and 60% and that to the Hongze Lake is more than 80%. Transferring water from the Hongze Lake to the Luoma Lake plays an important part in the compensation, and contributes to the reduction of the water shortage of user L and user P. The constraint for annually diverted water under scenario 3 limits the volume of diverted water to 7.6 billion m³. It is obvious that the diverted water from the Yangtze River can alleviate the water shortage in the water resources system. The problem of water scarcity mostly exists when the probability of water shortage in the Hongze Lake is greater than 90% and that of the Luoma Lake is greater than 40%, however, it is limited to 0.05–0.10 when water is allowed to be diverted from the Yangtze River (scenario 3). These results show that the role of alleviating the water shortage based on the inflow of the two lakes alone is limited. The water will indeed be in great shortage without water diversion from the Yangtze River, which has a greater influence on the inflow of the Hongze Lake than that of the Luoma Lake.

To illustrate the effectiveness of the water resource system, the least favorable condition from the time series is chosen as an example. In 1999, a year of extreme drought, the exceedance probability of inflow to both lakes was around 95%. Optimal operation reallocates the water, taking into account the space and time variability of the supply sources: the water shortage index is homogenized in time to avoid periods of intense water shortage, and it is also homogenized in space to guarantee fairness among users. Table 3 lists the monthly water shortage index in 1999 for each category of users under the three different scenarios. The increase of available water resources under scenario 3 results in the water shortage index being decreased to below 20% compared with other scenarios, under which the water shortage index varies between 40 and 60% throughout most of the year. These results thus demonstrate the large impact of the diverted water from the Yangtze River on the water supply. Under scenario 1, when the inflow from the Luoma Lake is reduced, user L faces a serious water shortage issue due to the limited amount of available water resources compared with scenario 2. The water shortage index of user L under scenario 1 is 10% higher than under scenario 2 from January to June. Note how the water scarcity is homogeneously distributed for the different users at all time steps, so that extreme water supply shortage is avoided for every user, thus meeting the requirements of the system. Figure 4 displays the monthly natural inflow and diversion of water to lakes and water demand in 1999 under three different scenarios.

As the economic cost of diverting water from the Yangtze River is high, different conditions of the volume of annually diverted water from the Yangtze River are set in order to evaluate and improve the cost-efficiency of the water transfer-supply system.

The optimized operation of an inter-basin water transfer system is an effective way to address the uneven distribution of regional water resources. A multi-scenario optimization model for the operation of an inter-basin water transfer-supply system is proposed in this paper to obtain a water transfer scheme that balances the cost–benefit relationship. The proposed method is applied to a real case for optimized operation of the eastern route of the South-to-North Water Diversion Project in China. The findings can be concluded as follows:

• (1)

  When the probability of exceeding the standard flow to the Hongze Lake is less than 50% and the probability of exceeding the standard flow to the Luoma Lake is less than 40%, the local water from the Hongze Lake and the Luoma Lake can meet the water demand of the users and there is no need to transfer water across the basin. When the Hongze Lake and the Luoma Lake are at low flows, the impact of water shortage conditions is more sensitive for the Hongze Lake than for the Luoma Lake.

• (2)

  With the diversion of a contracted annual volume of water from the Yangtze River, the water supply reliability is 89.1% and the water shortage index is 0.9%. In extreme drought years, the water shortage index can be controlled to within 5 and 10%.

• (3)

  When water is diverted from the Yangtze River at 60% of the annual contracted volume, the reliability of the water supply is 78.2% and the water shortage index is 2.8%, which is a compromise between balancing the water shortage index and water transferring volume regarding the cost of water transferring.

Conceptualization: M.C., B.X., L.W.; Methodology: M.C., W.L., Y.Z.; Formal analysis and investigation: M.C., W.L., Y.Z.; Writing – original draft preparation: M.C.; Writing – review and editing: M.C., Y.Z., L.W., W.L.; Funding acquisition: L.W., B.X., Y.Z., W.L.; Resources: L.W., B.X.; Supervision: L.W.

This study is supported by the National Natural Science Foundation of China (Grant No. 52209032), the China Postdoctoral Science Foundation Funded Project (Grant No. 2021M702313), the Fundamental Research Funds for the Central Universities (Grant No. 2018B10514), the Fundamental Research Funds for Jiangsu Province (Grant No. 2016001) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200160).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.