A Study of Initial Water Rights Allocation Coupled with Physical and Virtual Water Resources

Abstract

Virtual water exerts an indispensable influence on water resources, yet the existing studies on the water rights allocation of transboundary rivers hardly consider virtual water transfer (VWT). Therefore, in this paper, we used Taihu Lake as an example with data collected in 2017 that described both physical and virtual water use. We used these data to evaluate water rights allocation schemes by coupling virtual and physical water use. In order to achieve this goal, we first determined the physical water rights allocated for the four regions connected to the Basin. Next, we employed the multi-regional input–output (MRIO) approach to calculate the VWT among the four regions; then, we converted the VWT to the riparian level via the water efficiency coefficient. Finally, with virtual water included in the physical water rights allocation, we formulated a final water rights allocation for Taihu Lake. The results showed the following findings: (1) The ranking of the amount of physical water rights allocation is: Jiangsu > Zhejiang > Shanghai > Anhui. (2) Anhui and Jiangsu produce a net export of virtual water (2.259 billion m³ and 1.78 billion m³, respectively), while Zhejiang and Shanghai have a net import of virtual water (2.344 billion m³ and 1.695 billion m³, respectively), indicating that Anhui houses more water-consuming industries and is in greater need of economic restructuring. (3) The integration of virtual water makes a difference: Jiangsu achieved 16.208 billion m³ in terms of the amount of water rights allocated, Zhejiang achieved 6.606 billion m³, Shanghai achieved 3.040 billion m³, and Anhui achieved 4.319 billion m³, with a ranking of Jiangsu > Zhejiang > Anhui > Shanghai. The results detailed above prove that virtual water exerts an indispensable influence, and integrating virtual water can make the physical water rights allocation of transboundary rivers more equal and reasonable.

1. Introduction

Rapid socioeconomic development and frequent extreme climate events are leading to an increasing scarcity of water resources across the world [1,2]. In 2022, for instance, the Yangtze River Basin in China suffered a record-breaking drought, and its water levels dropped to half of the basin’s average. Water shortages cause significant conflicts or contradictions between the upper and lower parts of a basin within a country, as well as regional competition for water rights [3,4,5]. In order to resolve the water conflict between the upstream and downstream areas, many governments and scholars have offered possible solutions by allocating transboundary water resources [6,7,8]. Thus, the clarification of water rights in a transboundary river (that is, a river within a country with different administrative regions rather than international rivers that cross national borders) is not only the basis and prerequisite for a water rights trade market but also the basis for alleviating water conflicts between upstream and downstream areas.

Aside from these major physical water resources (mainly comprising surface water and groundwater), there is another form of water resource, so-called “virtual water” [9,10]. The concept of “virtual water” was initially proposed by Allan (1993) to refer to the water ‘embodied’ in a product, not in a real sense but in a virtual sense [9]. Based on this concept, many studies refer to “virtual water” as the water embedded in goods to describe the amount of water consumed during the production or manufacturing process of a commodity [10,11,12,13,14,15]. It is defined from the production side and is rooted in regional economic systems. Every sector, industry, or region contains virtual water. The transfer between sectors, industries, or regions would lead to the transfer of the water embedded in goods, which is known as “virtual water transfer”. As the volume of trade increases, the upstream–downstream virtual water transfer (VWT, or the virtual water quantity transferred (outflowed or inflowed) through trade) increases too. In other words, regions with net virtual water imports (inflow) have more (not immediately visible) water resources, while those characterized by net exports (outflow) lose water resources. This transfer volume, if converted and included as part of the available water in transboundary rivers, would yield an invisible influence on the actual amount of water resources in a basin [10,11,12,13]. In short, both physical and virtual water resources should be considered in research on water resource allocation [10,11,12,13,14,15]. However, the existing studies do not convert or integrate virtual water transfer into physical water resources in order to quantitively analyze the invisible influence of virtual water transfer on water rights allocation. Such studies help us to understand that virtual water transfers have a significant impact on physical water resources in a region; however, the existing work on transboundary water rights allocation focuses on physical water resources and neglects the impact of the virtual water that is embedded in trade [16,17,18,19,20,21,22,23,24,25,26,27,28]. Therefore, this paper combines and couples physical and virtual water to examine water rights allocation in transboundary river basins.

Moreover, in order to achieve the aims of this study, we constructed the following models. Regarding physical water rights allocation, since the concept of water resource management was proposed in 1908, developed countries, based on the status quo of their socioeconomic development and water regimes, have explored the systems of initial water rights allocation, including riparian ownership, the prior appropriation doctrine, and water rights permissions [29]. Although scholars have proposed various allocation rules, they have reached a consensus on several basic principles of water rights allocation: putting domestic water first, ensuring food security, respecting history and the status quo, and pursuing sustainable development [29,30,31,32,33,34,35,36]. As such, drawing on the results above, this paper constructs an index system for the water rights allocation of physical water resources in transboundary rivers that is grounded in the basic principles of the status quo: equity, efficiency, sustainability, and macro-regulation.

As for converting virtual water, there are both bottom-up [37] and top-down [38] approaches for building a measurement model. The input–output analysis approach is designed to produce an input–output table and, accordingly, to construct a data-based model to analyze the interdependencies between different sectors or industries of a national economy. It is able to quantify the amount of water resources allocated in trade in a more visual and accurate manner [39,40,41,42,43,44,45,46,47,48,49]. On this basis, this research used the multi-regional input–output (MRIO) approach to measure VWT. The amount of virtual water is usually calculated at the provincial level, while water rights are allocated at the riparian level. Thus, VWT needs to be converted from the provincial level to the riparian level. However, a few studies that focus on this topic convert VWT using the water efficiency coefficient [50,51,52]. Therefore, this paper also employed the proportion of the riparian water efficiency coefficient to the provincial water efficiency coefficient to quantify and convert the provincial VWT.

Based on the above steps, this paper also incorporates the transfer of riparian virtual water into the corresponding regional physical water rights allocation and obtains a water rights allocation scheme based on the coupling of physical and virtual water. Additionally, due to the subsidy of water resources from the virtual water net exporters to the net importers, in the allocation of physical water rights, the net importers should provide reverse compensation. As such, we assumed that the net virtual water output is a positive value and the net virtual water input is a negative value. Therefore, when coupling virtual water and physical water, if the region where the basin is located has a net virtual water output, it can increase the quantity of water rights allocated; if the region where the basin is located has a net virtual water input, compared to when virtual water is not considered, it will have a reduced portion of water rights allocation.

In general, both methods and principles of water rights allocation focus on physical water, ignoring the invisible effects that virtual water has on water rights allocation. In order to fill this research gap, this paper aims to: (1) determine the amount of allocated physical water in a transboundary river; (2) calculate the provincial VWT; (3) convert the VWT from the provincial level to the riparian level; and (4) combine the converted VWT with physical water for water rights allocation.

According to the above analysis, we constructed the research logic framework for this article. First, according to the allocation rules, this paper used Multiple Attribute Decision Making (MADM) to allocate physical water rights. Next, the MRIO approach was employed to measure the VWT in provinces where a transboundary river is located. After that, the provincial VWT was converted via the water efficiency coefficient to the riparian level. Finally, the converted VWT was integrated into a transboundary water allocation scheme based on “virtual water + physical water”, as shown in Figure 1.

The main contributions of this paper are as follows: (1) including virtual water in physical water rights allocation in order to make transboundary water rights allocation schemes more equitable and reasonable; (2) converting provincial VWT to reduce errors.

The rest of this paper is structured as follows: Section 2 describes the research framework and study area; Section 3 introduces the models; Section 4 presents the major results and discussion; and Section 5 presents the conclusions.

2. Materials and Methods

2.1. Study Area

2.1.1. Overview

Located in the southern part of the Yangtze River Delta, the Taihu Lake Basin is one of the most economically advanced and populated areas in China, housing four administrative regions: Anhui Province, Jiangsu Province, Zhejiang Province, and Shanghai City. In 2021, the total water consumption in the areas of the three provinces and one city reached 34.23 billion m³, while the Basin’s annual average actual supply of water resources was 19.6 billion m³, indicating a sizeable gap between demand and supply [53]. Worse still, the four regions all suffered from drought in 2022, leading to a more intense water quantity conflict. For this reason, the upstream and downstream regions along the Taihu Lake Basin tried their best to formulate an allocation scheme to ease such conflicts. In the meantime, as the main players in the Regional Integrated Development Plan for the Yangtze River Delta, the four regions are involved in frequent economic and trade activities. A VWT that is embedded in trade would yield an invisible influence on the actual amount of water resources in the regions. Hence, an equitable and reasonable water rights allocation scheme should consider both physical and virtual water.

According to the above analysis, it is evident that a significant supply and demand gap for physical water exists within the Taihu Lake basin, intensifying the competition for physical water resources among the four regions. At the same time, trade is frequent among the three provinces and one city where the Taihu Lake basin is located, resulting in a notable volume of the implied VWT. Therefore, this paper takes the Taihu Lake basin as its case study.

2.1.2. Date Source

The data on virtual water in this paper were collected from the Carbon Emission Accounts and Datasets (CEADs) [54], data on water consumption in the four regions were taken from the China Statistic Yearbook (2017) [55], and data on the physical water allocation in the Taihu Lake Basin were taken from the water-related Communiques of the four regions and the Taihu Basin Authority in 2017 [51,56,57,58,59]. This paper chose the year 2017 as the study period because the latest public input–output data from CEADs is in 2017.

2.2. Method

To achieve the coupling of virtual and physical water, the method is divided into three parts. The first part concerns the allocation of physical water rights. Based on the normalization of indicators, the TOPSIS method (relative closeness) is used to allocate the physical water rights of the basin [60]. The second part involves the calculation of the virtual water transfer between provinces in the basin. Based on the MRIO model, the virtual water output (input) of each province is calculated, and the net VWT quantity (output minus input) of each province is obtained. In the third part, according to the water efficiency coefficient, the VWT quantity at the provincial level is converted into the virtual water transfer amount corresponding to the coastal area of the basin; then, the VWT quantity of the coastal area is coupled with the physical water quantity in the first part, thereby achieving the coupling allocation of virtual and physical water.

According to the relevant policies, the initial allocation of water rights takes place after deducting the government’s reserved amount of water, including pre-allocated water for ensuring food security [61]. This principle also applies to the distributable water rights in this paper. Meanwhile, in actual engineering, there are two tiers of initial water rights allocation in China: (1) within the administrative regions of the basin, and (2) further distribution among different industries after the allocation of water rights to each region. The focus of this paper pertains to the allocation of physical water rights at the first level; that is, we consider the allocation between administrative regions within the basin and do not consider specific industries.

2.2.1. Modelling of Physical Water Rights Allocation

(1)

Constructing an index system of physical water rights allocation

Based on the “Opinions on Implementing the strictest Water Resource Management System” issued by the State Council and “the reply of the Ministry of Water Resources of the National Development and Reform Commission on the water allocation scheme of the Taihu Lake Basin”, coupled with the principles and indicators of other scholars [30,31,32,33,34,35,36,53,62], this paper constructed the following principles of physical water rights allocation: the status quo principle, the equity principle, the efficiency principle, the sustainability principle, and the macro-regulation principle. There are also indicator systems, which are only used to determine the amount of physical water allocation.

(1) The status quo principle. The main indicators that reflect the status quo principle include the current water supply volume in each region, per capita water consumption, water consumption per unit of cultivated land area, and the scale of existing water supply projects [16,53,63,64,65]. The specific meanings of the indicators selected under the status quo principle are as follows:

Current water use (P₁₁) refers to the current water use situation and also expresses each region’s different history of water use. Water use per capita (P₁₂) is the ratio between a region’s current water use and its population. Water use per farmland unit (P₁₃) is the ratio of the region’s current water use to its irrigation area. The current water supply scale (P₁₄) represents the water supply capacity of the project.

(2) The equity principle. In water rights allocation, the principle of fairness is particularly important. To reflect the fairness of water allocation, it is first necessary to ensure that everyone has the right to use water resources, and population indicators can reflect the principle of people-oriented distribution. The effective irrigated area is a basic element used to ensure food security in a region, and the effective irrigated area indicator reflects the fairness of land and water rights. These indicators can be obtained from the “Comprehensive Plan for Basin Water Resources” [29,31,33,35,62,64,66]. Moreover, the specific meanings of the indicators selected under the equity principle are as follows:

The annual average runoff volume (P₂₁) refers to the water yield of each region. Population (P₂₂) refers to the people who live in the same river basin and who should possess the same water rights. The effective irrigated area (P₂₃) indicates the area of cultivated land in each region that requires irrigation.

(3) The efficiency principle. On the basis of prioritizing the principle of fairness, it is also necessary to improve the efficiency and economic benefits of water resource utilization. The efficiency principle mainly considers the level of economic development and the efficiency of water resource utilization in each region. The level of economic development can reflect the position of each region in the entire river basin, with higher economic development indicating greater regional importance. Indicators such as the per capita GDP, per capita industrial output value, and per capita agricultural output value reflect the level of economic development in each region, while indicators such as the water consumption per CNY 10,000 of GDP, the water consumption per CNY 10,000 of industrial output value, and the water consumption per CNY 10,000 of agricultural output value reflect the water resource utilization efficiency in each region [16,22,29,33,35,53,61,62,66,67]. The specific meanings of the indicators selected under the efficiency principle are as follows:

Per capita GDP (P₃₁) is the ratio between a region’s GDP and its population. Industrial output per capita (P₃₂) is the ratio between a region’s industrial output value and its population. Agricultural output per capita (P₃₃) is the ratio between a region’s agricultural output value and its population. Water consumption per CNY 10,000 of GDP (P₃₄) refers to water resource use efficiency. A larger indicator value means lower-efficiency water resource use. Water consumption per CNY 10,000 of agricultural output (P₃₅) is the proportion between regional agricultural water consumption and the regional agricultural output value, and it also reflects the water resource use efficiency. Water consumption per CNY 10,000 of industrial output (P₃₆) is the proportion between the regional industrial water consumption and the regional industrial output value and also reflects water resource use efficiency.

(4) The sustainability principle. The principle of sustainability requires that the current use of water resources by humans does not exceed the carrying capacity of the regional water resources and that the discharge of pollutants does not exceed the capacity of the regional water environment in order to ensure that the use of water resources meets the principles of sustainable development [64,66]. The economic growth rate and population growth rate reflect the changing trend of future water demand in each region; the greening rate indicates the ecological environment’s water demand in each region; and the standard discharge rate of wastewater reflects the sewage treatment situation in each region. In addition, there are qualitative indicators that reflect the ecological environment, such as the rate of water and soil loss, the secondary salinization of land, non-point source pollution in agriculture, and river flow interruption. However, these indicators are difficult to determine and have little impact, so they were not selected [16,22,53,64,66]. Based on the above analysis, we selected the following indicators related to the sustainability principle and provided explanations for their meanings:

The economic growth rate (P₄₁) reflects the changing trend of water demand in each region in the future. The greening rate (P₄₂) is the ratio between the greenery area and the total area of the region; it determines the ecological water demand of each region. The population growth rate (P₄₃) determines the domestic water demand of each region; it must be guaranteed. The proportion of wastewater that meets the discharge standards (P₄₄) means that a water function area with high water quality standards should result in more initial water rights.

(5) The macro-regulation principle. The configuration must be based on and grounded in the fundamental interests of the majority of the regions. The government should comprehensively coordinate the relationship between local interests and overall interests, single project objectives, and the overall goal of the sustainable development of the entire basin from a macro perspective [16,22,61,62,64]. The government needs to consider the overall goals of the basin from a macro perspective and formulate corresponding policies for different regions, such as regional priority development policies, soil and water conservation policies, etc. Therefore, this article uses “policy inclination” as an indicator to measure the government’s macro-control efforts. In addition, the allocation of water rights in the basin must take into account the interests of vulnerable groups. Since the interests of vulnerable groups are often not effectively protected, this is one of the main factors that causes dissatisfaction among them. Currently, the protection of the interests of vulnerable groups can only be achieved through government macro-control, so this article uses the “protection of vulnerable groups” indicator for the principle of government macro-control [64]. As such, we selected the following indicators related to the macro-regulation principle and provided explanations of their meanings:

Policy inclination (P₅₁) means that the government has different key development areas or industries during different periods, including regional development policies, soil and water conservation policies, upstream priority policies, or policies for the introduction of a certain industry. The protection of vulnerable groups (P₅₂) refers to disadvantaged regions with undesirable geographical locations, a backward economic development level, and worsening ecological environments; these areas should be effectively protected regarding the allocation of water rights. Besides the term “transboundary river” in this paper refers to rivers that flow through different administrative regions within the same country rather than international rivers that cross national borders. Therefore, important indicators that affect international rivers, such as political factors [68], are not included.

Moreover, the indicator system is the foundation of water rights allocation and determines the rationality of water rights allocation. When setting up the indicator system, a comprehensive and overall analysis of the basin and its jurisdictional area must be conducted, and the factors affecting water rights allocation must be fully considered to construct a comprehensive and integrated indicator system. At the same time, the indicator system should also be a top-down, multi-level, multi-attribute, and multi-regional structural system that is an organic whole rather than a simple collection of multiple indicators. There are many types of indicator systems that affect water rights allocation, and different indicators can be generated from different perspectives. If all of them are listed, they will be numerous, and some indicators may have certain intersections or redundancies. Therefore, the selection of indicators should follow certain guidelines. The reasons and their sources of practical applications for selecting indicators are detailed in Appendix A,

Table A1. Sources of indicators and rational explanations of indicator selection.

Principle	Indicator	Research Literature or Documents	Reasons or Sources of Practical Application for Selection
Status quo B1	Current water use (100 million m3)	[16,53,63,64,65], among them, [53] is related documents	At present, these indicators are mainly used in practical engineering applications to reflect the principles of the current situation; see the water resources bulletin of the TaiHu Basin Authority of the Ministry of Water Resources.
	Water use per capita (m3/person)	[16,53,63,64,65]
	Water use per farmland unit (m3/mu)	[16,53,63,64,65]
	Current water supply scale (10,000 m3)	[16,53,63,64,65]
Equity B2	Annual average runoff volume (100 million m3)	[29,31,33,35,62,64,66], among them, [62] is related documents	Similarly, these indicators are mainly used in practical engineering applications to reflect the premises of the equity principle. These indicators can be obtained from the “Comprehensive planning of water resources in river basins” document.
	Population (10,000 people)	[29,31,33,35,62,64,66]
	Effective irrigated area (hectares)	[29,31,33,35,62,64,66]
Efficiency B3	GDP per capita (CNY 10,000)	[16,22,29,33,35,53,61,62,66,67], among them, [53,61,62,67] are related documents.	Firstly, according to relevant policies in China (Order No. 32 of the Ministry of Water Resources of the People’s Republic of China), the initial allocation of water rights is after deducting the government’s reserved water amount, such as the advance deduction of water for food security guarantees. Therefore, basic agricultural water consumption is a priority and does not fully benefit industrial and urban areas. Secondly, in the assessment of water utilize in various administrative regions in China, indicators such as P31-P36 are commonly used as a basis for determining whether an area has low water use efficiency. This is one of the reasons why these indicators were selected for this article, and it is not an arbitrary choice made to empower industrialized cities. On the basis of ensuring agricultural water security and proposing measures to safeguard food security, areas with low agricultural water use efficiency should choose to improve irrigation techniques or adjust crop structures within the limited water resources, which is also the incentive mechanism of the Chinese government in water allocation. In addition, actual water resource utilization efficiency data statistics, such as those from the Ministry of Water Resources of the People’s Republic of China, TaiHu, the Basin Authority of the Ministry of Water Resources, and so on, all use these indicators to measure efficiency principles. Finally, an approach of not considering the efficiency principle and blindly protecting underdeveloped areas by allocating more water is not conducive to regional economic development, nor does it conform to China’s policy (“Three red lines”) of improving water efficiency. Moreover, in addition to the efficiency principle, our principles also include the principle of fairness and the indicators for the protection of vulnerable groups, meaning that vulnerable groups are already accounted for.
	Industrial output per capita (CNY 10,000)	[16,22,29,33,35,53,61,62,66,67]
	Agricultural output per capita (CNY 10,000)	[16,22,29,33,35,53,61,62,66,67]
	Water consumption per CNY 10,000 GDP (m3)	[16,22,29,33,35,53,61,62,66,67]
	Water consumption per CNY 10,000 agricultural output (m3)	[16,22,29,33,35,53,61,62,66,67]
	Water consumption per CNY 10,000 industrial output (m3)	[16,22,29,33,35,53,61,62,66,67]
Sustainability B4	Economic growth rate (%)	[16,22,53,64,66]	First, these indicators for measuring sustainability are visible in local or national water resource bulletins. Second, the economic growth rate and population growth rate reflect the changing trends of future water demand in each region; the greening rate indicates the ecological and environmental water demand in each region; and the standard discharge rate of wastewater reflects the sewage treatment situation in each region. In addition, there are qualitative indicators that reflect the ecological environment, such as the rate of water and soil loss, the secondary salinization of land, non-point source pollution in agriculture, and river flow interruption. However, these indicators are difficult to obtain and have little impact (and thus do not satisfy the requirements of being comparable, quantifiable, and feasible), so they were not selected.
	Greening rate (%)	[16,22,53,64,66]
	Population growth rate (%)	[16,22,53,64,66]
	Proportion of waste water that meets discharge standards (%)	[16,22,53,64,66]
Macro regulation B5	Policy inclination (points)	[16,22,61,62,64]	First, the government must comprehensively coordinate the relationship between local interests and overall interests, as well as between individual goals and the overall goal of sustainable development in the entire basin. It must do so from a macro perspective to guide the smooth implementation of water rights allocation work. The government needs to consider the overall goals of the watershed from a macro perspective and formulate corresponding policies for different regions, such as regional priority development policies, soil and water conservation policies, and preferential policies for poverty-stricken areas. Therefore, this project uses “policy inclination” as an indicator to measure the government’s macro-control efforts. Second, these policies are evidenced in the relevant documents produced by the relevant governments. These include the “Opinions on Implementing the strictest Water Resource Management System”, the reply of the Ministry of Water Resources of the National Development and Reform Commission on the water allocation scheme of the Taihu Lake Basin”, and so on. This means that we are correct in using policy inclination indicators. In addition, the first-level allocation of initial water rights in the basin must comprehensively consider the vulnerable groups in the upstream, downstream, and left and right bank areas. Due to the lack of effective protections for the interests of vulnerable groups, their dissatisfaction is often triggered, which is one of the main reasons for a lack of social harmony. At present, the protection of the interests of vulnerable groups can only be achieved through government macroeconomic regulation.
	Protection of vulnerable groups (points)	[16,22,61,62,64]

.

Therefore, we designed a water allocation index system, as shown in

Table 1. Index system of physical water rights allocation.

Scheme	Principle	Indicator	Symbol	Attribute
Physical water rights allocation scheme A	Status quo B1	Current water use (100 million m3)	P11	Benefit-based indicator
		Water use per capita (m3/person)	P12	Benefit-based indicator
		Water use per farmland unit (m3/mu)	P13	Benefit-based indicator
		Current water supply scale (10,000 m3)	P14	Benefit-based indicator
	Equity B2	Annual average runoff volume (100 million m3)	P21	Benefit-based indicator
		Population (10,000 people)	P22	Benefit-based indicator
		Effective irrigated area (hectare)	P23	Benefit-based indicator
	Efficiency B3	GDP per capita (CNY 10,000)	P31	Benefit-based indicator
		Industrial output per capita (CNY 10,000)	P32	Benefit-based indicator
		Agricultural output per capita (CNY 10,000)	P33	Benefit-based indicator
		Water consumption per CNY 10,000 of GDP (m3)	P34	Cost-based indicator
		Water consumption per CNY 10,000 of agricultural output (m3)	P35	Cost-based indicator
		Water consumption per CNY 10,000 of industrial output (m3)	P36	Cost-based indicator
	Sustainability B4	Economic growth rate (%)	P41	Benefit-based indicator
		Greening rate (%)	P42	Benefit-based indicator
		Population growth rate (%)	P43	Benefit-based indicator
		Proportion of waste water that meets discharge standards (%)	P44	Benefit-based indicator
	Macro-regulation B5	Policy inclination (points)	P51	Benefit-based indicator
		Protection of vulnerable groups (points)	P52	Benefit-based indicator

.

(2)

Allocating physical water rights

Based on the data from these 19 indicators, using the TOPSIS method, we can determine the actual allocation of water rights in each coastal area of the watershed.

The TOPSIS method, also known as a technique for ordering preference according to similarity to an ideal solution, is an improvement on M. Zeleny’s compromise solution; it is based on the concept of the nearest ideal solution [60,62,63,64]. For multi-objective decision-making problems, the specific solution process of the TOPSIS method is as follows:

First, determining positive and negative ideal solutions. The positive ideal solution represents the best attribute values among all the alternative solutions, while the negative ideal solution corresponds to the worst attribute values.

Second, in a practical situation, attaining optimal values for all indicators is impossible. Based on the core idea of the TOPSIS method [60,62,63,64], the optimal solution is identified as the one with the shortest distance to the positive ideal solution and the longest distance to the negative ideal solution. Therefore, the key concern of the TOPSIS method is to measure the distance between each solution and both positive and negative ideal solutions.

In the allocation of water rights in a river basin, there are $n$ regions participating in the allocation, and $m$ evaluation indicators are set. The regions with shorter distances to the positive and negative ideal solutions should be allocated more water rights. Therefore, the distances of each region to the positive and negative ideal solutions can be used as the basis for water rights allocation.

Step 1: building a decision-making matrix

Suppose there are $n$ regions participating in the initial water rights allocation in the basin, and each region has $m\left(m=1,2,\cdots ,19\right)$ indicators; therefore, a decision-making matrix is built on the $m$ indicators of $n$ regions, as shown in Equation (1):

$$X=\left[\begin{array}{llll}{x}_{11}\hfill & x_{12}\hfill & \cdots \hfill & x_{1n}\hfill \\ x_{21}\hfill & x_{22}\hfill & \cdots \hfill & x_{2n}\hfill \\ ⋮\hfill & ⋮\hfill & \cdots \hfill & ⋮\hfill \\ x_{m1}\hfill & x_{m2}\hfill & \cdots \hfill & x_{mn}\hfill \end{array}\right]={\left(x_{ij}\right)}_{m\times n}$$

(1)

Step 2: normalizing the data

Considering the different standards for different indicators, the matrix $X$ was then normalized [16].

For benefit-based indicators:

$$y_{ij}=\frac{x_{ij}-\underset{i}{\min } x_{ij}}{\underset{i}{\max } x_{ij}-\underset{i}{\min } x_{ij}},i=1,2,\cdots ,m;j=1,2,\cdots ,n$$

(2)

where $\underset{i}{\max } x_{ij}$ is the maximum value of indicator $i$ in region $n$, and $\underset{i}{\min } x_{ij}$ is the minimum value of indicator $i$ in region $n$.

For cost-based indicators:

$$y_{ij}=\frac{\underset{i}{\max } x_{ij}-x_{ij}}{\underset{i}{\max } x_{ij}-\underset{i}{\min } x_{ij}},i=1,2,\cdots ,m;j=1,2,\cdots ,n$$

(3)

Step 3: constructing the projection indicator function

First, the decision-making matrix of the positive-ideal and negative-ideal solutions is determined as follows:

$$\begin{array}{l}{Y}_j^{+}=\max \left\{y_{1j},y_{2j},\cdots ,y_{mj}\right\}\\ Y_j^{-}=\min \left\{y_{1j},y_{2j},\cdots ,y_{mj}\right\}\end{array}$$

(4)

Thus, the positive-ideal and negative-ideal matrices are:

$$\begin{array}{l}{Y}^{+}={\left(y_{ij}^{+}\right)}_{m\times n}\\ Y^{-}={\left(y_{ij}^{-}\right)}_{m\times n}\end{array}$$

(5)

Next, the distance between each region and the positive-ideal solution is:

$$d_j^{+}={\left[{\displaystyle \sum _{i=1}^m{\omega }_i(y_{ij}-y_{ij}^{+}}{)}^2\right]}^{0.5}$$

(6)

where ${\omega }_i$ is the weight of indicator $i$; obviously, the smaller the $d_j^{+}$ value, the closer the region $j,j=1,2,\cdots ,n$ is to the positive-ideal point, so the region deserves more water rights.

According to the indicator weight ${\omega }_i$, $p_{51},p_{52}$ are qualitative indicators, and the rest are quantitative indicators. As such, this paper used an analytic hierarchy process (AHP) that combines both qualitative and quantitative indicators to determine the weights of the indicators of water rights allocation [62,63,64]. For specific explanations and solution processes for AHP, please refer to Attachment A.

The distance between each region and the positive-ideal solution is:

$$d_j^{-}={\left[{\displaystyle \sum _{i=1}^m{\omega }_i(y_{ij}-y_{ij}^{-}}{)}^2\right]}^{0.5}$$

(7)

Obviously, the bigger the $d_j^{-}$ is, the closer region $j$ is to the positive-ideal point, so it deserves more water rights.

Moreover, based on the premise of TOPSIS, $D_j$ is presented with relative proximity, as shown in Equation (8):

$$D_j=\frac{d_j^{-}}{d_j^{-}+d_j^{+}}$$

(8)

Step 4: determining the water rights allocation scheme

According to Equations (6)–(8), the initial water rights that should be allocated to each region are as follows:

$${\phi }_j=\frac{D_j}{{\displaystyle \sum _{j=1}^n{D}_j}}$$

(9)

The amount of initial water rights that each region receives is:

$$C_j={\phi }_j\cdot C_0$$

(10)

where $C_0$ represents the available water resources of the basin and $\left(C_1,C_2\cdots C_n\right)$ is taken as the scheme of the initial water rights allocation.

2.2.2. The Model for Virtual Water Transfer

The water resources implicitly contained in goods are generally referred to as “virtual water”. Therefore, such resources can be transferred through trade. If provinces $r$ and $s$ engage in direct trade, the water resources used in the production of goods in province $r$ are directly transferred to province $s$. If the goods produced in province $r$ are first purchased by province $p$ and used for production before being sold to province $s$, an indirect trade relationship is established between provinces $r$ and $s$. In this case, the virtual water of province $r$ is actually transferred to province $s$ through indirect trade. Therefore, based on the MRIO model, we can calculate the amount of interprovincial virtual water transfer.

Provincial VWT:

First, we should note that a transboundary river includes n basin provinces, referred to as basin province 1, basin province 2, …, basin province $n$, and that other provinces that are not part of the transboundary basin are grouped into one province, referred to as the other province $\left(n+1\right)$. Second, in combination with the multi-regional input–output table, we constructed a modified multi-regional input–output table. See the specific

Table A9. Multi-regional input–output table.

Output			Intermediate Use										Final Demand				Total Output
			Basin Province 1			…	Basin Province (n)			Basin Province (n + 1)			Basin Province 1	… …	Basin Province n	Other Province (n + 1)
Input			Industry 1	… …	Industry m	… …	Industry 1	… …	Industry m	Industry 1	… …	Industry m
Interm-ediate use	Basin province 1	Industry 1	$y_{11}^{11}$	… …	$y_{1m}^{11}$	… …	$y_{11}^{1n}$	… …	$y_{1m}^{1n}$	$y_{11}^{1(n+1)}$	… …	$y_{1m}^{1(n+1)}$	$f_1^{11}$	… …	$f_1^{1n}$	$f_1^{1(n+1)}$	$y_1^1$
		… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …
		Industry m	$y_{m1}^{11}$	… …	$y_{mm}^{11}$	… …	$y_{m1}^{1n}$	……	$y_{mm}^{1n}$	$y_{m1}^{1(n+1)}$	… …	$y_{mm}^{1(n+1)}$	$f_m^{11}$	… …	$f_m^{1n}$	$f_m^{1(n+1)}$	$y_m^1$
	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …
	Basin province n	Industry 1	$y_{11}^{n1}$	… …	$y_{1m}^{n1}$	… …	$y_{11}^{nn}$	… …	$y_{1m}^{nn}$	$y_{11}^{n(n+1)}$	… …	$y_{1m}^{n(n+1)}$	$f_1^{n1}$	… …	$f_1^{nn}$	$f_1^{1(n+1)}$	$y_1^n$
		… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …
		Industry m	$y_{m1}^{n1}$	… …	$y_{mm}^{n1}$	… …	$y_{m1}^{nn}$	… …	$y_{mm}^{nn}$	$y_{m1}^{n(n+1)}$	… …	$y_{mm}^{n(n+1)}$	$f_m^{n1}$	… …	$f_m^{nn}$	$f_m^{1(n+1)}$	$y_m^n$
	Other province (n + 1)	Industry 1	$y_{11}^{(n+1)1}$	… …	$y_{1m}^{\left(n+1\right)1}$	… …	… …	……	… …	$y_{11}^{n(n+1)}$	… …	$y_{1m}^{(n+1)(n+1)}$	$f_1^{(n+1)1}$	… …	$f_1^{n\left(n+1\right)}$	$f_1^{(n+1)(n+1)}$	$y_1^{(n+1)}$
		… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …	… …
		Industry m	$y_{m1}^{(n+1)1}$	… …	$y_{mm}^{(n+1)1}$	… …	… …	……	… …	$y_{m1}^{(n+1)(n+1)}$	……	$y_{mm}^{(n+1)(n+1)}$	$f_m^{(n+1)1}$	… …	$f_m^{(n+1)n}$	$f_m^{(n+1)(n+1)}$	$y_m^{n+1}$
Added Value			$v_1^1$	… …	$v_m^1$	… …	… …	……	… …	$v_1^{n+1}$	… …	$v_m^{n+1}$
Total input			$y_1^1$	… …	$y_m^1$	… …	… …	……	… …	$y_1^{n+1}$	… …	$y_m^{n+1}$
Direct water input			$w_n^r$

in Appendix B.

Based on a multi-regional input–output approach, we obtain the following:

$$Z^{rs}={\displaystyle \sum _{p=1}^{n+1}{W}^r{L}^{rp}{F}^{ps}}$$

(11)

$r,s$ refers to the basin province, $p$ stands for all provinces with which provinces $r,s$ trade, and $\left(n+1\right)$ denotes the number of provinces with which provinces $r,s$ trade. When $p=r$, it indicates the amount of virtual water transfer triggered by direct trade from basin province $r$ to basin province $s$. When $p\ne r$, it indicates that basin province $r$ exports intermediate products to province $p$, which are processed by province $p$ into final products and exported to basin province $s$, thus transferring the amount of water resources from basin province $r$ to basin province $s$, i.e., engaging in indirect virtual water transfer from basin province $r$ to basin province $s$.

$Z^{rs}$ denotes the virtual water transfer from basin province $r$ to basin province $s$. $W$ denotes the direct water coefficient matrix, and $W^r$ stands for the direct water coefficient matrix of basin province $r$. $L$ is famously known as the Leontief inverse and represents the gross output values that are generated in all stages of the production process of one unit of consumption; $L^{rp}$ refers to the submatrices of the Leontief inverse matrix for basin province $r$ basin province $p$. $F$ is the final demand matrix, and $F^{ps}$ is the submatrices of the final demand matrix for basin province $p$ to basin province $s$.

Similarly, we can obtain the virtual water transfer from basin province $s$ to basin province $r$:

$$Z^{sr}={\displaystyle \sum _{p=1}^{n+1}{W}^s{L}^{sp}{F}^{pr}}$$

(12)

Finally, we are able to obtain a net virtual water transfer volume from basin province $r$ to another basin province:

$$K{Z}^r={\displaystyle \sum _{s=1}^n\left(Z^{rs}-Z^{sr}\right)}$$

(13)

If $K{Z}^r\ge 0$, this means the basin province r has a net virtual water output, then its total water availability decreases. If $K{Z}^r<0$, this means that basin province $r$ has a net virtual water input and its total water availability increases.

2.2.3. Coupling Physical and Virtual Water

(1)

Riparian VWT

To further refine provincial VWT at the riparian level, this paper converted provincial VWT via the water efficiency coefficient and then distributed it to riparian areas within a province.

$${KZ}_b^r=\tau {KZ}^r$$

(14)

where $\tau$ is the conversion percentage, which represents the proportion of the water efficiency coefficient in the basin to the corresponding water efficiency coefficient in the province or city. ${KZ}_b^r$ is the net VWT of basin $r$.

(2)

Model coupled with physical water and virtual water

The physical and virtual water resources were determined and then coupled to formulate an initial water rights allocation scheme that integrates both physical and virtual water, as shown below:

$$C_r^{\prime }=C_r+{KZ}_b^r$$

(15)

where $C_r^{\prime }$ represents the amount of water allocated to region $r$.

3. Results

3.1. Physical Water Resources Allocation

3.1.1. Characteristic Value of Each Indicator

This paper examined the initial water rights allocation combining both physical and virtual water in the Taihu Lake Basin. The Basin encompasses Anhui Province (Xuancheng City), Jiangsu Province (Suzhou City, Wuxi City, Changzhou City, and Zhenjiang City), Zhejiang Province (Hangzhou City, Jiaxing City, and Huzhou City), and Shanghai City. This paper selected the mean values of the data of cities in Jiangsu Province and Zhejiang Province to obtain the characteristic values of indicators via Table 1, as shown in

Table 2. Characteristic values of indicators of physical water resources.

Indicators	P11	P12	P13	P14	P21	P22	P23	P31	P32	P33	P34	P35	P36	P41	P42	P43	P44	P51	P52
Anhui N1	0.24	503	331	1.3	0.1	36.4	11.8	2.8	1.91	0.37	214	1.85	72	8.5	0.082	58.0	58.3	6	7
Jinagsu N2	195	802	446	94.6	10.7	3186.5	1030.4	7.0	4.81	0.45	52	0.01	82	7.2	0.028	39.8	60.4	8	6
Zhejing N3	47.1	370	381	82.6	6.7	1987.0	642.6	13.6	7.97	0.24	35	0.01	21	7.8	0.06	37.8	57.2	8	6
Shanghai N4	98.2	418	524	28.4	2.8	848.1	274.3	18.6	9.82	0.06	33	0.005	75	6.9	0.028	30.0	70.5	7	6

.

3.1.2. Normalization of Indictor Values

Characteristic values were then normalized via Equations (2) and (3) to obtain the normalization of the indictor values (

Table 3. Normalization of indictor values.

Indicators	Anhui N1	Jinagsu N2	Zhejing N3	Shanghai N4
P11	0.00	1.00	0.24	0.50
P12	0.31	1.00	0.00	0.11
P13	0.00	0.60	0.26	1.00
P14	0.00	1.00	0.87	0.29
P21	0.00	1.00	0.62	0.26
P22	0.00	1.00	0.62	0.26
P23	0.00	1.00	0.62	0.26
P31	0.00	0.28	0.68	1.00
P32	0.00	0.37	0.77	1.00
P33	0.79	1.00	0.46	0.00
P34	0.00	0.90	1.00	1.00
P35	0.00	0.10	0.10	1.00
P36	0.16	0.00	1.00	0.11
P41	1.00	0.19	0.56	0.00
P42	1.00	0.00	0.59	0.00
P43	1.00	0.35	0.28	0.00
P44	0.08	0.24	0.00	1.00
P51	0.00	1.00	1.00	0.50
P52	1.00	0.00	0.00	0.00

).

3.1.3. Weights of Indicators

Regarding the weight of principle layer B on target A and the weight of indicator layer P on principle B, Appendix A presents the relevant data. Additionally, AHP was employed to determine the total weight of indicators relative to the target (A), as shown in

Table 4. Indicator weight.

P	A					The Total Weight of Indicators Relative to the Target (A)
	B1	B2	B3	B4	B5
	0.265	0.492	0.136	0.069	0.038
P11	0.556	0	0	0	0	0.1473
P12	0.190	0	0	0	0	0.0503
P13	0.190	0	0	0	0	0.0503
P14	0.064	0	0	0	0	0.0172
P21	0	0.2	0	0	0	0.0983
P22	0	0.4	0	0	0	0.1967
P23	0	0.4	0	0	0	0.1967
P31	0	0	0.2	0	0	0.0272
P32	0	0	0.2	0	0	0.0272
P33	0	0	0.2	0	0	0.0272
P34	0	0	0.1	0	0	0.0136
P35	0	0	0.2	0	0	0.0272
P36	0	0	0.1	0	0	0.0136
P41	0	0	0	0.520	0	0.0363
P42	0	0	0	0.201	0	0.0140
P43	0	0	0	0.200	0	0.0140
P44	0	0	0	0.078	0	0.0054
P51	0	0	0	0	0.667	0.0251
P52	0	0	0	0	0.333	0.0125

:

3.1.4. Allocation of Physical Water Resources

The allocation amount and proportion of physical water were calculated via Equations (6)–(10), as shown in

Table 5. Results of physical water resource allocation.

Region	Distance to Positive-Ideal Solution, ${\mathit{d}}_{\mathit{k}}^{+}$	Distance to Negative-Ideal Solution, ${\mathit{d}}_{\mathit{k}}^{-}$	Allocation Amount (100 Million m3)	Allocation Proportion
Anhui	0.8659	0.0992	16.83	5.51%
Jiangsu	0.1070	0.8233	144.91	47.50%
Zhejiang	0.2810	0.3444	90.18	29.56%
Shanghai	0.4767	0.2293	63.18	17.43%

. Specifically, cities in Jiangsu Province have the largest amount, at 14.491 billion m³, followed by cities in Zhejiang Province (29.56%), and then Xuancheng City in Anhui Province, with a value of 1.683 billion m³, accounting for 5.51%.

Moreover, to verify the stability of the physical water allocation results presented in this paper, we conducted a sensitivity analysis for the weights of the physical water allocation indicators and used Pearson’s correlation coefficient to test the similarity of the results under different scenarios (see

Table 6. The change rate of physical water rights for different weights.

	The Change Rate of Physical Water Rights	Anhui	Jiangsu	Zhejiang	Shanghai	Pearson’s Correlation Coefficient
Weight Variation Range
0.3%		0.6%	−0.6%	0.1%	−0.1%	0.99992
0.5%		1.2%	−1.0%	0.1%	−0.2%	0.99972
1%		1.9%	−1.8%	0.2%	−0.4%	0.99915

).

According to the relevant literature on sensitivity analyses [69,70], and in conjunction with the actual status of the indicators, there are 19 indicators in this paper. The calculated minimum indicator weight value is 0.00541, while the others are generally in the range of 0.01 to 0.09. In instances where there is a significant random increase or decrease in the indicator weights, it is possible that some indicator weights become negative and incorrect.

Just as we know, when the indicator value becomes negative, it has no practical significance. Moreover, this does not comply with the principles of allocation and does not conform to practical experience. Therefore, this paper selects weight variations of 0.3%, 0.5%, and 1% and then conducts Pearson’s correlation coefficient analysis for the three scenarios. We obtained the range of the rate of change of physical water rights allocation in four different regions (see Table 6).

In the above three cases (Table 6), the change rate of the proportion of physical water rights allocation is within the acceptable range. Additionally, the correlation coefficient was 0.99, indicating that it is safe to say that the overall physical water rights allocation is much less strongly affected when using different weights. Therefore, the allocation of physical water rights is reliable.

3.2. VWT Value

According to Equations (12)–(14), the import, export, and net export of virtual water among cities and provinces connected to the Taihu Lake Basin were calculated, as shown in

Table 7. VWT within the Taihu Lake Basin (100 million m³).

	Exporter	Jiangsu	Anhui	Zhejiang	Shanghai	Virtual Water Export
Importer
Jiangsu		/	20.43	13.06	9.36	42.85
Anhui		19.35	/	16.54	14.96	50.85
Zhejiang		2.74	3.38	/	4.68	10.80
Shanghai		2.96	4.45	4.64	/	12.05
Virtual water import		25.05	28.26	34.24	29.00

and Figure 2.

In this table, the rows show virtual water exports. Taking Jiangsu as an example, the first row indicates that Jiangsu exports virtual water to Anhui, Zhejiang, and Shanghai, with volumes of 2.043, 1.306, and 0.936 billion m³, respectively, totaling 4.285 billion m³. The columns show virtual water imports. Similarly, taking Jiangsu as an example, the first column indicates that Anhui, Zhejiang, and Shanghai import virtual water from Jiangsu, with volumes of 1.935, 0.274, and 0.296 billion m³, respectively, totaling 2.505 billion m³. Therefore, the net transfer of virtual water from Jiangsu is calculated by subtracting the total input from the total output, resulting in 1.780 billion m³.

According to Table 7, Anhui transfers the largest amount of virtual water to other provinces and cities, 5.085 billion m³, while Zhejiang transfers the smallest amount, at 1.08 billion m³. However, the net import of virtual water shows the opposite result: 3.424 billion m³ in Zhejiang. Moreover, according to Table 3, we can obtain a comparative diagram of virtual water transfer in these four regions (Figure 2).

3.3. Allocation Scheme Combining Physical and Virtual Water

According to Equations (14) and (15), we can obtain the allocation scheme comprising a physical water rights allocation scheme including virtual water, as shown in

Table 8. Water rights allocation scheme, including virtual water.

Region	Conversion Percentage $\mathit{\tau }$	Allocation Proportion ${\mathit{\phi }}_{\mathit{k}}$	Allocation Amount (100 million m3)
Anhui	1.17	14.31%	43.19
Jiangsu	0.96	53.72%	162.08
Zhejiang	1.03	21.89%	66.06
Shanghai	1.34	10.07%	30.40

and Figure 3.

Table 7 shows that, with virtual water included, the region that receives the largest amount of allocated water is still Jiangsu Province, with 16.208 billion m³, accounting for 53.72%. Meanwhile, Anhui and Shanghai experience relatively pronounced changes; the amount allocated to Anhui reaches 4.319 billion m³, while that for Shanghai declines to 3.04 billion m³, with Shanghai becoming the city with the smallest allocation quantity. From the perspective of absolute quantity change, the water allocation in Zhejiang has decreased by 2.41 billion m³, which is more than Shanghai. This shows that VWT exerts an essential influence on physical water resources, which proves the significance of integrating virtual water.

According to Figure 3, the integration of virtual water changes the amount and proportion of water rights allocated to all four regions. Specifically, the amount allocated to Anhui increases by more than two times in amount, while that received by Shanghai drops by nearly 75%, leading to the variation in allocation proportions.

4. Discussion

4.1. Physical Water Allocation

The results above (Table 5) are generally in line with the results of previous studies [71] (Figure 4). Jiangsu ranks first in terms of the allocation amount, followed by Zhejiang and Shanghai. The exception is Anhui Province; some scholars ignore Anhui in studies of water resource allocation as it comprises a relatively small portion of the basin’s area. In terms of the allocation proportion, Jiangsu drops by 6.43% compared with the results of previous studies, while Zhejiang and Shanghai increase by 5.30% and 6.65%, respectively. In addition, in this paper, Jiangsu still takes the lion’s share, 47.5%, whereas Shanghai ranks at the bottom with 17.43%.

According to Figure 4 and Table 5, the overall water allocation and distribution ratios are consistent with those presented in previous studies. This result is in line with the actual conditions: Jiangsu Province houses the most cities connected to the Taihu Lake Basin and thus requires the largest amount of water; meanwhile, Xuancheng City is located along the Basin and requires the least water. This indicates that the results related to water allocation in this article are applicable to the actual situation. The difference is that previous scholars’ research overlooked Anhui province. This is unfair to Anhui province, so we included the Anhui region in the allocation process.

4.2. Water Allocation after Coupling Physical and Virtual Water

According to Figure 2 and Table 7, Anhui and Jiangsu are net exporters of virtual water, with values of 2.259 billion m³ and 1.78 billion m³, respectively. This means that Anhui and Jiangsu subsidize Zhejiang and Shanghai in terms of virtual water. Thus, after incorporating virtual water into the allocation of physical water rights, it appears that the two provinces deserve more water rights in the allocation scheme. On the contrary, Zhejiang Province and Shanghai City are net importers, with 2.344 billion m³ and 1.695 billion m³, respectively. This indicates that Shanghai and Zhejiang are the recipients of subsidies; thus, they deserve fewer water rights.

Additionally, based on Figure 5, we can determine that the coastal areas of the three provinces and one city in the Taihu Lake Basin experienced significant changes in water rights allocation before and after including virtual water. It is clear that the impact of virtual water cannot be ignored. In addition, in the process of calculating the virtual water transfer, we found that the main reason for Anhui and Jiangsu’s net export of virtual water is that these two provinces mainly export agricultural products to Shanghai and Zhejiang, while the opposite is true for Shanghai and Zhejiang. Agricultural products have much higher virtual water content than industrial products, resulting in Anhui and Jiangsu being net exporters of virtual water. In terms of actual water use efficiency, Anhui and Jiangsu consume a large amount of water resources. To reduce the degree of development constraint in the context of uncertain future water supply and demand, it is increasingly urgent for these two provinces, especially Anhui, to adjust their industrial structure.

All these findings produce changing proportions and lead to the conclusion that virtual water plays an indispensable role in physical water rights allocation. Therefore, virtual water must be considered in the water rights allocation of rivers, especially transboundary rivers.

Moreover, water rights allocation is the foundation for alleviating water conflicts between upstream and downstream regions. In practical situations, due to climatic variations and differences in socio-economic development, some regions have relatively abundant water resources but lower demand for them, while others have relatively limited water resources but higher demand, as is the case in agricultural areas. In such cases, we can engage in water rights trading based on water rights allocations to achieve mutual benefits among regions.

5. Conclusions

Virtual water exerts a significant influence on water resources, yet current studies on water rights allocation in transboundary rivers barely pay attention to virtual water. Therefore, taking the Taihu Lake Basin as the case study, this work determined the physical water rights of the four regions (province/city) connected to the Basin. Next, this paper employed MRIO to measure the provincial VWT and then used the water efficiency coefficient to convert the VWT from the provincial level to the riparian level. Finally, virtual water was included to formulate the final water rights allocation scheme.

(1) In terms of physical water rights allocation, Jiangsu ranks first, followed by Zhejiang, Shanghai, and then Anhui.

(2) As for VWT, Anhui and Jiangsu are net exporters (Anhui > Jiangsu), whereas Zhejiang and Shanghai are net importers (Zhejiang > Shanghai).

(3) The integration of virtual water makes a difference to the amount and proportion of water rights allocated to all four regions. Anhui and Shanghai experience relatively obvious changes.

(4) Anhui is the largest net exporter of virtual water, indicating that it consumes more water than the other regions and is in greater need of economic restructuring.