**1. Introduction**

China is facing a grea<sup>t</sup> challenge as water is still a major constraint on the nation's economic and social development due to the growing population, urbanization, and industrialization at a time when there are serious water shortages, growing pollution, severity of droughts, and declining aquatic ecosystems. Although China is rich in water resources and ranks sixth in the world in terms of water volume, the available water in China is only 1998.6 m<sup>3</sup> per capita in 2014 and less than one-quarter of the world average which can be shown by the data from China Statistical Yearbook (2015). China's amount of water use reached 609.5 billion m<sup>3</sup> (Figure 1) in 2014. However, the annual

water scarcity across the country has exceeded 50 billion m<sup>3</sup> on average according to the data from Global Water Partnership.

**Figure 1.** Increasing water use in China. Data source: China Water Resources Bulletin (1997–2000) and China Statistical Yearbook (2000–2015).

With China's previous water resources managemen<sup>t</sup> system, the cost of using water was nearly zero which caused a similar external diseconomy of "tragedy of the commons". In that situation, injudicious development and overuse of water cannot be avoided and the negative impacts on environment came out including rivers drying up, ecosystem degradation, and environment deterioration.

At present, under the new scenarios of the most stringent water resources managemen<sup>t</sup> system, in order to address these water problems, China is establishing a legal framework including initial water rights, water licensing, and a water rights trade-off to reform water allocation mechanisms and property rights systems to fit more closely with China's developing and maturing market economy. In fact, the final distribution of wealth, however, does depend on how property rights are initially assigned. Just as the Coase Theorem presented, the initial allocation of property rights often matters for efficiency due to transaction costs cannot be neglected [1]. Therefore, assignment of initial water rights is particularly important for fairness of water use and water efficiency. Clarification of initial water rights in China is not only the basis and prerequisite for a water rights trade-off market but also an effective solution to the problem of water scarcity and water conflicts.

Initial provincial water rights are an important part of river basin initial water rights. Existing literature about initial provincial water rights optimal allocation is in pursuit of a more scientific and effective allocation plan. However, as the major reforms to the implementation of the new most stringent water resources managemen<sup>t</sup> system in China, the existing theory and practice of provincial initial water rights allocation should meet the new requirements of this system. Therefore, how to assign a reasonable allocation of initial provincial water rights, following the benchmark of the new most stringent water resources managemen<sup>t</sup> system, is not only the major element and core aspect of basin initial water rights allocation but also an important approach to enhancing the efficiency of water resources utilization and significant for achieving harmony between economic and social development and available water resources in China. Recently, initial provincial water rights optimal allocation has been an active research field both in foreign and domestic areas. A majority of literature in this area can be divided into four categories.

The first category focuses on using hybrid allocation method to solve the initial provincial water rights allocation problems. For instance, Wang Hao et al. [2] found water resources allocation in China should follow a "natural-artificial" dual knowledge and perception mode for modern river basin water cycling process. Wu Dan et al. [3] established the bi-level optimization model of the compound system for basin initial water rights allocation to realize the reasonable allocation of water rights in different regions and different industries. Considering the pollution limits of water functional zones, which is

the one "red line" of the most stringent water resources management, Ge Min et al. [4] proposed a provincial initial water rights incentive allocation model with total pollutant discharge constraints.

The second category pays close attention to multi-participation allocation model. For instance, Ralph [5] set up a generalized simulation model called Water Right Analysis Package (WRAP) which was implemented in the state of Texas for the state's 23 river basins. Yan-ping Chen et al. [6] divided the regions of the same basin into a disadvantaged group and an advantaged group, based on which they founded an evolutionary game model. They also adjusted the water rights of different regions according to the evolutionary stable strategy. Read et al. [7] established the model of negotiation with multiple-decision makers over water rights allocation.

The third category concerns an allocation model of multi-objective optimization. For instance, Feng-ping Wu et al. [8] established a multi-objective and semi-structural fuzzy optimization model in order to solve the problem of initial allocation of water rights of the first hierarchy. Xian-feng Huang et al. [9] created a multi-objective chaotic optimization algorithm. Condon et al. [10] presents the development of a water allocation model (WAM) for an integrated physical hydrology model. His managemen<sup>t</sup> model uses linear optimization to maximize satisfaction of demand.

The fourth category focuses on applying interactive or harmonious allocation method to tackle the initial provincial water rights allocation problems. For instance, Feng-ping Wu and Min Ge et al. [11] put forward principles for harmonious and disharmonious judgment of initial water rights allocation, and they also came up with an interactive method of initial water rights allocation which could fully assimilated the ideas of different apartments from different regions about the initial allocation of water rights. Furthermore, Wang et al. [12] built a harmonious model for water rights allocation, and Feng-ping Wu et al. [13] proposed the harmonious method of allocating basin water rights.

According to the existing literature, despite different perspectives, much research has applied a considerable amount of initial provincial water rights allocation methods in the pursuit of a more scientific and effective water rights allocation plan. However, along with the evolution of the social-economic-ecological complex system, water rights managemen<sup>t</sup> in China is now facing many new constraints. The first one is that China is implementing the most stringent mechanism of water resources managemen<sup>t</sup> which contains "three red lines", namely a "red line" for controlling the total water use, a "red line" for improving the water use efficiency and a "red line" for controlling the pollution of water function zones. Initial provincial water rights allocation must meet the new requirements of the water resources managemen<sup>t</sup> system in China. The second one is that China advocates the construction of an ecological civilization for which the improvement of water quality is an important guarantee. The third one is that China has put forward five concepts for development and policies for poverty alleviation, and how to realize the balanced and efficient use of water with initial provincial water rights allocation really needs further discussion.

For the new scenarios of water resources managemen<sup>t</sup> presented above, the existing studies of relevant aspects are inadequate as follows:


dynamic decision question for time, indicator, and allocation plan. We are concerned not only about the static analysis of the system, but also the dynamic development of the system.

•Thirdly, the existing indicator system studies are inadequate for meeting the new most stringent water resource managemen<sup>t</sup> requirements. Hence, the third contribution of this paper is that we design an index system of initial provincial water rights allocation by absorbing the concepts of "three red lines" and the idea of coordinated and sharable development of provinces. Based on the designed index system, we set up an initial provincial water rights allocation model with the total water use control by dynamic projection pursuit technique. Furthermore, we tackle the model with a self-adaptive chaotic optimization algorithm to acquire the solutions for province initial water rights allocation, and study the case of Taihu Basin. The outline of the paper can be depicted in Figure 2.

**Figure 2.** Outline of initial provincial water right allocation based on most stringent water resources management.

The rest of this study is organized as follows. Section 2 designs an index system of initial provincial water rights allocation with multiple principles. Section 3 establishes a dynamic projection pursuit allocation model of initial provincial water rights. Section 4 details a case study of Taihu Basin. Section 5 provides the conclusions.

### **2. Design of the Index System**

### *2.1. The Principles of Establishing Index System*

The principles of the establishing index system are important to ensure this method and conclusion are accepted by the administration and the public [13]. The existing literature presents different principles of initial provincial water rights allocation. In order to meet the new requirements of the most stringent water resources managemen<sup>t</sup> in China, we follow the principles of "three red

lines". Furthermore, we follow the principle of "coordinate development, share the future" to design the indicator system for the initial provincial water rights allocation.

### 2.1.1. Principle of Controlling the Total Water Use

As the key content of the most stringent water resources managemen<sup>t</sup> system, control gives dual attention to two dimensions of water quantity and quality. The principle of total water use is shown on the foundation of water resources capacity which means a macroscopic control over the water use of basins or provinces. It sets a bearing capacity of water resources within which people can ensure sustainable social and economic development through rational and efficient water use. As the main controlling factor, it aims to protect ecological environment, and also strengthen the constraining force of water resources managemen<sup>t</sup> and promote the optimal use of water resources.

### 2.1.2. Principle of Improving the Water Use Efficiency

The principle of improving the water use efficiency has water conservation as its main target. It can reflect controlling the process of water saving, in addition, it can reveal the high utilization rate of water resources and lower pollutant discharge, which is a benefit for water quality protection. At a macro level, this red line can control the water total amount of a basin or a province, furthermore, at a micro level, it is the quota managemen<sup>t</sup> to the total water use of industries, enterprises, and water users, which can directly influence not only the water quantity but also the water quality.

#### 2.1.3. Principle of Controlling Pollution of Water Function Zones

The principle of controlling the pollution of water function zones, which is mainly used for limiting the total pollutant discharge, safeguarding the proportion of drinking water sources meeting the required standard, and keeping the ecological base flow for eco-environmental needs. It protects water environment bearing capacity including water quality and water ecology. Furthermore, it restores the damaged water ecology, improves water quality, and decreases the amount of pollutants in the basin.

### 2.1.4. Principle of "Coordinate Development, Share the Future"

The principle of "coordinate development, share the future" leads a profound reform idea in China. At the present stage, initial water rights allocation research should satisfy bearable balanced development of environmental resources between regions, and also should include the idea of coordinated and sharable development. In fact, there is a natural difference in water resources endowment between different provinces including bad geographical location, backward economic development, and a worsening ecological environment. We should give full consideration to the contribution of different provinces for basin water resources managemen<sup>t</sup> in water pollution control and flood discharging. Moreover, in water rights management, we must ensure coordination and equality within initial provincial water rights allocation and protect the basic rights of disadvantaged groups. Then we are able to implement the poverty-reducing policy and share the achievements of development.
