流域水资源利用的极化程度研究——以黄河流域为例
顾世杰1,2, 鲁春霞1,2, 邱金根3
1. 中国科学院地理科学与资源研究所,北京 100101
2. 中国科学院大学,北京 100049
3. 重庆根创勘测规划咨询有限公司,重庆 400000
摘要

水资源过度利用对流域水资源实现可持续利用及生态环境具有很大的影响,量化水资源的开发利用程度对水资源合理利用具有重要的指导作用。基于此,本文提出了水资源利用极化概念旨在定性分析水资源利用是否存在超采;依据 ER指数、 TW指数以及方差的偏离度构建水资源利用极化指数模型,用来量化水资源利用的超采程度。并以黄河七个二级流域区为例,分别计算了地表水以及地下水资源可利用量、超采量、极化指数。结果显示:2012年黄河流域地表水资源可利用量为344.9亿m3,占地表水资源总量的56.21%;地下水资源可利用量为58.4亿m3,占地下水资源的58.74%。而且在黄河流域中下游水资源极化严重,其中黄河兰州至头道拐流域、龙门至三门峡流域段极化度最高,极化指数分别为:19.88、11.81。龙羊峡以上以及头道拐至龙门段不存在极化现象。总体而言,黄河流域水资源利用极化指数是7.95。水资源利用极化度的计算可为黄河流域水资源可持续利用提供重要的理论支撑。

关键词: 水资源研究; 水资源利用; 极化现象; 黄河
Quantifying the Degree of Water Resource Utilization Polarization: A Case Study of the Yellow River Basin
GU Shijie1,2, LU Chunxia1,2,*, QIU Jingen3
1. Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Chongqing GenChuang Survey Planning Consult Co Ltd, Chongqing, 400000, China
*Corresponding author: LU Chunxia, E-mail: lucx@igsnrr.ac.cn
Abstract

The overexploitation of water resources has a substantial influence on their sustainable utilization and the ecological environment in a river basin. Quantification of the development and utilization of water resources plays an important role in guiding the rational utilization of water resources. Based on this, this paper develops the concept of water resource utilization polarization (WRUP) in order to qualitatively analyze whether water resources are being overexploited in the process of utilization. An index model of WRUP was built to quantify the degree of water resources overexploitation. In addition, taking seven secondary basins of the Yellow River as examples, the available quantity, overdraft and polarization indexes of surface water and groundwater resources were calculated. The results show that there are 34.49×108 m3 of surface water available, which accounts for 56.21% of the total surface water volume. A total of 5.84×108 m3 of groundwater is available, which is 58.74% of the total groundwater resources. We also found that the water resources are heavily overexploited and that there is extensive polarization in the middle and lower reaches of the Yellow River. The highest polarization of water resources occurs from Lanzhou to Toudaoguai where the polarization index is 19.88 and from Longmen to Sanmenxia where it is 11.81. There is no polarization above Longyangxia or from Toudaoguai to Longmen. Overall, the polarization of water resources is 7.95 over the entire Yellow River area. These results provide a reference for the availability of water resources that can be used to determine the degree of overexploitation of the water resources in the Yellow River.

Keyword: water research; water resources utilization; polarization phenomenon; the Yellow River
1 Introduction

Water resources play important roles in daily life and economic development. Population growth and increases in economic activity have led to increased demand for water and to water pollution in recent years. These developments have created many problems, such as the destruction of the water balance, the appearance of groundwater funnel areas and ecological degradation because of a diminishing ecological water supply. The Yellow River is the decisive factor for the economy and life in the north of China. In fact, many problems have arisen recently, such as groundwater funnel-ing and surface water reduction, due to the overuse of water resources, and these problems have far-reaching impacts on the sustainable development of China's economy.

The sustainable utilization of water resources is the foundation of water security. Thus, the degree of water resource exploitation in a river system has become a topic of primary importance. The concept of a safe yield emerged in 1915 when it was proposed as a means to determine the amount of a water resource that could be exploited. William defined safe yield as the maximum amount of a water resource that could be supplied from a reservoir during a critical period (Alley W M, 2004 ). Economic feasibility and water quality factors were not considered in this concept. Sophocleous (2000) advanced the concept of a safe yield by considering the quality of an aquifer, and established the concept of sustainable yield in 2000. He believed that sustainable yield must take into consideration the sustainability of the ecological environment and, therefore, should be lower than the safe yield. Both the safe yield and the sustainable yield concepts have ambiguities and complexities. Moreover, these concepts consider only the water resource yield, without accounting for the degree of damage to a river ecosystem. Therefore, this paper introduces the polarization of water resource utilization to determine the situation with respect to the degree of water resource overexploitation.

The concept of polarization was originally defined in the physical sciences as a change in the equilibrium potential of an electrochemical reaction. The phenomenon occurs when something has diverged from certain conditions, making its nature deviate from its original state. In addition, the concept has been broadly used in fields such as economics and sociology. Francois (1955) first proposed the concept of growth poles in economics (Perroux F, 1955). Then the Esteban-Ray index model and the Lorenz-Curve (W indices) were built to determine significant differences in polarization (Esteban J M and Ray D C, 1994; Wolfson, 1994). Based on the W indices, the Tsui-Wang index was developed in 2000 to identify the polarization indices that satisfied a set of desirable axioms (Wang Y and Tsui K, 2000). In addition, other researchers have built models to measure the polarization index, such as the D Ambrosio and K-Z indices (Zhang X and Kanbur R, 2011).

Three models are commonly used to measure the polarization index of the economy. The three polarization index measures are the Esteban-Ray (Esteban J M and Ray D C, 1994) which we refer to as the ER index, the Tsui-Wang (Wang Y and Tsui K, 2000) index (TW index), and the Wolfson index (Wolfson, 1994). These methods divide the sample into several parts and calculate the deviation from the median or mean.

It is unfortunate that the polarization concept is used primarily in economics and sociology. In fact, the polarization phenomenon can be utilized in many fields.

There is also a polarization phenomenon associated with water resources. Guan (2016) identified appropriate indicators using the trapezoidal fuzzy number method and constructed an evaluation index system to measure comprehensive utilization efficiency of water resources. A fuzzy multi-attribute decision analysis approach (FMADAA) was also developed for evaluation of water resource security in nine provinces within the Yellow River basin (Liu K K et al., 2014).

This paper calculates the degree of polarization and quantifies the degree of overexploitation in the Yellow River basin as a way to address governance problems that have occurred and to protect the water resources in the basin.

2 Study area and research methods
2.1 Study area

The Yellow River is the third longest river in Asia and the second longest river in China, with an estimated length of 5464 km. The Yellow River is considered the birthplace of ancient Chinese civilization. The Yellow River covers a total drainage area of 7.53× 105 km2, and is divided into seven reaches from upstream to downstream according to differences in hydrogeology, water resource availability and water resource utilization. The reaches include above Longyangxia (Lyx), Longyangxia to Lanzhou (Lyx-Lz), Lanzhou to Toudaoguai (Lz-Tdg), Toudaoguai to Longmen (Tdg-Lm), Longmen to Sanmenxia (Lm-Smx), Sanmenxia to Huayuankou (Smx-Hyk), and below Huayuankou (Hyk). These divisions have also been adopted by the Chinese government. We chose the seven reaches as sites in this study, although we omitted Endorheic regions of the Yellow River because these areas are small and scattered.

A series of well-known problems have arisen in the Yellow River due to unreasonable use and overexploitation of water resources over the past few decades. The most serious problem is the break-off in the lower reaches that occurred for 19 years from 1972 to 1996. Groundwater funnel is another serious problem. According to incomplete statistics, there were 65 groundwater funnel areas in the Yellow River basin before 2006 due to overexploitation in some areas. In addition, a polarization phenomenon has emerged. This paper calculates the degree of polarization as a way to shed light on the governance problems that have occurred around the Yellow River and quantifies the degree of overexploitation in the Yellow River basin.

2.2 Concept of the water resource utilization polarization

Polarization phenomena exist in the utilization of a water resource. When more than the available water resources are extracted or a certain threshold is exceeded, the water resource declines, and the water and ecological balances of the river ecosystem deteriorate or are destroyed. These changes lead to polarization phenomena, such as a decline in the groundwater level, a decrease in runoff volume and the destruction of biodiversity.

Therefore, we established a conceptual framework of polarization for water resources utilization (Fig.1) and attempted to build a polarization index to assess the degree of water resource overexploitation. The Yellow River basin was used as an example to calculate a polarization index that reflects the degree of destruction and predicts whether utilization of the water resource is sustainable. This study also provides a quantitative method for measuring the degree of water balance overexploitation and the ecological balance in the Yellow River ecosystem.

Fig. 1 The two-grade district division of the Yellow River

Fig. 2 Relationship of the polarization of water resource utilization

2.3 Model of water resource utilization polarization

This study aims to measure the deviation of the exploitation of available water resources. We built an index model of water resource utilization polarization (WRUP) based on the TW index, ER index and variance (formula 1). The WRUP calculates the degree of water resource overexploitation in a river basin by considering the exploitation and water availability. Different water resources are available under different hydrogeological conditions. Therefore, the river polarization over large spans is calculated in subareas.

The WRUP is based on the availability of both surface water and groundwater. The alienation of the polarization reflects the difference between available water and exploited water. The method that calculates the deviation of the water resource exploitation from the available water is similar to a variance calculation. The groundwater or surface water will show polarization when the volume of water is below a threshold. The WRUP index is built as follows:

\[WRU{{P}_{i}}= \\ \left\{ \begin{align} {{\left( \frac{{{\left| \frac{{{W}_{sai}}-{{W}_{sei}}}{{{W}_{sai}}} \right|}^{2}}+{{\left| \frac{{{W}_{gai}}-{{W}_{gei}}}{{{W}_{gai}}} \right|}^{2}}}{2} \right)}^{r}},\text{ }{{W}_{sai}} <{{W}_{sei}},\text{ }{{W}_{gai}}<{{W}_{gei}},\text{ }r=\frac{1}{2} \\ {{\left| \frac{{{W}_{sai}}-{{W}_{sei}}}{{{W}_{sai}}} \right|}^{r}},\text{ }{{W}_{sai}}<{{W}_{sei}},\text{ }r=1 \\ {{\left| \frac{{{W}_{gai}}-{{W}_{gei}}}{{{W}_{gai}}} \right|}^{r}},\text{ }{{W}_{gai}}<{{W}_{gei}},\text{ }r=1 \\ 0,\text{ }{{W}_{sai}}>{{W}_{sei}},\text{ }{{W}_{sai}}>{{W}_{sei}}\text{ } \\ \end{align} \right. \ (1)\]

\[WRUP=\sum\limits_{i=1}
{n}{{{W}_{i}}W}RU{{P}_{i}}\ (2)\]

where n is the number of subareas, WRUPi is the ith subarea of the water resource polarization index, Wi is the area ratio, Wsai is the available surface water resources, Wsei is exploited surface water resources, Wgai is available groundwater resources, and Wgei is the exploited groundwater resources.

Available surface water is usually measured using the deductive method and indicates the sustainable level of water resource exploitation in a river. Surface water resource (Ws) is the water on the surface in a river, lake or ocean, and the quantity that is usually replaced by natural surface runoff. The available portion of surface water is calculated as the difference between the amount of unavailable surface water and total surface water. Unavailable water is composed of ecological runoff and discarded water (Wb) during the flood season. Least basic flow in non-flood season turns to ecological runoff. Part of the discarded water serves as ecological runoff during the flood season, and the other part is unmanageable water (Yao et al., 2005).Wn is the river water demand, which is normally represented by the maximum value among the base water flows, ecological water demand and sediment discharge water demand (Wang et al., 2007). Mathematically, this is expressed as:

Wsa=Ws - Wn-Wb (3)

Available groundwater, which is measured by a water balance model in this study, represents the sustainable volume of groundwater resource exploitation. A water balance model is used to describe the flow of water resources in and out of a river basin. This method is suited for situations with excessive groundwater exploitation, as occurs in the Yellow River, which forms a regional drawdown funnel (Wang et al., 2013). The water balance model is based on the dynamic balance of groundwater accumulation (Qc), which is equal to the sum of the groundwater yield (Qe) and the variable storage (Qv ) of groundwater. Groundwater accumulation is based on the groundwater amplitude and drainage area. Available groundwater resources must be less than the amount that exists, which is measured by water resources (Wa) and surface water resources (Ws). Available groundwater is expressed as follows:

Qc = Qe + Qv

We = Wa - Ws (4)

Wga=min(Qc, We)

2.4 Data availability

To calculate the polarization index of the Yellow River, the following data were collected: 1) Yellow River water resources; 2) Yellow River water resources utilization; 3) sediment discharges; and 4) hydrological data from the Yellow River. These data were collected from the Yellow River Water Resources Bulletin, the sediment from the Yellow River CommuniqueandThe Hydrological Year Book. In addition, this study is based on data for the Yellow River from the year 2012 because the data for this year is the most comprehensive and representative, based on overall analysis in the past ten years.

3 Results and discussion
3.1 water resource utilization polarization model

Water resource utilization polarization takes the term “ polarization” from economics and applies it to water resources utilization to describe the development of water resources. In this context the concept can be used for qualitative analysis of excessive water resources in river basins. The water resources utilization polarization index is proposed to quantitatively evaluate the degree of overexploitation of water resources in a basin. Jia (1999) establishes water resources development and utilization index factors, development and utilization rates, water supply conditions, water use composition, water supply composition and other eight index factors to evaluate the development and utilization of water resources in Xi'an. Yang (2007) and Xia (2007) both used an analytic hierarchy process model and principal component analysis to evaluate the water resources development and utilization in Hunan and Xi'an, respectively. At present, the evaluation of water resources development is limited to multi-factor comprehensive evaluation analysis. There has been no further study of the overexploitation of water resources.

The introduction of the concept of polarization of water resources utilization can determine whether there is over- exploitation of water resources and intuitively show the status quo of water resources development and utilization. Construction and calculation of a polarization index model of water resources utilization can quantitatively analyze the degree of exploitation of water resources, and accurately assess the utilization of water resources. It provides accurate references for water resources exploitation and utilization.

3.2 Water resources available in the Yellow River

3.3.1 Surface water availability in the Yellow River

This paper assessed the degree of polarization of the water resources of the seven reaches of the Yellow River using the WRUP model. Surface water availability was first estimated using formula (4). The amount of surface water usually refers to natural river runoff. River water demand is theoretically determined by selecting the maximum value of the base water flow, ecological water demand and sediment discharge water demand. In addition, river water demand is usually replaced by 30%-40% of the runoff in the actual calculation (Yao et al., 2005; Zhang, 2008; Guo, 2001). We selected 30% as the river water demand in this study. Discarded water is the amount of water that cannot be controlled or used during the flood period; it is the flood season runoff minus the controllable water use. The results are shown in Table 1.

Table 1 Available surface water and surface water yield in different reaches of the Yellow River (unit: 108 m3)

The results indicate that 34.49× 108 m3 of water is available, which accounts for 56.21% of the total surface water

volume. The distribution of the available water resources is uneven, and most of the available water resources are distributed in the upper reaches of the Yellow River.

Surface water availability in the middle and lower reaches is relatively small, but exploitation is high in these areas. Fig. 3 shows that the Lanzhou and Toudaoguai reaches, the Longmen to Sanmenxia reaches and the below Huayuankou reach have been over-exploited. The most heavily overused area is in the Lanzhou to Toudaoguai region.

Fig. 3 Comparison chart of surface water available (sa), surface water yield (sy) and surface water overexploitation (so) in different reaches of the Yellow River

3.2.2 Groundwater resources available around the Yellow River

Available groundwater is the sum of groundwater accumulation and yield (formula 5); it is less than the total volume of groundwater resources.

Groundwater accumulationis based on the amplitude and drainage area of groundwater. we calculated the groundwater availability, as shown in Table 2.

Table 2 Available groundwater and groundwater yields in different reaches of the Yellow River (unit: 108 m3)

Table 2 and Fig. 3 show that groundwater is severely over-exploited. The middle and lower reaches of the Yellow River, especially, represent the major areas where groundwater is overexploited. The most serious overexploitation occurs in the below Huayuankou area, where the volume of overexploited groundwater exceeds 1.35× 108 m3. Moreover, groundwater is overexploited in all areas below the Longmen region. One reason is that these areas are population centers that have large water demands. Groundwater recharge is small in these areas due to the overexploitation of surface water resources. In addition, the groundwater resources are overexploited by approximately 1.21× 108 m3 between the Sanmenxia and Huayuankou regions. A total of 0.36× 108 m3 from the Longyangxia and Lanzhou area are overexploited. When these areas are taken together, 5.84× 108 m3 of groundwater is available, representing 58.74% of total groundwater resources. In addition, the results show that the middle and lower reaches of the Yellow River exhibit heavy polarization.

3.3 Degree of polarization in sub-catchments of the Yellow River

The study calculates the polarization of water resources to determine the extent of overexploitation of the basin and the water resource availability needed to prevent destruction of the river basin ecosystem. The utilization of water resources from the Yellow River indicates polarization, especially in the middle and lower reaches. Therefore, this paper established a concept for describing the polarization of water resource utilization and built a model to calculate the degree of polarization of the Yellow River based on formulas 2 and 3. The results are shown in Table 3.

Table 3 Water resources polarization index in different reaches of the Yellow River

The utilization of water resources is always a subject of concern because unreasonable yields can lead to the destruction of the water balance and the ecological balance of a river ecosystem. The WRUP model is built to measure the degree of damage caused by the utilization of water resources in the Yellow River.

Table 3 and Fig. 4 indicate that the heaviest polarization occurs along the Lanzhou to Toudaoguai reaches, where the WRUP is 19.98. The region from Longmen to Sanmenxia is also overexploited, and both the surface water and groundwater are overexploited. This overexploitation leads to the degradation of the ecological environment and affects the lives of people in this basin. The WRUP index of the below Huayuankou region is 11.81. Water resources are in great demand in this region, which results in the polarization of both surface water and groundwater. The water resource polarization index is 10.78 between the Longmen and Sanmenxia reaches. The water resource polarization index is 2.75 and 6.55 in the Sanmenxia to Huayuankou and Longmen to Lanzhou reaches, respectively. These are the only regions with excessive groundwater. There is no polarization above the Longyangxia region due to the large water storage reservoir. There is also no polarization from Toudaoguai to Longmen because of the low water demand. Overall, the water resource polarization is 7.95 over the entire Yellow River area. In addition, the water resource polarization index is high, which affects the ecological environment and the everyday life of people living near the river.

Fig. 4 Comparison chart of ground water available (ga), ground water yield (gy) and ground water overexploitation (go) in different reaches of the Yellow River

Fig. 5 Water resource polarization index in different reaches of the Yellow River

4 Conclusions

The concept of WRUP is established to describe the utilization of water resources in a river. In addition, the WRUP model is built to measure the degree of damage due to the utilization of water resources. In this study, the model is used to calculate the availability of water resources based on the present situation in the Yellow River. This paper calculates the availability of water resources and the WRUP index of the Yellow River.

(1) A total of 34.49× 108 m3 of surface water is available in the Yellow River. In addition, 5.84× 108 m3 of groundwater is available. The overexploited water resource area is centered on the middle and lower reaches of the Yellow River. The areas with serious overexploitation of surface water resources are located from Lanzhou to Toudaoguai, where the utilization exceeds the amount of available water by 13.75× 108 m3. The area of groundwater overexploitation is centered from Longmen to Sanmenxia, and the volume of overexploitation is 4.72× 108 m3.

(2) Overall, the water resource polarization index is 7.95 for the entire Yellow River area and is highest from Lanzhou to Toudaoguai. In addition, there is also polarization from Longyangxia to Lanzhou, Longmen to Sanmenxia, Sanmenxia to Huayuankou and below Huayuankou. The areas above Longyangxia and from Toudaoguai to Longmen have no polarization, which means that the water resources in these areas are not overexploited.

The authors have declared that no competing interests exist.

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