Introduction

Freshwater plays unique roles for society and for economic development through provision (e.g., products, food), support (e.g., wastewater processing, supply of clean water), and enrichment (e.g., aesthetic, recreational, cultural) services (Yang et al. 2007). The growing demand for freshwater resources to sustain human activities, coupled with adverse effects of human activities, such as discharge of industrial wastewater and domestic sewage, are likely to cause a crisis in the near future if water resources are not appropriately managed (Charkhabi and Sakizadeh 2006). The shortage of water resources and water pollution is very serious in the arid and semi-arid areas of Northwestern China. Strengthening water quality management and conservation of impoverished water resources are indispensable for economic and social sustainable development.

Water quality management involves water quality monitoring, analysis, assessment, and reporting. Water quality assessment, a quantitative description of water quality, is a challenge within the study of the environment. Proper identification of water quality status in a river system based on limited observations is essential for meeting the goals of environmental management. Numerous methods have been proposed in the literature to assess water quality, including expert assessment (Croke et al. 2007; Nasiri et al. 2007), index assessment (Cude 2001), neural networks (Sudheer et al. 2006), and grey clustering (Wang et al. 2007). The pollution degree of water is a vague concept. Owing to inherent imprecision and fuzziness of classification criteria and the boundaries between different classes of water quality, difficulties of water quality classification and assessment always exist in conventional assessment methodologies such as water quality index (WQI) when describing integrated water quality. Conventional methods for water quality assessment do not consider the uncertainties involved either in measurement of water quality parameters or in the limits provided by regulatory bodies. Conventional assessment methods of the water quality parameters use crisp set, and concentrations values, which are close to or far from the limits, are included in same classes. A small increase/decrease in pollutant data near the boundary value results in a change in classification (Onkal-Engin et al. 2004; Shen et al. 2005). This fuzziness has led some environmental researchers to look for advanced assessment methods based on fuzzy set theory (Fisher 2003) such as fuzzy synthetic evaluation.

Fuzzy set theory is designed to interpret the uncertainties of the real situation. This method is suited to make decisions in complex systems when the context of the problem is unclear (Dahiya et al. 2007). A fuzzy set is defined in terms of a membership function which maps the domain of interest, e.g., concentrations, onto the interval [0, 1]. The shape of the curves shows the membership function for each set. The membership functions represent the degree, or weighting, of the specified value belonging to the set (Singh et al. 2008). Fuzzy set theory may be regarded as a generalization of classical set theory. In the classical set theory, the membership function of a set is 1 within the boundaries of the set, and 0 outside. The fuzzy synthetic evaluation method groups raw data into several different categories according to predetermined quality criteria using a set of functions designed to reflect the absence of sharp boundaries between adjacent criteria. It evaluates comprehensively the contributions of various pollutants according to predetermined weights, and decreases the fuzziness by using membership functions. Therefore, sensitivity is higher than for other index evaluation techniques (Onkal-Engin et al. 2004). A well-designed fuzzy synthetic evaluation may be capable of covering the uncertainties in the sampling and analysis process, comparing sampling results to quality standards for each parameter, and summarizing individual parameter values (Dahiya et al. 2007). Fuzzy synthetic evaluation has been widely used in environmental quality assessment (Chang et al. 2001; Haiyan 2002; Fisher 2003; Onkal-Engin et al. 2004; Shen et al. 2005; Zou et al. 2006; Dahiya et al. 2007; Icaga 2007; Singh et al. 2008), and has been proven effective in solving problems of fuzzy boundaries and in controlling the effect of monitoring errors (Haiyan 2002). Very limited information on the water quality status and comprehensive assessment of the Wei River in China is available. The aims of this article are to investigate the water parameters of the Wei River and to assess its current water quality status using fuzzy synthetic evaluation. The results provide a scientific basis for improved water resource management and protection of the river.

Materials and methods

Background of study site

Wei River originates from Gansu Province and passes through ca. 502 km in Shaanxi province. It is the largest tributary of the Yellow River in China. The Wei River valley is the major region for agriculture, industry, and commerce in Northwestern China. The river is a major source of water for drinking, industrial production, and agricultural activities in the central Shaanxi plain. The irrigation water for 55,400 km2 of farmland and fruit gardens in the central Shaanxi plain comes from the Wei River (Yang 2002). Although there are stringent rules in China for treatment of industrial wastes, disposal of untreated wastewater into drains and subsequently into the Wei River is very common, posing potential health and environmental risks to people living in central Shaanxi and downstream. Another source of stream and river pollution is surface runoff, directly discharged to streams without treatment. Assessment of water quality is very important for the exploitation and administration of the Wei River to protect human and ecological health.

Sampling and analysis

Twenty-five water samples were collected from the Baoji Xi’an reach of Wei River during October/November, 2006. The selection of sampling sites was based on the provincial environment monitoring sites and proximity to major pollutant sources such as agriculture, industry, and residential land use (Fig. 1). The samples were taken from 10 to 15 cm below the water surface using acid-washed, wide-mouth polyethylene plastic bottles. Standard procedures were followed for the collection of water samples (Chinese Environmental Protection Agency 2002a, HJ/T91-2002). Two bottles of water samples were collected at each site, one of which was acidified for metal analyses to minimize precipitation and adsorption on the walls of the container. The water samples were transported to the laboratory and analyzed for pH, electrical conductivity (EC), dissolved oxygen (DO), biological oxygen demand (BOD), chemical oxygen demand (COD), and fluoride by standard methods (Chinese Environmental Protection Agency 2002a, HJ/T91-2002). In order to analyze total metal concentration, the samples were digested without preliminary filtration using the concentrated hydrochloric acid digestion method. Mercury, arsenic, and selenium were analyzed in the water samples using atomic fluorescence spectrometer.

Fig. 1
figure 1

Map of water sampling sites along the Baoji Xi’an reach of the Wei River, China

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Fuzzy synthetic evaluation

The following procedure (Chang et al. 2001; Haiyan 2002; Shen et al. 2005; Singh et al. 2008) describes the fuzzy synthetic evaluation method.

(a) Select assessment parameters and establish assessment criteria:

It is crucial to select representative, rational, and accurate water quality assessment parameters to form an assessment factor set U based on the actual local situation. This is expressed as

$$ U = \left\{ {u_{1} ,u_{2} , \ldots ,u_{n} } \right\} $$
(1)

where n is the number of selected assessment parameters. The assessment criteria set V is established from National Surface Water Environmental Quality Standards of China.

$$ V = \left\{ {v_{1} ,v_{2} , \ldots ,v_{m} } \right\} $$
(2)

where m is the number of assessment criteria categories. The water quality is classified into five levels (Chinese Environmental Protection Agency 2002b, GB3838-2002; Table 1).

Table 1 National surface water environmental quality standards of China (mg l−1)
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(b) Establish membership functions of fuzzy environmental quality:

The membership functions represent the degree to which the specified concentration belongs to the fuzzy set. For the water quality assessment parameter, the smaller the better such as COD, the membership functions are

$$ r_{i1} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 1 \\ {{{(c_{i} - v_{i2} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{i2} )} {(v_{i1} - v_{i2} )}}} \right. \kern-\nulldelimiterspace} {(v_{i1} - v_{i2} )}}} \\ 0 \\ \end{array} \;\;\;\;\begin{array}{*{20}c} {c_{i} \le v_{i1} } \\ {v_{i1} < c_{i} < v_{i2} } \\ {c_{i} \ge v_{i2} } \\ \end{array} } \right. $$
(3)
$$ r_{ij} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 0 \\ {{{(c_{i} - v_{ij - 1} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{ij - 1} )} {(v_{ij} - v_{ij - 1} )}}} \right. \kern-\nulldelimiterspace} {(v_{ij} - v_{ij - 1} )}}} \\ {{{(c_{i} - v_{ij + 1} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{ij + 1} )} {(v_{ij} - v_{ij + 1} )}}} \right. \kern-\nulldelimiterspace} {(v_{ij} - v_{ij + 1} )}}} \\ \end{array} } \right.\;\;\;\;\begin{array}{*{20}c} {c_{i} \le v_{ij - 1} ,c_{i} \ge v_{ij + 1} } \\ {v_{ij - 1} < c_{i} \le v_{ij} } \\ {v_{ij} < c_{i} < v_{ij + 1} } \\ \end{array} \;\;\;\;j = 2,3,4 $$
(4)
$$ r_{i5} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 0 \\ {{{(c_{i} - v_{i4} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{i4} )} {(v_{i5} - v_{i4} )}}} \right. \kern-\nulldelimiterspace} {(v_{i5} - v_{i4} )}}} \\ 1 \\ \end{array} } \right.\;\;\;\;\begin{array}{*{20}c} {c_{i} \le v_{i4} } \\ {v_{i4} < c_{i} < v_{i5} } \\ {c_{i} \ge v_{i5} } \\ \end{array} . $$
(5)

For the water quality assessment parameter, the bigger the better such as DO, the membership functions are

$$ r_{i1} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 1 \\ {{{(c_{i} - v_{i2} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{i2} )} {(v_{i1} - v_{i2} )}}} \right. \kern-\nulldelimiterspace} {(v_{i1} - v_{i2} )}}} \\ 0 \\ \end{array} } \right.\;\;\;\;\begin{array}{*{20}c} {c_{i} \ge v_{i1} } \\ {v_{i2} < c_{i} < v_{i1} } \\ {c_{i} \le v_{i2} } \\ \end{array} $$
(6)
$$ r_{ij} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 0 \\ {{{(c_{i} - v_{ij - 1} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{ij - 1} )} {(v_{ij} - v_{ij - 1} )}}} \right. \kern-\nulldelimiterspace} {(v_{ij} - v_{ij - 1} )}}} \\ {{{(c_{i} - v_{ij + 1} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{ij + 1} )} {(v_{ij} - v_{ij + 1} )}}} \right. \kern-\nulldelimiterspace} {(v_{ij} - v_{ij + 1} )}}} \\ \end{array} } \right.\;\;\;\;\begin{array}{*{20}c} {c_{i} \ge v_{ij - 1} ,c_{i} \le v_{ij + 1} } \\ {v_{ij} < c_{i} \le v_{ij - 1} } \\ {v_{ij + 1} < c_{i} < v_{ij} } \\ \end{array} j = 2,3,4 $$
(7)
$$ r_{i5} (c_{i} ) = \left\{ {\begin{array}{*{20}c} 0 \\ {{{(c_{i} - v_{i4} )} \mathord{\left/ {\vphantom {{(c_{i} - v_{i4} )} {(v_{i5} - v_{i4} )}}} \right. \kern-\nulldelimiterspace} {(v_{i5} - v_{i4} )}}} \\ 1 \\ \end{array} } \right.\;\;\;\;\begin{array}{*{20}c} {c_{i} \ge v_{i4} } \\ {v_{i5} < c_{i} < v_{i4} } \\ {c_{i} \le v_{i5} } \\ \end{array} $$
(8)

where c i is the actual monitoring data for the ith assessment parameter, and v ij is the criteria value of the ith assessment parameter at the jth level (i = 1, 2, …, n; j = 1, 2, …, m).

(c) Calculate the membership function matrix:

Substituting the data of each assessment parameter at each monitoring site and the national standards into the membership functions, we can obtain the fuzzy matrix R, expressed as

$$ R = (r_{ij} )_{n \times m} = \left( {\begin{array}{*{20}c} {r_{11} } & {r_{12} } & \cdots & {r_{1m} } \\ {r_{21} } & {r_{22} } & \cdots & {r_{2m} } \\ \vdots & \vdots & \vdots & \vdots \\ {r_{n1} } & {r_{n2} } & \cdots & {r_{nm} } \\ \end{array} } \right) $$
(9)

where r ij (i = 1, 2, …, n; j = 1, 2, …, m) is the membership degree of the ith assessment parameter at the jth level.

(d) Calculate the weights matrix:

Water quality status cannot be ascertained according to a single water quality parameter. Each water quality parameter has its own contribution to water quality. Therefore, weight determination is an important and complex issue in comprehensive assessment. The weight of each assessment parameter is usually determined from the ratio of the parameter monitoring value to the corresponding environmental quality standard in typical fuzzy synthetic evaluation (Haiyan 2002; Shen et al. 2005). This weight determination method in water quality assessment does not consider the relationship among different monitoring sites, and the workload is heavy when there are multiple evaluation objects (Zou et al. 2006).

In this study, the entropy method was used to determine the weights of assessment parameters. The weight w i of the ith assessment parameter (Zou et al. 2006) is defined as

$$ w_{i} = {\frac{{1 - H_{i} }}{{n - \sum\limits_{i = 1}^{n} {H_{i} } }}} $$
(10)

where 0 ≤ w i  ≤ 1, \( \sum\nolimits_{i = 1}^{n} {w_{i} = 1} \). H i is the entropy of the ith assessment parameter, defined as

$$ H_{i} = - k\sum\limits_{j = 1}^{p} {f_{ij} \ln f_{ij} } ,\;\;\;\;i = 1,2, \ldots ,n $$
(11)

where \( f_{ij} = {{e_{ij} } \mathord{\left/ {\vphantom {{e_{ij} } {\sum\nolimits_{j = 1}^{p} {e_{ij} } }}} \right. \kern-\nulldelimiterspace} {\sum\nolimits_{j = 1}^{p} {e_{ij} } }} \), k = 1/ln p, p is the number of monitoring sites (25 in this article), and e ij is the normalization value of the ith assessment parameter at the jth monitoring site.

(e) Determine evaluation results:

Evaluation results can be obtained from the fuzzy matrix algorithm of W · R. Fuzzy matrix R = (a ij )n×m, Weight matrix W = (w i )1×n . The matrix algorithm results B is

$$ B = W \cdot R = \left( {b_{1} ,b_{2} , \ldots ,b_{m} } \right) $$
(12)

where \( b_{j} = \sum\nolimits_{i = 1}^{n} {w_{i} a_{ij} } \), j = 1, 2, …, m. The evaluation result is

$$ {\text{Class}} = \max \left( {b_{j} } \right),\;\;\;\;j = 1,2, \ldots ,m. $$
(13)

Here, the maximum value of b j determines the water quality class of the area studied.

Results and discussion

Status of water quality of Wei River

The measured results for the water quality parameters in the Wei River water at the locations sampled are shown in Fig. 2. The pH of samples varied from 6.75 to 7.62 with an average of 7.18, which falls within the range of National Surface Water Environmental Quality Standards of China (Chinese Environmental Protection Agency 2002b, GB3838-2002). EC varied from 420 to 900 μS cm−1 with an average of 578 μS cm−1. There is no distinct difference of pH and EC among the sampling sites. The fluoride content in water samples ranged from 0.24 to 1.09 mg l−1 with an average of 0.54 mg l−1, all falling into class I (1 mg l−1) (Chinese Environmental Protection Agency 2002b, GB3838-2002) except for two samples collected from Baoji urban area (site 3 and site 4) in which the fluoride contents are close to l mg l−1 (Fig. 2). The DO, BOD5, and COD concentrations ranged from 0.09 to 3.19, 0.4 to 78.0, and 24.8 to 239.1 mg l−1, respectively. The higher BOD5 and COD concentrations appeared in the water samples collected from the vicinal reach of Baoji (site 4), Xianyang (site 16) and Xi’an (site 21) cities. The trace elements As, Se, and Hg in the studied water samples ranged from 1.10 to 42.0, 0.01 to 0.66, and 0.93 to 3.82 μg l−1, respectively. Arsenic and Se concentrations in all the water samples were below the class I limitations for As and Se (50 and 10 μg l−1, respectively) in the National Surface Water Environmental Quality Standards of China (Chinese Environmental Protection Agency 2002b, GB3838-2002).

Fig. 2
figure 2

Monitoring water quality data in Wei River water samples

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Fuzzy synthetic evaluation

Fuzzy synthetic evaluation was applied to assess the water quality of the Wei River based on the monitoring data and the National Surface Water Environmental Quality Standards of China. In the original monitoring data, pH and EC values of all the .water samples were in the range of natural surface water quality (Chinese Environmental Protection Agency 2002b, GB3838-2002), and trace elements As, Se. and F concentrations in all measured water samples fell below the limitations of class I water quality. As a result, only DO, BOD5, COD, and Hg were selected as assessment parameters to form an assessment factor set U, U = {DO, BOD5, COD, Hg}. An assessment criteria set V was also established according to the National Surface Water Environmental Quality Standards of China (Chinese Environmental Protection Agency 2002b, GB3838-2002; Table 1). The values of the above four assessment parameters at the 25 sampling sites are shown in Fig. 2.

Membership functions of DO, BOD5, COD, and Hg to standards at five levels were established according to Eqs. 3–8. The membership functions of DO, BOD5, COD, and Hg are shown in Fig. 3. After substitution of the actual monitoring data from each sampling site into the membership functions, we obtain the fuzzy matrices of R1–R25 for the 25 water sampling sites. For example, the fuzzy matrix for sampling site 1 is

$$ R1 = \left( {\begin{array}{*{20}c} 0 & 0 & {0.45} & {0.55} & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & {0.29} & {0.71} & 0 \\ 0 & 0 & {0.07} & {0.93} & 0 \\ \end{array} } \right). $$
(14)
Fig. 3
figure 3

Membership functions for assessment parameters in this study

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Substituting the normalization values of all the original monitoring data into Eqs. 10 and 11, we obtain the entropies and the weights for DO, BOD5, COD, and Hg (Table 2). The weight matrix is

$$ W = (\begin{array}{*{20}c} {0.643} & {0.055} & {0.062} & {0.240} \\ \end{array}) . $$
(15)
Table 2 Entropies and weights of assessment parameters
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The fuzzy matrices for the other sampling sites are not shown this article. Fuzzy algorithm B · R gave the following result for sampling site 1:

$$ \begin{aligned} W \cdot R1\, & = \left( {\begin{array}{*{20}c} {0.643} & {0.055} & {0.062} & {0.240} \\ \end{array} } \right) \cdot \left( {\begin{array}{*{20}c} 0 & 0 & {0.45} & {0.55} & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & {0.29} & {0.71} & 0 \\ 0 & 0 & {0.07} & {0.93} & 0 \\ \end{array} } \right) \\ & = (\begin{array}{*{20}c} {0.055} & 0 & {0.324} & {0.621} & 0 \\ \end{array} ). \\ \end{aligned} $$

The assessment result can be obtained from the results of fuzzy operation W · R1 and Eq. 13. Since the membership degree of class IV (0.621) is higher than for class I (0.055), class II (0), class III (0.324). and class V(0), the water environmental quality at sampling site 1 belongs to class IV. In the same way, we obtain the fuzzy synthetic evaluation results for water quality at the other sampling sites (Table 3). Among the 25 water sampling sites, the water quality at 23 sampling sites belongs to class V (bad level), whereas two sampling sties belong to class IV (poor level). The water quality of Baoji Xi’an reach of Wei River is clearly badly polluted. The major pollutant is Hg. Fuzzy synthetic evaluation with the typical method for weight determination was also used to validate the effectiveness of the entropy method. The results show that the entropy method leads to the same assessment result as the traditional method. The entropy method decreases the calculation workload and is very effective in water quality evaluation.

Table 3 Fuzzy comprehensive assessment results of water quality of Wei River, China
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Conclusions

Water quality analysis of the samples from the Wei River indicates that pH and EC values are in the range of natural surface water quality, and As, Se, and fluoride concentrations are below the limitations of class I water quality. The concentration of BOD5, COD, and Hg in Wei River water indicates serious pollution. Spatial distributions of BOD5, COD, and Hg concentrations show that higher values appeared in the water from the vicinal reach of Baoji, Xianyang, and Xi’an cities.

Fuzzy synthetic evaluation with the entropy method for weight determination was used to assess the integrated water quality of Wei River, and the result of this method was compared with the typical fuzzy synthetic evaluation. The results show that the entropy method for weight determination is effective in water quality evaluation. The water quality comprehensive assessment results indicate that all the sampling sites belong to class V water quality (bad level) except for two sampling sites belonging to class IV water quality (poor level). The Baoji Xi’an reach of Wei River is polluted, with Hg as the major pollutant. The assessment results are consistent with the real situation of Wei River water quality. Strict enforcement of domestic and industrial wastewater discharge management are vital to protect the water resource and to improve the Wei River.