Front. Earth Sci. 2014, 8(2): 242–250 DOI 10.1007/s11707-013-0395-6
RESEARCH ARTICLE
A Bayesian method for comprehensive water quality evaluation of the Danjiangkou Reservoir water source area, for the middle route of the South-to-North Water Diversion Project in China Fangbing MA1,2,3, Chunhui LI1, Xuan WANG (✉)1,2, Zhifeng YANG1,2, Chengchun SUN2, Peiyu LIANG1,2 1 Key Laboratory for Water and Sediment Sciences of Ministry of Education, School of Environment, Beijing Normal University, Beijing 100875, China 2 State Key Laboratory for Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China 3 Shidu Town People’s Government, Beijing 102411, China
© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013
Abstract The Danjiangkou Reservoir is the water source for the middle route of the South-to-North Water Diversion Project in China. Thus, its water quality status is of great concern. Five water quality indicators (dissolved oxygen, permanganate index, ammonia nitrogen, total nitrogen, and total phosphorus), were measured at three monitoring sites (the Danjiangkou Reservoir dam, the Hejiawan and the Jiangbei bridge), to investigate changing trends, and spatiotemporal characteristics of water quality in the Danjiangkou Reservoir area from January 2006 to May 2012. We then applied a Bayesian statistical method to evaluate the water quality comprehensively. The normal distribution sampling method was used to calculate likelihood, and the entropy weight method was used to determine indicator weights for variables of interest in to the study. The results indicated that concentrations of all five indicators increased during the last six years. In addition, the water quality in the reservoir was worse during the wet season (from May to October), than during the dry season (from November to April of the next year). Overall, the probability of the water’s belonging to quality category of type Ⅱ, according to environmental quality standards for surface water in China, was 27.7%–33.7%, larger than that of its belonging to the other four water quality types. The increasing concentrations of nutrients could result in eutrophication of the Danjiangkou Reservoir. This method reduced the subjectivity that is commonly associated with determining indicator weights and artificial classifications, achieving more reliable results. These results indicate that it is important for the Received November 12, 2012; accepted May 19, 2013 E-mail:
[email protected]
interbasin water diversion project to implement integrated water quality management in the Danjiangkou Reservoir area. Keywords water quality evaluation, Danjiangkou Reservoir, Bayesian method, normal distribution sampling method, entropy weight method
1
Introduction
Due to global climate change and human interferences, water shortages and pollution are becoming more and more serious worldwide. Declining environmental water quality directly restricts the availability of water regionally, and accelerates the degradation of aquatic ecosystems (Cai et al., 2011; Jun et al., 2011). For regional water resources and ecological environmental security, it is necessary to characterize the overall status of the water quality quantitatively, and to guide water use planning based on comprehensive quantitative water quality evaluation (Zou et al., 2006; Liu et al., 2010; Tan et al., 2011; Wu et al., 2012). No uniform method for the water quality evaluation has been developed to date, mainly because a large number of water quality evaluation factors complicate the non-linear relationships that operate among factors and water quality types. Previously, the most commonly used water quality evaluation methods were single-factor evaluation methods, and aggregative index evaluation methods. These methods used clear concepts and were easy to operate (Xing et al., 2011). Some other water quality evaluation methods were
Fangbing MA et al. A Bayesian method for water quality evaluation of the Danjiangkou Reservoir
established based on the grey box theory and systems theories, to reflect fuzziness (the nonlinear and uncertain characteristics of water quality evaluations). These methods include the fuzzy mathematics evaluation method (Zou et al., 2006; Liu et al., 2010), the gray system evaluation method (Ip et al., 2009), the artificial neural network method (Ni and Bai, 2000; Jiang et al., 2007; Zhao et al., 2007), and the principal component analysis method (Parinet et al., 2004; Debels et al., 2005). All of these methods were widely used for water quality evaluations of individual water bodies, and of watersheds. These existing methods were used to provide information that formed an important foundation for promoting the rational development, planned use, and protection of water resources. However, these methods require large amounts of data, resulting in a large complex calculation workload when multiple evaluation indicators exist. In addition, it is difficult to obtain reliable results for areas with insufficient data in China. Thus, a simple and effective water quality evaluation method needs to be developed and used for regional water resources planning and management, in order to provide more reliable and accurate water quality evaluation results with limited raw data. Water quality evaluation is based on inference decisions, and uses multiple types of information to infer possibilities statistically (Cha et al., 2010; Schoen et al., 2010). As a statistical classification method that uses known information to infer probabilities, the Bayesian method has drawn much attention in recent years (Wu et al., 2011). This method uses objective probability estimates, or statistical analyses, to indicate the probability of unknown states with incomplete information. Next, this method is used to find the most likely reasons for the occurrence of a certain event, by using probabilistic logic that is based on the Bayesian theory. This method requires only simple calculations, and reliable results can be obtained for small samples data. Thus, the Bayesian method has been used widely for water quality evaluations of rivers, estuaries, lakes and reservoirs (Qian et al., 2004; Qian and Reckhow, 2007; Wu et al., 2011). The most important step in this method is to calculate the likelihood of the water quality indicators. When the water quality belongs to a certain type, the indicator values and standard values always introduce sampling errors, which are represented by a normal distribution. The normal distribution sampling method is known to estimate likelihood satisfactorily, and to obtain more reliable results (Chib, 1996; Unnikrishnan, 2010). Another important step for water quality evaluation is to calculate the weights of the water quality indicators. In previous studies, the weights of all indicators have been assumed to be equal (Liao et al., 2009). However, this assumption introduced subjectivity because the relative importance of various indicators was not considered. The entropy weight method can improve upon existing methods by reducing subjectivity (Jin et al., 2004; Zou et al., 2006; Chen et al.,
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2008), and also, is expected to calculate indicator weights that produce more reliable evaluation results. To solve the water shortage problem, China implemented the middle route of the South-to-North Water Diversion Project (SNWDP) in 2002. This project transfers water from the Danjiangkou Reservoir to Northern China, including Tianjin and Beijing city, for irrigation, domestic, and industrial uses. As such, the Danjiangkou Reservoir has received extensive attention from society (Yin et al., 2001; Li et al., 2009a). Because the environmental protection of water source areas directly impacts the quality of the diverted water, and the benefits of the middle route of the SNWDP, implementing effective environmental protection practices for water source areas is desirable, in order to ensure long-term water diversion for the project. Thus, it is important to use comprehensive water quality evaluation to understand the current situation, changing tendencies, and the spatial and temporal variation rules of water quality objectively and accurately. The objectives of this research were: (i) to identify and analyze spatial and temporal variations of water quality, and (ii) to develop a water quality evaluation method based on Bayesian theory, for the Danjiangkou Reservoir — water source area of the middle route of the SNWDP. The following steps were taken to meet these objectives: (i) a Bayesian method for water quality evaluation was developed, using the normal distribution sampling method to calculate likelihood, and the entropy weight method to determine indicator weights, (ii) the selected water quality indicators were analyzed to investigate changing trends in water quality in the Danjiangkou Reservoir, and (iii) a comprehensive evaluation of the water quality in the Danjiangkou Reservoir with the proposed Bayesian method was completed. The adopted methods improve upon existing methods used to address uncertain information, as well as the calculation efficiency, of water quality evaluations using low-quality data from the Danjiangkou Reservoir. Ultimately, this research is important for implementing effective environmental protection and management strategies for water in the Danjiangkou Reservoir, for the interbasin water diversion project.
2
Materials and methods
2.1
Overview of the Danjiangkou Reservoir
The Danjiangkou Reservoir (32°36′N–33°48′N, 110°59′ E–111°49′E), consisting of the Hanjiang and Danjiang Reservoir areas, lies in the upper Hanjiang basin, and distributes water to the Hubei and Henan provinces. The Danjiangkou Reservoir has a total drainage area of approximate 95,000 km2 (Zhang et al., 2009) (see Fig. 1). The reservoir is in a sub-tropical region with a temperate and subhumid climate. The annual mean temperature is between 14.4 ºC and 15.7 ºC. The annual
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mean precipitation is between 800 mm and 1,000 mm. Most of the rainfall (80%) occurs between May and October (Li et al., 2008; Li et al., 2009b). The topography in the Danjiangkou Reservoir region is very complex. Mountains and hills account for approximate 97% of the land area. The Danjiangkou Reservoir was built in 1968. It is the largest artificial freshwater lake in Asia, with a storage capacity of 1.741010 m3. Currently, the water level of the reservoir is 157 m. After the completion of the middle route of the SNWDP, the water surface area of the reservoir will increase from 750 km2 to 1,050 km2. The Danjiangkou Reservoir is a top-grade multipurpose reservoir with flood-control, electricity-generation, navigation and agricultural irrigation functions. Considering the availability and representativeness of the data, dissolved oxygen (DO), permanganate index (CODMn), ammonia nitrogen (NH3-N), total nitrogen (TN) and total phosphorus (TP) were selected as water quality evaluation indicators. Monthly data from the three monitoring sites (the Danjiangkou Reservoir dam, the Hejiawan and the Jiangbei bridge shown in Fig. 1), collected from January 2006 to May 2012, were selected for the changing trend analysis of the water quality. These data were provided by the National Environment Monitoring Center of China. The water quality was divided into five different types (i.e., Ⅰ, Ⅱ, Ⅲ, Ⅳ and Ⅴ) according to the environmental quality standards for surface water in China (GB3838-2002).
2.2 Water quality evaluation procedures based on the Bayesian method
The water quality evaluation procedures using the Bayesian method are shown in Fig. 2. First, we analyzed the changing trends of indicator concentrations at the three monitoring sites. Next, we used the normal distribution sampling method to calculate the likelihood, the Bayesian formula to calculate the posterior probability, and the entropy weight method to calculate the indicator weights. Finally, we calculated the posterior probability of the multi-indicator comprehensive evaluation and determined the probability of the water quality belonging to a certain type. 2.3
Methods
The Bayesian formula that was used to calculate the posterior probability P(yji|xjk) is shown below (Jensen, 1996): Pðyji ÞPðxjk jyji Þ Pðyji jxjk Þ ¼ X , s Pðyji ÞPðxjk jyji Þ
(1)
i¼1
where i is the number of standard types (i = 1, 2,…,5), j is the number of indicators (j = 1, 2,…,5), k is the number of representative sites (k = 1, 2, 3), yji is the standard value of
Fig. 1 Location and sampling sites in the Danjiangkou Reservoir.
Fangbing MA et al. A Bayesian method for water quality evaluation of the Danjiangkou Reservoir
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Fig. 2 Procedures for comprehensive water quality evaluation with the Bayesian method.
the jth indicator of the ith standard type, xjk is the value of the jth indicator at the kth site, P(yji|xjk) is the posterior probability of every indicator that belongs to a certain standard type, and P(yji) is the probability of the jth indicator that belongs to the ith standard type. Due to insufficient water quality information, this research assumes that the probability of each type is equal. Specifically, P(yj1)= P(yj2)= P(yj3)= P(yj4)= P(yj5)= 1/5; P (xjk|yji) is the likelihood of every indicator. Here, we adopted the normal distribution sampling method to estimate likelihoods. We calculated the comprehensive probability of the multi-indicator water quality evaluation by using Eq. (2). Pi ¼
m X j¼1
ωj Pðyji jxjk Þ,
(2)
where Pi is the weighted sum of the posterior probabilities of multi-indicators and represents the probability that the water quality at the kth site belongs to the ith standard type. ωj is the weight of the jth indicator, and 0£ωj £1; m X ωj ¼ 1. Here, we used the entropy weight method to j¼1
determine the weight of every indicator ωj.
3
Results and discussion
We analyzed the changing concentrations of five indicators
at the three monitoring sites and used the Bayesian method, the normal distribution sampling method and the entropy weight method to conduct a comprehensive evaluation of water quality in the Danjiangkou Reservoir. 3.1 Analysis of water quality indicator concentration changes
Figures 3(a)–3(e) show the monthly changes in concentrations of the water quality indicators at the three monitoring sites from January 2006 to May 2012. Figure 3(f) shows inter-annual changes of the five water quality indicators at the Danjiangkou Reservoir dam. The changes measured at the other two monitoring sites (the Hejiawan and the Jiangbei bridge), which were not shown here, were very similar to those at this site. Table 1 shows the categories of water quality criteria and the range of monitoring values for each indicator at the three sites. We can see from Figs. 3(a)–3(e) and Table 1 that the concentration values of DO, CODMn and NH3-N mainly fall within the type Ⅰ and type Ⅱ categories of environmental quality standards for surface water in China (GB3838-2002). In contrast, concentration values of TP mainly fall within type Ⅱ, and partly fall within type Ⅰ and type Ⅲ categories. Concentration values of TN mainly fall within type IV and partly type Ⅲ and type Ⅴ categories. To validate the results that indicate changes in the water quality indicators’ concentrations, we conducted a significance test of linear fit parameters for each indicator
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Fig. 3 Concentration changes of the indicators during 2006–2012 ((a) DO; (b) CODMn; (c) NH3-N; (d) TN; (e) TP; (f) inter-annual change of five indicators at the Danjiangkou Reservoir dam). Note: Dashed lines in (a) – (e) are water quality types of the environmental quality standards for surface water in China (GB3838-2002), solid lines in (a) – (e) represent the trend change of indicator concentrations.
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Table 1 Water quality criteria and the monitoring values of the indicators at the three sites DO/(mg$L–1)
CODMn/(mg$L–1)
NH3-N/(mg$L–1)
TN/(mg$L–1)
TP/(mg$L–1)
Type Ⅰ
≥7.5
£2
£0.15
£0.2
£0.01
Water quality National criteria
Monitoring sites
Type Ⅱ
≥6
£4
£0.5
£0.5
£0.025
Type Ⅲ
≥5
£6
£1
£1
£0.05
Type Ⅳ
≥3
£10
£1.5
£1.5
£0.1
Type Ⅴ
≥2
£15
£2
£2
£0.2
Danjiangkou Reservoir dam
6.71–11.5
1.14–3.3
0.01–0.371
0.909–2.55
0.005–0.034
Hejiawan
6.62–11.8
1–3.56
0.01–0.4
0.904–2.32
0.005–0.03
Jiangbei bridge
6.66–12
1.14–3.9
0.01–0.39
0.908–2.66
0.005–0.027
Note: In order to maintain standards for use and to meet protection objectives for surface water in China, five categories of suitability for water use have been established. Type Ⅰ indicates that the water is mainly suitable for use as source water and for the national nature reserve; Type Ⅱ indicates that the water is mainly suitable for first grade surface source protection zones for centralized drinking water, precious fish conservation areas, fish spawning sites, etc; Type Ⅲ indicates that the water is mainly suitable for second grade surface source protection zones for centralized drinking water, general fish conservation areas, swimming areas, etc; Type Ⅳ indicates that the water is mainly suitable for industrial use, and other amusement purposes that do not directly contact the body; Type Ⅴ indicates that the water is mainly suitable for agricultural and landscaping use.
Table 2 Significance test results (p) for linear fit parameters for trends for the five indicators Time scale Monthly
Inter-annual
Monitoring sites
DO
CODMn
NH3-N
TN
TP
Danjiangkou Reservoir dam
0.13674
0.3874
5.26933E – 5
5.16478E – 8
4.09747E – 4
Hejiawan
0.22912
0.68553
7.73886E – 6
4.29056E – 9
0.12361
Jiangbei bridge
0.22292
0.9473
1.88037E – 7
3.56097 E – 9
0.01822
Danjiangkou Reservoir dam
0.06692
0.95926
0.01394
0.00612
0.06765
Hejiawan
0.06917
0.61542
0.01201
0.01188
0.19165
Jiangbei bridge
0.11671
0.48039
0.00406
0.00702
0.11975
Note: p is less than 0.05 represents that the change is significant, or vice versa.
(Table 2). The results indicated that concentrations of NH3N, TN, and TP increased significantly, (p < 0.05) in most cases. Concentrations of DO and CODMn did show increases, but the changes did not reach statistical significance. The results illustrated in Fig. 3 and Table 2 show that the concentrations of all five indicators increased during the last six years, but at different rates. Concentrations of NH3-N, TN, and TP had a more notable tendency to increase than those of DO and CODMn. This indicates that nitrogen pollution and phosphorus pollution are becoming more and more serious. Effective management and control of industrial pollutants in the Danjiangkou Reservoir area restricted the growth of CODMn to some extent. Concentrations of NH3N, TN and TP were closely related to agricultural nonpoint pollution that resulted from the increasing population and rapid economic development, which have placed great pressure on the water environment of the Danjiangkou Reservoir. According to a general planning report for the South-to-North Water Diversion Project (2001)1), the water quality of the Danjiangkou Reservoir is required to reach a standard of at least type Ⅱ. Thus, it is important to
control nitrogen and phosphorous pollution in the reservoir. The trends of the five water quality indicators were essentially the same at all three sites (Figs. 3(a)–3(e)). Thus, we chose one of the three sites, the Danjiangkou Reservoir dam, to analyze the seasonal concentration changes of the five indicators. For this analysis, we used the averaged monthly data from 2006 to 2012. From Fig. 4 we can see that NH3-N and TP kept a smooth and slight increasing tendency in the wet season (from May to October). CODMn and TN had an obvious increase in the wet season compared with the dry season (from November to April of the next year) with continuous fluctuations. DO decreased from May to August, and fluctuated during September to October, and then, kept increasing. In addition, the concentration values of DO were lower in the wet season than those of the dry season on the whole. This indicated that the water quality is worse during the wet season than during the dry season. During the wet season, large amounts of urban, domestic and industrial effluents, nitrogen fertilizers, and sediment perturbation were carried into the reservoir by surface
1) General planning report of the South-to-North Water Diversion Project (2001). The Ministry of water resources of the People’s Republic of China (in Chinese)
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Fig. 4 Seasonal concentration changes of indicators at the Danjiangkou Reservoir dam.
runoff. As a result, the concentrations of the water quality indicators (e.g., CODMn, NH3-N and TP) were higher than those during the dry season. Thus, agricultural non-point pollution, water loss, and soil erosion caused by vegetation damage were the main causes of increased nitrogen concentrations in the reservoir, making nitrogen pollution become a very serious problem in the reservoir. In contrast, phosphorus pollution has not endangered water quality in the Danjiangkou Reservoir so far. Concurrently, the degradation of pollutants, as well as increases in rainfall and temperature during the wet season could accelerate the growth and metabolism of marine organisms, leading to an obvious reduction of DO, especially from May to August. According to the entropy weight method calculations, the weight matrix of DO, CODMn, NH3-N, TN and TP was (ωj)15=(0.127, 0.329, 0.174, 0.239, 0.131). The relative influence of the indicators on water quality in the Danjiangkou Reservoir was as follows: CODMn > TN > NH3-N > TP > DO. These results indicate that CODMn and nitrogen concentrations were the major pollutants. These findings were consistent with those from a previous study (Li et al., 2009a). We used the entropy weight method to determine the indicator weights and to obtain accurate evaluation results.
four types of environmental quality standards for surface water in China. These results are consistent with previous analyses of trends found in indicator concentrations, and results issued by government authorities (Bulletin of Chinese environmental conditions in 2011: freshwater environment, 2012)1). Comprehensive water quality evaluation is a systematic process that requires the consideration of multiple indicator properties. Physical, chemical, and biological factors contain uncertainty; and nonlinear relationships exist among evaluation indicators and water quality types. Meanwhile, water quality changes dynamically. All of these considerations complicate the comprehensive evaluation of the water quality in the Danjiangkou Reservoir. We adopted the Bayesian method to establish a water quality evaluation model and the normal distribution
3.2 Comprehensive water quality evaluation of the Danjiangkou Reservoir
To determine water quality type, we calculated the posterior probability of every indicator that belonged to each standard with Eq. (1), and the probability of the multiindicator with Eq. (2). Figure 5 shows a probability distribution box chart for each water quality type. The probability of the water quality belonging to type Ⅱ was 27.7%–33.7%, larger than that of belonging to the other
Fig. 5 Probability distribution box chart for the five water quality types.
1) Bulletin of Chinese environmental conditions in 2011: freshwater environment (2012). The Ministry of Environmental Protection of the People’s Republic of China (in Chinese)
Fangbing MA et al. A Bayesian method for water quality evaluation of the Danjiangkou Reservoir
sampling method to calculate likelihood. In addition, the influence of random sampling errors on the water quality evaluation was considered. We used the entropy weight method to determine the weight of every indicator, which provided a theoretical foundation for distributing weights. The Bayesian method was more convenient and effective than single-factor and aggregative index evaluation methods (Xing et al., 2011) for the comprehensive evaluation of water quality. In existing literature, researchers often use maximum probability principles to explain evaluation results in studies that use the Bayesian method (Liao et al., 2009). For example, if surface water has a maximum probability of belonging to type Ⅱ of environmental quality standards, then it is regarded as type Ⅱ. However, the results of the water quality evaluation are not determined precisely. They have fuzziness and uncertainty (Qian et al., 2004; Wu et al., 2011). Especially for those posterior probabilities with small disparity, the use of the maximum probability principle brings subjective deviation into determining the water quality type. In order to reduce this subjective deviation, posterior probability was used to represent the possibility and tendency of the water quality to belong to each type. This type of analysis potentially provides a basis for decision-makers that is more objective and reliable than that provided by single-factor or aggregative analyses. One of the most important advantages of the Bayesian method is that it can describe and address uncertainty in information during the evaluation process more precisely. We assumed that the priori probabilities of the water quality belonging to each water quality type were equal due to lacking water quality information. However, these priori probabilities were different in the Danjiangkou Reservoir. For example, larger probabilities were found for type Ⅱ and type Ⅲ categories than for the other three types. Thus, the determination of priori probabilities needs to be studied further to obtain more reliable and accurate results.
4
Conclusions
The Bayesian method was used in this study, along with the normal distribution sampling and entropy weight methods, to evaluate water quality in the Danjiangkou Reservoir. The study was based on the investigation of changes and spatiotemporal characteristics of five water quality indicators (DO, CODMn, NH3-N, TN and TP) measured from January 2006 to May 2012. The following conclusions can be drawn: 1) CODMn and nitrogen were the major pollutants in the reservoir, and the concentrations of all indicators increased during the last six years. Nitrogen pollution and phosphorus pollution in the water source area is becoming increasingly serious. 2) The seasonal concentration variations of five water
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quality indicators varied with changes in temperature, rainfall and runoff. Overall, the water quality of the Danjiangkou Reservoir was worse during the wet season than during the dry season. 3) Water quality evaluation results indicated that the probability of the water quality’s belonging to type Ⅱ was 27.7%–33.7%, larger than that of its belonging to the other four types defined by environmental quality standards for surface water in China. The methodology used in this study reduced both subjectivity and artificial classifications when determining indicator weights, and obtained more reliable calculation results than those obtained using other conventional methods. The Bayesian method was convenient for analyzing different sample sizes, and can be used objectively for comprehensive water quality evaluation. Increasing concentrations of nutrients will promote the occurrence of eutrophication in the Danjiangkou Reservoir. To reduce the concentrations of nitrogen and phosphorus, it is important for managers to implement integrated water quality management strategies to avoid eutrophication in the Danjiangkou Reservoir. These strategies should include the control of man-made pollution sources, control of fertilizer use on upstream farmlands, and increasing the vegetation coverage on the upper regions of the reservoir to prevent water loss and soil erosion. Acknowledgements This study was supported by the National Science and Technology Support Program (No. 2011BAC12B02), the National Science Foundation for Innovative Research Group (No. 51121003), and the Outstanding Doctoral Thesis Fund of Beijing Normal University (No. 105512GK). We are grateful to the editors and anonymous reviewers’ careful review of this paper, whom have contributed substantially to improving the paper.
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