A cloud model-based approach for water quality assessment

Environmental Research 148 (2016) 24–35

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A cloud model-based approach for water quality assessment Dong Wang a,n, Dengfeng Liu a, Hao Ding a, Vijay P. Singh b, Yuankun Wang a, Xiankui Zeng a, Jichun Wu a, Lachun Wang c a Key Laboratory of Surficial Geochemistry, Ministry of Education, Department of Hydrosciences, School of Earth Sciences and Engineering, State Key Laboratory of Pollution Control and Resource Reuse, Nanjing University, Nanjing 210046, China b Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A&M University, College Station TX77843, USA c School of Geographic and Oceanographic sciences, Nanjing University, Nanjing, China

art ic l e i nf o

a b s t r a c t

Article history: Received 6 January 2016 Received in revised form 26 February 2016 Accepted 3 March 2016

Water quality assessment entails essentially a multi-criteria decision-making process accounting for qualitative and quantitative uncertainties and their transformation. Considering uncertainties of randomness and fuzziness in water quality evaluation, a cloud model-based assessment approach is proposed. The cognitive cloud model, derived from information science, can realize the transformation between qualitative concept and quantitative data, based on probability and statistics and fuzzy set theory. When applying the cloud model to practical assessment, three technical issues are considered before the development of a complete cloud model-based approach: (1) bilateral boundary formula with nonlinear boundary regression for parameter estimation, (2) hybrid entropy-analytic hierarchy process technique for calculation of weights, and (3) mean of repeated simulations for determining the degree of final certainty. The cloud model-based approach is tested by evaluating the eutrophication status of 12 typical lakes and reservoirs in China and comparing with other four methods, which are Scoring Index method, Variable Fuzzy Sets method, Hybrid Fuzzy and Optimal model, and Neural Networks method. The proposed approach yields information concerning membership for each water quality status which leads to the final status. The approach is found to be representative of other alternative methods and accurate. & 2016 Elsevier Inc. All rights reserved.

Keywords: Analytic hierarchy process Cloud model Fuzziness Information entropy Multi-criteria decision-making Randomness

1. Introduction The past decades have witnessed increasing human and industrial impacts on the environment, contributing to the pollution of lakes, reservoirs, rivers, and estuaries, especially in developing countries. Water quality degradation has been acknowledged as one of the most serious environmental issues worldwide, because it may disrupt the ecological balance of water bodies and threaten regional environmental security. It is, therefore, no surprise that effective modeling and assessment of water quality degradation have attracted a great deal of interest (Adrian et al., 1994; Vega et al., 1998; Janssen and Carpenter, 1999; Singh et al., 2004; Hantush, 2007; Kalin et al., 2010; Ng et al., 2011; Ocampo-Duque et al., 2013). The term “eutrophication” has acquired a scientific and legal definition as “the enrichment of water by nutrients causing an accelerated growth of algae and higher forms of plant life to produce an undesirable disturbance to the balance of organisms n

Corresponding author. E-mail address: [email protected] (D. Wang).

http://dx.doi.org/10.1016/j.envres.2016.03.005 0013-9351/& 2016 Elsevier Inc. All rights reserved.

present in the water and to the quality of the water concerned, and therefore refers to the undesirable effects resulting from anthropogenic enrichment by nutrients” (Ferreira et al., 2011). The mechanism of eutrophication is complex because of the influences not only from natural processes but also from anthropogenic activities (Kitsiou and Karydis, 2011). The evaluation of eutrophication is essentially a multi-criteria decision-making process accounting for the transformation of qualitative and quantitative uncertainties. That is, to obtain a true eutrophication level one should first quantify the qualitative term “eutrophication” with an index, construct a multi-criteria decision-making model with the input index, and finally obtain the evaluation outcome using the constructed model. There are two types of uncertainty that should be considered in the eutrophication evaluation: (1) randomness, which is often exhibited in the monitoring and analysis of data related to eutrophication; and (2) fuzziness, which is often reflected in the evaluation of the classification standard, evaluation class, and degree of pollution (Wang et al., 2007). Various models have been proposed to determine the water quality condition, including eutrophication status. Based on the above uncertainties, the assessment models can be divided into four types: (1) models based on various statistical and stochastic

D. Wang et al. / Environmental Research 148 (2016) 24–35

techniques for randomness, such as modeling eutrophication and microbial risks using discriminant analysis (DA) (Pinto et al., 2012), frequently used multivariate statistical approach (Moya et al., 2015; Primpas et al., 2010; Qian et al., 2007), which includes cluster analysis (CA), factor analysis (FA) and principal component analysis (PCA); (2) models based on fuzzy membership function, fuzzy logic and fuzzy set theory for fuzziness (Kotti et al., 2013; Dahiya et al., 2007); (3) models based on machine learning and artificial intelligence for unknown patterns hardly captured in the assessment process (Ay and Kisi, 2014; Kuo et al., 2006; Aguilera et al., 2001); and (4) hybrid models based on two or more above models or techniques, such as neuro fuzzy networks with factor analysis (Chang et al., 2014), non-parametric probability distributions, and fuzzy inference systems (Ocampo-Duque et al., 2013). A new hybrid model considering randomness with fuzziness, named cloud model, developed by (Li et al., 2009; Wang et al., 2014b), is a more complete and efficient cognitive technique than the former membership function (Zadeh, 1965) based transformation. In statistics, probability distributions can be used to model the uncertainty of variables representing random phenomena called randomness. In fuzzy mathematics, the membership function is used to model the uncertainty of membership to fuzzy concepts called fuzziness. The cloud model can model both randomness and fuzziness with fixed parameters.The normal cloud model, based on the normal distribution and a membership function, has been widely applied in information science, including multi-criteria group decision making (Wang et al., 2014a, 2014b, 2014c), intelligent control, image segmentation, and so on. In hydrology, Liu et al. (2009) introduced the normal cloud model for the study of spatial and temporal rainfall distribution. Liu et al. (2014) proposed a cloud model-based risk analysis approach coupled with an artificial neural network. More applications making use of the attractive efficiency of the randomness-fuzziness coupled model are expected in the near future. Since randomness and fuzziness are widely considered in water quality assessment, the normal cloud model, quantifying both randomness and fuzziness by means of three fixed parameters, is more advantageous than single randomness or fuzziness type models. Moreover, a physical interpretation of these parameters corresponding to water quality evaluation can be given (see Appendix A), which makes the cloud model-based assessment feasible. The main objective of this study therefore is to introduce the cloud model into water quality assessment, and develop a cloud model-based eutrophication assessment approach. However, since eutrophication assessment is a multi-criteria decision-making process with different undetermined outcomes classified as eutrophication levels, there are three main issues that limit the efficient application of existing cloud model in information science. There issues can be stated as: (1) how to determine the values of parameters according to the given or missing quantitative boundaries of each status; (2) how to balance the weights of each criterion so as to attain the final outcome; and (3) how to recognize the final status or level of eutrophication by the degree of certainty which is a random variable in repeated assessments. The organization of the paper is as follows. Section 2 provides sufficient data and monitored values of eutrophication indices (Chl-a: Chlorophyll-A; TP: Total Phosphorus; TN: Total Nitrogen; COD: Chemical Oxygen Demand and SD: Clarity) to allow the remaining work to be reproduced, then discusses the three issues stated above and provides appropriate solutions; next, a complete cloud model-based water quality assessment approach is proposed. Section 3 illustrates the application of the technique to typical lakes and reservoirs in China, and assesses the validity of the proposed cloud model-based approach by comparison with four other methods. The conclusions are given in Section 4. In

25

Appendix A, basic concepts of the cloud model are briefly introduced, in the context of eutrophication evaluation.

2. Data and methods 2.1. Data and monitored values of eutrophication indices In China, the Ministry of Environmental Protection and the Ministry of Water Resources employ professionals, engineers and scientists whose primary responsibility is to collect water quality data, such as chlorophyll-A, total phosphorus, total nitrogen, chemical oxygen demand, clarity, and so on. These data are subject to a variety of national standards and professional standards, which assure and control the quality of data. These standards also regulate data sampling, monitoring, inspection, analysis, and interpretation. The data were obtained mainly from branches of the Ministry of Environmental Protection and the Ministry of Water Resources. Monitored values of eutrophication indices of 12 typical lakes and reservoirs employed in this study can be found in (Shu, 1990); the study lakes and reservoirs were Qionghai Lake in Sichuan Province, Erhai Lake in Yunnan Province, Bosten Lake in Xinjiang Uygur Autonomous Region, Yuqiao Reservoir in Tianjin Municipality, Ci Lake in Hubei Province, Chao Lake in Anhui Province, Gantang Lake in Jiangxi Province, Moguhu Reservoir in Xinjiang Uygur Autonomous Region, West Lake in Zhejiang Province, Xuanwu Lake in Jiangsu Province, Moshui Lake in Hubei Province, and Dongshan Lake in Guangdong Province. 2.2. A cloud model-based assessment approach Recognizing the status of eutrophication by outcomes or uncertainty degrees, the normal cloud model can realize the transformation between qualitative concept and quantitative data. The model represents the cognition of qualitative concept “eutrophication” (Fig. 1), which makes it applicable in water quality evaluation. Note that in Fig. 1 the x-axis represents the values of an eutrophication index, and the y-axis represents the certainty degree of an eutrophication level. In addition, physical interpretation of the parameters corresponding to water quality evaluation can be developed, based on the original description of model parameters (Table 1). The cloud model-based eutrophication assessment approach can be illustrated in Fig. 2, and summarized as below: Step1: Determine eutrophication criteria (Chl-a, TP, TN, COD, SD). Step2: Determine parameters (Ex, En, He) of each model, based on given levels (I, II, III, IV, V, VI), and the corresponding bilateral boundaries, before the cloud is completely modeled;. Step3: Calculate the hybrid entropy–AHP (Analytic Hierarchy Process) weights;. Step4: Substitute the observed data into cloud models repeatedly to obtain the distributions of certainty degrees, and further final outcomes corresponding to all levels. Finally, the eutrophication status (level) can be determined, based on the status (level) with maximum certainty degree calculated from the cloud model. 2.2.1. Strategies for three issues Since eutrophication assessment is a multi-criteria decisionmaking process, based on local environmental legislation with outcomes classified as various levels (Shu, 1990) (Table 2), three issues exist when employing the normal cloud model for eutrophication evaluation: (1) How to determine parameters, especially En and He, according

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The modified equations are applicable for fixed intervals, noting that on level VI of criterion Chl-a (Chlorophyll-A), TP (Total Phosphorus), TN (Total Nitrogen), COD (Chemical Oxygen Demand), and on level I of criterion SD (Clarity), Bmax is missing. Here a polynomial regression analysis technique was employed to attain the pseudo-boundary (Fig. 4), assuming that the increasing tendency of Bmax was in accordance with level L and could be recognized. After that, the half cloud model which is half of a complete cloud model was employed particularly on levels I and VI of each criterion, since cognition in this situation was monotonous but not symmetrical, and when the quantitative data reached zero or infinity even beyond the pseudo-boundary, the corresponding certainty degree reached 1. After attaining all quantitative boundaries of the levels of all criteria from the environmental legislation and polynomial regression technique, all parameters were determined as in Table 3. Fig. 1. Normal cloud model corresponding to the concept “eutrophication”.

to fixed or even missing quantitative boundaries of individual levels; (2) how to determine the weight of each criterion so that the final certainty degree can be attained; and (3) how to recognize the final eutrophication status or level by the certainty degree, since it is controlled by He and is a random variable in repeated assessment. 2.2.1.1. Strategy for issue 1: parameter determination. For the determination of (Ex, En, He), (Du et al., 2008) suggested Eq. (1) for a bilateral boundary of the form (Bmin, Bmax):

Ex = (Bmin + Bmax )/2 { En = (Bmax − Bmin )/6 He = k

(1)

where Bmin and Bmax are the minimum and maximum values that can be accepted by a qualitative concept; that is, in eutrophication assessment Du et al. (2008) mean the minimum and maximum values corresponding to a certain eutrophication level in each criterion to obtain the value of Ex. For example, for level II of Chl-a, Bmin ¼ 1, and Bmax ¼ 2 (see Table 2), the corresponding parameters can be obtained as Ex¼1.5 and En ¼1/6. Note that k is a constant and can be adjusted according to the practical situation. In the present study, the algorithm of He was modified as follows: Since hyper-entropy He is the uncertainty degree of entropy En, while in Eq. (1) He is assumed as a constant irrelevant to En, it is assumed that He can be adjusted by a linear relationship with En:

He = k⋅En

(2)

In this way, k intuitively controls the ‘atomization’ degree of the normal cloud model (Fig. 3) and essentially reflects the variation of cognition of different evaluations. Here k is assumed as 0.1 to balance the variation and robustness of assessment (Liu et al., 2014).

2.2.1.2. Strategy for issue 2: calculation of weights. The Analytic Hierarchy Process (AHP) has been widely applied in multi-criteria analyses (Saaty and Shang, 2011). (Cai, 1997) employed the AHP in water quality weight calculation, and ranked the relative importance of the five eutrophication criteria from high to low as: Chl-a, SD, TP, TN and COD, and finally determined the AHP-based weight ri as 0.455, 0.251, 0.154, 0.086 and 0.054, respectively. Here a comprehensive weight calculating algorithm coupled with entropy is proposed, which is expected to balance the potential subjective uncertainty of the simple AHP approach. Regarded as a measurement of disorder or uncertainty of a system, the notion of “entropy” taken from the theoretical foundation of the modern information theory (Shannon, 1948) has been introduced in hydrology and water quality, particularly in uncertainty analyses (Singh et al., 2014; Singh, 2015; Wang et al., 2014a). In eutrophication assessment, entropy of the observed data under the ith criterion can be calculated by: n

Hi = −

∑ pk ln pk k=1

(3)

where Hi represents the uncertainty of observed water quality data of one criterion with n potential intervals or statements; pk is the frequency of the kth statement and if pk ¼0 then 0 ln 0 = 0. Now the entropy-based weight of the ith criterion ωi can be attained, based on the normalized entropy Hi′ (Zhang and Singh, 2012), as:

Hi′ =

Hi ln n

(4)

1 − Hi‵

ωi =

m

m−

∑

Hi‵

i=1

(5)

where m is the number of criteria. For the feasibility of entropy-based weight in the water quality assessment, the entropy-based weight, unlike the AHP-based weight,

Table 1 Original descriptions of parameters and further interpretations in water quality assessment. Original descriptions of parameters

Interpretations in water quality assessment

 Ex (Expectation):The most representative and typical sample of the qualitative  The central tendency of the quantitative values representing “eutrophication” concept

 En (Entropy): Uncertainty measurement of a qualitative concept  He (Hyper-entropy): Uncertain degree of entropy En

 The average scope of the universe that can be accepted by “eutrophication”  The measurement of variation of certainty degrees from assessments by different evaluators

D. Wang et al. / Environmental Research 148 (2016) 24–35

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Fig. 2. Framework of cloud model-based eutrophication assessment approach. (Chl-a: chlorophyll-A; TP: total phosphorus; TN: total nitrogen; COD: chemical oxygen demand; SD: clarity). Table 2 Quantitative boundaries of eutrophication levels of all criteria. Levels

I II III IV V VI

Eutrophication criteria Chl-a(mg/m3)

TP(mg/m3)

TN(mg/m3)

COD (mg/L)

SD(m)

r1 r2 r4 r 10 r 65 465

r 2.5 r5 r 25 r 50 r 200 4200

r30 r50 r300 r500 r2000 42000

r 0.3 r 0.4 r2 r4 r 10 428

Z 10 Z5 Z 1.5 Z1 Z 0.4 o 0.4

(Chl-a: chlorophyll-A; TP: total phosphorus; TN: total nitrogen; COD: chemical oxygen demand; SD: clarity).

criterion controlling the decision-making is less compared to others. In this manner, low entropy contributes to low weights. In order to balance the potential subjective uncertainty of the simple AHP approach, a hybrid entropy-AHP weights algorithm is given as Eq. (6):

Wi =

riωi m

∑

riωi

i=1

(6)

Results are shown in Table 4. After calculating the final hybrid entropy–AHP weights of various criteria, the certainty degree U in one simulation can be obtained: m

does not reflect the subjective importance of criteria, but indicates the relative severity of “competition” of each criterion. For instance, if the observed data have a central tendency under a certain criterion which corresponds to a low entropy, the “competitiveness” of the

U=

∑ Wiμi i=1

(7)

where μi is the certainty degree evaluated by the cloud model of each criterion.

Fig. 3. Cloud models (Ex¼ 0, En ¼100) with different k.

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Fig. 4. Polynomial regression of the quantitative boundaries of all criteria. (Chl-a: chlorophyll-A; TP: total phosphorus; TN: total nitrogen; COD: chemical oxygen demand; SD: clarity). Table 3 Cloud model parameters of eutrophication levels of all criteria. Levels

I II III IV V VI

Chl-a(mg/m3)

TP(mg/m3)

TN(mg/m3)

COD (mg/L)

SD(m)

Ex

En

He

Ex

En

He

Ex

En

He

Ex

En

He

Ex

En

He

0.50 1.50 3.00 7.00 37.50 160.50

0.17 0.17 0.33 1.00 9.17 31.83

0.02 0.02 0.03 0.10 0.92 3.18

1.25 3.75 15.00 37.50 125.00 464.00

0.42 0.42 3.33 4.17 25.00 88.00

0.04 0.04 0.33 0.42 2.50 8.80

15.00 40.00 175.00 400.00 1250.00 4890.00

5.00 3.33 41.67 33.33 250.00 963.33

0.50 0.33 4.17 3.33 25.00 96.33

0.15 0.35 1.20 3.00 7.00 19.00

0.05 0.02 0.27 0.33 1.00 3.00

0.01 0.00 0.03 0.03 0.10 0.30

14.50 7.50 3.25 1.25 0.70 0.20

1.50 0.83 0.58 0.08 0.10 0.07

0.15 0.08 0.06 0.01 0.01 0.01

(Chl-a: chlorophyll-A; TP: total phosphorus; TN: total nitrogen; COD: chemical oxygen demand; SD: clarity). Table 4 Weights of criteria for eutrophication assessment. Criteria

Entropy

Entropy weight ω

AHP weight r

Entropy-AHP weight W

Chl-a TP TN COD SD

1.474 1.705 1.352 2.138 1.589

0.243 0.187 0.272 0.083 0.215

0.455 0.154 0.086 0.054 0.251

0.499 0.130 0.106 0.020 0.244

(Chl-a: chlorophyll-A; TP: total phosphorus; TN: total nitrogen; COD: chemical oxygen demand; SD: clarity).

2.2.1.3. Strategy for issue 3: recognizing the degree of final certainty. Since the degree of certainty of the cloud model is a random variable controlled by He in repeated assessments, with fixed quantitative values of water quality criteria. Two sub-strategies are suggested as the final certainty degree: the mode of distribution of certainty degree (sub-strategy 1), which can be interpreted as the most acceptable or popular outcome in repeated simulations; and the mean of distribution of certainty degree (sub-strategy 2), which can be interpreted as the central tendency of outcomes in repeated simulations. Here we compared the statistical performances of the

D. Wang et al. / Environmental Research 148 (2016) 24–35

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Table 5 Final certainty degrees of 720, 7 10 and 0 by the cloud model (0, 10, 1) in repeated simulations. Strategies

Quantitative values

STD of final certainty degrees

Number of assessments 500

1000

2000

5000

10,000

50,000

Mean

 20  10 0 10 20

0.136 0.600 1 0.605 0.139

0.136 0.599 1 0.598 0.137

0.139 0.600 1 0.600 0.137

0.138 0.600 1 0.600 0.139

0.139 0.600 1 0.601 0.139

0.138 0.601 1 0.600 0.138

0.0012 0.0007 0 0.0023 0.0007

Mode

 20  10 0 10 20

0.133 0.616 1 0.639 0.121

0.136 0.625 1 0.604 0.111

0.131 0.601 1 0.608 0.137

0.124 0.618 1 0.613 0.132

0.141 0.617 1 0.627 0.131

0.128 0.620 1 0.622 0.128

0.0055 0.0074 0 0.0118 0.0085

two sub-strategies under various generating scenarios:

 Parameters of cloud model were fixed at Ex¼0, En ¼10, He¼ 1 (k¼0.1), without loss of generality;

 Quantitative values of the criteria were fixed at x ¼ 7 20, 710 and 0; and

 The number of simulations varied from 500, 5000, 50,000. The final certainty degree results are listed in Table 5 from which the following can be deduced: (1) The cognitive transformation is symmetrical about Ex, with outcomes under various assessments of pairs of (  20, 20) and (  10, 10) being generally the same by both sub-strategies. Also, the transformation is nonlinear and non-exponential.

Since the mapping essentially obeys the normal membership function with parameters disturbed by the Gaussian noise, outcomes of the cloud model have the patterns of a normal distribution, such as symmetry, nonlinearity, non-exponential behavior, etc. (2) Outcomes of the two sub-strategies depend on various quantitative values: For x ¼0, both certainty degrees are the same as 1; for x ¼  20 and 20, the outcomes of sub-strategy 1 are higher than those of sub-strategy 2; and the situation is unlike that for x ¼  10 and 10, with certainty degrees of sub-strategy 2 being higher than the other. Further, distributions of the certainty degrees of  20 and 20 are positive-skewed, of which means are larger than modes; while distributions of certainty degrees of  20 and 20 are negative-skewed, of which modes are larger than means. The phenomenon can be

Fig. 5. (a) Distributions of certainty degree of  20 by the cloud model (Ex¼ 0, En ¼10, He¼ 1) in different repeated simulations. (b) Distributions of certainty degree of  10 by the cloud model (Ex¼ 0, En¼ 10, He¼ 1) in different repeated simulations.

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D. Wang et al. / Environmental Research 148 (2016) 24–35

illustrated from the distributed patterns of certainty degrees (Fig. 4(a) and (b)). For brevity, we here only provide the distributions of certainty degrees of  10 and  20. (3) Sub-strategy 2 (mean) seems to have a stronger robustness than sub-strategy 1 (mode), with lower STDs of outcomes from various numbers of assessments. By contrast, outcomes by sub-strategy 1 are more variant in different simulations and non-convergence can occur, even though the number of simulations reaches 50,000. In order to balance the accuracy, robustness and computational expense in repeated simulations, sub-strategy 2 (mean) was selected for determining the final certainty degree from practical water quality assessments for which the number was set as 2000 ( Fig. 5).

3. Results and discussion 3.1. Eutrophication status assessment using cloud model-based approach Observed water quality data from the 12 lakes and reservoirs were used in the cloud model with parameters as given in Table 3. After weight calculation, distributions of certainty degrees on each level for all cases were computed and are illustrated in Fig. 6(a)– (d). From Fig. 6, we obtain different distribution patterns of certainty degrees at each level of the various cases. Not all levels have distributions for most cases and the distribution ranges are also different for those levels that have distributions. We performed

sub-strategy 2, and the final certainty degrees at each level of all cases were determined with the mean of certainty degrees obtained from 2000 simulations, and the final eutrophication levels were obtained with the maximum certainty degrees indicating the most probable membership. Results are shown in Table 6. Note that the numbers of zeros indicate that there is no membership at the level corresponding to the non-distribution patterns in Fig. 6. 3.2. Comparative results The validity of the proposed cloud model-based approach was assessed by comparison with other four methods: the Scoring Index (SI) method (Shu, 1990), the Variable Fuzzy Sets (VFS) method (Chen and Guo, 2005), the Hybrid Fuzzy and Optimal model (HFO) method (Wang et al., 2007), and the Neural Networks (NNs) method (Cui, 2012). Results of the various methods are compared in Table 7. The ensuing discussion can be summarized as follows: (1) Generally speaking, results from the various methods are in accordance with each other, and especially, the results of 5 lakes (Chao Lake, Gantang Lake, Xuanwu Lake, Moshui Lake and Dongshan Lake) are exactly the same. For other lakes, there are no more than two different outcomes, except for Bosten Lake whose final levels are III (Scoring Index (SI) method and Hybrid Fuzzy and Optimal model (HFO) method), IV (cloud model-based approach and variable fuzzy sets (VFS) method), and V (Neural Networks (NNs) method). Furthermore, results from the cloud model-based approach are

Fig. 6. (a) Distributions of certainty degrees on each level of cases of Qionghai Lake, Erhai Lake and Bosten Lake. (b) Distributions of certainty degrees on each level of cases of Yuqiao Reservoir, Ci Lake and Chao Lake. (c) Distributions of certainty degrees on each level of cases of Gantang Lake, Moguhu Reservoir and West Lake. (d) Distributions of certainty degrees on each level of cases of Xuanwu Lake, Moshui Lake and Dongshan Lake.

D. Wang et al. / Environmental Research 148 (2016) 24–35

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Fig. 6. (continued)

generally the same as those from the other methods that are compared. That is, the 83% (10/12) results are exactly the same as those from the variable fuzzy sets (VFS) method and scoring index (SI) method; and the 75% (9/12) results are exactly the same as those from the hybrid fuzzy and optimal model (HFO) methods and the neural networks (NNs) method. The above results show high consistency between various methods. (2) The eutrophication of each lake and reservoir can be generally classified by 4 status levels from low to high, considering the overall results from all methods: Qionghai Lake and Erhai Lake, most of whose levels are III; Bosten Lake and Yuqiao reservoir, most of whose levels are VI; Ci Lake, Chao Lake, Gantang Lake and West Lake, most of or even all of whose levels are V; Mogu Lake, Xuanwu Lake, Moshui Lake and Dongshan Lake, most of or even all of whose levels are VI. The same conclusion can also be drawn by the cloud model-based approach individually, with the final levels from III to VI. Actually, for each case, results from the cloud model-based approach are the most probable among all results, which show high representativeness of the cloud model-based approach amongst all methods. (3) By indicating the degree of certainty belonging to a certain eutrophication level, the certainty degree provides more detailed information than the simple final level. For instance, although the final levels of Bosten Lake and Yuqiao Reservoir are IV, the certainty degree of level IV of Yuqiao Reservoir (0.1280) is higher than that of Bosten Lake (0.0863), which shows that the eutrophication level of Yuqiao Reservoir is more likely to be IV than of Bosten Lake. Another example is Ci

Lake and Chao Lake whose levels are both V, whereas the certainty of level V of Ci Lake is 0.3764, much higher that than of Chao Lake (0.1446). Considering the local test and water supply conditions that Ci Lake was environmentally more serious than Chao Lake, it can be seen that the cloud modelbased approach can not only indicate the eutrophication level accurately, but also further reveal the severity of eutrophication at the same level.

4. Conclusions A cloud model-based approach is proposed for eutrophication assessment, considering different types of uncertainties and three technical issues in practical water quality evaluation. Comparing with four alternative methods using observed data from lakes or reservoirs in China, final eutrophication level outcomes produced by the proposed model are found to be most probable and representative, thus demonstrating the validity of the model. Besides, the evaluation process ensures that the method also reveals the severity of eutrophication at each level, which provides much more information on the eutrophication status than other methods. In this research, we employed the most popular normal cloud model for water quality assessment. The cloud model type needs to be extended for further applications. Given that the construction of a comprehensive cloud model from one-dimensional cloud models is complicated, an easier multi-dimensional cloud modeling strategy is worth exploring.

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Fig. 6. (continued)

Fig. 6. (continued)

D. Wang et al. / Environmental Research 148 (2016) 24–35

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Table 6 Results by cloud model-based assessment approach. Cases

Final certainty degrees

Final eutrophication levels

Level I

Level II

Level III

Level IV

Level V

Level VI

Qionghai Lake Erhai Lake Bosten Lake Yuqiao Reservoir Ci Lake Chao Lake

0.0259 0.0000 0.0000 0.0000 0.0000 0.0000

0.0010 0.0000 0.0000 0.0000 0.0000 0.0000

0.2322 0.1700 0.0030 0.0010 0.0000 0.0000

0.1012 0.0493 0.0863 0.1280 0.0000 0.0000

0.1293 0.0000 0.0503 0.1030 0.3764 0.1446

0.0001 0.0000 0.0000 0.0001 0.0001 0.1345

III III IV IV V V

Gantang Lake Moguhu Reservoir West Lake Xuanwu Lake Moshui Lake Dongshan Lake

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.1476 0.0365 0.1203 0.0057 0.0000 0.0000

0.0280 0.1077 0.0711 0.8018 0.9827 0.8988

V VI V VI VI VI

Table 7 Comparison of eutrophication levels using various methods. Cases

Assessment methods

Qionghai Lake Erhai Lake Bosten Lake Yuqiao Reservoir Ci Lake Chao Lake Gantang Lake Moguhu Reservoir West Lake Xuanwu Lake Moshui Lake Dongshan Lake

Scoring index

Variable fuzzy sets

Hybrid fuzzy and optimal model

Neural networks

cloud modelbased

III III III IV

IV III IV IV

III III III IV

III IV V V

III III IV IV

V V V V

V V V VI

IV V V V

V V V VI

V V V VI

V VI VI VI

VI VI VI VI

V VI VI VI

V VI VI VI

V VI VI VI

Acknowledgment The authors gratefully acknowledge the helpful review comments and suggestions on earlier version of the manuscript by the Editor, Associate Editor and the reviewers. This study was supported by National Key Technology Support Program (2013BAB05B01-3), National Natural Science Foundation

of China (No. 41571017, 51190091, 41071018), Program for New Century Excellent Talents in University (NCET-12-0262), China Doctoral Program of Higher Education (20120091110026), Qing Lan Project, the Skeleton Young Teachers Program and Excellent Disciplines Leaders in Midlife-Youth Program of Nanjing University.

Appendix A. methodology: cloud model The cloud model is a cognitive model, which can realize the transformation between qualitative concept and quantitative data based on probability and statistics and fuzzy set theory. In the cloud model, it is possible to measure the deviation of a cognition process from a fuzzy membership function when the cognition does not strictly satisfy a certain membership function, e.g. Gaussian function, by adding a stochastic disturbance to the membership degree. Based on the normal distribution and Gaussian membership function, and with three parameters (Ex, En, He), the normal cloud model is the most important cloud model, and has been studied and widely applied in information science (Li et al., 2009; Wang et al., 2014b). The definition of the normal cloud model is as follows: Let U be the universe of discourse and A˜ be a qualitative concept in U. If x ∈ U is a random instantiation of concept A˜ , which satisfies x ∈ N (Ex, En′ 2), En′ ∈ N (En, He2), and the certainty degree of x belonging to concept A˜ satisfies −

y = μ∼ =e A (x )

(x − Ex)2 2(En )2

′

(A.1)

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then the distribution of x in the universe U is called a normal cloud. In this way, the normal cloud model can effectively integrate the randomness and fuzziness of concepts by the three parameters as follows:

 Ex (Expectation) is the mathematical expectation of the cloud drops belonging to a concept in the universe. It can be regarded as the most representative and typical sample of the qualitative concept. En (Entropy) represents the uncertainty measurement of a qualitative concept. It is relevant for both the randomness and the fuzziness of the concept. In one aspect, En contributes to the extent of random dispersion of cloud drops, with another parameter He, and in other aspect, it is essentially the measurement of fuzziness, representing the average scope of the universe that can be accepted by the concept. He (Hyper-entropy) is the uncertainty degree of entropy En.





Note that ∀ x ∈ U , the mapping μ A∼(x ) is a one-to-many mapping in nature, that is, the certainty degree of x belonging to the concept A˜ is a probability distribution rather than a fixed number. Given the parameters, the cloud model with N drops can be generated by the following algorithm. Algorithm Forward normal cloud transformation (FNCT) Input: Three parameters Ex, En, He and the number of cloud drops N.Output: N cloud drops and their certainty degree. Steps: Generate a normally distributed random number Eni′ with expectation En and variance He . 2. Generate a normally distributed random number x i with expectation En and variance Eni′. 1.

−

(x − Ex )2 2(En′)2 i .

3.

Calculate yi = e

4.

x i is a cloud drop in the universe and Yi is the certainty degree of x i belonging to the concept A˜ . Finally, repeat steps 1–4 until N cloud drops are generated.

5.

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