A multidimension cloud model-based approach for water quality assessment

Environmental Research 149 (2016) 113–121

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A multidimension cloud model-based approach for water quality assessment Dong Wang a,n, Debiao Zeng a, Vijay P. Singh b, Pengcheng Xu a, Dengfeng Liu a, 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, PR China b Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A & M University, College Station, TX 77843-2117, 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 14 March 2016 Received in revised form 26 April 2016 Accepted 9 May 2016

Lakes are vitally important, because they perform a multitude of functions, such as water supply, recreation, fishing, and habitat. However, eutrophication limits the ability of lakes to perform these functions. In order to reduce eutrophication, the first step is its evaluation. The process of evaluation entails randomness and fuzziness which must therefore be incorporated. This study proposes an eutrophication evaluation method, named Multidimension Normal Cloud Model (MNCM). The model regards each evaluation factor as a one-dimension attribute of MNCM, chooses reasonable parameters and determines the weights of evaluation factors by entropy. Thus, all factors of MNCM belonging to each eutrophication level are generated and the final eutrophication level is determined by the certainty degree. MNCM is then used to evaluate eutrophication of 12 typical lakes and reservoirs in China and its results are compared with those of the reference method, one-dimension normal cloud model, related weighted nutrition state index method, scoring method, and fuzzy comprehensive evaluation method. Results of MNCM are found to be consistent with the actual water status; hence, MNCM can be an effective evaluation tool. With respect to the former one-dimension normal cloud model, parameters of MNCM are improved without increasing its complexity. MNCM can directly determine the eutrophication level according to the degree of certainty and can determine the final degree of eutrophication; thus, it is more consistent with the complexity of water eutrophication evaluation. & 2016 Elsevier Inc. All rights reserved.

Keywords: Multi-dimension normal cloud model Eutrophication evaluation Entropy weight

1. Introduction Lakes play a remarkable role in a variety of functions, such as fishing, habitat and water supply. However, these functions are restricted to a certain extent by the problem of eutrophication (Schindler, 2012). In recent years, eutrophication, triggered by human activities, has been regarded as a worldwide environmental concern, which threatens drinking water security and restricts sustainable socio-economic development (Shu, 1990). Eutrophication is defined as “the enrichment of water by nutrients, such as phosphates, nitrates and so on, causing an accelerated growth of algae and higher forms of plant life to produce an undesirable disturbance to the balance of organisms present in the water and to the quality of the water concerned, and therefore refers to the undesirable effects resulting from anthropogenic n

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

http://dx.doi.org/10.1016/j.envres.2016.05.012 0013-9351/& 2016 Elsevier Inc. All rights reserved.

enrichment by nutrients” (Ferreira et al., 2011). It is, therefore, important to develop efficient methods for evaluation of eutrophication (Pinto and Maheshwari, 2011). Traditional methods for the assessment of eutrophication include the trophic state index (TSI) (Carlson, 1977), comprehensive fuzzy assessment method (Newton et al., 2003; Dustin and Miller, 2001), eutrophication assessment based on quantile regression (Xu et al., 2015), computer-automated decision support system (Asheesh et al., 2013), comprehensive eutrophication state index model (Wang, 2012), artificial neural network model (Cui, 2012,) and improved fuzzy synthetic evaluation model (Rui et al., 2013). These methods apply under particular conditions and have certain limitations. For instance, artificial neural networks are deficient in the precise analysis of each performance index; quantile regression is highly sensitive to the abnormal parameter; and the comprehensive fuzzy method has difficulty in differentiating the contiguous typical indications (Xu et al., 2015). Although these methods of eutrophication assessment are helpful, they do not systematically consider two uncertainties:

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D. Wang et al. / Environmental Research 149 (2016) 113–121

randomness and fuzziness (Wang et al., 2007; Li et al., 2009b; Wang et al., 2014). Li et al. (1995) introduced the concept of membership cloud and membership cloud generators, which provided a new way of combining fuzziness and randomness. The cloud model, that involves the transformation of qualitative notion and its quantitative instances, can systematically consider the randomness and fuzziness of eutrophication assessment. The normal cloud model is the most rudimentary model for its adoption of normal distribution and membership function. The normal cloud model has been widely used in the fields of information sciences, including data mining (Liu et al., 2009; Wang et al., 2003), intelligent control (Jia et al., 2014), image segmentation (Qin et al., 2011), and risk assessment (Zhang et al., 2012). Normal cloud models have also been developed in the aerial fields to help make decisions on alternative routes for aircraft (Sun et al., 2014). The main aim of this paper is to propose a multidimension normal cloud model (MNCM) based on the cloud model theory and the corresponding one-dimension normal cloud model (ONCM). The one-dimension normal cloud method is based on one-dimension normal cloud, while the multi-dimension normal cloud method is an extension of the one-dimension normal cloud method. It takes the one-dimension normal cloud method as each dimension of MNCM, and determines the final certainty by the multi-dimension normal cloud. Considering the randomness of membership degree, Li et al. (1995) proposed cloud models as a new cognition model of uncertainty, based on the probability theory and fuzzy sets theory in 1995. Therefore, the originality of the MNCM is as follows: (1) it is based on the cloud model which can synthetically present randomness and fuzziness. (2) It proposes the weight formula on the basis of Shannon entropy. (3) In contrast with the ONCM, the MNCM can objectively indicate the randomness and fuzziness which can be shown by the hyper entropy He. The MNCM can judge the eutrophication of different lakes which are on the same eutrophication level. In addition, because of different demands, lake functions vary with different evaluation criteria. According to the aforementioned analysis, water quality assessment is an obscure and fuzzy concept, because it is decided by human demands and self-identities. Furthermore, many elements in the lake health assessment are nonlinear and indeterminate (Karr,1999; Norris and Thoms,1999). Therefore, employment of the MNCM based on the cloud model, which can synthetically describe randomness and fuzziness of the concept “risk” and implement the uncertain transformation between the concept and its quantitative factors, is applicable to the characteristics of lake functions. A weight formula was therefore proposed based on the Shannon entropy and the analytical hierarchy process (AHP), which can balance the subjective uncertainty with calculation of conventional weights. This paper is organized as follows: Section 2 introduces the basic theory of one-dimension and multi-dimension cloud models. The multi-dimension cloud-based eutrophication assessment, including the framework for assessment, determination of model parameters, and comprehensive cloud model of evaluation factors, is discussed in Section 3. In Section 4, the MNCM is used to evaluate 12 typical lakes in China, followed by comparison with other assessment methods. Finally, conclusions are stated in Section 5.

2. Methodology 2.1. One-dimension normal cloud Definition 1: 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), so the degree of certainty of x belonging to concept A satisfies

2

μA(x)=e

−

( x − Ex)

2(En′) 2

(1)

then the distribution of x in the universe U is called one-dimension normal cloud, and x is defined as a cloud drop. The normal cloud model can effectively integrate the randomness and fuzziness of concepts by three parameters as follows:


Ex (Expectation), 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. Ex can be determined as Ex¼(Bmin þBmax)/2, where Bmin and Bmax are the boundaries of the particular variable. The specific equation is discussed in Section 3.2. En (Entropy) represents a measurement of uncertainty of a qualitative concept. It is relevant with both the randomness and the fuzziness of the concept. On one hand, En measures the random dispersing extent of cloud drops, with another parameter He. On the other hand, it is essentially a measurement of fuzziness, representing the average scope of the universe that can be accepted by the concept. He (Hyper-entropy) is the degree of uncertainty of entropy En.

2.2. Multidimensional normal cloud model The multidimension normal cloud method is an extension of the one-dimension normal cloud method. It takes the one-dimension normal cloud method for each attribute of the multi-dimension normal cloud, and determines its certainty. Let U{x1,x2,…,xm} be an m dimension universe of discourse with precise values, and C be a qualitative concept in U { x1,x2,…,xm}. If x ∈ U is a random instantiation of concept C, which satisfies

( (

)

2

)

X(x1,x2 ,…,xm )~N Ex Ex1Ex2 ,…,Exm ,En‵ ( En‵1,…,Enm ‵) , and

(

En′ En′1,En′2 ,…,En′m

)

( (

)

2

)

He ( He1, He2 , ..., Hem ) ,

~N En En1, En2 ,…,Enm ,

and the degree of certainty of x belonging to concept C satisfies −

μ(x ( x1,x2 ,…,xm ))=e

m ( x −Ex 2 j j

∑

j=1 2 ( En′ j

) )2 ,

j= 1,2,…m

(2)

then the distribution of x in the universe U is called multi-dimension normal cloud. Based on these concepts, the MNCM can be described by the following algorithm (Li and Liu, 2010). Algorithm Multidimension forward normal cloud transformation

Steps: 1. Generate a normally distributed random number X(x1,x2,…,xm), with expectation Ex ( Ex1,Ex2 ,…,Exm ) and variance En ( En1,En2 ,…,Enm ). 2. Generate a normally distributed random number

En′(En′1,En′2 ,…,En′m ), with expectation En ( En1,En2 ,…,Enm ) and variance He ( He1,He2 ,…,Hem ). − ∑m j=1

(xj − Exj )2 2

2 (Enj ) 3. Calculate: μ (x (x1, x2, ... , xm )) = e , j = 1, 2, ... , m , so a particular cloud drop of normal cloud is (X(x1,x2,…,xm),μ( x (x1,x2,…,xm))).

D. Wang et al. / Environmental Research 149 (2016) 113–121

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other elements into phosphate, so TP is usually regarded as an evaluation index. Total Nitrogen (TN): Nitrogen is one of important nutrients and also the limiting nutrient element of some phytoplankton. So TN is usually regarded as an evaluation index. Chlorophyll-A (Chl-a): The blooms of phytoplankton, such as algae, is the direct cause of eutrophication. The density of chlorophyll-A can indicate the number of phytoplankton. So Chl-a is usually regarded as an evaluation index. Water Transparency (SD): Water transparency indicates the extension of light in the depth direction. The deterioration of water transparency will influence the photosynthesis of plants, which will destroy the balance of water ecological system. Chemical Oxygen Demand (COD): Chemical oxygen demand reflects the degree of water polluted by reducing agents. To make the results correspond to the practical situation of lakes, this paper chooses chlorophyll-A (Chl-a), total phosphorus (TP), total nitrogen (TN), chemical oxygen demand (COD) and water transparency (SD) as evaluation factors, which are all related with the Chl-a (Shu, 1993). The specific evaluation criteria are detailed in (Shu, 1990). On this basis, the evaluation factors and their classification standards have been determined, and three digital characteristics of cloud model were determined according to the following method (Ding and Wang, 2013). As to the determination of numerical characteristics (Ex, En, He), (Du et al., 2008) suggested Eq. (3) when giving bilateral constrains in the form of interval [Bmin, Bmax ]: If a variable has an upper as well as a lower boundary, like this: VQa [Bmin, Bmax ]. VQa just means the value of a certain variable. Ex, which is one of the digital characteristics of cloud model, can be determined as

4. Repeat steps 1–3 until N cloud drops are generated.

3. Multidimension cloud-based eutrophication assessment 3.1. Framework for assessment The framework of the water eutrophication evaluation method for the MNCM is as follows. ● Determine the appropriate eutrophication evaluation factors and their number, determine the suitable classification index, and divide them into N levels. ● To determine the m evaluation factors, choose an evaluation factor Xj, according to the determined eutrophication evaluation standard to determine the scope of the corresponding evaluation index in level (a, b) and the weight of each evaluation factor. ● Determine three digital characteristics of the cloud model and establish the comprehensive cloud mode which synthetically considers m evaluation factors belonging to certain eutrophication by the forward normal cloud generator. ● Repeat these steps until N m-dimension normal cloud models corresponding to the N eutrophication levels are produced. ● From measured data of a lake, the certainty of each lake belonging to each eutrophication level can be calculated by combining the weight of each evaluation factor and finally the eutrophication level of this lake can be determined. The flow chart of this method is shown in Fig. 1: 3.2. Selection of cloud model parameters

Ex = (Bmin + Bmax ) / 2

The Chinese National Environmental Monitoring Centre proposed TP, TN, Chl-a, COD and SD as the basic evaluation factors of eutrophication. Total Phosphorus (TP): Phosphorus is the main element resulting in eutrophication, excessive input of TP is the essence of cause of eutrophication. And phosphorus tends to combine with

(3)

In Eq. (3), Bmin and Bmax are the minimum and maximum values of VQa, respectively. If a variable has only a single boundary, like: VQa[Bmin, þ 1] or VQa[  1,Bmax], its default boundary parameter or expectation can be determined according to the upper and lower bounds of the value, then cloud parameters would be calculated Start

Determine the evaluation criteria dividing it into N levels

Determine the evaluation factors, defining its number as m dimension. Define the scope of Xj as (a,b)

Data reading

Define the weights of the evaluation factors:

The digital characteristics of the cloud model follow as )

If produce N m-dimensional normal cloud

Yes

Obtain the certainty belonging to each eutrophication level, Determining the water eutrophication level END Fig. 1. Flow chart of the multidimension normal cloud method.

No

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D. Wang et al. / Environmental Research 149 (2016) 113–121

Table 1 Numerical characteristics (Ex, En, He) of the multidimension normal cloud model.

Table 3 Numerical characteristics of the cloud model for SD.

Cloud

Ex

En

He

Cloud

Ex

En

He

C1, Ⅰ level C2, Ⅱ level C3, Ⅲ level C4, Ⅳ level C5, Ⅴ level C6, Ⅵ level

Ex1 ¼(a þ b)/2 Ex2 ¼(b þc)/2 Ex3 ¼(c þd)/2 Ex4 ¼(d þ e)/2 Ex5 ¼(e þ f)/2 Ex6 ¼ eþ f

Ex6/3 Ex6/3 Ex6/3 Ex6/3 Ex6/3 Ex6/3

k k k k k k

C1, Ⅰ level C2, Ⅱ level C3, Ⅲ level C4, Ⅳ level C5, Ⅴ level C6, Ⅵ level

15.00 7.50 3.75 1.25 0.70 0.20

5 5 5 5 5 5

0.01 0.01 0.01 0.01 0.01 0.01

according to Eq. (3). Due to the multidimension cloud model comprehensively considering the evaluation level of each evaluation factor, En, which is one of the digital characteristics of cloud model, can be determined by the maximum range of one evaluation factor and En of this evaluation factor is unchanged. For example, the lower boundary of TP is 200 mg m  3 in the Ⅵ level, that is 50 mg m  3 in the Ⅴ level, so Ex of TP is 250 mg m  3 in the Ⅵ level, then En of TP is 250/3 mg m  3 according to the “3En rule” (Liu et al., 2005) of the normal cloud model. He, which is the last digital characteristic of cloud model, can be set as an appropriate constant k (kr0.5). The final parameters of evaluation factor of cloud model are shown in Table 1. In Table 1, a–e represent the boundary values of eutrophication classification index. For instance, the six evaluation spaces of TN areⅠ[a,b], Ⅱ[b,c], Ⅲ[c,d], Ⅳ[d,e], Ⅴ[e,f], Ⅵ[f, þ1], in which a ¼0, b ¼30, c¼50, d ¼300, e¼ 500, f ¼2000. These boundary values are decided according to the specific evaluation criteria which are discussed in (Shu, 1990) and the specific evaluation criteria are shown in Table 2. Hence, the digital characteristics of these four evaluation factors (TP, TN, COD and Chl-a besides SD) corresponding to the cloud model can be obtained. Because the classification standard of SD is different from that of Chl-a, TP, TN and COD, it must be managed separately. Parameter of SD are shown in Table 3. 3.3. Determining the weights of evaluation factors This paper uses the entropy weight method (Sun et al., 2013; F. Yan and Zou, 2014; H. Yan and Zou, 2014) to determine the weight of each evaluation factor and the main calculation steps are as follows: ● Suppose there are m evaluation objects, and each evaluation object has n indices. Then, build a normalized judgment matrix: R = (rij )m × n . ● Calculate the proportion of the first i object in the first j evam luation index: Pij=rij/∑i = 1 rij . ● Calculate the entropy of the first j evaluation index: m 1 ej= − ln m ∑i = 1 Pij·ln Pij . ● Calculate the entropy weight of the first j evaluation index: n wj=(1 − ej ) /∑ j = 1 (1 − ej ). Five weights of evaluation factors by the entropy weight Table 2 Classification criteria. Classification

TP (mg m

Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ

r 2.5 r 5.0 r 25 r 50 r 200 4200

3

)

TN (mg m r 30 r 50 r 300 r 500 r 2000 42000

3

)

Chl-a (mg m r1.0 r2.0 r4.0 r10 r65 465

3

)

COD

SD (m)

r 0.3 r 0.4 r 2.0 r 4.0 r 10 410

Z 10.0 Z 5.0 Z 1.5 Z 1.0 Z 0.4 o 0.4

method are as follows: [TP, TN, Chl-a, COD, SD]¼ [0.2046, 0.2544, 0.2734, 0.0766, 0.1910]. 3.4. Generation of comprehensive cloud model of evaluation factors This paper utilizes five evaluation factors, so the established cloud model is a 5-dimension normal cloud model. Among them, TP, TN, Chl-a, COD, SD are each regarded as one dimension of this 5-dimension normal cloud model. It takes a comprehensive cloud model whose eutrophication level is Ⅱ level as an example to explain the process of establishing the 5-dimension normal cloud model. The digital characteristics and weights of each evaluation factor of the comprehensive cloud model whose eutrophication level is Ⅱ level are shown in Table 4. According to the multidimension normal cloud generator, the 5-dimension normal cloud model will now be developed. Because the concentration of an evaluation factor of water is not negative, the points, where xi <0, i = 0,1,2…m , must be abandoned in the process of development. In addition, the equation for calculation of certainty is changed for considering the weights of evaluation factors as m

−

μ ( x ( x1, x2 , x3,…,xm ) )=e

∑ [aj * j =1

( xj − Exj )2 ] 2 2 ( En′ j ) , j=1, 2, 3, … ,m,

(4)

If the concentration of an evaluation factor of water exceeds the maximum concentration range, that is to say, the concentration is in the highest level of evaluation factor, then the contribution of the evaluation factor to the overall certainty is 1. For example, the concentration of TP of Moshui Lake in Wuhan is 500 mg m  3, which exceeds the maximum concentration range (200 mg m  3) of TP. So we take x1=Ex1 when calculating the certainty ( μ ( x ( x1, x2, … , xm ) )), that is to say that the contribution of this evaluation factor's concentration to the overall certainty is 1.

4. Application: case studies 4.1. Initial results The MNCM was used to evaluate eutrophication levels of 12 representative lakes in China (Shu, 1990). The results of evaluation are shown in Table 5. Qionghai Lake, Erhai Lake and Bositen Lake did not encounter Table 4 Digital characteristics and weights of each evaluation factor of the comprehensive cloud model whose eutrophication level is Ⅱ.

Ex En He a

TP

TN

chl-a

COD

SD

3.75 83.33 0.050 0.2046

40.00 833.33 0.10 0.2544

1.50 25.00 0.02 0.2734

0.35 4.67 0.01 0.0766

7.50 5.00 0.01 0.1910

D. Wang et al. / Environmental Research 149 (2016) 113–121

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Table 5 Evaluation results of the multi-dimension normal cloud method. Lake

TP (mg m  3) TN (mg m  3) Chl-a (mg m  3)

COD (mg/L)

SD (m) μ (x)

Result Actual situation

μ (Ⅰ)

μ (Ⅱ)

μ (Ⅲ)

μ (Ⅳ)

μ (Ⅴ)

μ (Ⅵ)

Qionghai Lake Erhai Lake Bositen Lake Yuqiao Reservoir Cihu Lake Chaohu Lake

130 21 50 26 87 140

410 180 969 1020 1540 2270

0.88 4.33 4.91 16.2 15.38 14.56

1.43 3.38 5.42 5.16 4.4 4.34

2.98 2.4 1.46 1.16 0.65 0.27

0.4175 0.5020 0.3630 0.3380 0.2307 0.1123

0.7071 0.8750 0.6782 0.6457 0.4587 0.2309

0.8118 0.9833 0.8292 0.7977 0.6011 0.3228

0.8599 0.9800 0.9296 0.9057 0.7450 0.4427

0.6072 0.5248 0.7143 0.7709 0.8559 0.7246

0.0802 0.0465 0.1076 0.1303 0.2230 0.3164

Ⅳ Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ

Gantang lake Mogu Lake West Lake in Hangzhou Xuanwu Lake in Nanjing

135 332 136

2140 2660 2230

77.7 82.4 95.94

6.96 14.6 10.18

0.36 0.49 0.37

0.0346 0.0037 0.0147

0.0729 0.0079 0.0312

0.1059 0.0129 0.0465

0.1622 0.0248 0.0758

0.6062 0.2148 0.3895

0.7366 0.9997 0.7941

Ⅵ Ⅵ Ⅵ

708

6790

202.1

8.86

0.31

0.0000 0.0000 0.0000 0.0000 0.0123

0.9546

Ⅵ

500

16,050

262.4

13.6

0.15

0.0000 0.0000 0.0000 0.0000 0.0074

0.9997

Ⅵ

No water obstacles. No water obstacles. No water obstacles. No water obstacles. Algal bloom partly Algal bloom partly with water obstacles Algal bloom totally Algal bloom totally Algal bloom in large area Algal bloom totally with fish death in large degree Algal bloom totally

670

7200

185.1

14.8

0.26

0.0000 0.0000 0.0000 0.0000 0.0000 0.9999

Ⅵ

Algal bloom totally

Moshui Lake in Wuhan Dongshan lake in Gugngdong

the problems of water obstacles. So it is reasonable to classify them as Level Ⅲ and Level Ⅳ. The Cihu Lake and Chaohu Lake have come across the situation of algal bloom partly, so it is true and effective to be defined as Level Ⅴ. On the contrary, the algal bloom appeared all over the lake with regard to Xuanwu Lake in Nanjing, Moshui Lake in Wuhan and Dongshan Lake in Guangdong, which has influenced the ecological system of the fish and diatoms and created eyesores. Therefore, they are classified as Level Ⅵ which conformed to the practical situation. 4.2. Results by reference method The MNCM, ONCM, score formula method (Shu, 2003) and fuzzy comprehensive evaluation method (Chen and Guo, 2005) were compared for evaluating eutrophication levels of 12 representative lakes and reservoirs in China, and the results of evaluation are shown in Table 6. 4.3. Comparison between MNCM and ONCM Both of the models are similar in choosing parameters, determining evaluation factors and the underlying concept, however,

the MNCM is an improved model over the ONCM in the modeling process and selecting parameters, without increasing modeling complexity. (1) The MNCM simplifies the process of modeling: The number of cloud models is reduced, and the calculation times of the certainty are decreased. The MNCM considers all evaluation factors and establishes only one comprehensive multidimension cloud model for each evaluation level, that is to say, six four-dimension normal clouds are established in order to evaluate the eutrophication level. However, the ONCM needs to establish a one-dimension normal cloud model at each evaluation level of each evaluation factor. In other words, it needs to build 24 one-dimension normal cloud models to assess eutrophication. At the same time, the calculation times of certainty of the MNCM also decrease. For the same nutritional level, the MNCM only needs to calculate one certainty so that the last certainty can be determined, while the ONCM needs to calculate four kinds of certainty, and then calculate these four kinds of certainty to determine the last certainty.

Table 6 Assessment results of each evaluation method. Lake

Qionghai Lake Erhai Lake Bositen Lake Yuqiao Reservoir Cihu Lake Chaohu Lake Gantang Lake Mogu Lake West Lake in Hangzhou Xuanwu Lake in Nanjing Moshui Lake in Wuhan Dongshan lake in Gugngdong

Relevant weighted nutrition state comprehensive index method

Score formula method

Fuzzy comprehensive evaluation method

ONCM method

MNCM method

Chl-a

TP

TN

COD

SD

Comprehensive index

Ⅰ Ⅳ Ⅳ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ Ⅵ

Ⅴ Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ Ⅴ Ⅵ Ⅴ

Ⅳ Ⅲ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ Ⅵ Ⅵ

Ⅲ Ⅳ Ⅴ Ⅴ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ

Ⅲ Ⅲ Ⅲ Ⅳ Ⅴ Ⅵ Ⅵ Ⅴ Ⅵ

Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ Ⅵ

Ⅳ Ⅲ Ⅳ Ⅴ Ⅴ Ⅴ Ⅴ Ⅴ Ⅴ

Ⅳ Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ

Ⅳ Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ Ⅴ Ⅵ Ⅵ

Ⅳ Ⅲ Ⅳ Ⅳ Ⅴ Ⅴ Ⅵ Ⅵ Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅴ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Ⅵ

Note: MNCM: multidimension normal cloud model; ONCM: one-dimension normal cloud model.

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D. Wang et al. / Environmental Research 149 (2016) 113–121

(2) The MNCM improves the selection of cloud model parameters. 1) Selection of digital feature En: En represents the evaluation scope of the cloud model corresponding to the eutrophication Ex level. The MNCM chooses 3 i , ( i = 1, 2, … , 6), as En covers the scope of all the eutrophication levels and it can get each certainty of cloud model corresponding to each evaluation level. Ex −Ex The ONCM chooses i 3 i −1 , ( i = 1, 2, … , 6), as En only covers the scope of two eutrophication levels adjacent to a certain eutrophication level, so it can only obtain three certainties of cloud corresponding to the three evaluation levels. Taking the cloud model corresponding to the Ⅴ eutrophication level as an example, En of TP which is one of the evaluation factors is 83.3 in the MNCM, while that is 29.2 in the ONCM. 2) Selection of digital feature Ex of SD: Ex represents the central value of each evaluation factor, whose accuracy can reflect the characteristics of the evaluation factor in the nutrition level. Ex of the MNCM is the central value of the upper and lower bounds of one nutrition (a, b) of SD, that is to say, Ex¼(a þb)/2. Ex of the ONCM is the lower value of one nutrition (a, b) of SD, that is to say, Ex¼a. Take the cloud model corresponding to the Ⅲ eutrophication level as an example, the range of SD is as follows: [a, b] ¼[1.5, 5.0]. Ex of MNCM is 3.25 and Ex of the ONCM is 1.5. Table 7 uses the cloud model corresponding to the Ⅲ eutrophication level as an example to show the different values of En and Ex of SD between MNCM and ONCM. 3) Selection of digital feature He: He represents the condensation degree of the cloud droplet in the cloud model, reflecting the number and differences between evaluation factor arrays (TP, TN, Chl-a, SD) corresponding to one certainty. The bigger He is, the bigger the fuzziness and the randomness of the value of evaluation factor will be. The certainty of evaluation results will also be smaller. Therefore, He, the digital feature, cannot be too big or too small. It is determined, based on the upper bound of the evaluation factor. According to the evaluation criterion, the maxima of TP, TN, Chl-a, SD are 200, 2000, 65, 10. The He values of the MNCM are, respectively, 0.05, 0.1, 0.02 and 0.01, while the He value of the ONCM is unanimously 0.01. Different values of He between the MNCM and the ONCM are shown in Table 8. Taking the digital feature He as an example, different values of He between the MNCM and the ONCM are shown in Table 8, in which the horizontal coordinates represent the evaluation factors, and the longitudinal coordinates represent the values of He. For example, according to the evaluation criteria, the upper bound of TP is 250, and the values of He of the MNCM and the ONCM are 0.05 and 0.01, respectively. That is to say, the values of He of the MNCM are different, based on the different values of the upper bound of the evaluation factor, while the value of He of the ONCM is constant. The value of He of the MNCM is improved over the ONCM. Thus, it can be seen that the MNCM simplifies the modeling Table 7 Different values of the MNCM and the ONCM in the Ⅲ eutrophication level. Digital feature

Evaluation factor

ONCM method

MNCM method

En

TP TN Chl-a SD COD

3.75 44.00 0.50 0.17 0.28

83.33 833.33 25.00 5.00 4.67

Ex

SD

1.50

3.25

Note: MNCM: multidimension normal cloud model ONCM: one-dimension normal cloud model.

Table 8 Different values of He between the MNCM and the ONCM. Digital feature

Evaluation factor

ONCM method

MNCM method

He

TP TN Chl-a COD SD

0.01 0.01 0.01 0.01 0.01

0.05 0.10 0.02 0.01 0.01

Note: MNCM: multidimension normal cloud model ONCM: one-dimension normal cloud model.

process by reducing the number of cloud models and decreasing the calculation times of the certainty as compared with the ONCM without increasing the complexity of modeling. Meanwhile, the MNCM has been improved in respect of the selection of En, He, and Ex of SD. 4.4. Discussion of comparison between MNCM and other methods A comparative analysis was made between the MNCM and other common methods (the relevant weighted nutrition state comprehensive index method, the score formula method, and the fuzzy comprehensive evaluation method). (1) The results of the MNCM are consistent with the results of other evaluation methods, which verify the validity of the MNCM method. For example, for the eutrophication level judgment of Erhai Lake, Bositen Lake, Cihu Lake, Chaohu Lake, Xuanwu Lake in Nanjing, Moshui Lake in Wuhan, Dongshan Lake in Guangdong, the evaluation results of the MNCM are consistent with all of the common methods used here. For the eutrophication judgment of Qionghai Lake, Yuqiao Reservoir, Mogu Lake, the evaluation results of the MNCM are consistent with those of the most common method. (2) The MNCM makes up for the limitation of common evaluation methods. 1) The relevant weighted nutrition state comprehensive index method can make a comprehensive evaluation of the degree of water eutrophication, considering multiple evaluation factors. But this method has the following disadvantages: The formula of the relevant weighted nutrition state comprehensive index method is established on the basis of the content of Chl-a in water and the formulas of TSIM ( TP ), TSIM ( TN ), TSIM ( SD) are established on the basis of correlation between TP, TN, SD and Chl-a. If the content of Chl-a in water is abnormal because of external influences, the evaluation results will be inaccurate. 2) The score formula method is quick and easy to assess the degree of water eutrophication, but the evaluation standard and evaluation values of each evaluation factor's eutrophication level are divided artificially and the influence of subjective factors is inevitable, so it cannot evaluate the water eutrophication level objectively. In the relevant weighted nutrition state comprehensive index method, the weights of evaluation factors are calculated according to the measured data of water, which is closely related to the evaluation factors, and there are so many subjective factors that it cannot evaluate the water eutrophication level objectively. 3) The fuzzy comprehensive evaluation method can make a comprehensive evaluation of the degree of water eutrophication, considering all selected evaluation factors and take the complexity and fuzziness of the assessment process into full consideration, reducing the influence of artificial factors to a minimum. But the method itself gets blurred and it cannot eliminate the influence of uncertainty factors in the process of

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evaluation, so the evaluation results will not be accurate. The MNCM is established through the consideration of all evaluation factors, selecting 3 digital features of cloud model reasonably and determining the weight of each evaluation factor by the entropy method to construct the cloud model and to determine the water eutrophication level by the certainty degree. This not only can avoid inaccurate assessments because of a too strong certain evaluation factor, but also can maximally reduce subjective factors. As a result, it can effectively analyze the uncertainty of randomness and fuzziness, so that it is more consistent with the complexity of water eutrophication evaluation. (3) According to the certainty degree, the MNCM can determine the water eutrophication level more directly. Taking Qionghai Lake and Bositen Lake as examples, according to the evaluation standard, four evaluation factors of Qionghai Lake and Bositen Lake are respectively in different nutritional levels: five evaluation factors (TP, TN Chl-a, COD, SD) of Qionghai Lake are, respectively, in eutrophication levelsⅠ, Ⅴ, Ⅳ, Ⅲ, and Ⅲ, and five evaluation factors (TP, TN Chl-a, COD, SD) of Bositen Lake are, respectively, in eutrophication levels Ⅳ, Ⅳ, Ⅴ, Ⅴand Ⅲ. The eutrophication level of five evaluation factors of Qionghai Lake and Bositen Lake and final eutrophication level of these two lakes obtained by the MNCM are shown in Table 6. The following analysis is based on the certainty degree of the two lakes. Here horizontal coordinates are expressed as eutrophication level and vertical coordinates are expressed as 4 evaluation factors and final eutrophication levels of the two lakes. The figure shows that it is difficult to directly determine the eutrophication level of the lake based on the five eutrophication levels of the evaluation factors. The certainty degree of two lakes corresponding to each eutrophication level are, respectively, as follows: Qionghai Lake [μ(Ⅰ), μ(Ⅱ), μ(Ⅲ), μ (Ⅳ), μ(Ⅴ), μ(Ⅵ) ] ¼[ 0.4175, 0.7071, 0.8118, 0.8599, 0.6072, 0.0802], Bositen Lake [μ(Ⅰ), μ(Ⅱ), μ(Ⅲ), μ(Ⅳ), μ(Ⅴ), μ(Ⅵ) ] ¼ [0.3630, 0.6782, 0.8292, 0.9296, 0.7143, 0.1076]. The eutrophication levels of both lakes are all level IV by the maximum certainty. (4) According to the certainty degree, the MNCM can judge the eutrophication of different waters whose eutrophication levels are on the same level. Taking Gantang Lake and Mogu Lake as examples, the certainty of Gantang lake is that μ(Ⅴ)¼ 0.6062, μ (Ⅵ)¼0.7366 and the certainty of Mogu Lake is that μ(Ⅴ)¼ 0.2148, μ(Ⅵ)¼ 0.9997. The levels of both lakes are all level Ⅵ, but the eutrophication degree of Mogu lake is higher than that of Gantang lake. Cihu Lake and Chaohu Lake are in the same situation. The certainty of Cihu Lake is that μ(Ⅳ)¼0.7450, μ (Ⅴ)¼0.8559, μ(Ⅵ) ¼0.2230 and the certainty of Chaohu Lake is that μ(Ⅳ)¼0.4427, μ(Ⅴ)¼ 0.7246, μ(Ⅵ) ¼0.3164. The levels of both lakes are all level Ⅴ, but the eutrophication degree of Chaohu Lake is closer to the Ⅵ level and the eutrophication degree of Cihu Lake is closer to level Ⅳ, so the eutrophication degree of the Chaohu Lake is higher than that of Cihu Lake, which is conforming to the actual situation of the water barrier. Cihu Lake has the appearance of the algal bloom partly and is unable to see. Chaohu Lake also has the appearance of the algal bloom partly and encounters the disturbance of water supply in summer; Gantang Lake has the appearance of the algal bloom and is hard to see and Mogu Lake has the appearance of the algal bloom to a certain degree, resulting in substantial loss of fish. So the eutrophication degree of these four lakes from high to low is Mogu Lake, Gantang Lake, Chaohu Lake, Cihu Lake, respectively. Other methods can only judge the eutrophication level of water and they cannot accurately judge the degree of eutrophication of water whose

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eutrophication levels are on the same level. This is a particular advantage of the MNCM compared to other evaluation methods. The aforementioned analysis compares the eutrophication levels of Chaohu Lake and Cihu Lake by the MNCM. The largest certainty of both lakes is level V, which expresses that both of them are at the eutrophication level V. In the contrast of certainty corresponding to the eutrophication level Ⅳ, the certainty of Cihu Lake is greater than the certainty of Chaohu Lake. In contrast of certainty corresponding to the eutrophication level Ⅵ, the certainty of Chaohu Lake is greater than the certainty of Cihu Lake. In other words, the eutrophication degree of Cihu Lake is closer to level Ⅳ and the eutrophication degree of Chaohu Lake is closer to level Ⅵ.

5. Conclusions From the above analysis we can draw the following conclusions. (1) MNCM is a comprehensive normal cloud model and corresponds to each eutrophication level considering all the evaluation factors. Combining with the weights of evaluation factors, the eutrophication level of the water is determined by the certainty degree. Through comparative analysis, it is found that the evaluation results of the multi-dimension normal cloud model are consistent with those of the reference method and the classification results are more consistent with the actual situation of each lake water barrier compared with other reference methods. (2) Compared to the ONCM, the MNCM has a clearer modeling procedure, a more concise algorithm and a more credible evaluation. The MNCM improves the selection of cloud model parameters (3) Judging the eutrophication level of water by the certainty degree avoids the influence of subjective factors and human factors, whereas the relevant weighted nutrition state comprehensive index method is influenced by the content of Chla, the score formula method is influenced by the artificial factor, and the fuzzy comprehensive evaluation method itself has fuzziness and uncertainty. Hence, the MNCM can be more comprehensive, objective and accurate to evaluate the eutrophication of water. Results of comparative analysis by the MNCM, the ONCM, the relevant weighted nutrition state comprehensive index method, the score formula method and the fuzzy comprehensive evaluation method show that the MNCM is more comprehensive, objective and accurate to evaluate the eutrophication level of water. Despite the above merits, the MNCM has its disadvantage. Because the choice of parameters of the multidimension normal cloud model does not have a verdict, studies on a reasonable determination of the three characteristics of the model are needed in the future. The case study of 12 representative lakes in China has shown a positive application of the MNCM in the field of water environment. Since the MNCM is still in the phase of theory, it needs to be applied and validated for more study regions in the future.

Acknowledgments The authors gratefully acknowledge the helpful review comments and suggestions on earlier version of the manuscript by the

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D. Wang et al. / Environmental Research 149 (2016) 113–121

Editor, Associate Editor and the reviewers. This study was supported by the National Natural Science Fund of China (Nos. 41571017, 51190091, and 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. We also wish to thank the editors and reviewers for your time and we appreciate it very much.

Appendix. The computational program, using Matlab, to establish the multi-dimension cloud drops clc; clear; a ¼6; b ¼12; N ¼2000; s ¼ [130,410,0.88,2.98;21,180,4.33,2.4;50,969,4.91,1.46;26,1020, 16.2,1.16;87,1540,15.38,0.65;140,2270,14.56,0.27;135,2140,77.7,0.36; 332,2660,82.4,0.49;136,2230,95.94,0.37;708,6790,202.1,0.31;500, 16050,262.4,0.15;670,7200,185.1,0.26];. He ¼ 0.1; Ex_1 ¼ [1.25,3.75,15,37.5,125,250]; Ex_2 ¼ [15,40,175,400,1250,2500]; Ex_3 ¼ [0.5,1.5,3,7,37.50,75]; Ex_4 ¼ [15,7.5,3.75,1.25,0.7,0.2]; En_1 ¼ 83.33; En_2 ¼ 833.33; En_3 ¼ 25; En_4 ¼ 5; He_1 ¼ 0.05; He_2 ¼0.1; He_3 ¼0.02; He_4 ¼ 0.01; x ¼ zeros(a,N,b); y ¼ zeros(a,N,b); u ¼ zeros(a,N); u_ss ¼ zeros(b,6); u_s ¼ zeros(1,6); x_1¼ zeros(a,N); x_2¼ zeros(a,N); x_3¼ zeros(a,N); x_4¼ zeros(a,N); y_1 ¼ zeros(a,N); y_2 ¼ zeros(a,N); y_3 ¼ zeros(a,N); y_4 ¼ zeros(a,N); u_1 ¼ zeros(a,N); u_2 ¼ zeros(a,N); u_3 ¼ zeros(a,N); u_4 ¼ zeros(a,N); for j ¼ 1:12 for i ¼1:6 [x_1(i,:),x_2(i,:),x_3(i,:),x_4(i,:),y_1(i,:),y_2(i,:),y_3(i,:),y_4(i,:), u(i,:),u_1(i,:),u_2(i,:)] ¼ test_1(Ex_1(i),En_1,Ex_2(i),En_2,Ex_3(i), En_3,Ex_4(i),En_4,He_1,He_2,He_3,He_4,N,s(j,1),s(j,2),s(j,3),s(j,4)); if i ¼ ¼1 && s(j,4) 4 Ex_4(i) s(j,4) ¼ Ex_4(i); end if i ¼ ¼6 if s(j,1) 4 Ex_1(i) s(j,1) ¼ Ex_1(i); end if s(j,2) 4 Ex_2(i)

s(j,2) ¼ Ex_2(i); end if s(j,3) 4 Ex_3(i) s(j,3) ¼ Ex_3(i); end end u_s(i) ¼exp( (0.2216*(s(j,1)  Ex_1(i))^2/(2*En_1^2) þ0.2755*(s (j,2)  Ex_2(i))^2/(2*En_2^2) þ0.296*(s(j,3)  Ex_3(i))^2/(2*En_3^2) þ 0.2069*(s(j,4)  Ex_4(i))^2/(2*En_4^2))); end u_ss(j,:) ¼ u_s; end

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