Study of the selection of indicator parameters in ...

Study on the selection of indicator parameters in marine water quality evaluation and the evaluation methodology ZHANG Yinga,b, PAN Delu*b, WANG Difengb, FU Dongyanga,b Lab of Ocean Remote Sensing and Information Technology GuangDong Ocean University, Zhanjiang, 524088, GuangDong, China; bState Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,State Oceanic Administration,Hangzhou 310012 , ZheJiang, China a

ABSTRACT In order to obtain the indicator types which must be introduced in marine water quality evaluation as well as the suitable evaluation methodology, GB3097-1997 National Marine Water Quality Standards is, in the first place, analyzed to establish a hypothetical sample which is consisting of 2000 stances, each stance containing the information of 21 indicators. And then a stepwise discriminant method is utilized to filter the 21 indicators in accordance with their water quality classification discriminant abilities. And finally, 6 indicators with significant discriminant ability, biochemical oxygen demand(BOD5), oil type(Oil), total phosphorus(P), cadmium(Cd), cyanide(HH) and chemical oxygen demand(COD), are selected and the water quality evaluation chart of the corresponding six indicators is also established. Theoretically, the water quality indicator types and the suitable evaluation methodology, which must be introduced when the water quality evaluation is done in all the waters under the jurisdiction of China, are discussed in this paper, providing theoretical basis for the subsequent marine water quality evaluation based on field observation. Keywords: Marine water quality,Indicator filtration,Stepwise discriminant analysis,Water quality evaluation model

1. INTRODUCTION The content of marine water quality evaluation is to analyze the time and space distribution of water quality in 1-2 accordance with the composition and content of the main materials in marine water bodies . However, the compositions of the main materials in the water bodies are numerous. Moreover, water quality monitoring data are of years of continuous accumulation, which makes the evaluation of marine water quality difficult. There are many 3-4 domestic and overseas methods about water quality evaluation, such as single factor index method , aggregative index 4-6 7-9 method and grading evaluation method etc. in the early stage. In the recent period, the methods are fuzzy theory, 9-16 grey system theory, projection pursuit and neural network etc.. However, the above mentioned methods all utilize water quality indicators as many as possible to establish water quality evaluation model. Therefore, both the large calculated quantity and the relevance among water quality indicators influence the effect of the evaluation model. In order to discuss what the indicators which must be introduced in marine water quality evaluation are how to establish effective water quality evaluation model with limited indicators. In accordance with GB3097-1997 National Marine Water Quality Standards is, a hypothetical sample is established in this paper. Stepwise discriminant analysis is utilized to obtain indicator parameters and the corresponding evaluation model which must be introduced to water quality evaluation. And it provides theoretical basis for the selection of water quality indicators and method of water quality comprehensive evaluation in the subsequent field observation on marine water quality evaluation.

2. ESTABLISHMENT OF THE HYPOTHETICAL SAMPLE 17

National Marine Water Quality Standards is applicable to all the waters under the jurisdiction of the People’s Republic of China. It stipulates various evaluation standards of utilizing function water quality in the waters. This standard contains 35 water quality evaluation indicators. However, too many indicator parameters are bound to bring * [email protected]; phone 021-61900263; fax 021-61900263

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difficulty in modeling. Moreover, the numerous indicator parameters were not considered when The Marine Environment Bulletin was published. Therefore it is essential to figure out the indicator parameters which must be introduced in water quality evaluation. In order to theoretically discuss the necessary categories of water quality indicators, the 35 indicators in National Marine Water Quality Standards (Table 1) is analyzed and they have the following features: ① Indicators whose interval values cannot be quantized, such as indicators represented by No.1; ② Indicators whose interval values can be quantized but the values are the same, such as indicators represented by No.13; ③Indicators whose interval values can be quantized but the values are different , such as indicators represented by No.9 to No.12 and No.14 to No.17. In accordance with the theory of mathematical statistics analysis, indicators which can be quantized and have significant separating capacity shall be analyzed. There are 21 water quality indicators with the above mentioned features. Hypothetical samples are randomly produced in accordance with the interval values of the 21 indicators in National Marine Water Quality Standards. Each category of water quality contains 500 data points. There are 2000 data points in total in the four categories of water qualities. It is equivalent that information of water quality of 2000 sampling stances is established. Table 1. Sea water quality standard.

Units：mg/L

No.

Indicator

First kind

Second kind

Third kind

1

Floatable Substance

……

……

9

Dissolved Oxygen ＞

6

5

4

3

10

Chemical Oxygen Demand ≤

2

3

4

5

11

Biochemical Oxygen Demand ≤

1

3

4

5

12

Inorganic Nitrogen ≤

0.2

0.3

0.4

0.5

13

Non-ionic Ammonia ≤

14

Labile Phosphate ≤

0.015

0.03

0.045

15

Mercury ≤

0.00005

0.0002

0.0005

16

Cadmium ≤

0.001

0.005

17

Plumbum ≤

0.001

0.005

……

……

The sea can't appear the oil film, foam and other floating material.

Fourth kind The sea can't appear clearly the oil film, foam and other floating material.

……

0.02

0.01 0.01

0.05

……

3. FILTRATION OF WATER QUALITY INDICATORS AND EVALUATION METHODS It can be known in accordance with the established water quality hypothetical sample that the classification of water qualities of the data points (i.e. hypothetical stances) in the sample (There are four categories in total). Moreover, each data point contains multi-information (21 water quality indicators). While our target is to figure out the indicators which must be introduced in water quality evaluation and establish corresponding discrimination model by analyzing the hypothetical sample. And this is exactly the problem to be solved by stepwise discriminant analysis method. 3.1 Algorithm principle Discriminant analysis is a multivariate statistics analysis method. It aims at training the discrimination function from the existing known category of sample data. And then classify the data of unknown category utilizing the

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18

discrimination function . While stepwise discriminant analysis introduces the variable quantities with the strongest discriminant ability through inspection during the process of establishing discrimination functions. That is to establish the final discriminate functions with the few variable quantities with strong discriminant ability. Therefore, the 19 calculation of stepwise discriminant analysis incorporates two parts : filtrating variable quantities and establishing discriminant functions. 3.1.1 Filtrating variable quantities Suppose: given N samples in A categories. Each sample point has N sample points in A total categories can be represented as follows：



2 m X x1ak , xak ,, xak ; a  1,2,, A; k  1,2,, N

n1 , n2 ,, na n1  n2    na  N  .

m variable

quantities. Then, the value of

 ，as for different categories, the numbers of samples are as follows respectively

（1）Calculate the mean value and general average of varies categories of variable quantities. （2）Calculate the dispersion matrix W and the total dispersion matrix T in varies categories. （3）Filtrating variable quantities step by step. Wilks principle: dispersion matrix W in the totality and total dispersion matrix T constitute the Wilks statistical magnitude   W T . The smaller the value of  is, the stronger the discriminant ability the variable quantity has. ① Process of variable quantity selection. If l 1 variable quantities have been introduced in the discriminant L  function after L 1 steps of calculations, in the totality the dispersion matrix is W in the totality and total dispersion L  matrix is T . And calculate Wilks statistical magnitude i  wiiL tiiL in the variables which are not selected and figure out the minimum i . The variable with the strongest discriminant ability can be figured out by   min( i ) . Doing F inspection on

x

, Calculate

F

: F 

If

F  F  A  1, N  A  l 

,

x can

N  A  l t L   w L   A 1 w L 

(5)

be selected in the discriminant function.

② Process of variable quantity elimination. If L variables have been introduced in the discriminant function, Wilks  L1  L 1 statistical magnitude i  wii( L1) tii( L1) of all selected variables shall be calculated in the current W and T matrix.   max(  i ) F x x F with the weakest discriminant ability is figured out by . Doing inspection on , calculate : N  A  l  1 w L 1  t L 1 (6) F   A 1 t L 1 If F  F  A  1, N  A  l  1 , it is considered that the discriminant ability of x is not significant and it shall be eliminated from the discriminant function. 3.1.2 Establishing discriminant function After filtering the variables, the corresponding discriminant function can be established. Generally speaking, two20 class problems are solved under Fisher principle and multi-class problems are solved by Bayer principle . It is a fourclass problem in this paper. Therefore, Bayers principle is adopted: Calculate the conditional probability of which th th category the n sample belongs to, and classify the n samples to the category of large conditional probability. Suppose 1 2  th  X x , x ,, xl   l (l  m) variables are introduced and the sample belongs to the a category, the discriminant function is as 21 follows :

Fl  X   ln qa   cai x i   coa , i, j  l , a  1,2,, A il

Among which,

q a  na N ,

ca  N  a  w xa , i 

jl

L ij

i 

coa  

1  cai  xai  2 il

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(7)

3.2 Filtration of water quality indicators The process of filtering the 21 water quality indicators in the hypothetical sample step by step is given in Table 2. Each step follows Wilks principle, which is filtering the indicators in the principle of maximum F inspection value. A parameter with significant discriminant ability is selected each time. In the next step, observing whether the F inspection value of the introduced parameter in the last step is still larger, if so, the introduced parameter will not be eliminated. Filtering the indicators step by step till the established function can fully distinguish the four categories of water qualities. Table 2. Selection process of water quality indicators. Step

Step 1

Statistic

pH

Dissolved Oxygen

Chemical Oxygen Demand

Biochemical Oxygen Demand

Inorganic Nitrogen

Labile Phosphate

Mercury

Cadmium

Plumbum

Hexavalent Chromium

F

104.5

10091.

10251.

10483.7

9951.2

4016.1

3262.2

4390.5

2562.1

4616.4

Wilks

0.864

0.062

0.061

0.06

0.063

0.142

0.169

0.132

0.206

0.126

Be elected

Step 2

Step 3

Step 4

Step 5

F

27.88

652.51

711.60

2762.72

620.88

675.60

920.58

491.97

836.16

995.10

Wilks

0.057

0.03

0.029

0.088

0.031

0.03

0.025

0.034

0.026

0.024

Don't eliminate F

24.78

430.93

492.41

1630.2

415.84

603.92

576.65

491.77

318.73

347.4

Wilks

0.016

0.01

0.01

0.031

0.01

0.009

0.009

0.01

0.011

0.011

Don't eliminate

Be elected

F

19.63

350.32

393.88

611.94

347.96

592.30

353.31

481.21

256.28

258.10

Wilks

0.009

0.006

0.006

0.01

0.006

0.01

0.006

0.005

0.006

0.006

Don't eliminate

Don't eliminate

Be elected

F

11.85

274.911

325.477

589.004

273.831

572.005

314.078

479.938

245.343

253.377

Wilks

0.005

0.004

0.003

0.006

0.004

0.006

0.004

0.005

0.004

0.004

Don't eliminate

Don't eliminate

Don't eliminate

F

11.58

252.205

307.051

354.687

249.844

455.26

253.673

401.978

172.211

175.815

Step 6

Wilks

0.003

0.002

0.002

0.003

0.002

0.003

0.002

0.003

0.002

0.002

Be elected

Don't eliminate

Step

Statistic

Total Chromium

Arsenic

Cuprum

Zinc

Selenium

Nickel

Cyanide

Sulfide

Volatile Phenol

Oil Type

Benzex

F

4696.7

3935.4

1545.2

2723.8

3076.1

4892.8

6272.24

4901.66

2342.2

6929.06

7518.2

Wilks

0.124

0.145

0.301

0.196

0.178

0.12

0.096

0.12

0.221

0.088

0.081

F

1011.3

473.11

227.12

895.71

797.84

1071.6

1657.7

1005.0

882.95

1669.86

673.62

Wilks

0.024

0.035

0.044

0.025

0.027

0.023

0.017

0.024

0.026

0.017

0.03

Step 1

Step 2

Step 3

Don't eliminate

Don't eliminate

Be elected F

363.14

450.08

222.59

333.08

513.00

383.58

500.20

349.02

314.16

1544.76

352.28

Wilks

0.011

0.01

0.013

0.011

0.01

0.011

0.01

0.011

0.012

0.03

0.011

Don't eliminate Step 4

F

280.77

449.41

192.36

257.37

300.85

300.60

480.32

278.18

268.95

1543.0

258.64

Wilks

0.006

0.005

0.007

0.006

0.006

0.006

0.005

0.006

0.006

0.017

0.006

Don't eliminate

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Step 5

Step 6

F

276.547

257.518

131.447

233.901

283.27

296.491

479.053

275.672

250.639

497.362

241.058

Wilks

0.004

0.004

0.004

0.004

0.004

0.004

0.003

0.004

0.004

0.005

0.004

Be elected

Don't eliminate

F

182.281

247.312

130.455

150.776

235.792

194.396

457.715

195.59

175.699

460.716

177.892

Wilks

0.002

0.002

0.003

0.002

0.002

0.002

0.003

0.002

0.002

0.003

0.002

Don't eliminate

Don't eliminate

th

In accordance with the above mentioned principle, when it is filtered to the 6 step, i.e. the six water quantity indicators biochemical oxygen demand (BOD5), oil type (Oil), total phosphorus (P), cadmium (Cd), cyanide (HH) and chemical oxygen demand (COD) are introduced, the established discriminant function is able to exactly classify the 2000 data points into the correct categories. Till now, it is not necessary to introduce other water quality indicators. Namely, as for all the sea waters in the jurisdiction of China, the six water quantity indicators biochemical oxygen demand (BOD5), oil type (Oil), total phosphorus (P), cadmium (Cd), cyanide (HH) and chemical oxygen demand (COD) are enough to establish an effective water quality evaluation model. 3.3 Water quality evaluation methodology Three discriminant functions shall be established with the selected six water quality indicators under the Bayers principle so that the four categories of water quality and the formulas of the three discriminant functions are as follows: F1  14.240  1.317 X BOD5  8.327 X Oil  66.990 X P  278.333 X Cd  20.332 X HH  1.890 X COD F2  3.198  0.964 X BOD5  11.662 X Oil  11.420 X P  391.691 X Cd  29.996 X HH  0.663 X COD F3  1.895  0.007 X BOD5  4.601 X Oil  191.507 X P  421.105 X Cd  4.206 X HH  0.173 X COD

Among which, X BOD , X Oil，X P，X Cd，X HH，X COD represent the contents of biochemical oxygen demand, oil type, total phosphorus, cadmium, cyanide and chemical oxygen demand respectively. It can be known by calculation that the classification capacity of the first discriminant function is the strongest and its contribution rate for classification is 94.1%. The contribution rate for classification of the second discriminant function is 4.5% while that of the third discriminant function is 1.4%. 5

So far, we have obtained water quality classification equations set on the six indicators. And then institute the 2000 data points in the hypothetical sample, a three-dimensional water quality classification space （ Fig.1 ） ， a six parameters water quality evaluation chart, can be obtained. Central positions of various water qualities in the space can be found (Table 3). As for a stance to be classified, the six indicators shall firstly be converted into the position coordinates （F1，F2，F3）in the chart space. And then it can be classified in accordance with the minimum distance between the stance and various central coordinates. Table 3. Sea water quality standard. water quality type

F1

F2

F3

First kind

-9.886

1.823

-0.548

Second kind

-4.325

-1.435

1.353

Third kind

3.091

-2.009

-1.17

Fourth kind

11.12

1.621

0.365

4.

CONCLUSION

1. No matter it is based on site observation or remote sensing observation, marine water quality evaluation abides by National Marine Water Quality Standards. Therefore, a water quality evaluation model theoretically appropriate to all

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sea waters in China can be obtained by establishing hypothetical samples in accordance with the above mentioned national standards and analyzing the sample with multivariate statistics’ method.

4\ 3\ O

2\

First kind of water quality Second kind of water quality

A +

1

Third kind of water quality Fourth kind of water quality

0\ 1

Ai&

.............

2\ -3

...... talkG ` ::...... ........

10

F2

-15

15

-5

-10

F1

Figure 1. Six parameters water quality evaluation chart

2. Indicator categories which must be introduced in water quality evaluation can be obtained by utilizing stepwise discriminant analysis method. The indicators parameters which must be introduced in water quality evaluation in all sea waters in China are as follows: biochemical oxygen demand (BOD5), oil type (Oil), total phosphorus (P), cadmium (Cd), cyanide (HH) and chemical oxygen demand (COD). 3. Three discriminant functions are required to be established for the above mentioned indicators under the criterion of Bayers. And therefore, a three-dimensional water quality evaluation chart of six parameters can be obtained. Utilizing this chart, automatic evaluation of water quality conditions in all sea waters in China can be achieved. And it provides theoretical basis for the selection of water quality indicators and method of water quality comprehensive evaluation in the subsequent field observation on marine water quality evaluation.

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