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Factor analysis and discriminant analysis of wastewater quality in Vidyaranyapuram sewage treatment plant, Mysore, India: a case study Ayesha Sulthana, K. C. Latha, Ramya Rathan, R. Sridhar and S. Balasubramanian
ABSTRACT Wastewater treatment plant monitoring is an essential part of effective wastewater management. The analysis of eight physico-chemical parameters of untreated wastewater was carried out at Vidyaranyapuram sewage treatment plant, Mysore, India. Factor analysis (FA) was applied to the untreated wastewater data matrix, and pollution was found to be the most contributing factor, explaining 22.31% of the total variance (chloride, biochemical oxygen demand, chemical oxygen demand and total dissolved solids). The second most contributing factor was found to be nitrification which explained 21.11% of the total variance (pH and nitrate), whereas the salinization factor contributed 16.98% of the total variance (total solids and total suspended solids). FA regression scores could not satisfactorily classify the data matrix with respect to the seasonal variations. Discriminant analysis (DA) was used to find the seasonal variations in the data matrix, and the
Ayesha Sulthana (corresponding author) K. C. Latha Ramya Rathan S. Balasubramanian Department Of Water and Health – JSS University, S.S. Nagar, Mysore -570 015, Karnataka, India E-mail:
[email protected] R. Sridhar Department of Computer Science, Sri Ramakrishna Mission Vidyalaya, Coimbatore -641020, Tamil Nadu, India
standard mode DA explained 66.6% of total variance by grouping the cases with respect to seasons. Key words
| discriminant analysis, factor analysis, seasonal changes, wastewater characterization
INTRODUCTION Wastewater treatment is a challenging environmental task. The pollution control board in Mysore, Karnataka has set up many plans to monitor the sources and factors responsible for high pollution. Wastewater quality differs with increase in population, seasonal variation, vacations and inflows of tourists. Regular monitoring of physical and chemical parameters of wastewater is necessary to plan the appropriate treatment required with respect to the seasonal variations. Routine monitoring of wastewater parameters like pH, biochemical oxygen demand (BOD), chemical oxygen demand (COD), total solids (TS), total suspended solids (TSS), total dissolved solids (TDS), nitrate, chloride and phosphorus in the long term will generate a highly voluminous and complex data matrix, which leads to complications in deriving meaningful conclusions (Chapman ; Dixon & Chiswell ; Reghunath et al. ; Boyacioglu & Gunduz ). Generally the data monitoring of water quality is understood by applying statistical techniques (Yidana et al. ). Multivariate statistical techniques are used for the quantitative examination of a doi: 10.2166/wst.2013.782
large number of variables and to understand the latent structure of the data (Timm ; Babbie ). Multivariate statistical techniques offer a higher level of explanation of complicated water quality data sets (Arslan ; Zhang et al. ). Therefore multivariate analysis like factor analysis (FA) and discriminant analysis (DA) are applied to better understand water quality data matrices (Singh et al. ; Shrestha & Kazama ; Indrani et al. ; Smeti et al. ). The natural and anthropogenic factors leading to the temporal and spatial variations influencing surface and freshwater quality can be verified by these statistical techniques (Boyacioglu ; Reisenhofer et al. ; Helena et al. ; Singh et al. ). Identification of possible determinants or sources which impact on water and ecological systems will suggest helpful means for the fast alleviation of water pollution issues in addition to the candid management of water resources (Mellinger ; Farnham et al. ; Lambrakis et al. ; Mendiguchia et al. ). These possible factors can be identified by cracking the complex data matrices to derive meaningful interpretations by
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the application of different multivariate statistical techniques, such as cluster analysis (CA), principal component analysis (PCA), FA and DA (Davis ; Massart & Kaufman ; Brown et al. ; Vega et al. ; Lee et al. ; Adams et al. ; Wunderlin et al. ; Voncina et al. ; Reghunath et al. ; Bengraine & Marhaba ; Grande et al. ; Liu et al. a, b; Simeonov et al. ; Saadia et al. ; Ouyang et al. ; Panda et al. ; Zhou et al. ; Wu et al. ; Krishna et al. ; Lin et al. ; Li & Zhang ). Better management of environmental systems can be successfully achieved by the application of multivariate statistical techniques to environmental data (Chen et al. and Liu et al. a, b). These analyses determine the variables that contribute most to pollution under different sets of seasonal variations; this gives important information for environmentalists and decision makers to modify treatment processes accordingly. Focusing on the seasonally influenced variables contributing to high pollution will help guide environmental scientists in introducing pretreatment procedures which can aid efficient wastewater treatment before proceeding with regular wastewater treatment. The present study aims to determine the factors responsible for variations in the physical and chemical parameters of untreated wastewater through PCA and also to verify the variables showing seasonal variations through DA.
MATERIALS AND METHODS Description of study area Mysore district (area 128.42 sq. km, latitude 11 450 to 12 400 N and longitude 75 570 to 77 150 E) lies in southern Karnataka, India. Based on the undulating topography of Mysore city, it is divided into ‘drainage district A’, ‘drainage district B’, ‘drainage district C’, ‘drainage district D’ and ‘drainage district E’. Southern drainage districts A and D are allocated to the 60 million liters per day (MLD) Rayankere sewage treatment plant (STP). Southwestern drainage connects to the 67.65 MLD Vidyaranyapuram STP of drainage district B and the northern drainage system is connected to the 30 MLD Kesare STP of drainage district C. The provision of a sewage treatment facility to drainage district E (11 sq. km) is under planning and progress. Vidyaranyapuram STP (latitude 12.273681 to 12.270031 N and longitude 76.650737 to 76.655947 E) was constructed in 2002 with an area of 27.21 sq. km and a sewer length of 7,000 meters. It is a W
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biological treatment plant situated next to the solid waste disposal area at the foothills of Chamundi Hills; the treated wastewater of Vidyaranyapuram STP crosses the Dalvai Lake and reaches the drinking water source that is the Kabini River. More than 50% of the sewage generated in Mysore city is received by Vidyaranyapuram STP; therefore it was selected as a study area. The Vidyaranyapuram STP consists of two facultative aerated lagoons with sedimentation basins each having a surface area of 50,544 m2 (312 m length × 162 m width) and a volume of 176,904 m3 (312 m length × 162 m width × 3.5 m depth). The surface aeration is enabled by 36 blowers of 20 hp each which are operated successfully to ensure reduction in the accumulated sludge and foul odor. In addition to that the STP has two maturation ponds each having a surface area of 24,940 m2 (172 m length × 145 m width) and a volume of 37,410 m3 (172 m length × 145 m width × 1.5 m depth). The mean detention time of wastewater in each facultative lagoon is 11.8 days whereas in each maturation pond it is 2.5 days. The total saving on operational and maintenance cost is about 40%, considering the cost of power. The overall power usage is about 4% of what is required to operate a conventional STP. Therefore Mysore City Corporation with this technology is able to save electricity and operate the STP with less manpower. Although the capacity of the STP is 67.75 MLD, the inflow rate of wastewater varies under many influencing factors like seasonal changes, tourist inflow etc., and there will be an approximate difference of 7 to 9 MLD between the raw wastewater received and the treated wastewater liberated due to seepage. Data
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The performance of the wastewater treatment plant is monitored routinely by analyzing the physical and chemical parameters of raw wastewater influent and treated wastewater effluent. Among the chemical parameters, nitrogen compounds are targeted the most because of their importance in the life cycles of living entities. In wastewater, nitrogen is largely present as organic nitrogen and in forms of ammonia, and it is also present as nitrite and nitrate in small quantities. Total Kjeldahl nitrogen and quantification of total ammonia nitrogen are the indicator tests of wastewater quality which measure the sum of organic nitrogen and ammonia in milligrams per liter (mg/L). However, both of these are involved tests of wastewater quality that the laboratory of Vidyaranyapuram STP is not equipped to perform.
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Based on the guidelines of the City Sanitation Plan, Mysore, Karnataka, the quality of wastewater from STPs is analyzed with physical parameters like TS, TDS and TSS, with chemical parameters like pH, BOD, COD, chloride, nitrate and phosphorus. To perform the analysis of physical and chemical parameters the sample was drawn from sampling point 1 (untreated wastewater influent flowing towards facultative aerated lagoon 1), sampling point 2 (treated effluent in maturation pond 1) and sampling point 3 (treated effluent in maturation pond 2). For the present study the data generated from untreated wastewater influent from sampling point 1 are taken into account (Table 1). These data were collected at daily intervals during the period October 2009 to June 2011 (607 × 8 ¼ 4,856 data points) from Vidyaranyapuram STP. Among all the wastewater quality parameters (pH, BOD, COD, chloride, nitrate, TS, TDS and TSS), ‘total phosphorus’ was not included in the multivariate analysis due to the discontinuous data records.
with eigenvalues greater than one are considered to be the best and were included in FA (Kaiser ). Interpretation of the factors is improved through varimax rotation, which reduces the contribution of less significant variables ( Johnson & Wichern ).
Factor analysis
D ¼ a þ v1 X1 þ v2 X2 þ v3 X3 ¼ ::::::::vn Xn
Discriminant analysis DA determines statistically significant independent variables, which allows their separation into predefined groups. To discriminate between variables of different groups, it builds a linear combination of observed predictor variables to form the discriminant function of the respective group. Important discriminant water quality variables which classify the groups effectively can be identified through this analysis (Wunderlin et al. ). DA will predict which case belongs to the respective group by the following linear equation:
FA reduces a large number of observed variables to a new set of fewer variables in decreasing order of importance. It detects the underlying structural relationship between the variables, to classify them into factors. The variables within each factor are related to each other based on their measure of similarity (Norusis ; Liu et al. a, b). Factor extraction is done through PCA, where the linear combination of variables accounting for the highest variance is Factor 1. The factor contributing to the second highest variance without any correlation with the first factor is Factor 2 and so on. The eigenvalue explains the portion of variance accounted for by each factor; hence factors Table 1
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(1)
where D ¼ discriminant function, a ¼ constant, v ¼ the discriminant coefficient, X ¼ respondent’s score, n ¼ number of predictor variables.
RESULTS AND DISCUSSION Factor analysis A Pearson correlation study was conducted as a main part of the FA to detect the multicollinearity and singularity of
Descriptive statistics
Mean N
Range
Minimum
Maximum
statistic
statistic
statistic
statistic
Statistic
Std. error
Std. deviation
Variance
statistic
statistic
pH
607
9.80
0.00
9.80
7.7551
0.03918
0.96528
0.932
BOD
607
252.00
98.00
350.00
268.8537
0.98483
24.26351
588.718
COD
607
263.00
167.00
430.00
301.2622
1.90044
46.82188
2192.289
TS
607
1021.00
979.00
2000.00
1626.4959
5.04680
124.33995
15460.422
TDS
607
1935.92
340.00
2275.92
1606.2689
9.32183
229.66549
52746.239
Chloride
607
652.00
38.00
690.00
349.8151
3.06861
75.60242
5715.725
TSS
607
250.00
30.00
280.00
59.0190
0.83601
20.59704
424.238
Nitrate
607
56.00
24.00
80.00
45.8425
0.44182
10.88530
118.490
Valid N (listwise)
607
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Table 2
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Correlation matrixa for physico-chemical parameters of untreated wastewater
pH
Correlation
COD
TS
TDS
Chloride
TSS
Nitrate
pH
1.000
0.222
0.270
0.139
0.041
0.172
0.112
0.378
BOD
0.222
1.000
0.293
0.174
0.175
0.198
0.003
0.134
0.270
0.293
1.000
0.076
0.131
0.223
0.086
0.251
TS
0.139
0.174
0.076
1.000
0.349
0.144
0.281
0.335
TDS
0.041
0.175
0.131
0.349
1.000
0.324
0.169
0.080
0.172
0.198
0.223
0.144
0.324
1.000
0.005
0.071
COD
Chloride
Sig. (1-tailed)
BOD
TSS
0.112
0.003
0.086
0.281
0.169
0.005
1.000
0.013
Nitrate
0.378
0.134
0.251
0.335
0.080
0.071
0.013
1.000
0.000
0.000
0.000
0.156
0.000
0.003
0.000
0.000
0.000
0.000
0.000
0.471
0.000
pH BOD
0.000
COD
0.000
0.000
TS
0.000
0.000
0.031
0.031
0.001
0.000
0.017
0.000
0.000
0.000
0.000
0.000
TDS
0.156
0.000
0.001
0.000
Chloride
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.025
0.448
0.040
TSS
0.003
0.471
0.017
0.000
0.000
0.448
Nitrate
0.000
0.000
0.000
0.000
0.025
0.040
0.372 0.372
a
Determinant ¼ 0.334.
the parameters (Table 2). Since the determinant of the matrix was 0.334, greater than 0.0001, all the parameters were involved in the FA. Bartlett’s test was highly significant ( p < 0.001) and the Kaiser–Meyer–Olkin (KMO) value of 0.580 (Table 3) met the standard of adequacy for the data to yield reliable factors through this analysis. Three components out of eight were extracted with eigenvalues greater than one to form a new, smaller set of factors than the original set of data (Kowalkowski et al. ), which is shown in the Scree plot (Figure 1). This analysis yielded 60.42% of the total variance (Table 4) in the data; varimax rotation was performed to equalize the relative importance of factors (Richman ). Before rotation, Factor 1 accounted for 24.26% of the total variance and after rotation it accounted for 22.31% of the total variance (Table 4). The regression scores of the FA could not satisfactorily classify the data matrix with respect to the seasonal variations.
Table 3
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KMO and Bartlett’s test
KMO measure of sampling adequacy
0.580
Bartlett’s test of sphericity
661.179 28 0.000
Approx. chi-square df Sig.
Figure 1
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Scree plot of eigenvalues vs principal component number.
Factor 1 accounted for 22.31% of the total variance and was highly associated with chloride, BOD, COD and TDS (Table 5). Chloride ions combine with cations to form inorganic dissolved solids, whereas organic matter contributing to organic dissolved solids is measured in terms of BOD and COD (Thirumalini & Kurian ). Therefore this factor can be termed the pollution factor. Factor 2 explained 21.11% of the total variance. The high positive loading of nitrate and negative loading of pH (Table 5) indicates a nitrification process, where ammonia is rapidly converted to nitrates, lowering the pH ( Jain ). Increase in nitrogen content leads to anthropogenic eutrophication (Kuppusamy & Giridhar ), therefore this factor can be termed the nitrification factor.
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Table 4
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Total variance explained by the physico-chemical parameters of untreated wastewater
Initial eigenvalues
Extraction sums of squared loadings
Rotation sums of squared loadings
Total
% of variance
Cumulative %
Total
% of variance
Cumulative %
Component Total
% of variance
Cumulative %
1
1.941
24.264
24.264
1.941
24.264
24.264
1.785
22.318
22.318
2
1.788
22.350
46.614
1.788
22.350
46.614
1.689
21.118
43.436
3
1.105
13.808
60.422
1.105
13.808
60.422
1.359
16.985
60.422
4
0.847
10.585
71.006
5
0.724
9.046
80.052
6
0.675
8.436
88.488
7
0.500
6.246
94.734
8
0.421
5.266
100.000
Extraction method: PCA.
Table 5
|
0.391
inorganic solids in wastewater. The Monsoon season showed the highest positive contribution to the nitrification factor with a maximum mean of 0.30 among the rest. The highest positive contribution to the salinization factor was observed in the summer season with the high mean value of 0.37 among the other seasons, and this may be again due to a high rate of evaporation of water content leading to accumulation of a high amount of dissolved salts.
0.757
0.111
Discriminant analysis
0.134
0.172
0.910
0.381
0.423
0.576
Rotated component matrixa of physico-chemical parameters of untreated wastewater
Component 1
2
3
0.160
Chloride
0.695
COD
0.624
0.364
BOD
0.616
0.236
TDS
0.568
0.229
pH
0.219
TSS TS
0.814
Nitrate
Extraction method: Principal component analysis. Rotation method: Varimax with Kaiser normalization. a
Rotation converged in eight iterations.
Factor 3 accounted for 16.98% of the total variance and was highly loaded with negative TSS and moderate positive TS (Table 5). This factor represents the large influence of the total dissolved salts, which is positively correlated with the total solids and negatively correlated with the total suspended solids (Pratap ); hence this factor can be termed the salinization factor (Hongmei et al. ). The relationship between the three regression factor scores and the seasons was analyzed. The summer season showed the highest positive contribution to the pollution factor with a maximum mean of 0.14 when compared with other seasons; this may be due to the rise in temperature resulting in a high rate of evaporation which leads to a high concentration of organic and
DA using standard mode method was performed to understand the seasonal variations in untreated wastewater matrix. Seasonal DA was performed on untreated wastewater data after dividing them into three seasons, viz. monsoon (July–October), winter (November–February) and summer (March–June). This grouping was done with respect to the seasons of Mysore, Karnataka (Padmanabha & Belagali ). The parameters contributing most to this seasonal grouping were assessed. Two seasonal discriminant functions (DF) were created to discriminate eight parameters (Table 6). Both the functions were significant (p < 0.001) according to Wilks’ lambda test (Najafpour et al. ) (Table 7). Table 6
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Function
Eigenvalues for two DFs for eight parameters of untreated wastewater
Eigenvalue
% of
Cumulative
Canonical
variance
%
correlation
1
a
0.456
67.4
67.4
0.560
2
0.220a
32.6
100.0
0.425
a
First two canonical DFs were used in the analysis.
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Table 7
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Wilks’ lambda test of DFs for temporal variation
Test of function(s)
Wilks’ lambda
Chi-square
df
Sig.
1 through 2
0.563
345.165
16
0.000
2
0.819
119.637
7
0.000
The first DF explained 67.4% of the variance whereas 32.6% of the variance was explained by the second DF. Nitrate, pH and COD contributed strongly to the seasonal variations against other parameters in function 1, whereas the parameters TS and TDS moderately contributed in function 2 (Table 8). The classification function coefficient of each parameter with respect to that particular season explains the
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seasonal variation (Table 9). Fisher’s linear discriminant function coefficients were taken to build the following models. Discriminant function model for monsoon season: D1 ¼ 209:806 þ 14:241pH þ 0:239 BOD þ 0:027 COD þ 0:110 TS þ 0:015 TDS 0:023 chloride þ 0:393 TSS þ 0:567 nitrate (2) Discriminant function model for winter season: D2 ¼ 222:177 þ 15:757 pH þ 0:240 BOD þ 0:047 COD þ 0:105 TS þ 0:012 TDS 0:018 chloride þ 0:412 TSS þ 0:700 nitrate (3) Discriminant function model for summer season:
Table 8
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Standardized canonical discriminant function coefficients of temporal variation
D3 ¼ 228:581 þ 16:061pH þ 0:225 BOD þ 0:036 COD þ 0:111 TS þ 0:015 TDS 0:018 chloride þ 0:395 TSS þ 0:670 nitrate (4)
of untreated wastewater
Function 1
2
0.789
0.655
BOD
0.006
0.362
COD
0.477
0.257
TS
0.325
0.558
TDS
0.321
0.425
pH
Chloride
0.217
0.061
TSS
0.197
0.243
Nitrate
0.800
0.061
It can be seen in the above equations that the coefficient values of the parameters pH, nitrate, BOD and COD differed according to different seasons and accounted for most of the expected seasonal variation, therefore they were selected as seasonal variables to construct box plots (Figures 2(a)–2(d)). Only 66.6% of original group cases were classified into groups, shown in classification matrix (Table 10).
CONCLUSION Table 9
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Classification function coefficients of three seasons
Season Monsoon
pH
Winter
Summer
14.241
15.757
16.061
BOD
0.239
0.240
0.225
COD
0.027
0.047
0.036
TS
0.110
0.105
0.111
TDS
0.015
0.012
0.015
0.023
0.018
0.018
0.393
0.412
0.395
Chloride TSS Nitrate (Constant) Fisher’s linear DF.
0.567
0.700
0.670
209.806
222.177
228.581
Dimension reduction of the complex data matrix of untreated wastewater was achieved by the application of multivariate statistical tools. In this case study, 60.4% of the variance was explained by FA by considering six parameters (factor loading >0.60) out of eight parameters, that is by utilizing 75% of the original data. The organic pollution factor contributed most to the variance in the data when compared to eutrophication and salinization factors. Discriminant function 1 explained 67.4% of variance by pointing to three parameters (nitrate, pH and COD) and 66.6% of seasonal variation was explained by group classification. DA was found to be the more efficient data reduction technique than FA; it can be used to analyze variations in a large volume of data.
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Figure 2
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(a) Temporal variation of pH in STP, (b) temporal variation of BOD in STP, (c) temporal variation of COD in STP, (d) temporal variation of nitrate in STP.
Table 10
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Classification resultsa,c for DA of seasons
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Predicted group membership
Original
Count
%
Cross-validatedb
Count
%
a
Monsoon
Winter
Summer
Total
Monsoon Winter Summer Monsoon Winter Summer
77 18 26 60.6 7.5 10.8
12 153 40 9.4 63.8 16.7
38 69 174 29.9 28.8 72.5
127 240 240 100.0 100.0 100.0
Monsoon Winter Summer Monsoon Winter Summer
74 20 28 58.3 8.3 11.7
15 149 41 11.8 62.1 17.1
38 71 171 29.9 29.6 71.3
127 240 240 100.0 100.0 100.0
66.6% of original grouped cases correctly classified. Cross-validation is done only for those cases in the analysis. In cross-validation, each case is classified by the functions derived from all cases other than that case.
b c
Season
64.9% of cross-validated grouped cases correctly classified.
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ACKNOWLEDGEMENTS This work is supported by MANF-UGC, New Delhi, India. The authors like to acknowledge the Mysore City Corporation and management authorities of Vidyaranyapuram STP, Mysore in conducting this case study.
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First received 20 July 2013; accepted in revised form 27 November 2013. Available online 11 December 2013