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176 CHAPTER 7 ASSESSMENT OF GROUNDWATER QUALITY USING MULTIVARIATE STATISTICAL ANALYSIS 7.1 GENERAL Many different sources and processes are known to contribute to the deterioration in quality and contamination of water, both surface and groundwater. So a thorough understanding of the nature and extent of contamination in an area requires detailed hydrochemical data (Helena et al 1999). Unfortunately, very few studies have so far been undertaken combining the effects of multiple water quality variables in order to evaluate the water quality, the extent and nature of contamination (Shuxia et al 2003). Conventional techniques including Stiff and Piper plots only consider major and minor ions to assess the chemical quality of water, whether surface or groundwater. Considering the limitations of these traditional methods to express the water quality and also the recent advances in analytical capabilities and the availability of larger numbers of chemical parameters, wide ranging statistical techniques are now needed to assess the water quality, nature and extent of contamination. In this regard, factor analysis is useful for interpreting groundwater quality data and relating those data to specific hydro-geologic and anthropogenic processes (Bakac 2000). Multivariate data can be defined as an observational unit characterized by several variables. An example of data appropriate for multivariate analysis is the chemical quality of water, which depends on

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176

CHAPTER 7

ASSESSMENT OF GROUNDWATER QUALITY USING

MULTIVARIATE STATISTICAL ANALYSIS

7.1 GENERAL

Many different sources and processes are known to contribute to the

deterioration in quality and contamination of water, both surface and

groundwater. So a thorough understanding of the nature and extent of

contamination in an area requires detailed hydrochemical data (Helena et al

1999). Unfortunately, very few studies have so far been undertaken combining

the effects of multiple water quality variables in order to evaluate the water

quality, the extent and nature of contamination (Shuxia et al 2003).

Conventional techniques including Stiff and Piper plots only consider major

and minor ions to assess the chemical quality of water, whether surface or

groundwater. Considering the limitations of these traditional methods to

express the water quality and also the recent advances in analytical capabilities

and the availability of larger numbers of chemical parameters, wide ranging

statistical techniques are now needed to assess the water quality, nature and

extent of contamination. In this regard, factor analysis is useful for interpreting

groundwater quality data and relating those data to specific hydro-geologic

and anthropogenic processes (Bakac 2000).

Multivariate data can be defined as an observational unit

characterized by several variables. An example of data appropriate for

multivariate analysis is the chemical quality of water, which depends on

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177

factors like composition of host rock, slope of ground, movement of water,

etc. The chemical characteristics of water play a vital role vis-a-vis potable,

agricultural and industrial purposes. Cluster analysis is one statistical tool to

group similar pairs of correlation in a large symmetric matrix. It reduces even

large data set into groups with similar characteristics. It provides logical and

pair-by-pair comparison between various chemical constituents. The results

of cluster analysis can be presented in a two-dimensional hierarchical

diagram, by which the natural breaks between the groups become obvious.

An observer can pick up groups at any desired level of similarity or

dissimilarity (Parks 1966; Till 1974; Rao 2003; Bhabesh et al 2007).

Statistical associations do not necessarily establish cause-and-effect

relationships, but do present the information in a compact format as the first

step in the complete analysis of the data. That can assist in generating

hypothesis for the interpretation of hydro-chemical processes.

Statistical techniques, such as cluster analysis, can provide a

powerful tool for analyzing water-chemistry data. These methods can be

grouped into distinct populations (hydro-chemical groups) that are significant

in the geologic context, as well as from a statistical point of view. Cluster

analysis was successfully used (Alther 1979; Williams 1982; Farnham et al

2000) and applied to classify water-chemistry data (Ciineyt Giiler et al 2002).

Mapping of groundwater contamination is often complicated by

infrequent and uneven distribution of monitoring locations, analytical errors

in sample analyses, and large spatial variation in observed contaminants

over short distances due to complex hydro geologic conditions. While

numerical simulation modeling is commonly used to delineate

groundwater contamination plumes, this approach may be limited by

insufficient knowledge of local hydrostratigraphic conditions. Also,

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managing and mapping extensive water quality datasets can be difficult due

to the multiple locations, times, and analysis that may be present.

An alternative to numerical simulation modeling uses statistical

analysis of groundwater quality data to infer zones of potential

contamination. Many studies have been conducted using Principal

Component Analysis (PCA) in the interpretation of water quality

parameters. PCA is a multivariate statistical procedure designed to

classify variables based on their correlations with each other. The goal of

PCA and other factor analysis procedures is to consolidate a large number

of observed variables into a smaller number of factors that can be more

readily interpreted. In the case of groundwater, concentrations of different

constituents may be correlated based on underlying physical and

chemical processes such as dissociation, ionic substitution or carbonate

equilibrium reactions. PCA helps to classify correlated variables into

groups more easily interpreted as these underlying processes. The number

of factors for a particular dataset is based on the amount of non-random

variation that explains the underlying processes. The more factors extracted,

the greater is the cumulative amount of variation in the original data.

Environmental monitoring system has been carrying out a lot of

water quality monitoring programs in recent years, but many of those

monitoring programs contain complicated data sets. These include physical

properties, aggregate organic constituents, nutrients and inorganic

constituents and biological and microbiological situations. These are difficult

to analyze and interpret on account of the latent interrelationships among

parameters and monitoring sites. Thus, it is necessary to extract meaningful

information from large and complicated data sets without missing useful

information. It is also essential to optimize the monitoring network by

recognizing the representative parameters, delineating monitoring sites and

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identifying latent pollution sources (Pekey et al 2004). The application of

multivariable statistical methods offers a better understanding of water quality

for interpreting the complicated data sets. Traditional multivariable statistical

methods such as FA and Correlation matrix have been widely accepted in

water quality assessment.

The objective of the study is to extract information about:

the similarities or dissimilarities between the monitoring

periods and monitoring sites

significant parameters responsible for temporal and spatial

variations in water quality.

expose hidden factors accounting for the structure of the data

and

the influence of the possible sources on the water quality

parameters.

The final results may be helpful for effective water quality management

as well as rapid solutions on pollution problems (Morales et al 1999).

7.2 FACTOR ANALYSIS

Factor analysis attempts to explain the correlations between the

observations in terms of the underlying factors, which are not directly

observable (Yu et al 2003). There are three stages in factor analysis

(Gupta et al 2005):

For all the variables a correlation matrix is generated.

Factors are extracted from the correlation matrix based on

the correlation coefficients of the variables.

To maximize the relationship between some of the factors

and variables, the factors are rotated.

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The first step is the determination of the parameter correlation

matrix, which has been done in the previous stage. It is used to account for

the degree of mutually shared variability between individual pairs of water

quality variables. Then, Eigen values and factor loadings for the correlation

matrix are determined. Eigen values correspond to an Eigen factor, which

identifies the groups of variables that are highly correlated among them.

Lower Eigen values may contribute little to the explanatory ability of the data.

Only the first few components are needed to account for much of the

parameter variability. Once the correlation matrix and Eigen values are

obtained, component loadings are used to measure the correlation between the

variables and components. Component rotation is used to facilitate

interpretation by providing a simpler factor structure (Zeng and Rasmussen

2005).

This study evaluated the possibility that a smaller group of water

quality parameters/locations might provide sufficient information for water quality

assessment. Principal component analysis was applied to a groundwater quality

data set collected from the study area of Tirupur Region, Tirupur District, Tamil

Nadu, India, using ‘the Statistical Package for the Social Sciences Software-

SPSS 14.0 for Windows’. Water quality monitoring was conducted at 62

sample locations within the study area during the seasons (June–July 2006,

November–December 2006 and June-July 2011). The selected parameters for

the estimation of groundwater quality characteristics are: Turbidity, pH, total

hardness (TH), total dissolved solids (TDS), calcium (Ca2+

), magnesium

(Mg2+

), sodium (Na+), potassium (K

+), bicarbonate (HCO3

-), sulphate (SO4

2-),

chloride (Cl-) nitrate (NO3

-), fluoride (F) and iron (Fe).

7.2.1 Spatial variation of groundwater quality using factor analysis

The whole study area was analyzed for factor analysis, for the pre-

monsoon (2006), post-monsoon (2006) and post-monsoon (2011). Factor

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analysis is a multivariate statistical technique used not only to condense but

also to simplify the set of large number of variables to smaller number of

variables called factors. This technique is helpful to identify the underlying

factors, which determine the relationship of the observed variables. It

provides an empirical classification scheme of clustering of statement into

groups called factors.

7.2.1.1 Spatial variation of groundwater quality for the pre-monsoon

(2006)

The Factor Analysis (FA) generated three significant factors for the

pre-monsoon period, which are explained as 75.922 % of the variance in data

sets. Table 7.1 gives the rotated factor loadings, communalities, Eigen values

and the percentage of variance explained by these factors. In order to reduce

the number of factors and enhance the interpretability, the factors are rotated.

The rotation usually increases the quality of interpretation of the factors.

There are several methods of the initial factors matrix to attain simple

structure of the data. In this regard, Principal Components Analysis (PCA)

is widely used. After PCA rotation, each original variable tends to be

associated with one (or a small number) of the factors and each factor

represents only a small number of variable. Table 7.2 shows the summary

statistics of water quality parameters for the pre-monsoon (2006). The

parameters are grouped based on the factor loadings and the following factors

are identified:

Factor 1 (F1): TDS, TH, Ca, Cl, F, SO4, Na, K, HCO3 and NO3

Factor 2 (F2): Turbidity, Mg and Fe

Factor 3 (F3): pH

F1, F2 and F3 have been explained as 55.609 %, 13.011 % and

7.301 % of the variance respectively. The F1 has a high positive loading in

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TDS, Na, Cl, K, TH, Ca, SO4, HCO3, NO3 and F which are 0.987, 0.93, 0.911,

0.894, 0.88, 0.844, 0.817, 0.767, 0.686 and 0.408 respectively. High positive

loading indicated strong linear correlation between the factor and the

parameters. The relationships of factor loadings on the groundwater variables

are shown in Figure 7.1 for pre-monsoon (2006).

Table 7.1 Rotated factor loadings of groundwater samples for the

pre-monsoon (2006)

Sl.No ParametersFactors

Communalities1 2 3

1 Turbidity 0.425 0.792 -9.981 0.818

2 TDS 0.987 -5.364 0.025 0.978

3 pH 0.146 0.174 0.911 0.882

4 TH 0.880 -5.982 -0.147 0.800

5 Ca 0.844 -9.348 -0.127 0.736

6 Mg 0.798 9.544 -0.176 0.668

7 Cl 0.911 4.397 -0.065 0.837

8 F 0.408 -0.361 -0.154 0.32

9 SO4 0.817 -0.178 0.183 0.732

10 Na 0.930 -0.124 0.122 0.895

11 K 0.894 0.16 0.079 0.831

12 HCO3 0.767 0.108 -0.059 0.604

13 Fe 0.315 0.851 -0.042 0.826

14 NO3 0.686 -0.456 0.157 0.702

15 Eigen value 7.785 1.822 1.022 10.629

16 % of Variance 55.609 13.011 7.301 75.922

17 Cumulative % 55.609 68.62 75.922 -

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Table 7.2 Summary statistics of groundwater quality parameters for the

pre-monsoon (2006)

Sl.

NoParameters Minimum Maximum Mean Variance

Std.

Deviation

1 Turbidity 2 18 6.65 11.15 3.339

2 TDS 399 3672 1291.97 500709.18 707.608

3 pH 7.30 8.25 7.70 1.00 1.00002

4 TH 192 956 460 37055.06 192.497

5 Ca 35 288 105.94 2373.14 48.715

6 Mg 13 107 50.76 472.32 21.733

7 Cl 31 1092 333.71 61172.14 247.33

8 F 0 2 0.90 0.22 0.4649

9 SO4 4 382 85.94 4898.88 69.992

10 Na 24 720 180.5 19124.29 138.291

11 K 7 224 66.6 2175.10 46.638

12 HCO3 129 733 346.9 16565.27 128.706

13 Fe 0 1.20 0.124 0.05 0.2193

14 NO3 6 520 79.47 8873.11 94.197

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Figure 7.1 Distribution of variables among factors given by factor

analysis for the pre-monsoon (2006)

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7.2.1.2 Spatial variation of groundwater quality for the post-monsoon

(2006)

The FA generated three significant factors for the post-monsoon

period, which are explained as 74.458 % of the variance in data sets.

Table 7.3 gives the rotated factor loadings, communalities, Eigen values and

the percentage of variance explained by these factors. The factors are rotated.

The rotation increases the quality of interpretation of the factors. There are

several methods of the initial factors matrix to attain a simple structure of the

data. For this purpose, PCA is widely used. Table 7.4 shows the summary

statistics of water quality parameters for the post-monsoon (2006). The

parameters are grouped based on the factor loadings and the following factors

are indicated:

Factor 1 (F1): TDS, Cl, TH, Ca, Fe, Mg, SO4, F, NO3 and HCO3.

Factor 2 (F2): pH and K

Factor 3 (F3): Na and Turbidity

F1, F2 and F3 have been explained as 51.946 %, 13.825 % and

8.687 % of the variance respectively. F1 has a high positive loading in

TDS, Cl, TH, Ca, Fe, Mg, SO4, F, SO4, and NO3 which are 0.966, 0.966,

0.947, 0.864, 0.842, 0.798, 0.777, 0.701 and 0.568 respectively. The high

positive loading indicated strong linear correlation between the factor and the

parameters. The relationships of factor loadings on the groundwater variables

are arrayed in Figure 7.2, for post-monsoon (2006).

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Table 7.3 Rotated factor loadings for the post-monsoon (2006)

ParametersFactors

Communalities1 2 3

Turbidity 0.517 0.246 0.549 0.629

TDS 0.966 -0.031 -0.120 0.949

pH -0.412 0.566 -0.212 0.536

TH 0.947 0.151 -0.127 0.935

Ca 0.864 -0.037 -0.434 0.937

Mg 0.798 -0.098 0.119 0.661

Cl 0.966 0.104 -0.104 0.955

F 0.701 0.018 0.069 0.497

SO4 0.777 0.236 -0.249 0.722

Na 0.605 -0.028 0.615 0.745

K 0.400 0.528 0.357 0.567

HCO3 0.186 -0.861 0.171 0.804

Fe 0.842 0.161 -0.123 0.749

NO3 0.568 -0.637 -9.354 0.737

Eigen value 7.272 51.946 51.946 111.164

% of Variance 51.946 13.825 8.687 74.458

Cumulative % 51.946 65.771 74.458 -

Table 7.4 Summary statistics of water quality parameters for the post-

monsoon (2006)

Parameters Minimum Maximum Mean Variance Std. Deviation

Turbidity 0 38 7.58 5.925 35.107

TDS 198 5,119 1,164.68 831.18 690859.402

pH 7.07 8.85 7.68 0.34695 0.12038

TH 114 2,558 696 470.821 221672.451

Ca 15 1,023 149.27 164.461 27047.35

Mg 0 319 74.56 61.638 3799.299

Cl 18 2,249 359.89 403.596 162890.069

F 0 1 0.40 0.330 0.1090

SO4 0 427 79.47 85.331 7281.335

Na 8 220 88.63 50.552 2555.483

K 1 91 22.82 19.732 389.361

HCO3 53 650 186 134.099 17982.609

Fe 0 1.20 0.166 0.2055 0.0422

NO3 0 125 34.05 25.408 645.555

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Figure 7.2 Distribution of variables among factors given by factor

analysis for the post-monsoon (2006)

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7.2.1.3 Spatial variation of groundwater quality for the pre-monsoon

(2011)

The FA generated three significant factors for the pre-monsoon

(2011), which are explained as 72.879% of the variance in data sets. Table 7.5

gives the rotated factor loadings, communalities, Eigen values and the

percentage of variance explained by these factors. Among the several

methods of the initial factors matrix to attain simple structure of the data,

PCA is widely used. Table 7.6 expresses the summary of statistics of

water quality parameters for the pre-monsoon (2011).

Table 7.5 Rotated factor loadings of groundwater samples for the pre-

monsoon (2011)

Sl.No ParametersFactors

Communalities1 2 3

1 Turbidity 0.139 0.073 0.781 0.635

2 TDS 0.813 0.544 0.098 0.967

3 pH -0.266 0.111 0.788 0.704

4 TH 0.963 0.139 0.073 0.934

5 Ca 0.838 0.813 0.544 0.715

6 Mg 0.841 -0.266 0.111 0.709

7 Cl 0.910 0.963 0.067 0.960

8 F -0.084 0.838 0.047 0.223

9 SO4 0.738 0.841 0.014 0.852

10 Na 0.518 0.910 0.359 0.928

11 K 0.291 -0.084 -0.013 0.788

12 HCO3 -0.122 0.738 0.334 0.525

13 Fe 0.771 0.518 0.793 0.603

14 NO3 -0.003 0.291 0.838 0.661

15 Eigen value 5.433 2.855 1.915 10.203

16 % of Variance 38.808 20.395 13.676 72.879

17 Cumulative % 38.808 59.203 72.879 -

The parameters are grouped based on the factor loadings and the

following factors are explained.

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Factor 1 (F1): TDS, TH, Ca, Mg and K

Factor 2 (F2): Cl, F, SO4, Na and HCO3

Factor 3 (F3): Turbidity, pH, Fe and NO3

F1, F2 and F3 have been explained as 38.808%, 20.395% and

13.676% of the variance respectively. The F1 has a high positive loading

in TH, Mg, Ca, TDS and K which are 0.963, 0.841, 0.838, 0.813 and 0.291

respectively. The high positive loading indicated strong linear correlation

between the factor and the parameters. The relationships of factor loadings

on the groundwater variables are furnished in Figure 7.3, for pre-monsoon

(2011).

Table 7.6 Summary statistics of groundwater quality parameters for the

pre-monsoon (2011)

Sl.

NoParameters Minimum Maximum Mean Variance

Std.

Deviation

1 Turbidity 0 18 6.40 12.704 3.564

2 TDS 543 5990 1763.71 1034541.291 1017.124

3 pH 6.60 8.00 7.56 0.088 0.2969

4 TH 212 3600 776.68 277367.107 526.657

5 Ca 28 913 166.02 19395.951 139.269

6 Mg 0 480 92.15 5554.766 74.530

7 Cl 34 3190 541.24 265453.231 515.222

8 F 0 2.10 0.70 1018.741 31.9177

9 SO4 0 1210 158.8905 34280.769 185.15066

10 Na 24 1120 224.45 40603.498 201.503

11 K 7 269 67.40 3725.359 61.036

12 HCO3 138 787 411.02 23009.524 151.689

13 Fe 0 1.10 0.191 0.031 0.1760

14 NO3 0 569 76.118 7113.857 84.3437

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Figure 7.3 Distribution of variables among factors given by

factor analysis for the pre-monsoon (2011)

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7.3 CORRELATION OF PHYSICOCHEMICAL PARAMETERS

OF GROUNDWATER

Correlation coefficient is a commonly used measure to establish the

relationship between two variables. It is simply a measure to exhibit how

well one variable predicts the other (Kurumbein and Graybill 1965). It is used

to account for the degree of mutually shared variability between individual

pairs of water quality variables. The application has been broadened to study

the relationship between two or more hydrologic variables, and also to

investigate the dependence between successive values of a series of

hydrologic data. The analytical data of 62 groundwater samples for the

seasons spread over the study area are correlated. The groundwater quality

parameters considered for correlation are Turbidity, TDS, pH, TH, Ca, Mg,

Cl, F, SO4, Na, K, HCO3, Fe and NO3. In general, highly polluted

groundwater samples have low oxidation-reduction potential because of the

reducing atmosphere (Sunil Kumar Srivastava and Ramanathan 2007). The

results are summarized in Tables 7.7, 7.8 and 7.9 for the seasons.

7.3.1 Correlation of physicochemical parameters of groundwater for

the pre-monsoon (2006)

During the pre-monsoon (2006), the study illustrated that TDS

showed good positive correlation with Na and K. Also the pairs of TDS-

TH, TDS-Ca, TDS-SO4, TH-Ca, TH-Mg, Cl-Na, Cl-K, Na-SO4 and Na-K

have more significant correlations. TDS-Mg, HCO3, TDS-NO3, TDS-TH-Cl,

TH-Na, TH-HCO3, Ca-Cl, Ca-Na Na-NO3 and Turb-Fe have good positive

correlations. Further, TH- SO4, TH-K, Ca-Mg, Ca-SO4, Ca-K, Ca-HCO3,

Mg-Cl, Mg-Na, Mg-K, Mg-HCO3, Cl-SO4, Cl-HCO3, Na-HCO3, K-HCO3,

TH-NO3, Mg-SO4, Mg-K, Mg-NO3 pairs exhibit positive correlations. The

details are illustrated in Table 7.7.

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7.3.2 Correlation of physicochemical parameters of groundwater

for the post-monsoon (2006)

During the post-monsoon (2006), the study proved that TDS

showed good positive correlation with Ca and Cl, and TH with Cl. The

pairs of TH-Ca, TH-Fe, Ca-Cl, Mg-Cl, Cl-Fe also showed more significant

correlation. TDS-Mg, TDS-SO4, TDS-Na, TDS-Fe, TH-Mg, TH-SO4, Ca-

SO4, Ca-Fe, Cl-SO4, also indicated good positive correlations. Also, the pairs

of TDS-Fe, TDS-NO3, TH-F, Ca-Mg, Ca-F, Ca-NO3, Mg-F, Mg-SO4, Mg-Fe,

Cl-F, Cl-Na exhibited positive correlations. The details are given in Table 7.8.

7.3.3 Correlation of physicochemical parameters of groundwater

for the pre-monsoon (2011)

During the pre-monsoon (2011), the study evolved that TDS

showed good positive correlation with Cl and TH. The pairs of TDS-TH,

TDS-Na, TH-Ca, TH-Mg, Mg-Cl and Na-K showed more significant

correlations. Also TDS-Ca, TDS-Mg, TDS-SO4, TH-SO4, Ca-Cl, Cl-SO4, Cl-

Na and Na-SO4 indicated good positive correlations. Further TDS-K, TH-Fe

and Cl-Fe exhibited positive correlations. The details are given in Table 7.9.

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193

Table 7.7 Correlation of physicochemical parameters of groundwater during the pre-monsoon (2006)

Parameters Turbidity TDS pH TH Ca Mg Cl F SO4 Na K HCO3 Fe NO3

Turbidity 1.0000 `

TDS 0.3671 1.0000

pH 0.1111 0.1331 1.0000

TH 0.3373 0.8379 0.0628 1.0000

Ca 0.3036 0.8272 0.0662 0.8201 1.0000

Mg 0.3559 0.7533 0.0376 0.8031 0.6011 1.0000

Cl 0.3831 0.3287 0.0887 0.7724 0.7865 0.6775 1.0000

F -0.0294 0.3749 0.0061 0.3574 0.4173 0.3093 0.3860 1.0000

SO4 0.2188 0.8106 0.1574 0.6705 0.6371 0.5768 0.6539 0.2893 1.0000

Na 0.2868 0.9688 0.1506 0.7396 0.7251 0.6244 0.8885 0.3427 0.8108 1.0000

K 0.4459 0.9049 0.1619 0.6814 0.6271 0.6211 0.8817 0.2904 0.7187 0.8848 1.0000

HCO3 0.3351 0.7215 0.1143 0.7048 0.6831 0.6755 0.6208 0.1423 0.5213 0.6203 0.6491 1.0000

Fe 0.7451 0.2560 0.1297 0.1801 0.1606 0.2275 0.3013 -0.0338 0.1372 0.1880 0.4337 0.2752 1.0000

NO3 -0.0032 0.7016 0.0711 0.5396 0.5110 0.5273 0.4796 0.3352 0.7037 0.7417 0.5340 0.4448 -0.10344 1.0000

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Table 7.8 Correlation of physicochemical parameters of groundwater during the post-monsoon (2006)

Parameters Turbidity TDS pH TH Ca Mg Cl F SO4 Na K HCO3 Fe NO3

Turbidity 1.0000 `

TDS 0.3707 1.0000

pH -0.1936 -0.3611 1.0000

TH 0.4946 0.9079 -0.3348 1.0000

Ca 0.2267 0.9066 -0.2854 0.8601 1.0000

Mg 0.3872 0.7995 -0.3380 0.7003 0.5477 1.0000

Cl 0.4209 0.9772 -0.3165 0.9331 0.8813 0.8045 1.0000

F 0.4296 0.6283 -0.1685 0.6847 0.5260 0.6296 0.6350 1.0000

SO4 0.3718 0.7410 -0.1627 0.7560 0.7786 0.5205 0.7666 0.4072 1.0000

Na 0.5315 0.7410 -0.2966 0.4535 0.2900 0.4614 0.5360 0.3647 0.4021 1.0000

K 0.2825 0.3785 0.0215 0.3769 0.1973 0.2787 0.4132 0.2225 0.2705 0.3939 1.0000

HCO3 -0.1226 0.2196 -0.4344 -0.0066 0.1179 0.3164 0.0723 0.1121 -0.0833 0.2526 -0.1984 1.0000

Fe 0.3763 0.7800 -0.2796 0.8587 0.7407 0.573 0.8070 0.4917 0.6718 0.4364 0.413 0.0093 1.0000

NO3 0.1834 0.5479 -0.4688 0.4392 0.5888 0.3573 0.4536 0.3892 0.2958 0.3175 -0.1023 0.0093 0.3976 1.0000

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Table 7.9 Correlation of physicochemical parameters of groundwater during the pre-monsoon (2011)

Parameters Turbidity TDS pH TH Ca Mg Cl F SO4 Na K HCO3 Fe NO3

Turbidity 1.000

TDS 0.218 1.000

pH 0.410 -0.075 1.000

TH 0.108 0.817 -0.274 1.000

Ca 0.172 0.767 -0.150 0.836 1.000

Mg -0.066 0.708 -0.171 0.801 0.591 1.000

Cl 0.104 0.950 -0.235 0.910 0.789 0.803 1.000

F -0.227 -0.070 -0.183 -0.022 -0.019 -0.027 -0.039 1.000

SO4-0.209 0.709 -0.487 0.726 0.585 0.582 0.769 0.004 1.000

Na 0.056 0.810 -0.232 0.545 0.367 0.427 0.752 -0.048 0.754 1.000

K 0.153 0.669 -0.001 0.309 0.201 0.170 0.571 -0.068 0.495 0.841 1.000

HCO30.212 0.272 0.360 -0.093 0.020 0.026 0.089 -0.153 -0.124 0.294 0.323 1.000

Fe 0.196 0.575 -0.070 0.679 0.475 0.596 0.634 -0.061 0.546 0.456 0.347 -0.116 1.000

NO30.166 0.464 0.279 0.087 0.137 0.026 0.261 -0.020 0.172 0.538 0.515 0.345 -0.032 1.000

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7.4 CLUSTER ANALYSIS

The assumptions of cluster analysis techniques include

homoscedasticity (equal variance) and normal distribution of the variables

(Alther 1979). However, an equal weighing of all the variables requires long-

transformation and standardization (z-scores) of the data. Comparisons based

on multiple parameters from different samples are made and the samples are

grouped according to their ‘similarity’ to each other. The classification of

samples according to their parameters is termed Q-mode classification. This

approach is commonly applied to water-chemistry investigations in order to

define groups of samples that have similar chemical and physical

characteristics. This is because rarely is a single parameter sufficient to

distinguish between different water types. Individual samples are compared

with the specified similarity/dissimilarity and linkage methods are then

grouped into clusters. The linkage rule used here is Ward’s method (Ward

1963). Linkage rules iteratively link nearby points (samples) by using the

similarity matrix. The initial cluster is formed by linkage of the two samples

with the greatest similarity. Ward’s method is distinct from all the other

methods because it uses an analysis of variance (ANOVA) approach to

evaluate the distances between clusters. Ward’s method is used to calculate

the error sum of squares, which is the sum of the distances from each

individual to the center of its parent group (Judd 1980). This form smaller

distinct clusters than those formed by other methods (StatSoft.Inc.1995).

Cluster analysis has been carried out to substitute the geo-

interpretation of hydogeochemical data. Cluster analysis has been useful in

studying the similar pair of groups of chemical constituents of water. The

similarity/dissimilarity measurements and linkage methods used for clustering

greatly affect the outcome of the Hierarchical Cluster Analysis (HCA) results.

After a careful examination of the available combination of

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similarity/dissimilarity measurements, it was found that using Euclidean

distance (straight line distance between two points in c-dimensional space

defined by c variables) as similarity measurement, together with Ward’s

method for linkage, produced the most distinctive groups. In these groups

each member within the group is more similar to its fellow members than to

any other member from outside the group. The HCA technique does not

provide a statistical test of group differences; however, there are tests that can

be applied externally for this purpose (Ciineyt Giiler et al 2002). It is also

possible in HCA results that one single sample that does not belong to any of

the groups is placed in a group by itself. This unusual sample is considered as

residue. The values of chemical constituents were subjected to hierarchical

cluster analysis. Based on the indices of correlation coefficients, similar pairs

groups of chemical constituents have been linked. Then the next most similar

pairs of groups and so on, until all the chemical constituents have been

clustered in a dendrogram by an averaging method (Davis 1973; 1986).

7.4.1 Cluster analysis of groundwater samples

A 14 X 14 matrix of correlation coefficients is computed to perform

cluster analysis (Tables 7.7, 7.8 and 7.8). Correlation matrices of various

stages of clustering were then obtained. Hierarchical dendrogram for the

clustering, (Figures 7.4, 7.5 and 7.6) for the pre-monsoon (2006), post-

monsoon (2006) and pre-monsoon (2011), of the determined physical and

chemical parameters for all the studies sites were plotted. Dendrogram in CA

provided a useful graphical tool for determining the number of clusters that

describe the underlying process leading to spatial variation (Papaioannai.et al

2010). The CA results established that the parameters were principally

separated into two big clusters.

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Cluster 1 (10 parameters are included) F, Fe, Turbidity. pH,

Mg, K, Ca, SO4, NO3 and Na)

Cluster 2 Cl, HCO3 and TH

A careful consideration of the content of clusters reveals that during

the pre-monsoon the first cluster included dominant chemical parameters (F,

Fe, Mg, K, Ca, SO4, NO3, and Na) and two physical parameters (Turbidity

and pH). The second cluster consisted of two chemical parameters (Cl and

HCO3) and one physical parameter (TH). During the post-monsoon, the first

cluster included dominant chemical parameters (F, Fe, Turbidity, K, NO3,

Mg, Na, SO4, Ca and HCO3) and one physical parameter (Turbidity). The

second cluster included one chemical parameter (Cl) and one physical

parameter (TH). In all the seasons, the physical parameter TDS was seen

clustering as independently.

Figure 7.4 Dendrogram for cluster analysis of groundwater for the pre-

monsoon (2006)

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Figure 7.5 Dendrogram for cluster analysis of groundwater for the

post-monsoon (2006)

Figure 7.6 Dendrogram for cluster analysis of groundwater for the pre-

monsoon (2011)

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The data analysis gave an idea of how the single physicochemical

parameters should be compared and related with all the physicochemical

values simultaneously, not individually. For instance, within a group of water

samples (Figure 7.4) like (Cl, HCO3 and TH), there is a stronger relation

between the group of chemical parameters (Cl and HCO3) and the physical

parameter (TH) or with parameters like (SO4, NO3 and Na) to the chemical

parameters (F, Fe, Mg, K and Ca) and physical parameters (Turbidity and

pH). The study revealed that in all the seasons the clustering parameters

were more or less same type.