CHAPTER 7 ASSESSMENT OF GROUNDWATER QUALITY USING MULTIVARIATE STATISTICAL ANALYSIS

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

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,

178 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

179 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.

180 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 (Ca 2+ ), magnesium (Mg 2+ ), sodium (Na + ), potassium (K + ), bicarbonate (HCO - 3 ), sulphate (SO 2-4 ), chloride (Cl - ) nitrate (NO - 3 ), 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 premonsoon (2006), post-monsoon (2006) and post-monsoon (2011). Factor

181 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, SO 4, Na, K, HCO 3 and NO 3 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

182 TDS, Na, Cl, K, TH, Ca, SO 4, HCO 3, NO 3 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) Factors Sl.No Parameters 1 2 3 Communalities 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 SO 4 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 HCO 3 0.767 0.108-0.059 0.604 13 Fe 0.315 0.851-0.042 0.826 14 NO 3 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 -

183 Table 7.2 Summary statistics of groundwater quality parameters for the pre-monsoon (2006) Sl. No Parameters 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 SO 4 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 HCO 3 129 733 346.9 16565.27 128.706 13 Fe 0 1.20 0.124 0.05 0.2193 14 NO 3 6 520 79.47 8873.11 94.197

184 Figure 7.1 Distribution of variables among factors given by factor analysis for the pre-monsoon (2006)

185 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, SO 4, F, NO 3 and HCO 3. 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, SO 4, F, SO 4, and NO 3 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).

186 Table 7.3 Rotated factor loadings for the post-monsoon (2006) Parameters Factors 1 2 3 Communalities 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 SO 4 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 HCO 3 0.186-0.861 0.171 0.804 Fe 0.842 0.161-0.123 0.749 NO 3 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 postmonsoon (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 SO 4 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 HCO 3 53 650 186 134.099 17982.609 Fe 0 1.20 0.166 0.2055 0.0422 NO 3 0 125 34.05 25.408 645.555

187 Figure 7.2 Distribution of variables among factors given by factor analysis for the post-monsoon (2006)

188 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 premonsoon (2011) Sl.No Parameters Factors 1 2 3 Communalities 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 SO 4 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 HCO 3-0.122 0.738 0.334 0.525 13 Fe 0.771 0.518 0.793 0.603 14 NO 3-0.003 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.

189 Factor 1 (F1): TDS, TH, Ca, Mg and K Factor 2 (F2): Cl, F, SO 4, Na and HCO 3 Factor 3 (F3): Turbidity, ph, Fe and NO 3 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. No Parameters 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 SO 4 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 HCO 3 138 787 411.02 23009.524 151.689 13 Fe 0 1.10 0.191 0.031 0.1760 14 NO 3 0 569 76.118 7113.857 84.3437

190 Figure 7.3 Distribution of variables among factors given by factor analysis for the pre-monsoon (2011)

191 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, SO 4, Na, K, HCO 3, Fe and NO 3. 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-SO 4, TH-Ca, TH-Mg, Cl-Na, Cl-K, Na-SO 4 and Na-K have more significant correlations. TDS-Mg, HCO 3, TDS-NO 3, TDS-TH-Cl, TH-Na, TH-HCO 3, Ca-Cl, Ca-Na Na-NO 3 and Turb-Fe have good positive correlations. Further, TH- SO 4, TH-K, Ca-Mg, Ca-SO 4, Ca-K, Ca-HCO 3, Mg-Cl, Mg-Na, Mg-K, Mg-HCO 3, Cl-SO 4, Cl-HCO 3, Na-HCO 3, K-HCO 3, TH-NO 3, Mg-SO 4, Mg-K, Mg-NO 3 pairs exhibit positive correlations. The details are illustrated in Table 7.7.

192 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-SO 4, TDS-Na, TDS-Fe, TH-Mg, TH-SO 4, Ca- SO 4, Ca-Fe, Cl-SO 4, also indicated good positive correlations. Also, the pairs of TDS-Fe, TDS-NO 3, TH-F, Ca-Mg, Ca-F, Ca-NO 3, Mg-F, Mg-SO 4, 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-SO 4, TH-SO 4, Ca-Cl, Cl-SO 4, Cl- Na and Na-SO 4 indicated good positive correlations. Further TDS-K, TH-Fe and Cl-Fe exhibited positive correlations. The details are given in Table 7.9.

Table 7.7 Correlation of physicochemical parameters of groundwater during the pre-monsoon (2006) Parameters Turbidity TDS ph TH Ca Mg Cl F SO 4 Na K HCO 3 Fe NO 3 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 SO 4 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 HCO 3 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 NO 3-0.0032 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 193

Table 7.8 Correlation of physicochemical parameters of groundwater during the post-monsoon (2006) Parameters Turbidity TDS ph TH Ca Mg Cl F SO 4 Na K HCO 3 Fe NO 3 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 SO 4 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 HCO 3-0.1226 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 NO 3 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 194

Table 7.9 Correlation of physicochemical parameters of groundwater during the pre-monsoon (2011) Parameters Turbidity TDS ph TH Ca Mg Cl F SO 4 Na K HCO 3 Fe NO 3 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 SO 4-0.209 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 HCO 3 0.212 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 NO 3 0.166 0.464 0.279 0.087 0.137 0.026 0.261-0.020 0.172 0.538 0.515 0.345-0.032 1.000 195

196 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 longtransformation 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 geointerpretation 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

197 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), postmonsoon (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.

198 Cluster 1 (10 parameters are included) F, Fe, Turbidity. ph, Mg, K, Ca, SO 4, NO 3 and Na) Cluster 2 Cl, HCO 3 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, SO 4, NO 3, and Na) and two physical parameters (Turbidity and ph). The second cluster consisted of two chemical parameters (Cl and HCO 3 ) and one physical parameter (TH). During the post-monsoon, the first cluster included dominant chemical parameters (F, Fe, Turbidity, K, NO 3, Mg, Na, SO 4, Ca and HCO 3 ) 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 premonsoon (2006)

199 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 premonsoon (2011)

200 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, HCO 3 and TH), there is a stronger relation between the group of chemical parameters (Cl and HCO 3 ) and the physical parameter (TH) or with parameters like (SO 4, NO 3 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.