evaluating the groundwater quality variations using factor analysis combined with information entropy theory

introduction the chemical characteristic of groundwater as a major source of water supply for human life is an important factor in determining the usage of it for agriculture, industry and drinking. useful techniques and different methods of studying the chemical composition of groundwater such as correlation coefficient, descriptive statistics, factor analysis and cluster analysis provide an understanding of the main factors that contribute to groundwater salinity and also sources of contamination. shannon proposed entropy as a measure of uncertainly, a theory recently applied in various fields. although the ability of the entropy theory has quantified to evaluate uncertainty for hydrological variables and parameters in models of water resources systems, studies have not fully explored its application for describing and evaluating large-scale characteristics of groundwater quality. the three objectives of this study included: (1) applying cluster analysis and gis technique to recognition of spatial classification of groundwater resources; (2) using factor analysis to interpret major factors that affect groundwater quality in lenjanat, and (3) investigating the stability and spatial variation of influential factors. materials and methods in this study, 155 groundwater samples were collected from lenjanat plain, isfahan province. the analyzed concentrations of 10 ions including (ca), (na), (k), (mg), (hco3), (cl), (f), (no3), (so4) and (ec), and 11 metallic species including (as), (ba), (cd), (cr), (cu), (fe), (mn), (ni), (pb), (sb) and (se) has been used. finally, 14 parameters with a moderate to high correlation coefficient were chosen to assess the groundwater quality in this plain. in this study, different methods including geostatistics, information entropy theory, and   multivariate statistical methods were employed to assess groundwater quality. in order to extract the most important factors in groundwater quality change, the factor analysis method was used. factor analysis is a multivariate statistical technique that reduces the major variables to fewer factors which can be used to develop the best interpretable model. this study employed hierarchical agglomerative cluster analysis on standardized data using ward’s method with squared euclidean distance. information entropy theory using in this study was another important part of the research process. shannon introduced the entropy concept into information theory by suggesting entropy as a measure of information or uncertainty. discussion and results multivariate analysis and clustering of the data and parameters performed using 14 selected parameters which had a high to moderate correlation. in the first step, normalized values of 14 parameters of 155 samples were used for clustering and factor analysis. factor analysis of quality parameters revealed that 70.67% of groundwater quality changes in lenjanat plain are controlled by three factors that expression of each factor is described in the following. table 1 presents the rotated common factors for the percentage of variance and the total cumulative percentage of variance. table 1: the varimax rotated common factors for loadings, the percentage of variance and the total cumulative percentage of variance parameter component 1 2 3 ca -0.05 0.41 0.73 na 0.04 0.79 0.35 mg 0.06 -0.04 0.76 f 0.27 0.78 -0.15 no3 0.21 0.08 0.69 so4 0.14 0.81 0.29 ec -0.07 0.56 0.71 as -0.92 -0.14 0-.11 cr 0.47 0.02 -0.07 cd 0.95 0.06 0.10 cu 0.95 0.08 0.097 mn -0.96 -0.08 -0.10 ni 0.48 0.16 -0.02 pb 0.88 -0.006 0.12 eigenvalue 5.48 3.14 1.27 total variance (%) 39.19 22.42 9.07 cumulative variance (%) 39.19 61.61 70.67 factor 1: this factor indicates high relation with five elements including as, cd, cu, mn and pb accounts of 39.19% of the total variance in groundwater quality parameters. the existence of these parameters in groundwater is the result of human activities and pollutions generated from industrial areas in this plain. factor 2: the impact on the groundwater quality change by this factor is equal to 22.42%. the main source of sodium and sulfate in this plain is the presence of crystal and inter-beds of gypsum and salt deposits in the region. in addition, the use of chemical fertilizers and industrial & residential sewage discharge are another causes of sulfate and fluoride concentration. factor 3: this factor controls 9.07% of groundwater quality variance in lenjanat plain. according to the geological structure of region, source of ca and mg in the groundwater is generally natural and these elements could have been derived from erosion of limestone, dolomite and their minerals. existence of no3 in factor 4 and as an effective agent in destroying the quality of water show the infiltration of wastewater and the nitrate fertilizers used in farmland to subsurface. the information entropy for each selected groundwater monitoring well is calculated and the groundwater monitoring wells are ranked according to their calculated information entropy values. in the next step, the ranking values of groundwater monitoring wells were summed up for each parameter classified by each common factor. table 2 shows some of the results. finally, the magnitude of the sum of ranks was used to determine the stability of groundwater quality. the smaller values indicate more unstable groundwater qualities. except for as, cd and mn which have the lowest entropy and the maximum weight, all parameters show similar entropy and entropy weight. accordingly, all parameters except three mentioned parameters have been constant changes and many of these changes can be attributed to the geological formations. on the other hand, high entropy weight than other parameters indicate the higher influence. so, the heavy metals concentrations in groundwater are the most effective parameters in quality change. table 2: entropy and entropy weight values of parameters   ca na mg f no3 so4 ec as cr cd cu mn ni pb entropy value 7.21 7.19 7.26 7.21 7.24 7.23 7.22 6.92 7.24 6.46 7.21 6.87 7.20 7.22 entropy weight 11.06 11.06 11.06 11.06 11.06 11.06 11.06 11.08 11.06 11.12 11.06 11.09 11.06 11.06     the entropy value and weight of each factor that are presented in table 3 show that the highest entropy weight are associated with factor 1, and afterwards, factors 3 and 2. according to the results, the greatest impact on groundwater quality of lenjanat plain is related to parameters of the factor 1 and factor 3 and finally, factor 2. the correlation between entropy value of each parameter and corresponding factor is presented in table 4. table 3: the entropy values and entropy weight for different factors sample information entropy value entropy weight f1 f2 f3 f1 f2 f3 1 0.23459 0.167692 0.208551 0.358671 0.213175 0.285365 2 0.232756 0.168242 0.212976 0.358844 0.213154 0.28506 3 0.23459 0.157132 0.192494 0.357811 0.213457 0.285887 . . . . . . . 154 0.226236 0.098825 0.183919 0.355484 0.21604 0.284169 155 0.222986 0.134493 0.193117 0.357315 0.214337 0.284751 sum 34.707 21.643 28.946 55.426 33.193 44.251 table 4: correlation between entropy value of each parameter with the corresponding factor score pb mn cu cd as parameter 0.860 0.964 0.881 0.858 0.924 factor 1 scores & entropy value - - so4 f na parameter - - -0.811 -0.775 -0.781 factor 2 scores & entropy value - ec no3 mg ca parameter - -0.724 -0.723 -0.751 -0.731 factor 3 scores & entropy value     conclusions according to the minimum and maximum salinity in the plain, it can be expressed that the most important factor in groundwater quality variance is located in the plain. correlation between various parameters of quality shows that most influence on electrical conductivity is due to calcium, sodium and sulfate. the same changes and fluctuations in weight of factor 1 (39.2% of the variation in factor load) with the entropy value of heavy metals indicates the importance of this factor in determining the concentration of heavy metals. this factor has a manmade origin and is not connected with the natural environment and geological formations. strong negative correlation between the factor score and entropy value of heavy metals shows that the origin and changes in parameters of factor 2 (with 22.4% change in factor load) and 3 (with 9.1% changes in factor load) is due to natural factors and human activities has the lowest impact.