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## Application of multivariate statistics and geostatistical techniques to identify the spatial variability of heavy metals in groundwater resources | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Caspian Journal of Environmental Sciences | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مقاله 2، دوره 13، شماره 4، زمستان 2015، صفحه 333-347
اصل مقاله (641 K)
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نوع مقاله: Research Paper | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نویسندگان | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

F. Khanduzi؛ A. Parizanganeh؛ A. Zamani | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{}University of Zanjan | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

The performance of geostatistical and spatial interpolation techniques for estimation of spatial variability of heavy metals and water quality mapping of groundwater resources in Ramiyan district (Golestan province- Iran) were investigated. 24 spring/well water samples were collected and the concentration of heavy metals (Ni, Co, Pb, Cd and Cu) was determined using Differential Pulse Polarography. Multivariate and geostatistical methods have been applied to differentiate the influences of natural processes and human activities as to the pollution of heavy metals in groundwater across the study area. The results of the Cluster Analysis and Factor Analysis show that Ni and Co are grouped in the factor F1, whereas, Pb and Cd in F2 and Zn and Cu in F3. The probability of presence of elevated levels for the three factors was predicted by utilizing the most appropriate Variogram Model, whilst the performance of methods, was evaluated by using Mean Absolute Error, Mean Bias Error and Root Mean Square Error. The spatial structure results show that the variograms and cross-validation of the six variables can be modeled with three methods, namely,the Radial Basis Fraction, Inverse Distance Weight and Ordinary Kriging. Moreover, results illustrated that Radial Basis Fraction method was the best as it had the highest precision and lowest error. The Geographic Information System can fully display spatial patterns of heavy metal concentrations, in groundwater resources of the study area. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژهها | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Groundwater resources؛ Heavy metals contamination؛ Geostatistical؛ Multivariate statistics؛ Interpolation؛ Spatial mapping | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

اصل مقاله | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(Received: Feb. 29.2015 Accepted: July. 22.2015)
The performance of geostatistical and spatial interpolation techniques for estimation of spatial variability of heavy metals and water quality mapping of groundwater resources in Ramiyan district (Golestan province- Iran) were investigated. 24 spring/well water samples were collected and the concentration of heavy metals (Ni, Co, Pb, Cd and Cu) was determined using Differential Pulse Polarography. Multivariate and geostatistical methods have been applied to differentiate the influences of natural processes and human activities as to the pollution of heavy metals in groundwater across the study area. The results of the Cluster Analysis and Factor Analysis show that Ni and Co are grouped in the factor F1, whereas, Pb and Cd in F2 and Zn and Cu in F3. The probability of presence of elevated levels for the three factors was predicted by utilizing the most appropriate Variogram Model, whilst the performance of methods, was evaluated by using Mean Absolute Error, Mean Bias Error and Root Mean Square Error. The spatial structure results show that the variograms and cross-validation of the six variables can be modeled with three methods, namely,the Radial Basis Fraction, Inverse Distance Weight and Ordinary Kriging. Moreover, results illustrated that Radial Basis Fraction method was the best as it had the highest precision and lowest error. The Geographic Information System can fully display spatial patterns of heavy metal concentrations, in groundwater resources of the study area.
Water is the basic requirement for all life on earth and an increase in the population and urbanization necessitates growth of agricultural and industrial sectors, increasing demand for fresher water. When surface water is not available; the alternative is to depend on Groundwater (GW) (Subramani The aquifer is the main source for drinking and irrigation critical for the local residents. 24 well/spring samples were collected and analyzed by voltametric method for determination of such heavy metals. The presence and concentration of heavy metals were determined and the results were compared to the maximum contaminant level, specified by WHO and the Institute of Standards and Industrial Research of Iran (ISIRI). This study aims at investigating the contents of Cu, Ni, Zn, Cd, Pb and Co in the groundwater resources of Ramiyan, including the analysis of their spatial distribution as well as unveiling their possible sources by integrating multivariate statistical and geostatistical methods.
Golestan Province is located in the Southeast of the Caspian Sea in Northern Iran. The study area is Ramiyan district, with an area of 780.73 km
The samples for the assessment of groundwater pollution with heavy metals were collected from twenty four stations (wells/springs) in the study area (Fig 1, Table 1). The sampling was carried out in summer 2012 and from each station three replicate samples were selected for analysis. The glassware and vessels were treated in 10% (v/v) nitric acid solution for 24 hrs and were washed with distilled and de-ionized water. The samples were collected in polypropylene containers, labeled and a few drops of HNO
The multivariate analysis provides techniques, such as the Principle Component Analysis (PCA), Factor Analysis (FA) and Cluster Analysis (CA) for classifying the inter-relationship of measured variables (Zamani The first step in the geostatistical estimation, is a provision of a model that can facilitate the computation of semivariogram value for any possible sampling intervals. The most commonly used models are the Spherical, Exponential, Gaussian and Pure Nugget effect (Isaaks & Srivastava, 1989). The semivariogram plays a fundamental role in the analysis of geostatistical data by employing the Kriging Method. Prior to performing Kriging, a valid semivariogram model has to be selected and the model parameters have to be estimated (Pang Where, denotes the semivariogram, is the spatial interval, which is designated as lag; is the observed paired data, when the interval and are the measured values, when the Z(x) values are as xi+h, respectively. Valid models which are commonly fitted to the experimental semi variograms include the spherical, Gaussian and exponential functions. These are characterized by a sill, which represents the covariance accounted for by the model and a range that signifies the extent of spatial correlation. The value of the semi variograms is referred to as the nugget effect, where the model approaches the abscissa. These significant geostatistical parameters can indicate the spatial variation and relativity of regionalized variables under a certain scale (Yang
Kriging Method was used as estimating tool in sustainable management of groundwater. It is a geostatistical interpolation technique that considers both the distance and the degree of variation between known data points when estimating values in unknown areas (Sahoo & Jha, 2014). This technique is an exact interpolation estimator, which is used to detect the best linear unbiased estimate. The optimum linear unbiased estimator must have a minimum variance of error of estimation (Einax & Soldt, 1999; Ahmadi & Sedghamiz, 2008). In order to estimate the values of some locations which are not sampled, it is necessary to solve the following linear equation: (2) denotes the estimate of the unknown value and are the weights of known neighboring points . Kriging is an estimating method that is stable on weighty mobile average coincident. This estimator is known as a best unbiased linear estimator. Spherical, circular, Gaussian and exponential functions are available models when the Kriging method is ordinary (Nas, 2009). Goovaerts describes the detail of the method (Goovaerts, 1997). Because it uses statistical models, it allows a variety of map outputs, including predictions, prediction standard errors, probability, and quantile maps. Among the various forms of Kriging, ordinary Kriging has been used widely as a reliable estimation method (Nas, 2009). In interpolation with the Inverse Distance Weighted (IDW) method, a weight is attributed to the point to be measured. In other words weight is the function of inverse distance and closer points have more influence in estimating unknown points (Eslami These weights are controlled on the bases of power ten. So, with an increase of power, the effect of the points (that are farther) diminishes, whilst a lesser power distributes the weights more uniformly between neighboring points. In this method the distance between the points counts, so that, the points of equal distance have equal weights (Balakrishnan (3) Where designates the weight of point which is the distance between point i and the unknown point, which is the weight on the bases of power ten and n is the number of data points (Karandish & Shahnazari, 2014). Kriging in geostatistics is similar to inverse distance weighting except that the weights are based not only on the distance between the measured sampling points but also on the overall spatial arrangement among the sampling points. The basic assumption in kringing is that the sampling points that are close to each other are similar than those that are away. Kriging is regarded as an optimal spatial interpolation method, which is a type of weighted moving average (Gorai & Kumar, 2013). The Radial Basis Functions (RBF) Methods are a series of exact interpolation techniques, where the surface must go through for each measured sample value. The basis of each function has a different shape and results in a slightly different interpolation surface (Kazemi Poshtmasari (4) Where signifies the source of random error, is the measured value of an attribute at point and epsilon is the associated random error. The term represents the smoothness of the function f and the second term represents its proximity to the data (Karydas
The adequacy and validity of the developed semivariogram models was tested satisfactorily by a technique called cross-validation. The idea of cross-validation consists of removing a datum at a time from the data set and reestimating this value from remaining data by using different variogram models. The interpolated and actual values are compared, and the model that yields the most accurate predictions is retained (Burrough & McDonnell, 1998; Karimi Nezhad (5) (6) (7) Where Z (xi) is the observed value at point xi, Z*(xi) is the predicted value at point x and N denotes the number of samples.
The results of the analysis of target metal ions i.e., Co, Ni, Zn, Cd and Pb in samples from 24 wells/springs under study are given in Table (2). The results show that Co, Ni, Pb and Cd are evident in 100% of the samples and Zn and Cu are detected in 96% and 88% of the samples, respectively. The concentration of investigated metals (in µg/L) in the samples were found to be below their MCL and in the ranges of 5.69 -92.44 for Zn, 1.23 -7.06 for Pb, 0.14-8.40 for Cu, 0.01-0.99 for Cd, 1.23 -21.79 for Ni and 0.49 -7.79 for Co. The geographical location of the sampling stations and the average concentrations of metals at each station are shown in Table (1).
Two main groups of elements have been determined using the Cluster Analysis Method, one group includes Ni and Co and the other comprises of Pb, Cd, Zn and Cu (Fig. 2).
The major objective of the Factor Analysis (FA) is to reduce the contribution of less significant variables so as to further simplify even more of the data structure given by the PCA. This goal can be achieved by rotating the axis defined by the PCA and the construction of new variables, which are also called Varifactors (Shrestha & Kazama, 2007). Prior to such analysis, the raw data is commonly normalized to avoid misclassifications, due to the varied order of magnitude and range of variation of the analytical parameters (Tabachnick & Fidell, 2007). This process reduces the dimensionality of data by a linear combination of original data, to generate new latent variables which are orthogonal and uncorrelated to each other (Nkansah Nickel and cobalt, contained in the first factor, are typical emitted elements of electronic plants. The second factor includes cadmium and lead elements which are emitted by the agricultural activities and the metallurgical plant. The third factor is loaded with zinc and copper, which are emissions of batteries, pigments and fungicides. The heavy metal grouping has been explored in plotting the first three principle components generated from these parameters (Fig. 3).
The geostatistical analysis is to be assumed that the distribution behavior of the metal ions in the sampling stations is normal. The random and normal distribution assumptions were checked by the (K-S) (Kolmogorov-Smirnov) Methods. Alternatively, the homogeneity and normal distribution in the data, can be achieved by transforming the obtained data to another mathematically presentation, which lowers the difference between the data. This can be achieved by using the logarithmic form of data. The normality of heavy metal data set was checked by the Kolmogorov–Smirnov Test. It is often observed that environmental variables are lognormal (McGrath After the logarithmic transformation of the original data, a normal distribution can be obtained. Thus, the following calculations must be performed on the logarithms of the data. After normalizing the data Semivariogram parameters were generated for each theoretical model. Then, the confidence level of all variograms was evaluated using the ratio of nugget variance to sill which is regarded as a criterion for classifying the spatial dependence of ground water quality parameters. If this ratio is less than 25%, then the variable has strong spatial dependence; if the ratio is between 25 and 75%, the variable has moderate spatial dependence and the ratio greater than 75%, represents weak spatial dependence (Taghizadeh The most appropriate theoretical model was selected, which was based on highest R2 and lowest RSS (Table 5).
The attributes of the semivariograms for each factor are summarized in Table (5). Semivariograms show that the first and second factors are appropriate with the Exponential Model, whereas, the third factor fits well with the Gaussian Model. The values of R2 illustrate that the semivariogram models give good descriptions of the spatial structure of the heavy metals of groundwater. The nugget/sill ratios can be regarded as the criterion to classify the spatial dependence of data sets (Liu
The applicability of different semivariogram models is tested by cross-validation and best model is selected (Table 6). In this study, ordinary kriging (OK), IDW and RBF were utilized to estimate six heavy metal concentrations. Comparisons between different methods were carried out by the MAE, MBE, and RMSE statistical parameters. In this research, the Radial Basis Functions Method (Inverse Multiquadric Model) was found to be the most suitable method for the estimation of Ni mapping. Whereas, statistics for the geostatistical method also show that Ordinary Kriging for Pb (Exponential Model), Zn and Cu (Gaussian Model); the Inverse Distance Weighted method for Co (power 2) and Cd (power 3) provides a much better estimation for results of concentrations, than the other methods (Table 6). After plotting the values of heavy metal concentrations of groundwater for various sample locations, drinking water quality maps for heavy metal concentrations, can be drawn to demonstrate locations, where the water is almost clean or to some extent at risk (Fig 4).
Filled contour map of Co Filled contour map of Ni
Filled contour map of Cd Filled contour map of Pb
Filled contour map of Cu Filled contour map of Zn
Due to the complexity and a large variation of environmental data sets, the application of geostatistical and multivariate statistical methods is recommended. The main objective of this study was to determine the best estimators for providing heavy metals maps in ground water resources in Ramyian district. The application of multivariate statistical and geostatistical methods were performed on six heavy metals and three principal components were identified, so as to represent the variability of heavy metals in groundwater sources. From the spatial distributions of 6 heavy metals, it was evident that the parent materials and anthropogenic factors played important roles in heavy metal concentrations of GW in Ramiyan. The effects of these two factors varied with that of the heavy metals. The results of the Cluster Analysis (CA) and Factor Analysis (FA) on the heavy metals, showed that Ni and Co was grouped in factor F1, Pb and Cd in F2 and Zn and Cu in F3. The probability of the presence of elevated levels of the heavy metals studied in the groundwater was predicted by using the best-fit semivariogram model. The performance of methods was evaluated by utilizing the Mean Average Error (MAE), Mean Bias Error (MBE), and Root Mean Square Error (RMSE). Moreover, results showed that Radial Basis Functions (RBF), Inverse distance weighted (IDW) and Ordinary Kriging (OK) methods were the best methods employed to estimate the Ni; Co and Cd; Pb, Zn and Cu mappings, respectively. The Geographic Information System (GIS) can fully display the spatial patterns and relationships among landscape indices and heavy metal concentrations, in the groundwater of this area of study. Application of different multivariate statistical techniques interprets complex data matrices and better understanding of water quality. Although the concentrations of investigated metals in the collected samples were found to be below their maximum contaminant level values reported by WHO and ISIRI but the source of heavy
metals contamination should be investigated specially in hot points within the studied area.
Sincere gratitude to Rural Water and Wastewater Company (Golestan Province, Iran) for partial financial support (Grant Number 4987). The authors gratefully acknowledge Younes Khosravi’s contribution to this work.
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