Evaluation of Interpolation Models in Zoning of Heavy Metals in Soil (Case Study: Herris Area)

It is inevitable to analyze the existing contaminant elements in soil as the most important source of nutrition for human. Heavy metals are considered and referred among these elements. The contaminated soils of urbanized regions are directly related to human, while these elements are absorbed by plants in agricultural fields, through which they enter the human food cycle. The excessive increase of these elements in soil results in the growing incidence of certain diseases such as cancer. Moreover, the irresolvability of these materials may have dangerous impacts on the human digestion as well as nervous systems. Contamination, due to heavy metals in soil, have even resulted in some animals’ death.
There are various factors involved in soil contamination. One of main factors is the incorrect use and increasingly irregular exploitation of nature by human beings. In Iran, inappropriate economic exploitation of agricultural fields and aberrant use of chemicals have led to the higher concentration of heavy metals in soil, turning to a crucial problem in certain areas. The most significant cause of soil contamination is the wrong use of chemical fertilizers, resulting in the agglomeration of heavy metals in soil. Therefore, it is inevitable to identify the spatial distribution of these elements. The geo-statistical instruments have facilitated the quantification of soil spatial characteristics, whereby leading to the probability of spatial interpolation.
Objective of the study are: (i)To prepare zoning maps of elements including Zinc, Copper, Iron, Manganese, Potassium, and Lead using mathematics and geo-statistics methods as well as choosing the most optimum technique of spatial interpolation by comparing RMSE, MAE and MBE;(ii)To analyze the probable spatial correlation between the concentration of these elements in agricultural soils;(iii)To distinguish the regions affected by the excessive contamination higher than the threshold limit of general index and WHO standard and also Iran’s Soil and Water Research Institute’s standard.

Materials and Methods
Harris Town is located in the north-western Iran between 38°04° and 38°24° latitudes of northern hemisphere and of 46°22° and 47°22° geographical longitudes of eastern hemisphere.
Statistical Analyses
In this research, first of all, 370 samples of soil were randomly selected from this region and the concentrations of abovementioned elements were measured in the laboratory. Then, the accuracy of the measured data was examined by applying 3Sigma Validation Test. At the next stage, the spatial distribution of the elements of Zinc, Iron, copper, Manganese, and Potassium was examined using Mathematics and geo-statistics interpolation models. These methods which are based on the first principle of geography include certain mathematical methods such as the Inverse Distance Weighting, Local Polynomial, and Radial Basis Functions and geo-statistics methods such as Ordinary Kriging (OK), Simple Kriging (SK), and Universal Kriging (UK) with Circular, Globular, Gaussian, and Exponential Variogram Models.
Kriging is one of the geo-statistical interpolation methods, which is based on Weighted Moving Average. One of the features distinguishing it from other interpolation methods is that it is regarded as the Best Linear Unbiased Estimator. The first stage in statistical analyses is the computation and drawing of variogram. In fact, variogram represents the variability of samples based on their distance. The next stage is the selection of the best theoretical model for fitting to experimental variogram. The modeled variogram shows the spatial self-correlation of data, and describes range, sill and nugget. The Kriging interpolator is divided into different methods. The models being tested in this research are Ordinary, Universal and Simple Kriging.
Inverse Distance Weighting
The Inverse Distance Weighting is a radix point method which acts based on the first principle of geography. In this interpolation method, the weighting parameter operates according to the criterion that an increase in the distance from the sampled points to the passive point leads a decrease in its effect in the expected (predicted) value.
Local Polynomial Method
Polynomial interpolation is a method for finding a formula, the figure of which passes through the data. The Universal Polynomials identify the fitted surface to data by considering all existing data in the analysis, while local polynomials performs this action for a limited number of points within a considered oval. This method allocates the least proportional squares among the identified points in the oval shape area as the point weight. Thus, interpolation is performed based on the allocated weight of the relations of the first, second and/or third grades among the variables in the neighboring points of X, Y, and Z along with the minimization of estimated errors.
Radial Basis Functions
This method is a manner of artificial neural networks in which the predicted values are higher than the maximum observed and lower than the existing minimum observed. Indeed, the surface fitting by these functions acts like a plastic membrane so as to minimize the total surface curvature. The Radial Basis Functions performs interpolation based on five principal functions. The main core of these functions is the sum of squares values. In this method, a function is considered for each location (place), where the linear combination of these functions is used for predicting the amount of function in the passive location as the final function. In this study, five functions including Spline Function, Quite Regular, Spline with tension, Multi-Quadric function, Reverse Multi-Quadric Function and Spline Function with the thin surface were used.
Validation Criterion of Interpolation Methods
In this research, the observed data were divided in two groups of experimental and control, with the proportion of 80 to 20. At the beginning, by applying the experimental data, a surface was fitted for the data using each interpolation method. Jackknife Cross-Validation Method was used to determine errors vector. The basis of this method is that when fitting the surface, one of the data is omitted each time, fitting is performed by using other data and the data deviation from the predicted value is recorded. Then, the control data is inserted in the fitted model and the amount of data deviation from the fitted model is being reported.
In order to examine the accuracy and validation of each method in the zoning of the aforementioned heavy metals, Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Basin Error (MBE) were applied. The closer the values of (RMSE), (MAE), and (MBE) to zero, the more efficient (effective) the performance of the fitted model.

Results and Discussion
All obtained numbers for the spatial correlation between the elements are of positive value, and this represents a direct relation in the reciprocal transformations of elements. Among the results obtained, the spatial correlation between two metals of Zinc and Copper is more intense, as with 46%, include the most intense relation as compared to each pair of other elements. Meanwhile, the correlation between the two elements of Manganese and Potassium has the least value with 1%.
By using the QQ chart, it was found the data of Potassium, Zinc, Iron and Manganese have a relatively high skewedness and far from normal distribution.
As it was previously indicated, variogram explains the relation between sample variability as well as their interaction. In order to choose the best model of experimental variogram, the proportion of nugget to sill was used, in which the least value represents the best model (Figure 3).
By using Arc GIS Software, the most optimum model for the preparation of zoning maps was examined. Among the various models, deviation vectors were drawn from the measured value for the fitted surface. These vectors were drawn for both sets of data. By comparing the measured data and the global index of soil contamination and WHO standard, it was found that the highest volume of elements of Iron, Copper, and Manganese are not located in the permissible range, while the amount if this element is located in the impermissible range in the whole region under study. (Figures 4 to 8).