Disjunctive Kriging Research Articles

Geographical distribution of reference value of aging people's left ventricular end systolic diameter based on the support vector regression

AimThe aim of this paper is to analyze the geographical distribution of reference value of aging people's left ventricular end systolic diameter (LVDs), and to provide a scientific basis for clinical examination. MethodsThe study is focus on the relationship between reference value of left ventricular end systolic diameter of aging people and 14 geographical factors, selecting 2495 samples of left ventricular end systolic diameter (LVDs) of aging people in 71 units of China, in which including 1620 men and 875 women. By using the Moran's I index to make sure the relationship between the reference values and spatial geographical factors, extracting 5 geographical factors which have significant correlation with left ventricular end systolic diameter for building the support vector regression, detecting by the method of paired sample t test to make sure the consistency between predicted and measured values, finally, makes the distribution map through the disjunctive kriging interpolation method and fits the three-dimensional trend of normal reference value. ResultsIt is found that the correlation between the extracted geographical factors and the reference value of left ventricular end systolic diameter is quite significant, the 5 indexes respectively are latitude, annual mean air temperature, annual mean relative humidity, annual precipitation amount, annual range of air temperature, the predicted values and the observed ones are in good conformity, there is no significant difference at 95% degree of confidence. The overall trend of predicted values increases from west to east, increases first and then decreases from north to south. ConclusionIf geographical values are obtained in one region, the reference value of left ventricular end systolic diameter of aging people in this region can be obtained by using the support vector regression model. It could be more scientific to formulate the different distributions on the basis of synthesizing the physiological and the geographical factors. Highlights: -Use Moran's index to analyze the spatial correlation. -Choose support vector machine to build model that overcome complexity of variables. -Test normal distribution of predicted data to guarantee the interpolation results. -Through trend analysis to explain the changes of reference value clearly.

Application of Disjunctive Kriging for Estimating Economic Grade Distribution in an Iron Ore Deposit: A Case Study of the Choghart North Anomaly, Iran

Abstract Most significant iron ore deposits in Iran are located in Central Iran Zone. These deposits belong to the Bafq mining district. The Bafq mining district is located in the Early Cambrian Kashmar-Kerman volcanic arc of Central Iran. Linear estimation of regionalized variables (for example by inverse distance weighting or ordinary Kriging) results in relatively high estimation variances, i.e. the estimates have very low precision. Assessment of project economics (or other critical decision making) based on linear estimation is therefore risky. Non-linear estimation methods like disjunctive kriging perform better and the lower estimation variance allows less risky economic decision-making. Another advantage of disjunctive kriging is that it allows estimation of functions of the primary variable, which here is the grade (Fe %) of the ore. In particular it permits estimation of indicator functions defined using thresholds on the primary variable. This paper is devoted to application of disjunctive kriging method in Choghart North Anomaly iron ore deposit in Central Iran, Yazd province, Iran. In this study, the Fe concentration of Choghart North Anomaly iron ore deposit was modelled and estimated. The exploration data consists of borehole samples measuring the Fe concentration. A Gaussian isofactorial model is fitted to these data and disjunctive kriging was used to estimate the regionalized variable (Fe %) at unsampled locations and to assess the probabilities that the actual concentrations exceed a threshold value at a given location. Consequently a three dimensional model of probability of exceeding a threshold value and the estimated value are provided by disjunctive kriging to divide the ore into an economic and uneconomic part on the basis of estimation of indicator functions using thresholds grades defined on point support. The tools and concepts are complemented by a set of computer programs that are applied to the case study. The study showed that disjunctive kriging can be applied successfully for modeling the grade of an ore deposit. Results showed that the correlation between the estimated value and real value at locations close to each other is 81.9%.

COMPARISON ANALYSIS OF INTERPOLATION TECHNIQUES FOR DEM GENERATION USING CARTOSAT-1 STEREO DATA

Digital Elevation Model (DEM) can be generated using several techniques such as photogrammetric technique, interferometry, Lidar, etc. In photogrammetric technique, a DEM generation using stereo images, accuracy of generated DEM is also dependent on interpolation techniques. The process of interpolation is conducted to generate DEM as a continuous data from the point map that contained height information as a discrete data. In this research, point map was extracted from Cartosat-1 stereo image and from geodetic single frequency GPS in differential mode. Different interpolation techniques were applied on these data sets with different combination within these data sets. In this study, analysis of DEM interpolation was conducted with deterministic interpolators such as inverse distance weighted (IDW), global polynomial, local polynomial, and radial basis functions (RBF); and probabilistic interpolators such as simple kriging, ordinary kriging, universal kriging, indicator kriging, probabilistic kriging, disjunctive kriging, and cokriging. The accuracy of generated DEMs through different interpolation techniques were evaluated with ground point data collected from geodetic single frequency GPS in differential mode. Based on the analysis, the range error of DEMs generated was between 1.29 m to 2.96 m. Interpolation method with the least error was ordinary kriging using point map data and GPS points, while the highest error was obtained from global polynomial method.

Geospatial patterns and background levels of heavy metal in deposited particulate matter in Bushehr, Iran

Dust storm transportation and deposition in Bushehr, Iran, caused adverse effects on regional air quality and human health. To evaluate the impact of these phenomena, it is critical to clarify the chemical characteristics and trace the sources of heavy metals in a dust storm. In this paper, we give an overview of the spatial distribution and chemical properties of heavy metals by collecting deposited particulate matter samples at ten stations from August 2011 to July 2012. The samples were analyzed using inductively coupled plasma for Cd, Co, Fe, Pb, Ni, and V, and using hydride generation for As. Multivariate gap statistical analysis was used to investigate the concentration and source of metals. Based on the comparison between the original data and background levels, geostatistics, disjunctive kriging, and pollution index IPOLL techniques were used to quantify their geospatial patterns and assess the contamination levels of the heavy metals. Results of the fitted models with disjunctive kriging technique showed that As and V were fitted to the Gaussian model with a range of 1.95 and 4.74 km, respectively. Fe and Pb were fitted to the exponential model with a range of 1.37 and 1.06 km, Cd was fitted to the spherical model with a range of 4.74 km, Co was fitted to the rational quadratic model with a range of 1.44 km, and Ni was fitted to the circular model with a range of 14.98 km. Agglomerative hierarchical clustering and Gap statistic methods classify the sampling periods in two main groups; dust and non-dust. The results presented a wide range of metal pollution. In the non-dust period, the mean predominant values showed moderate pollution for Ni; while the dust period had extremely severe pollution for As and Ni, and very severe pollution for Fe and V. Overall, the IPOLL values in dust periods followed the sequence of As > Ni > V > Fe > Cd > Co > Pb. In the dust period, over 70 % of metals in the deposited particulate matter were from external origins. With exception of Fe, all the metals had weakly spatial dependence, indicating that entry of metals was by dust storm. Monitoring of the source of the deposited particles showed that in the periods of occurrence of dust, the dusts originated from Syria and Iraq, and entered Iran.

Risk assessment of heavy metal soil pollution through principal components analysis and false color composition in Hamadan Province, Iran

BackgroundIn the process of decision making to combat heavy metals pollution, it is essential to have accurate quantitative information about heavy metals and their pollution hot-spots. The main purpose of this study was to determine spatial distribution of several elements (As, Sb, Cr, Cd, Ni, Co, Cu, Zn, Pb, Fe and V) on surface soils of Hamadan Province (Iran). It also sought to create a holistic view to determine the position, level, and anomaly of classified elements through principal components analysis (PCA), false color composition (FCC), inverse overlay method, and weighted linear combination. Finally, it tried to identify possible sources of pollution in the hotspots. Interpolation of heavy metal concentrations was performed using geostatistical methods and correlation analysis for locations. The most appropriate interpolation method was selected based on mean absolute error (MAE) and mean bias error (MBE) indices.ResultsAccording to Pearson’s correlation analysis, the elements were categorized in four groups (Fe, V, and Co; Cu, Ni, and Cr; Pb, Zn, and As; Sb and Cd). For Fe, Zn, As, and Pb, the best method was disjunctive kriging. For Co, Sb, Ni, and Cr, ordinary kriging was the most appropriate. Radial basic functions was also the best method for Cd and Cu.ConclusionsOverlaying of zoning maps of the elements and land use and geological layer maps showed that the distribution pattern of the studied elements did not fully conform to the existing land use pattern. Although the most influential factor on the concentration of elements in the studied soils was bedrocks, extensive use of chemical fertilizers should not be ignored. Moreover, urban pollution can also contribute to Pb contamination of soil.

Support and Information Effect Modeling for Recoverable Reserve Estimation of a Beach Sand Deposit in India

Application of geostatistics in estimating recoverable reserves of beach sand deposit is rare. This paper made an attempt to estimate local recoverable reserves using disjunctive kriging and discrete Gaussian model considering support and information effects for a beach sand deposit located in the eastern part of India. The dependence of different selective mining unit (SMU) sizes and different production sampling strategies on the estimated tonnage, metal quantity, and the ore tonnage versus metal quantity relationships has been examined. The results of the study show that nonlinear geostatistics should be used for more precise assessment of the grade, ore tonnage, and metal quantity and their relationships, which are necessary for recoverable reserve estimation. In selective mining operation, both support and information effects have significant influence on recoverable reserve. Recoverable reserve estimation based on SMU involves estimating grade distributions of mining unit with much bigger support than the available drill core sample data. Information effect comes into picture from the real scenario where the actual grades of the blocks remain unknown even during mining. At the mining stage, discrimination of ore and waste blocks is carried out based on estimated grades of the production samples and it is likely that the blocks might be misclassified as either ore or waste and thus sent to wrong destination. Information effect modeling makes the estimation more reliable by taking care of misclassification.

Using Nonlinear Geostatistical Models in Estimating the Impact of Salinity on Crop Yield Variability

Three nonlinear geostatistical models—disjunctive kriging (DK), indicator kriging (IK), and probability kriging (PK)—were used to develop conditional probability (CP) maps based on soil salinity thresholds for two crops, alfalfa (Medicago sativa L.) and corn (Zea mays L.). The CP maps divide alfalfa and corn fields into zones with different probabilities to reach a specific yield potential (YP) at a specific soil salinity threshold. The objectives of this study were to: (i) compare the performance of the DK, IK, and PK models in developing CP maps; (ii) compare actual alfalfa and corn yield samples with the YP estimated by the three models; and (iii) provide guidance for precision management of agriculture by considering the output of the models used in this study. Yield data were collected at alfalfa and corn fields to compare the actual data with those estimated by the models. The results of this study show that the CP maps developed using the three geostatistical models are efficient in assessing the impact of soil salinity on the spatial variability of alfalfa and corn yield. The comparison of the actual yield data with the estimated CP maps from the three models showed good agreement. The IK and PK models generated very similar estimates for each of the zones; however, the zones generated by both of these models are slightly different from the zones generated using the DK model. The information from this study can be used for precision management of agricultural resources.

Three-Dimensional Variation of Electrical Conductivity in a Paddy Rice Soil Based on the Disjunctive Kriging Method

The aim of the study was using the disjunctive kriging method to analyze the three dimensional variation of soil electrical conductivity in a costal saline land in the Yangste delta of China. Fifty six soil apparent Electrical Conductivity (ECa) profiles, which inversed by the procedure that combine the EM38 linear model, were selected as the datum source of 3D spatial variability. Firstly, for facilitating the selection of crops risk evaluation threshold value, ECa was transferred to ECe according to the experience model. Secondly, the ECe distribution at the ten layers was transformed with a standard normal distribution by lognormal transformation. At last, the spatial variability of soil electrical conductivity of the all 10 layer was predicted by the disjunctive kriging method and the layers were stacked one by one. It presented a superior visualization of spatial distribution of ECe in 3D space directly that 2D interpolation can’t achieve. The higher ECe, the higher the salinity is. From the top surface map, the spatial distribution of soil salinity can be easily recognized, which is helpful in management on fertility, analyzing experimental data to reduce subjective judgment and developing and applying agronomic practices.

Spatial patterns of heavy metals in soil under different geological structures and land uses for assessing metal enrichments

One hundred and thirty composite soil samples were collected from Hamedan county, Iran to characterize the spatial distribution and trace the sources of heavy metals including As, Cd, Co, Cr, Cu, Ni, Pb, V, Zn, and Fe. The multivariate gap statistical analysis was used; for interrelation of spatial patterns of pollution, the disjunctive kriging and geoenrichment factor (EFG) techniques were applied. Heavy metals and soil properties were grouped using agglomerative hierarchical clustering and gap statistic. Principal component analysis was used for identification of the source of metals in a set of data. Geostatistics was used for the geospatial data processing. Based on the comparison between the original data and background values of the ten metals, the disjunctive kriging and EFG techniques were used to quantify their geospatial patterns and assess the contamination levels of the heavy metals. The spatial distribution map combined with the statistical analysis showed that the main source of Cr, Co, Ni, Zn, Pb, and V in group A land use (agriculture, rocky, and urban) was geogenic; the origin of As, Cd, and Cu was industrial and agricultural activities (anthropogenic sources). In group B land use (rangeland and orchards), the origin of metals (Cr, Co, Ni, Zn, and V) was mainly controlled by natural factors and As, Cd, Cu, and Pb had been added by organic factors. In group C land use (water), the origin of most heavy metals is natural without anthropogenic sources. The Cd and As pollution was relatively more serious in different land use. The EFG technique used confirmed the anthropogenic influence of heavy metal pollution. All metals showed concentrations substantially higher than their background values, suggesting anthropogenic pollution.

Comparative evaluation of the most common kriging techniques for measuring mineral resources using Geographic Information Systems

This study evaluates and compares the performances of ordinary, simple, universal, and disjunctive kriging techniques for measuring mineral resources using geographic information systems. These techniques differed in terms of their relative complexities, underlying assumptions, and analytical goals. The methodology consisted of selecting the best kriging techniques, based on their performances in the validation stage, for estimating the depth, thickness, and mass of a mineral resource by interpolating four surfaces representing the surface topography, mineral resource grade, and elevations of the upper and lower surfaces of the mineral resource. The methodology was tested on a phosphate layer detected in the Al-Abiad Mine in Jordan. The total measured phosphate resources were found to be about 1.3 million metric tons. They existed at depths varying from 6.9 to 19.4 m below the ground surface and had thicknesses ranging from 0.2 to 2.3 m. However, it can be concluded that the more complex the spatial behavior of the surface, the more complex is the kriging technique needed to interpolate that surface. Moreover, the deeper and thicker the mineral resource and the denser the spatial distribution of the exploration boreholes, the larger are the relative accuracies of the chosen kriging techniques for interpolating the required surfaces and the greater are the relative accuracies of the estimated depth, thickness, and mass of the mineral resource.

Application of cross-validation technique for zoning of groundwater levels in Shahrekord plain

Water is one of the essential natural resources for the development of life on the earth. In this study we apply Disjunctive Kriging (DK) and Radial Basis Functions (RBF) for zoning of groundwater levels. In study area the groundwater levels data have high skewness. Due to samples unsuitable distribution, data was normalized using logarithmic and QQPlot methods. Also geostatistical different methods were evaluated using cross-validation technique. Results showed that Disjunctive Kriging (DK) compared to Radial Basis Function (RBF) has the higher accuracy and the best model of Semivariogramis Exponential model. Also the groundwater levels decreases from north to south of the Shahrekord plain, Iran. Finally, Disjunctive Kriging was selected as the most appropriate method of investigation for the groundwater levels zoning Sahrekord plain.

Spatial assessment of soil salinity in the Harran Plain using multiple kriging techniques

The Harran Plain is located in the southeastern part of Turkey and has recently been developed for irrigation agriculture. It already faces soil salinity problems causing major yield losses. Management of the problem is hindered by the lack of information on the extent and geography of the salinization problem. A survey was carried out to delineate the spatial distribution of salt-affected areas by randomly selecting 140 locations that were sampled at two depths (0 to 30 and 30 to 60 cm) and analyzed for soil salinity variables: soil electrical conductivity (EC), soluble cations (Ca(2+,) Mg(2+), Na(+), and K(+)), soluble anions (SO (4) (2-) , Cl(-)), exchangeable Na(+) (me 100 g(-1)) and exchangeable sodium percentage. Terrain attributes (slope, topographical wetness index) were extracted from the digital elevation model of the study area. Variogram analyses after log transformation and ordinary kriging (OK) were applied to map spatial patterns of soil salinity variables. Multivariate geostatistical methods-regression kriging (RK) and kriging with external drift (KED)-were used using elevation and soil electrical conductivity data as covariates. Performances of the three estimation methods (OK, RK, and KED) were compared using independent validation samples randomly selected from the main dataset. Soils were categorized into salinity classes using disjunctive kriging (DK) and ArcGIS, and classification accuracy was tested using the kappa statistic. Results showed that soil salinity variables all have skewed distribution and are poorly correlated with terrain indices but have strong correlations among each other. Up to 65 % improvement was obtained in the estimations of soil salinity variables using hybrid methods over OK with the best estimations obtained with RK using EC(0-30) as covariate. DK-ArcGIS successfully classified soil samples into different salinity groups with overall accuracy of 75 % and kappa of 0.55 (p < 0.001).

Using Disjunctive Kriging as a Quantitative Approach to Manage Soil Salinity and Crop Yield

Disjunctive kriging (DK) is a nonlinear geostatistical model that provides unbiased estimates of the conditional probability (CP) that the true value of the property of interest does not exceed a defined threshold. It has important implications in aiding management decisions by providing growers with a quantitative input that can be used for evaluating the variability of the crop productivity at different zones in fields. The objectives of this study are (1) to identify the yield potential percentage (YP%) for several crops at different zones in fields under multiple soil salinity thresholds; (2) to evaluate the YP% of whole fields for several crops under multiple soil salinity thresholds; and (3) to provide guidelines to help growers decide which crops to grow. To achieve these objectives, the DK technique was applied to data from a project conducted in the southeastern part of the Arkansas River Basin in Colorado to generate CP maps. Two data sets of soil salinity (316 and 136 points) that were collecte...

Risk Zone Mapping of Lead Pollution in Urban Groundwater

Groundwater samples (n = 230) were collected from various parts of the Karachi City (Pakistan), Karachi is an urban coastal City situated at the southern most part of the Pakistan along the Arabian Sea. The groundwater samples were subjected to electrothermal atomic absorption spectroscopy (EAAS) for the analysis of Pb. Variable Pb levels were observed in groundwater samples from different parts of the city. The relative higher concentrations of Pb were found in the industrial area of the Lyari River vicinity and along the coastal belt. GIS risk zone model based on disjunctive kriging were generated and areas associated with higher risk for Pb contamination were classified on the map. The outcomes of the study stressed that GIS spatial analysis could be a useful tool for the assessment and forecasting of health risk in complex urban environmental setup.

Understanding the Dynamics of Transfer of Satellite Rainfall Error Metrics From Gauged to Ungauged Satellite Gridboxes Using Interpolation Methods

Knowledge of error characteristics of high resolution satellite rainfall data at different spatial/temporal scales is useful, especially when the scheduled Global Precipitation Mission (GPM) plans to provide High Resolution Precipitation Products (HRPPs) at global scales. Satellite rainfall data contain errors which need ground validation (GV) data for characterization, while satellite rainfall data will be most useful in the regions that are lacking in GV data. Therefore, a critical step to bridge this gap is to assess spatial interpolation schemes for transfer of the error characteristics from GV regions to non-GV regions. In this study, a comprehensive assessment of kriging methods for spatial transfer (interpolation) of error metrics is performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method is also performed to quantify the added benefit (if any) of using geostatistical methods. Four commonly used satellite rainfall error metrics are assessed for transfer to non-GV satellite gridboxes: Probability of Detection (POD) for rain, False Alarm Ratio (FAR), bias (BIAS), and Root Mean Squared Error (RMSE). Results show that performance of a kriging scheme is strongly sensitive to the timescale for which the errors are interpolated (monthly and weekly) wherein the extent of coverage by GV data plays an equally sensitive role. While most kriging techniques perform well according to correlation measure at climatologic timescales for a range of GV data coverage, only DK and OK appear to retain accuracy at the shorter timescales (monthly and weekly). However, scalar assessment metrics such as mean and standard deviation of error (i.e., difference between true and interpolated errors) reveal a completely different picture of accuracy of each interpolation method. In terms of such assessment measures, the overall performance ranking of the kriging methods is as follows: OK=DK >; IDW >; IK. Assessment of kriging methods also revealed that the transfer accuracy is sensitive to error metric type. The ranking of error metrics with highest accuracy in transfer is: POD >; FAR >; RMSE >; BIAS. Overall, the assessment of kriging methods revealed that these best linear unbiased spatial estimators may not be appropriate transfer methods for transfer of satellite rainfall error metrics at time scales shorter than a week. It is worthwhile now to pursue more non-linear transfer methods (such as neural networks) and other kriging methods that use additional spatial information on the rainfall process (such as co-kriging) to further constrain the interpolation uncertainty.

Application of spatial statistics as a screening tool for sustainable flood retention basin management

AbstractIn the context of climate change and the EU flood directive, this paper analyses and explores sustainable flood retention basins (SFRB) as adaptive structures contributing to water resources management and flood risk control. A dataset of 371 potential SFRB (including many operating reservoirs) characterized by 40 variables have been surveyed across central Scotland. However, the spatial properties of these SFRB, such as water storage (which relates to flooding depth) in different regions, are ambiguous. This paper uses geostatistics on the Scottish dataset. Spatial analysis showed that ordinary kriging, which is a spatial interpolation method, could be successfully applied to estimate numerical values for all key flood control variables everywhere in the study area. Moreover, the probability that certain threshold values relevant to flood control managers were exceeded can also be calculated by using disjunctive kriging. The findings provide an effective screening tool in assessing flood control using SFRB.

Geostatistics for radiological evaluation: study of structuring of extreme values

Geostatistics applied to radiological evaluation of nuclear premises provides sound methods to estimate radiological activities, together with their uncertainty. Quantification and risk analysis of contaminated areas are initially performed by applying geostatistical methods relying on the multi-Gaussian assumption. However, the application of the classical bi-Gaussian model for disjunctive kriging proves sub-optimal due to the spatial structuring of high and low values. The beta model which pertains to the class of Hermitian isofactorial models is potentially better suited to radiological evaluation as it allows a continuous evolution from a mosaic to a pure diffusive model. In the test case, disjunctive kriging estimates are obtained by applying in turn the beta model and the pure diffusive model. The comparison of estimation outcomes shows rather limited differences, primarily located in and around the homogeneous contaminated areas.

Assessing the Spatial Variability of Total and Available Cadmium in Soils of the Angouran Area, NW Iran

This study characterized and mapped the spatial variability patterns of total and available cadmium in soils of the Angouran area by geostatistical methods. Multivariate statistical techniques were also used to determine the significant factors influencing the spatial distribution. Results from the spatial analysis and ordinary kriging-interpolated maps showed that the two variables under investigation have different spatial structure dependences and opposite spatial distribution patterns. This distribution is a result of changes in the soil properties induced by cultivation practices in farmland. The estimated probability maps created by disjunctive kriging also indicated that the probability of exceeding the threshold value for available Cd (0.8 mg/kg) is high in farmland where total cadmium concentrations are low. The discriminant analysis conducted in this study revealed that the two main land use patterns (farmland and pasture) are different in terms of available cadmium concentrations. Results from the two-way ANOVA showed that soil pH was the most important factor controlling the availability of cadmium in soils. Due to obvious decreases in soil pH caused by extended use of ammonium-based fertilizers on the farmland, unavailable cadmium in soil has apparently became more available. This study concluded that precision agriculture strategies should be adopted in the study area to minimize the environmental impacts of some agricultural practices.

Heavy metals assessment and identification of their sources in agricultural soils of Southern Tehran, Iran

A detailed investigation was conducted to evaluate heavy metal sources and their spatial distribution in agricultural fields in the south of Tehran using statistics, geostatistics, and a geographic information system. The content of Cd, Cu, Co, Pb, Zn, Cr, and Ni were determined in 106 samples. The results showed that the primary inputs of Cr, Co, and Ni were due to pedogenic factors, while the inputs of Zn, Pb, and Cu were due to anthropogenic sources. Cd was associated with distinct sources, such as agricultural and industrial pollution. Ordinary kriging was carried out to map the spatial patterns of heavy metals, and disjunctive kriging was used to quantify the probability of heavy metal concentrations higher than their recommended threshold values. The results show that Cd, Cu, Ni, and Zn exhibit pollution risk in the study area. The sources of the high pollution levels evaluated were related to the use of urban and industrial wastewater and agricultural practices. These results are useful for the development of proper management strategies for remediation practices in the polluted area.

Spatial distribution and mapping of risk elements pollution in agricultural soils of southern Tehran, Iran

In order to evaluate risk elements and their spatial distribution in agricultural fields south of Tehran, statistics, geostatistics and geographic information system (GIS) were used. The content of Hg, As, Pb, Mo, and Be were determined in 106 samples. The results showed that primary inputs of As and Hg were due to anthropogenic sources, while Pb, Mo and Be were associated with pedogenic and anthropogenic factors. Ordinary kriging was carried out to map the spatial patterns of risk elements and disjunctive kriging was used to quantify the probability of risk elements concentrations higher than their guide value. The results show that As, Hg, Mo and Be exhibit pollution risk in the study area. The high pollution sources evaluated were related with usage of urban and industrial wastewater for agricultural practice. The results of this study are helpful for risk assessment of environmental pollution for decision making for vegetable production and ecosystem improving.