Groundwater is the main water resource for agricultural demands in arid and semiarid regions. An Sustainable agriculture requires a precise management and scheduling on utilizing these resources which in turn needs adequate knowledge about spatial variability of groundwater level for a given time period. As traditional interpolation methods do not consider spatial correlation between groundwater level observations, geostatistical methods are used for spatial variability analysis and mapping of groundwater level. In this study first a semivariogram is used to investigate the spatial correlation of groundwater level data from 59 observation wells in Kuhpayeh-Sagzi aquifer (Esfahan Province). Semivariogram analysis was performed for groundwater level data from 2002 to 2009 and for wet (Ordibehesht) and dry (Mehr) seasons. Also Kriging is used to interpolate groundwater level data over the study area and the results are compared with those achieved by inverse distance weighing method. Geostatistical analysis is performed using GS+. Based on results obtained in this study, the best semivariogram model for groundwater level for all time periods was spherical. Moreover the ratio of nugget effect (C0) to Sill showed that groundwater level data are strongly correlated over space for all years and for both wet and dry seasons. The smallest range of influence (36850 m) was found for wet season in 2002-2003 and the largest range of influence (40220 m) was found for dry season in 2007-2008. The cross-validation results showed the better performance of ordinary Kriging in comparison to inverse distance weighting. Based on the generated maps, the lowest groundwater level was seen in southeast and highest groundwater level was seen in center, south and southwest of the study area.

Saturated hydraulic conductivity and the other hydraulic properties of soils are essential vital soil attributes that play role in the modeling of hydrological phenomena, designing irrigation-drainage systems, transportation of salts and chemical and biological pollutants within the soil. Measurement of these hydraulic properties needs some special instruments, expert technician, and are time consuming and expensive and due to their high temporal and spatial variability, a large number of measurements are needed. Nowadays, prediction of these attributes using the readily available soil data using pedotransfer functions or using the limited measurement with applying the geostatistical approaches has been receiving high attention. The study aimed to determine the spatial variability and prediction of saturated (Ks) and near saturated (Kfs) hydraulic conductivity, the power of Gardner equation (α), sorptivity (S), hydraulic diffusivity (D) and matric flux potential (Фm) of a calcareous soil.
Material and The study was carried out on the soil series of Daneshkadeh located in the Bajgah Agricultural Experimental Station of Agricultural College, Shiraz University, Shiraz, Iran (1852 m above the mean sea level). This soil series with about 745 ha is a deep yellowish brow calcareous soil with textural classes of loam to clay. In the studied soil series 50 sampling locations with the sampling distances of 16, 8 , and 4 m were selected on the relatively regular sampling design. The saturated hydraulic conductivity (Ks), near saturated hydraulic conductivity (Kfs), the power of Gardner equation (α), sorptivity (S), hydraulic diffusivity (D) and matric flux potential (Фm) of the aforementioned sampling locations was determined using the Single Ring and Droplet methods. After, initial statistical processing, including a normality test of data, trend and stationary analysis of data, the semivariograms of each studied hydraulic attributes were calculated in various directions and their surface semivariograms were also prepared to determine the isotropic or anisotropic behavior of each studied soil attributes. Since all of studied soil hydraulic attributes were isotropic variables, therefore, the omnidirectional semivariograms were calculated and different theoretical models were fitted to them. The best fitted semivariogram models were determined using the determination coefficient, R2, and the residual sum of the square, RSS. The parameters of the best fitted models to the experimental semivariograms were also determined. The prediction of study hydraulic attributes was carried out using the parameters of semivariogram models by applying the ordinary Kriging approach. Predictions were also carried out using the Inverse Distance Weighing approach. The results of predictions were compared to each other using the Jackknifing evaluation approach and the suitable prediction method was determined and zoning was performed using the results of introducing prediction method. All of the semivariogram calculations and modeling, prediction of zoning of study hydraulic attributes were performed using the GS 5.1 software packages.
Results indicated that all of the studied soil hydraulic attributes belonged to the weak to moderated spatial correlation classes and the spherical model was the best fitted model for their semivariograms (except for Kfs and D that their best semivariogram models were exponential). The sill of all semivariograms ranged between 0.0003 to 0.419 for the S and Kfs, respectively. The nugget effects and the Range parameter of all semivariograms were located between 0.00015 to 0.108 for the S and Фm, and 211 to 6.4 m for Ks and D, respectively. Results also indicated that 3.5 and 50% of total variation of D and Ks was spatially structured and the other was random, respectively. The spatial correlation classes of near saturated soil hydraulic conductivity and soil hydraulic diffusivity were week, whereas, the spatial correlation classes of the other studied soil hydraulic attributes were moderate. Results revealed that the Inverse Distance Weighting method was the most suitable approach for the prediction of all studied soil hydraulic attributes in the present study. Comparison of the calculated statistical evaluation measures (i.e. Determination coefficient, R2, Mean residual error, MRE, mean square error, MSE, Normalized mean square error, NRMSE and geometric mean error ratio, GMER) and the final determined order of precision showed that the most and the least accurate predictions were obtained for Ks and Фm, respectively.
It is suggested in the cases that we need to map the hydraulic attributes or need their quantities in a large number; geostatistical prediction be performed using the limited measurements to reduce the needed time and costs.

Groundwater is always considered one of the important water resources, especially in arid and semi-arid regions of the world, such as Iran. In recent decades, it has decreased drastically due to excessive use. The objective of this study was to determine the best interpolation method and evaluation of the spatiotemporal variations for the groundwater level in the Sahneh-Biston plain of Kermanshah province during three decades from 1991 to 2020. At first, four Gaussian, linear, spherical, and power semi-variograms were obtained for observations. Then, the best semi-variogram and interpolation methods were selected among the evaluated methods for zoning the groundwater level in the region. The lowest value of the sum of RMSE, MBE, and MAE error criteria and the highest coefficient of determination (R2) between observations and estimates in all three decades and the average of the entire period were calculated and considered to evaluate the most appropriate semi-variogram and interpolation methods for spatial distribution. The results showed that the ordinary kriging method with Gaussian semi-variogram is the best method to estimate the groundwater level in the Sahneh-Biston plain. The average difference between the minimum and maximum groundwater levels based on the observation wells of the study area and the zonation method is from 1279 to 1372 meters and 1289 to 1409 meters during the studied period time, respectively. The groundwater level is placed in more depth with the proximity to the central and southern regions. The maximum decrease and increase of groundwater level variations have been 12 and 19 meters during three decades, respectively. Also, the underground water level variations during these three decades showed that both the second and third decades compared to the first decade and the third decade compared to the second decade have increased in more than 50% of the region. This increase can be caused by the optimum management and water use in these years. Therefore, groundwater level monitoring provides effective help for experts and users in planning and optimal management of groundwater for the sustainable development of water resources.

This research, carried out in order to evaluation of the inverse distance weighting method and kriging, (ordinary and lognormal kriging) for estimate Organic carbon and Bulk density in paddy fields of the Iranian Institute of Rice Research in Rasht. Spatial variability characteristics of variables were determined by semivariograms. The function used for quantifying the structure of regional variable. Estimation of Kriging carried out by 6 than 40 neighbors in 70 percentage range of search radius. For estimation variable used to method inverse distance weighting of exponent value 1 than 5. The best models for organic carbon and bulk density were spherical. Four statistics of mean error, root mean square error, reduced variance and percent error were used to compare the methods. Exponent value was in the estimation inverse distance weighting for Organic carbon 1 and Bulk density 4. Results show that kriging is the accuracy better of inverse distance. Beside the best estimator was ordinary kriging for Organic carbon and lognormal kriging for Bulk density.

Isohyetal map is the prerequisite of hydrology, meteorology and climatology studies. Precipitation distribution in a region is related to regionalization method of precipitation data. Khuzestan elevation fluctuates from sea level up to 3712 meter while the elevations of meteorological stations fluctuate from 3 meter up to 875 meter. Due to the complex topography of Khuzestan province and the lack of high elevation meteorological stations with long-term data, it is necessary to determine the appropriate interpolation method for monthly and annual precipitation data in this region. In this study, in order to determine the best method for regionalization of precipitation data, seven interpolation methods were compared together. These methods are ordinary kriging, Cokriging, kriging with external drift, regression kriging, inverse distance weighting, spline and three-dimensional linear gradient. The monthly average and annual long-term data were used from 37 meteorological stations (synoptic, climatology and rain gage) over the 22-year period (1984-2005). In variography analysis, five variogram models (spherical, exponential, Gaussian, linear and linear to sill) were fitted to precipitation data and the best one was selected based on higher correlation coefficient and higher structured component to unstructured ratio. Cross validation technique was used to compare the interpolation methods and the best one was chosen based on regression analysis, and calculation of some error indices like as root mean square error and mean bias error. The probability distribution of precipitation data were tested for normality with Anderson Darling (AD) method. The results showed that precipitation data had normal distribution throughout the year except January and December. Non-normal data in other months were normalized with logarithmic transformation. Variography analysis results showed that structured component in more than 85% of the months was more effective than unstructured component. Our results confirmed that precipitation data had strong spatial structure. Effective ranges of precipitation data vary from 81.1 Km (in warm months) to 250.3 Km (in cold months). Also spatial structure of warm months was weaker than cold months. The goodness of fit results for different variogram models showed that the optimal model was the spherical model. These results were obtained based on evaluation of different interpolation • The optimum power in Inverse Distance Weighting method among the five powers (1-5) was the power 3. It was also found that in this method the variation of adjacent point’s number does not have significant differences in results. • The Cokriging method was removed from calculations, because spatial correlation was not strong enough in cross variogram models for different months,. • Altitude variable and altitude, longitude, latitude variables were selected as covariate variables in kriging with external drift and regression kriging methods, respectively. • The results of three-dimensional linear gradient method showed that meridional, zonal and altitudinal gradients are positive in all months. In other words, precipitation increase from west to east and south to north of region and also increase with increase in altitude. • Selection of regression kriging and kriging with external drift methods as the best methods based on the regression analysis showed that there is a consistency between results of these methods with real data. So that it can be considered as a result of using elevation as covariate variable. • Regression kriging was selected as the best interpolation method in monthly precipitation data based on error indices and regression analysis results in Khuzestan province. • In annual precipitation data, Regression kriging and ordinary kriging methods were selected as the best interpolation methods based on regression analysis and calculation of error indices. But precipitation of highland area was underestimated by using ordinary kriging method. Considering the importance of precipitation in the highland area and slight difference of root mean square error between these two methods, regression kriging was selected as the best interpolation method for annual precipitation data. In this study, long-term weighted average of annual precipitation data in Khuzestan province was calculated by using regression kriging. It was 391 mm, which is 41 mm more than the amount reported by the Iran meteorological organization. Among the interpolation methods which were investigated in this study, regression kriging method is introduced as the most suitable interpolation method in Khuzestan province for monthly average and annual precipitation data. The average annual precipitation obtained from regression kriging map was 41 millimeter more than the average reported by the Iran Meteorological Organization. This difference is due to accurate estimation of precipitation over highland area of this region.

Determining the variability of soil parameters is a necessity for precision agriculture. To achieve higher yield with better management، knowledge of physico-chemical properties of soil in the fields is essential. Geostatistics is one of the methods developed for investigating the spatial variability of soil properties. For this purpose، 188 soil samples were taken from the Eastern farms of Mazandaran province in 2009. Soil samples were analyzed and the amounts of organic carbon (OC)، P، K، Fe، Mn، and Cu were determined. The spatial correlation of variables and the best fitted model were determined by variogram. Analysis indicated that OC، K، P، and Mn were best fitted to Gaussian model. Also، Fe and Cu were best fitted to exponential and spherical models، respectively. The effective ranges of these parameters were 58، 26، 58، 5، 58، and 3 km، respectively. In order to determine the distribution map، Kriging، Inverse Distance Weighted (IDW) and Splines (RBF) methods were used. The precision of interpolations were calculated using mean base error (MBE)، mean absolute error (MAE)، and root mean square error (RMSE). The results showed that kriging method had a higher accuracy compared to IDW and RBF. Kriging was the best method to estimate OC، P، K، and Cu because it had the highest precision and lowest error. IDW and RBF had the highest precision for estimation of Mn and Fe، respectively، in this area.

The knowledge about spatial variability of precipitation is a key issue for regionalization in hydro-climatic studies. Measurements of meteorological parameters by the traditional methods require a dense rain gauge network. But, due to the topography and cost problems, it is not possible to create such a network in practice. In these cases the spatial distribution pattern of precipitation can be produced using different methods of interpolation. Interpolation could be done only based on the data of the main variable (i.e. through univariate methods) or on the information obtained from both the main and one or more auxiliary variables (i.e. through multivariate methods). The classical interpolation methods such as arithmetic mean and linear regression (LR) methods are independent of the spatial relationship between observations, while geostatistical methods (such as kriging) use the spatial correlation between observations in the estimation processes (Isaaks and Srivastava, 1989). The previous studies showed that the choice of interpolation method depends on data type, desired accuracy, area of interest, computation capacity, and the spatial scale used. Hence, different interpolation methods, including geostatistical methods (OK, SK, Sklm, KED, UK and COK), univariate deterministic methods (IDW, LPI, GPI and RBF) and linear regression (LR) were compared to estimate monthly and annual precipitation in Sistan and Baluchestan Province. The auxiliary variables used in the multivariate approaches were DEM, distance to Sea and spatial coordinates. Study area Sistan and Baluchistan Province is located in southeast of Iran and covers an area of 181471 km2. It is located between the latitudes 25˚03ʹand 31˚27ʹN and the longitudes 58˚50ʹ and 63˚21ʹE. The precipitation data collected from 50 precipitation stations over the same period of 25 years (1988-2012) were used in this study. Interpolation methods Detailed description of geostatistical interpolation methods used in this study including OK, SK, Sklm, KED, UK and COK are provided in the variety of resources, such as Goovaerts (1997) and Deutsch and Journel (1998). In geostatistics the most important tool for investigating the spatial correlation between observations is the semivariogram. In practice, experimental semivariogram is calculated from the following equation: (1) where is the experimental semivariogram, N(h) is the total number of data pairs of observations separated by a distance h, Z(ui) and Z(ui+ h) are the observed values of the variable Z in locations ui and ui +h, respectively. After calculating experimental semivariogram, the most appropriate theoretical model is fitted to the data. Unknown values are estimated using the semivariogram model and a geostatistics estimator. Comparison method and evaluation criteria To assess the accuracy of interpolation methods and the best method for estimating precipitation, cross-validation technique is used (Isaaks and Srivastava, 1989). Evaluation criteria are including the Root Mean Square Error (RMSE) and the Mean Bias Error (MBE). Statistical analysis showed a high coefficient of variation of precipitation in August, September and July. Kolmogorov-Smirnov test showed that precipitation data are normally distributed over the study area. The precipitation semivariogram was considered isotropic as a little change was seen for different directions. Results of autocorrelation analysis showed a high spatial correlation of precipitation in all periods (except for January and February) with a spherical semivarioram model. This confirms the results of previous studies (Lloyd, 2005; Haberlandt, 2007; Mair and Fares, 2010). The maximum sill was observed for months January, February and March with a higher amount of mean and variance. The maximum radius of influence was seen for January (511 km) followed by May (205 km). The performance of UK was evaluated using the trend function of the first and the second order polynomial. The evaluation results indicate that the first order polynomial is the more accurate one. The cross validation results showed that the best method for precipitation estimation was linear regression (precipitation versus elevation) for April, KED for May, UK for June and September, RBF for July, August, October, December, January, February and annual precipitation and SK for November and March. The LPI and GPI methods did not perform well in any of the time periods. This could be possibly due to large changes in surface topography of province. RBF method had the highest accuracy in most of the periods. The estimated values in this method are based on a mathematical function that minimizes total curvature of the surface, generating quite smooth surfaces (Zandi et al., 2011). Geostatistical methods had the highest accuracy for other periods. One of the reasons for good performance of geostatistical methods may be due to the low density of the meteorological stations. It confirms other researchers’ results (Creutin and Obled, 1982; Goovaerts, 2000). The use of elevation as covariate has improved the estimation results only for April and May. However, the distance to Sea did not improve the estimation results in any cases. The reasons for little improvement of the precipitation estimation through the multivariate methods could be due to the complex topography, low density of meteorological stations, and low correlation between precipitation and covariates. Geostatistical interpolation methods, in deterministic and linear regression methods, were evaluated for precipitation data in Sistan and Balouchestan province. According to the results of cross-validation, linear regression (elevation- precipitation) for April, geostatistical methods for May, June, September, December and March and RBF method for other periods had the highest accuracy. According to the estimation error maps produced by the geostatistical methods, the highest estimation errors were seen in the area with a low density of stations and the boundaries of the province. These areas are recommended for developing the meteorological network in the future. Also, due to the variability of climate, distance from Oman Sea and changes in the surface topography for the precipitation stations, we recommend that the province is divided into more homogeneous regions and the proposed approaches are investigated in each section, separately.

In most of hydrometeorological studies and water resources management, flood and drought forecasting, irrigation planning and climate change studies, access to rainfall data and especially its spatial distribution (precipitation map), are of particular importance. Different models are used for spatial interpolation of rainfall data that generally fall into two categories of statistical and geostatistical methods. In statistical methods, interpolation is based on linear and nonlinear regression between main variable and covariate, but in geostatistical methods such as Kriging, spatial correlation of the sampled points is take in to account. There are many problems with spatial estimation of rainfall data especially in complex topography. Using correlated covariates is one of the answers to overcoming this problem. The altitudinal range of Mazandaran province fluctuates between -61 to 5610 meters, which creates various climates in this province. Besides, presence of the Caspian Sea in the north and Alborz Mountains Range in the south of the province make further complicates in spatial rainfall estimation, especially in the impassable heights of the province, which are a major water resource for large rivers. Since the elevated meteorological station in Mazandaran province is located on 2134 m, no rainfall data is available in area between 2134 to 5610 meters. So, this study was aimed to compare four interpolation methods include inverse distance weighting, Kriging, Co-kriging, and three-dimensional linear gradient. Also in this study, the role of covariates in precipitation estimation was investigated. Spatial data interpolation methods are used to estimate a variable at a particular point from actual data measured at adjacent points. The Inverse Distance Weighting method obtains the unknown quantity and performs the interpolation, by weighting the data around the estimated point. The interpolation methods use a set of points with known values around points with unknown data to estimate their values. This method is based on a geographical law that each phenomenon is related to other phenomena, but more depended to the close phenomena. Kriging as an advanced interpolation method is suitable for data with locally defined trends. This method can interpolate with the least variance of estimation that its error rate depends on the variogram specification. Co-Kriging is a suitable method when a covariate is present in all parts of network. In 3D Linear Gradient method, it is assumed that there is a linear trend along the length, width, and height of the region. In this study, in order to evaluate different interpolation methods of rainfall (Inverse Distance Weighting, Kriging, Co-Kriging, 3D linear gradient) the data from 25 synoptic and rain gauge stations were used in Mazandaran province. Surveying the statistical period of stations (1991-1991), the data of 2012 used to select the best interpolation method. Since the height of stations in Mazandaran province varies between -2120 and -21 m, precipitation data is not available for altitudes above 2200 meters. Therefore, altitude variable was used as an auxiliary variable in this study to obtain the most accurate estimation of altitude rainfall. In this study GS + and Mini tab software was used to calculate the estimated values of the models, Arc GIS software to prepare maps and Excel software for other calculations. Root Mean Square Error and Mean Bias Error were used to select the best interpolation method in this study. In variographic analysis, 5 types of semivariable models (Spherical, Gaussian, exponential, Linear and Linear to Sill models) were fitted to the data. The coefficient of determination and the ratio of structural changes to total variations were used to select the best half-variance. The best-chosen model has closer amounts of the coefficient and ratio to the number one. P-value and correlation coefficient were used to select the best covariate. Due to the importance of auxiliary variables in spatializing precipitation data, the variables of latitude, longitude, and altitude were used for the three-dimensional gradient equation. In order to better understanding of the studied methods, the map of annual precipitation changes in the province was plotted with different methods; then comparing them, the best rainfall map was selected. In this study, in order to determine the best interpolation method for monthly and annual precipitation data of Mazandaran province, four interpolation methods (Inverse Distance Weighting, Kriging, Co-kriging and three-dimensional linear gradients) were compared. Examination of Root Mean Square Error and Mean Bias Error revealed that the best interpolation method for long-term monthly precipitation was the 3D linear gradient method. But, the problem with this method and the other investigated methods in this study was overestimation of precipitation in high and low estimation stations in coastal and plain areas of the province. The overestimation was occured due to the lack of the number of station above altitudes of 2000 m in Mazandaran province. Therefore, the estimation of precipitation in the province's highlands had error. The outcomes of the best semicircle model in this study showed that the best models (except for July with low coefficient of determination) were spherical and exponential models. The results also showed that in hot months the spatial structure of precipitation data became weaker. Also, the impact of precipitation data in this province is about 30 km. The outcomes of correlation between monthly and annual precipitation data with latitude, longitude and altitude revealed that the altitude parameter had a significant correlation with other auxiliary parameters (latitude and longitude), in all months except July. Also, the correlation of latitude and longitude variables with precipitation was significant in some months. Therefore, it can be concluded that altitude parameter was the best auxiliary variable among the others to estimate monthly and annual rainfall in Mazandaran province. Distribution graph of annual rainfall variations with altitude along with regression equation indicated relatively good fit of linear equation to altitude rainfall fluctuations. Based on the results, the importance of the role of latitude and longitude variables for spatial precipitation data was determined. Therefore, latitude, longitude, and altitude variables were used for the three-dimensional gradient equation. Survey of annual precipitation maps showed that the three-dimensional linear, Co-Kriging and gradient methods had the most reasonable estimation of the spatial variability of precipitation in the province. According to the rainfall-altitude diagram, the average rainfall in the province is reduced to 500 mm of annual rainfall per 1000 meters. From the annual precipitation map survey with the selected method, it can be seen that only the western coasts of the province experience more than 1000 mm of rainfall per year. The slope of rainfall variations with altitude in the west of the province is more than east and due to the complex topography of the west of the province the west coast has more rainfall than the western altitudes.

Evaluation of changes in groundwater quality and sustainable management of water resources is of crucial importance in plains. In this regard, the importance of information about the quality of groundwater for various uses is time-consuming and expensive involving data collection. The survey of conventional estimators to find the best parameters, through which other parameters can be derived at lower costs, is essential. In this study, the data collected from 94 production wells in the Dezful Plain, namely: SAR, Na, Ca, TDS, Ec and TH, are used to check the status of the groundwater quality of the plain and select the best procedure for estimating the parameters studied by geostatistial methods. The results indicated that the Cokriging method with the Gaussian variogram and cross variogram models were the best geostatistical based on the highest R2 and lowest NMAE and NRMSE. These parameters were then employed to prepare a map showing the water quality in the specified zone. The results of the zoning maps indicate that the quality of groundwater resources in parts of the southeastern and eastern regions of the plain is not satisfactory for drinking and irrigation.

To study on competence of nonparametric geostatistical models including Indicator Kriging, Probability Kriging, Indicator Cokriging and Probability CoKriging, in zoning the probability of presence of Persian oak (Quercus brantii Lindl) regeneration in a forest stand to suggest the most suitable model and produce its related map, a forest stand with an area about 200 ha in nearby Yasouj was inventoried. Using a systematic random grid, 150 m by 250 m, general and silvicultural characteristics of the forest stand were inventoried in circular sample plots with an area of 1000 m2. the number of Persian oak regeneration were counted
To study on competence of nonparametric geostatistical models including Indicator Kriging, Probability Kriging, Indicator Cokriging and Probability CoKriging, in zoning the probability of presence of Persian oak (Quercus brantii Lindl) regeneration in a forest stand to suggest the most suitable model and produce its related map, a forest stand with an area about 200 ha in nearby Yasouj was inventoried. Using a systematic random grid, 150 m by 250 m, general and silvicultural characteristics of the forest stand were inventoried in circular sample plots with an area of 1000 m2. the number of Persian oak regeneration were counted in four small-circular plots with a radius of 1.55 m located with a distance of nine meters from the center of the main plots in line with the four main geographic directions. Using Geostatistic Analysis in ArcGIS10.2, the models of circular, spherical, tetraspherical, pentaspherical, exponential, gaussian, rational quadratic, hole effect, k-bessel, J-Bessel and stable were fited on the variogram. The cross validation method was used to evaluate the accuracy of the model. The results showed that the pantaspherical model of probability kriging have the strongest spatial structure (75.63%) and the highest level of credit in aspect of accuracy, ME (-0.0106), ASE (0.4424), RMSE (0.4470) and RMSS (1.0113) and would be suggested as the suitable model. After drawing semivariogram of regenerations and fixing the suggested model on that, they indicated on anisotropy in semivariogram quantity.
four small-circular plots with a radius of 1.55 m located with a distance of nine meters from the center of the main plots in line with the four main geographic directions. Using Geostatistic Analysis in ArcGIS10.2, the models of circular, spherical, tetraspherical, pentaspherical, exponential, gaussian, rational quadratic, hole effect, k-bessel, J-Bessel and stable were fited on the variogram. The cross validation method was used to evaluate the accuracy of the model. The results showed that the pantaspherical model of probability kriging have the strongest spatial structure (75.63%) and the highest level of credit in aspect of accuracy, ME (-0.0106), ASE (0.4424), RMSE (0.4470) and RMSS (1.0113) and would be suggested as the suitable model. After drawing semivariogram of regenerations and fixing the suggested model on that, they indicated on anisotropy in semivariogram quantity. The map of spatial distribution of regeneration could be an applicable guide in plantation projects in Zagros Region.