spatial variability

Soil penetration resistance (PR) and soil shear strength (SS) are used to evaluate soil erodibility. Some soil properties such sand, silt, clay, bulk and particle density, total porosity, organic carbon and CaCO3 and also some land characteristics such as percentage and direction of slope, altitude, type and density of vegetation can affect SS and PR. For example, PR values exceed 2.5 MPa, while root elongation is significantly restricted. Most of soil properties have temporal and spatial variabilities. Therefore, it is necessary to use geostatistical methods to simultaneously use quantitative information and geographic location of variables. The forest, range and cultivated soils of Fandoghloo region of Ardabil are located in sloping lands and are subject to erosion. Therefore, it is necessary to know the state of spatial variability of soil SS and PR as two important indicators affected by compaction and also effective on soil erosion in the mentioned area. The main objectives of this research were: 1) Investigating the spatial variabilities and drawing maps of soil SS and PR in forest, range and cultivated lands of Fandoghloo region of Ardabil,  2) Investigating the correlations between soil SS and PR with other soil characteristics in the study area,  3) Determining semivariogram parameters such as semivariogram models, spatial dependence classes and effective range for soil variables, 4) Comparison of the accuracy of geostatistical methods (ordinary kriging (OK) and  inverse distance weighting (IDW)) in the interpolation of SS and PR.

 This study was conducted in the forest, range and cultivated lands of Fandoghloo region of Ardabil located at the 25 km of Ardabil city, northwest of Iran (48° 32ʹ 45ʺ to 48° 33ʹ 5ʺ E and 38° 24ʹ 10ʺ to 38° 24ʹ 25ʺ N) at summer 2023. Totally, 80 geo-referenced samples were taken from 0-10 cm soil depth with 50×50 m intervals (15 ha) in cultivated (n=37), range (n=23) and forest (n=20) land uses. Sand, silt, clay, organic carbon (OC) and particle density (PD) were measured in the disturbed soil samples. Bulk density (BD) and field water content (FWC) were measured in the undisturbed soil samples taken by steal cylinders with 5 cm diameter and height. Total porosity was calculated using BD and PD. Soil penetration resistance (PR) was directly measured in the field at three replicates using a cone penetrometer. Soil shear strength (SS) was obtained using shear vane in saturation condition in the field at three replicates. The best fitted semivariograms model (Gaussian, spherical and exponential) was chosen by considering the minimum residual sum of square (RSS) and maximum determination coefficient (R2) for soil variables. Ordinary Kriging (OK) and inverse distance weighting (IDW) interpolation methods were used to analyze spatial variability of soil SS and PR. Spatial distribution maps of soil variables were provided by Arc GIS software. Normality test of data by Kolmogorov–Smirnov test and Pearson correlations were done using SPSS software. Figures were prepared using Excel software. The accuracy of OK and IDW methods in estimating soil SS and PR was evaluated by mean error (ME), mean absolute error (MAE), root mean square error (RMSE) and concordance correlation coefficient (CCC) criteria. The CCC indicates the degree to which pairs of the measured and estimated parameter value fall on the 45° line through the origin.

According to the results of coefficient of variation (CV) from the study area, the most variable (CV=58.3 %) soil indicator was PR in range land use, whereas the least variable (CV= 3.95 %) was PD in cultivated land use. The Pearson correlation coefficient (r value) indicated that there are significant correlations between OC with sand (r=0.59) and FWC (r=0.78) and between PR with SS (r=0.31). Also, significant correlations were found between PR with FWC (r=-0.45) and silt (r=-0.36) and between SS with OC (r=0.38), sand (r=0.48) and silt (r=-0.34). The spatial dependency classes of soil variables were determined according to the ratio of nugget variance to sill expressed in percentages: If the ratio was >25% and <75%, the variable was considered moderately spatially dependent; if the ratio was >75%, variable was considered weakly spatially dependent; and if the ratio was <25%, the variable was considered strongly spatially dependent. The strong spatial dependences with the effective ranges of 752 m was found for PR. The medium spatial dependences with the effective ranges of 787 m was obtained for SS. The silt and FWC variables had the least (636 m) and the highest (2282 m) effective range, respectively. The range of influence indicates the limit distance at which a sample point has influence over another points, that is, the maximum distance for correlation between two sampling point. The models of fitted semivariograms were Gaussian for PR and spherical for SS. The high values of CCC and low values of RMSE values indicated the more precision and high accuracy of OK compared with IDW interpolation method in estimating PR in the studied area. According to the RMSE and CCC values, IDW was better than OK to predict SS. Generally, the spatial maps showed that the highest values ​​of soil PR were observed in range land use and the lowest values ​​of soil SS were observed in cultivated land use of the study area.

Results showed that PR negatively related to the silt and FWC. Also, SS negatively related to the silt and positively related to the sand and OC. The strong spatial dependency was found for PR and medium spatial dependency was determined for SS in the studied area. The silt revealed the smallest effective range (636 m) among the studied variables. As a suggestion, for subsequent study, soil sampling distance could be taken as 636 m instead of 50 m in order to save time and minimize cost.

Soil chemical properties variability and value of their variability have specific importance in sustainable production. Measuring methods of these which usually possible with soil testing, in a large scale are so timing and cost consuming. One of methods which use for monitoring these properties and decrease the costs of sampling in large scale is interpolation. Interpolation has many methods and each one has a different accurate in various conditions. In current research three ordinary interpolation methods were used for interpolation some chemical properties of Khuzestan’s agricultural soils. These variables in this research were Total Nitrogen (TN), Absorbable Phosphorous (P), Absorbable Potassium (AK), Calcium Carbonate percent (CaCo3%), Organic Carbon percent (OC%),  Electrical Conductivity (EC), and Soil Acidity (pH), which measured in 270 soil samples. Due to the skewness and Kurtosis of these data, it was found they have not a normal distribution. In order to normalize the data, after deleting the outdated data, logarithm and Cox-box method were used.   The interpolation methods which used were kriging (OK), Radial Basic Functions (RBF), and Inverse Distance Weighted (IDW). Mean absolute error (MAE), mean bias error (MBE), and root mean square error (RMSE) were used for detecting the optimum method. Examination of variographic results showed that the spatial structure (correlation ratio) of absorbable phosphorus (0.243) and absorbable potassium (0.159), strong, total nitrogen weak (measurement error 0.816) and the other parameters had a moderate spatial structure. Based on the results of this table, the ordinary kriging method with exponential model can be considered as the best and most accurate method (MAE = 0.01515, RMSE = 0.0890, MBE = 0.0006 and R2 = 0.912) for interpolation the total nitrogen.However, the best method for interpolation of organic carbon, absorbable phosphorus, absorbable potassium, calcium carbonate, acidity and electrical conductivity of soil are RBF, ordinary kriging (spherical model), ordinary kriging (spherical model), RBF, ordinary kriging (with exponential model) and RBF respectively.The results showed that the IDW method was not a suitable method for interpolating any of the parameters. From the prepared maps, it can be clearly seen the non-uniformity of fertilization, amount of absorbable phosphorus in the southern parts of the study area is higher but amount of absorbable potassium in the northern and central parts of the study area has been more.While in the eastern and western part of the study area and in places where the pH is above 7.7, the amount of calcium carbonate in soils is at its highest level of 46 to 49 percent. Preparing maps with appropriate accuracy by geostatistical methods for parameters that have good spatial dependence is a suitable method for monitoring and land management at the macro level.

The expansion of cities and the subsequent policy of condensation has made congestion as one of the most important determinants of urban problems. The present study, with a descriptive-exploratory and survey approach, has analyzed the variations of congestion types and their spatial developments in Bijar in two time periods 2006 and 2016. Using statistical block data, trends of index changes and their distribution throughout the city have been studied. Spss, Excel, GIS software was used for statistical analysis and graphical representation of maps. According to the results, there is a direct and significant relationship between population density and building density in Bijar city. The west and northwest boundaries of the city are drawn. In 2006, about 11/10% of the total area and 24/89% of the city population were in the high density of construction area, which in 2016 amounted to 12/13% and 31/59% of the total urban area. According to the results, there is an inverse relationship between congestion and distance from downtown with decreasing congestion distance from downtown. Also, R2 coefficient showed that in year 2006 almost 60% of congestion changes were explained by variable distance from downtown but This has fallen to 95% in 2016, a decrease that reflects the more spatial distribution of neighborhood-level construction in recent times. The results of weight regression also show that three variables of land price in west and southwest, population density in north, central and southwest and distance to neighborhood center in west and southwest are the most important factors affecting The transitions are in the building density of Bijar.

Heavy metals are known to be the most dangerous environmental pollutants because they do not decompose by physical processes and therefore remain for a long time and will be effective in biochemical cycles and ultimately in the human food chain, disrupting biological reactions and damaging organs. And they will even die. Therefore, in order to control the quality of the environment, it is important to study the heavy elements in the soil. So far, much research has been done to identify contaminated areas and implement sustainable land use policies with respect to the risk of contamination. In this study, the spatial distribution of nickel in surface soils (0-10 cm) in parts of Qom province with urban-industrial, agricultural and uncultivated land uses with an area of 883 Km2 was investigated. In this study, geostatistical tools (ordinary kriging) were used. Sampling was performed at 209 points on a grid with distances of about 1.5 × 1.5 km in agricultural and urban land use and about 2×2 km in uncultivated land use. Concentration of total nickel and absorbable soil was measured by atomic absorption spectrometer. Statistical and geostatistical studies were performed by SPSS, Variowin and WINGSLIB software and contamination map was drawn with Surfer16 software. The results showed that the concentration of nickel in any of the forms in the region did not show toxicity. But there were significant differences in land uses. Existing industries, parent materials, and nickel-rich basic and ultra-basic rocks, the use of phosphate fertilizers and sewage sludge may have increased nickel, and the direction of westerly winds has led to the transfer of nickel in the region.

Nowadays, the exploitation of the renewable energy sources such as wind plays a key role in human life. Although, Iran has a high potential for wind power generation, there is not an efficient energy planning yet. Environmental variables such as wind speed vary according to spatial points, so it seems reasonable to consider that there exists a spatial correlation between wind speed data at different locations. In geostatistics the spatial autocorrelation of data could be investigated by calculating the experimental semivariogram. The parameters of the fitted semivariogram model may be then used to better estimate the wind speed at unknown locations through kriging algorithms.
In order to describe the behaviour of wind speed at a particular location, the data distribution should be first fitted by a suitable distribution function. There are different wind speed distribution models used to fit the wind speed distributions over a period of time. Among them, Weibull distribution function has been found to be the best all over the world because of its great flexibility and simplicity.
The aim of this study was to simulate the daily mean and maximum wind speed probability distribution by using Weibull distribution function and to investigate spatial variability of the wind speed data. This study was also aimed to interpolate and map the means of Weibull distribution functions of daily mean wind speed data observed at stations spread over Iran.
Study Area and Data Set
The study is based on a long term (20 years) wind data recorded in 104 synoptic stations spread over Iran. The wind data are recorded at 10m above the ground level (a.g.l.) and contain daily mean and maximum wind speed (m/s).
The Weibull Distribution Function
For each sites, the daily mean and maximum wind speed data were fitted by a two-parameter Weibull distribution, whose parameters (shape and scale) were determined through the maximum likelihood (ML) technique. The Weibull probability density function is defined as follows: where V is wind speed (m/s), 𝑐 is the scale parameter (m/s) and 𝑘 is shape parameter (dimensionless). The high and low 𝑘 values indicate the sharpness and the broadening of Weibull peak, respectively. The Weibull probability density function curve could be draw if the 𝑘 and 𝑐 values are obtained. This could be done through different ways, among which is maximum likelihood method as: where Vj is the wind speed for jth sample and n is the number of sample data. Equation (3) is an implicit equation and could be solved through an iteration method.
Interpolation Two interpolation methods including inverse distance weighing and ordinary kriging were used to estimate the theoretical mean values of the previously determined Weibull distributions of the wind speed data at unsampled locations.
Inverse Distance Weighing (IDW)
In absence of data spatial autocorrelation, IDW is usually used as an alternative method for spatial estimation of random field. IDW is a weighted averaging interpolator in which data is weighted according to their distance to the estimation point such that more distant points get less weight than closer points.
Ordinary Kriging (OK)
OK is the most popular kriging approach used in the spatial interpolation of the regionalized variables. It needs the parameters of the best fitted semivariogram model to incorporate spatial dependence of data into the estimation process. The semivariogram quantifies the dissimilarity between observations as the separation distance between them increases.
According to the obtained results, Semnan and Bandar-Abbass had the lowest and highest shape (k) factor of the fitted weibull distribution functions to the daily maximum wind speed data, respectively. For daily mean wind speed data, Nehbandan and Bandar-Abbass had the lowest and highest shape (k) factor of the fitted theoretical Weibull distributions, respectively. A high k value means less variation of the wind speed.
The annual duration of daily wind velocity of exceeding 4 m/s is also calculated for each site in order to obtain a first diagnostic sign of the most promising areas in terms of wind energy potential. According to the results, Cities of Rafsanjan, Zabol, Torbate Jam, Khodabandeh, Ardebil, Bijar and Kahnouj are of the most potential areas in terms of high wind speed.
The auto-correlation analysis showed that wind speed is moderately correlated in space with spatial structure model of spherical and a correlation distance of about 500 km (Figure 1 (a)). There was no apparent drift within the range of 500 km. The best semivariogram model was selected according to the cross validation results as well as highest correlation coefficient (r) and lowest residual sum of squares (RSS) functionally of GS software.
To predict the spatial distribution pattern of wind speed over Iran, Weibull mean wind speed data were interpolated over a point grid superimposed to the map of Iran by using IDW and OK. The cross validation results showed both methods performed similarly however the maps generated were visually different. Besides, unlike IDW, OK represented the map of estimation error which is useful in decision-making as it is provides a measure of uncertainty.
According to wind speed map generated by OK (Figure 1 (b)), eastern Iran (e.g. the cities of Zabol, Rafsanjan and Torbate Jam), as well as northwestern provinces (e.g. Ardebil) are the most promising areas for wind energy planning.
The spatial variability of wind speed and duration across Iran has been investigated. First, the frequency distribution of daily mean and maximum wind speed data during recent 20 years was simulated by using Weibull function. Then the mean values of the theoretical Weibull probability distribution functions are used to investigate the spatial variability and predict the spatial distribution pattern of wind speed across the country. According to the results, wind speed is moderately correlated in space with an influence range of about 500 km. The maps of wind speed at 10 m a.g.l. generated using IDW and OK encourage the utilization of wind energy on the eastern, and northwestern regions. Besides, additional measurements may be considered in areas of highest estimation uncertainty.

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.

The Siberian high (SH) is a quasi-stationary and semi-permanent surface high pressure system residing over the Eurasian continent during winter with its climatological–mean central pressure exceeding 1030 hPa. This most important atmospheric center of action controls the climate of a wide area of this continent. The SH forms generally in October mainly in response to strong radiative cooling over the snow covered Eurasian continent in the lower troposphere and persists until around the end of April in 90-110 °E and 40-55° N (Shahgedanova; 2002، 70.، Takaya and Nakamura; 2005، 4423.، Gong and Ho; 2002، 2،. Shahgedanova، 2002). The Asia climate is mainly affected by the SHI activity at winter. Despite the prominence and large spatial extent of SH in northern hemisphere، its spatial and temporal variations are not comprehensively known (Panagiotopoulos et al.، 2005، 2005، p. 1411). The global warming has been intensified in middle of 1970s and significant changes of mean sea level pressure (MSLP) in northern hemisphere and changes of atmospheric circulation on many regions (Trenberth and Hurrell; 1994، 303.، Nakamura et al; 1997، 2215.، Wang et al; 2007، 12) have been reported. A variation in temperature results in sea level pressure decrease according to barometric relation. In other words، the SH is expected to be weakened by the global warming as has been occurred after the 1976/1977 (Panagiotopoulos et al.; 2005، 1411). The obtained findings by Hori and Ueda (2006، 4) and Romanić et al (2014)، verify the same relation between global warming and SH weakening. Panagiotopoulos et al. (2005، 1411) have shown that the SH has experienced a negative trend of -2. 5 hPa in each decade during 1978-2001 while a slighter rate has been reported during the later decades (Jeong et al; 2011، 8). A plenty of studies have considered the temporal variability of SHI while the spatial variability and also the simultaneous spatial and temporal variability of SHI during global warming period have been often neglected. Thus، the present research aims to study the spatial and temporal variation of SHI during global warming period. Matarials and

2. 1. Data The present research has used the sea level pressure (SLP) data (Kalnay et al.، 1996) are obtained from the NCEP/NCAR Reanalysis 1 (NOAA National Center for Environmental Prediction). These data are gridded at 2. 5º latitude by 2. 5º longitude meshes، and cover 65 years (1948-2013). The SHI index is defined as the maximum pressure in SH spatial domain and the spatial and temporal variations have been considered during the global warming through the analysis of this index. The annual global land temperature anomalies data was also extracted from national climatic data center to consider the intensified global warming. Having collected the needed data and using regression method، the studied period (1948-2013) was divided into two parts presenting two discrete periods having different global warming intensities. Two mentioned periods were named intensified and slight global warming. The significance of spatial and temporal variability of SHI during two mentioned global warming periods were discussed through the compare means tests. 2. 2. Siberian High IntensityIn this research، the SHI is defined as maximum of December to February mean SLP over northern Mongolia between 40 and 65°N and 80–120°E. The same or similar definitions of the SHI have been utilized in many previous studies. 2. 3. Slight and intensified global warmingThe time series of data during 1880-2013 were used to consider the annual global land temperature anomalies data using regression method. The obtained results indicated that the pattern of mentioned data during 133 years can be divided into three smaller periods. Three periods of 1880-1933، 1934-1973، and 1974-2013 have the negative، near zero، and greater upper zero anomalies، respectively. The recent period (1974-2013)، having higher slope and increasing rate، was considered as intensified global warming while the 1934-1973 was considered as the slight global warming period having the slope near zero. Result and discussion3. 1. Temporal variabilityThe SHI were obtained during DJF through gridded. The weakening of SHI and its intensification recovery are evident during 1970-1980 and recent decades، respectively. The SHI decreased during intensified global warming (1974-2013) compared to slight global warming (1948-1973). The remarkable point is the noticeable reduction of variance during intensified global warming indicating a great change in annual SHI during intensified global warming. Regarding the maximum and minimum of SHI during two studied periods، it can be concluded that the variance decrease is due to decreasing maximum، meaning that the SHI variation range is decreased because of a decrease in SHI maximum3. 2. Spatial variabilityThe SHI centers location during intensified global warming shows that the centers have been focused toward zone 1 and 94. 17% of them are in zone 1 while only 5 and less than 1% of them are located in zone 2 and other zones respectively. The longitude and altitude time series of SHI also show a decrease of SHI centers distribution that more SHI centers have been formed in 50°N and 90°E since 1974. After the specification of SHI centers displacement، it is expected that their range is changed. Thus، two 1020/5 (reported as SH boundary in many references، for example IPCC; 2013، 224) and 1034 (more than 95% of SHI centers have a pressure higher than 1034 hPa and contour has been noticed as a area in which most SHI centers are formed) contours were plotted during two studied periods. Having extracted the mentioned contours during DJF at 1948-2013، the average of each contour was calculated and plotted during two global warming periods.

Starting the average sea level pressure changes in northern hemisphere from 1970 a noticeable change was observed in spatial and temporal of SHI resulting a dramatic change in average Earth''s temperature. The SHI has been weakened as the intensified global warming started (1974-2013) and the annual variation range has shown a considerable decrease compared to the period before (1948-1973). This annual variation decrease is due to a decrease in maximum and an increase in a minimum of SHI. It''s noteworthy that the decrease in maximum SHI has had a more dominant effect. The spatial SHI variations during intensified global warming (which is significant in error level lower than 0. 01) has been resulted in a reduction in spatial distribution of SHI centers in such a way that the SHI centers have been shifted toward 50°N and 90°E as the average global temperature increases. Additionally، the isobar 1020. 5 hPa (as maximum SH distribution) and 1034 hPa (as an area in which most SHI centers are formed) have been shifted toward west. A remarkable area decrease has been observed in 1034 hPa isobar during intensified global warming which is justified regarding the reduction of maximum SHI. Regarding the point that a significant change of atmospheric circulation has been occurred at mid-1970 in many areas of the world، it seems that the spatial variability of SHI have been due to noticeable changes in atmospheric circulation in such a way that the Aleutian low shifting toward west during 1977-1988 winters and variabilities of ocean temperatures during last 1970s have resulted in a long-term NAM/NAO and have led to SHI shifting consequently. Meanwhile، the important issue is that all of the mentioned changes have been coincident with a noticeable change in land temperature. Thus، it can be concluded that the global temperature increase have resulted in changes in atmospheric circulation and reorganizing the climate system. A scrutinized understanding of details، physical mechanisms، and real dynamics resulted in such changes necessitates a more comprehensive study and more data.

Salinity is a highly important problem in arid and semi- arid region. In Iran، about 235،000 km 2 (or 14. 2% of the total area of the country) area is salt-affected، which is equivalent to about 50% of irrigated lands in Iran (Pazira 1999). Irrigating of these lands causes to transfer salts to the area of root growth and thus increases the osmotic pressure and reduces the absorption of the nutrient elements and product. Some of researchers believe that this process is one of the disasters that threats development of human societies. Esfahan province is exposed to the danger of salinity. Esfahan province is located in the central arid region of Iran. Of 105،000 km 2 total area، an area of 5000 km 2 is used for crop and fruit production. Soil and water salinity is the major limitation to achieve optimum crop yields. However، the classical soil survey methods of field sampling، laboratory analysis and interpolation of these field data for mapping، especially in large areas، are relatively expensive and time-consuming but to get informed about distribution of salinity in soil is very important for recognizing critical threshold، planning، management، operation of source، and suitable distribution of water to correct the soil saline. Soil chemical properties commonly have spatial dependence at regional scale (Yost et al.، 1982). Regional assessment of soil properties requires evaluation of their spatial distribution. In recent years، environmental scientists have come to appreciate the merits of geostatistics and kriging for investigating and mapping Soil chemical properties in un-sampled areas. There are a large number of reports to natural resource distributions. Geostatistic method such as Ordinary Kriging is a class of statistics used to analyze and predict the values associated with spatial or spatiotemporal phenomena. It incorporates the spatial (and in some cases temporal) coordinates of the data within the analyses. Many geostatistical tools were originally developed as a practical means to describe spatial patterns and interpolate values for locations where samples were not taken. Three functions are used in geostatistics for describing the spatial or the temporal correlation of observations: these are the correlogram، the covariance and the semivariogram (hasani pak، 1999). The last is also more simply called variogram. The following parameters are often used to describe variograms: nugget: The height of the jump of the semivariogram at the discontinuity at the origin، sill: Limit of the variogram tending to infinity lag distances and range: The distance in which the difference of the variogram from the sill becomes negligible. In applied geostatistics the empirical variograms are often approximated by model function ensuring validity (Chiles and Delfiner 1999). Some important models are (Chiles and Delfiner، 1999; Cressie، 1993): The exponential variogram model، the spherical variogram model and The Gaussian variogram model. In assessments of some variables، spatial correlation structure is the same in all directions، or isotropic. In this case the variogram depend only on the magnitude of the lag vector، h = h، and not the direction، and the empirical variogram can be computed by pooling data pairs separated by the appropriate distances، regardless of direction. Such a variogram is described as omnidirectional. In many cases، however، a property shows different autocorrelation structures in different directions، and an anisotropic variogram model should be developed to reflect these differences. The most commonly employed model for anisotropy is geometric anisotropy، with the variogram reaching the same sill in all directions، but at different ranges. However some Geostatistical methods such as kriging need valid variograms. Cross validation is used to find the best model among the competitors. “Cross Validation” allows us to compare estimated and true values using the information available in our sample data set (Houlding، 2000). Study area: This research was conducted in Isfahan province (Fig1). It is located in the center of Iran in a predominantly arid or semiarid climate condition and is about 6800 km2 around Zayandehroud River. Mean annual precipitation and temperature are 120 mm and 14. 5 Co and Annual evapotranspiration is 1500 mm. The soils are classified as Aridisols. The area covers different land uses including agricultural، industrial، urban and uncultivated lands. In this study، soil sampling strategy was random stratify. In this method، the region was stratified in to regular- sized grid cells of 4 × 4 km and within each cell a sampling location was chosen randomly. A total of 255 soil samples (0-20 cm) were collected (Fig 2). At each sampling point the coordinates were obtained using a portable GPS and its land use was recorded. After calculation، 46. 5% of the sampling locations occurred in agricultural lands، 43. 5% in uncultivated lands and 10% in industrial and urban area (Fig2). Soil samples were air dried and ground to pass through a 2 mm sieve، Electrical conductivity was measured in a 1:2. 5 soil-water ratio suspension. Statistics including mean، variance، maximum، minimum، coefficient of variation (CV) and comparison average EC in different land use were calculated. The results of factor analysis were used to calculate the autocorrelation value between observed points and produce a minimum unbiased variance estimate. This variance is calculated as a function of variogram model. Variogram is calculated using the relative location of the samples (Soderstrom، 1998). The experimental variogram is calculated for several lag distances this is then generally fitted to a theoretical model and the parameters in suitable model are then used in the kriging procedure (Mohamadi، 2007). The next step is cross validation of the prediction models. The cross-validation technique is used to choose the best variogram model among candidate models and to select the search radius and lag distance that minimizes the kriging variance. Cross-validation is achieved by eliminating information، generally one observation at a time، estimating the value at that location with the remaining data and then computing the difference between the actual and estimated value for each data location. To compare different interpolation techniques، we examined the difference between the known data and the predicted data using the Mean Square Reduced Error (MSE). Correlation coefficient (Pearson) computed between real and estimated data with ordinary kriging. Distribution map of EC was produced using the ordinary kriging and use from maximum 16 point and minimum 3 point in estimation. The descriptive statistical parameters were calculated with Microsoft EXELE and SPSS (version 11). Maps were produce with Surfer (version 8) and ILWIS (version 3. 0) and geostatistics analyses were carried out with VARIOWIN and WINGSLIB. The average EC was 6. 9 dSm-1 with range of 1-74 dSm-1 in Isfahan surface soils (Table 1). EC values don’t follow a normal distribution and had a strongly skewed distribution (Fig 4a) therefore these values were transformed to logarithm and the log-transformed data fit an approximately normal distribution (Fig 4b). The average EC between different land uses was compared by using one-way ANOVA. The results showed that there is a significant difference in the soil salinity between uncultivated and agricultural area، but there is no significant difference between uncultivated and urban-industrial area. Soil salinity mean in the uncultivated area is at least three times higher than other land uses (Fig 3). The study of the spatial variability of EC is begun with the computation of directional variograms for EC in different directions. The best variograms was fitted in directions of 45 degrees، and a spherical theoretical covariance model fitted on variogram (Fig 6). The next step، cross validation of the prediction models computed with MSE and Pearson coefficient. MSE was minimum and Pearson coefficient was high (77%) and this parameter is identifier. Therefore valid variogram parameters (sill= 21000، rang= 0. 6 and nugget effect =0. 127) use for kriging and mapping (Table 2). According to the map of salt distribution in the top soil of study area (Fig 7)، all lands are saline (Ec> 4dS. m-1) but critical accumulation of salt is in the eastern region، especial Segzi plain. Segzi plain is located in the Eastern part of Isfahan province in the center of Iran and is about 40 kms from Isfahan center. The climate of the area according to the Gowsen method is found to be dry and semi-desert، respectively (Mojiri et al.، 2011). In Segzi plain are gypsum mines and wind can transport particles of chalk and sand that cause erosion and air pollution in Esfahan. Rainfall in east of Esfahan in comparison with center and west are lower and temperature is higher so there are more salt in compare to central and west parts. Moreover comparison of maps (salt distribution and land use) delineate، agricultural lands have lower salinity. Because irrigation and leaching are continued and transfer salt to deeper part. Moisture regime in study area is aridic. In this regime evapotranspiration is high and suction gradient transfer salinity solution to soil surface (Richards، 1954). The important result of this research was obtain concentration map of salt with this hope that this survey can be effective step in chose best decision in management of salinity lands to intention improvement and reformation this land. According result of this research، to be near with Lut deserts، low average rainfall، high annual temperature and high evaporation in eastern parts than western parts، are the most important parameters in accumulation of salt in this part of study area.