IntroductionRainfall erosivity, the propulsion or power of causing erosion in separation and transport of soil particles, is in relation to water erosion. Rainfall erosion is causing loss of soil, damage to agriculture and infrastructures which is followed by water pollution. Changes in rainfall patterns exacerbate risk of erosion globally. Rainfall erosivity plays an effective role in soil erosion and represents potential erosion in the study areas. Following the rainfall erosion, all types of water erosion can be occurred. Consequently, it not only makes soil to be eroded but also lead to filling of dam reservoirs, channels, water pollution and ecological changes. Regarding these mentioned problems, it is necessary to investigate various aspects of water erosion. Under the same condition, rate of soil loss is directly proportional to the rainfall erosivity. This can be expressed as erosivity factors which are based on rainfall characteristics. Various researchers have attempted to provide factors that are based on rainfall characteristics using simultaneous measurement of soil splash (or soil loss) and rainfall characteristics to determine relationships between them. Various factors have been proposed throughout the world. These factors are different because of geographical location, scale, local conditions and type of instruments. The concept of rainfall erosivity was proposed by wischmeier and smith (1958) in order to consider the effects of climate on soil erosion. Rainfall erosivity can be determined either using direct measurements or appropriate factors. Direct measurement method is a suitable method to determine rainfall erosivity which is done by measuring the amount of splashed soil. Event-based measurement of erosivity of rainfall for broad area is difficult and time-consuming. Therefore, researchers have attempted to provide factors that are based on rainfall characteristics using simultaneous measurement of soil loss and rainfall characteristics and relationships between them. For different areas, rainfall erosivity can be determined using these characteristics without direct measurement. In general, rainfall erosivity factors can be divided into two groups: 1) factors based on energy and intensity of rainfall; 2) factors based on readily available data. One of the most famous factors is EI30 which is based on kinetic energy and intensity of rainfall. One limitation in using this factor and also other factors which are based on rainfall erosivity is that they need long-term data (>20years) recorded with short intervals. Such data are recorded in the stations equipped with rain gauge. Therefore, due to lack of these long-term data, researchers have proposed factors that use available rainfall data (i.e., daily and monthly data). This recent factors are computed based on regional sediment analysis or its relationship with EI30.The purpose of this study is to prepare rainfall erosivity map for Kerman province with semi-arid climate and to determine the most suitable interpolation method. Although such a map has been produced by Nicknami (2014) for Iran, it's not available for Kerman specifically.

Rainfall spatial analysis methods are very helpful since there are not enough rainfall gauge stations and watersheds are scattered in large extent. There are many different methods for estimating average precipitation such as; arithmetic method and Thiessen polygon. However, the arrangement and location of data and their correlations are not considered by classic methods. Thus, Geostatistical techniques are applied instead. In the present article, 22 meteorological stations from within and around the basin with data collection period of 30 years were selected for the analysis. The geostatistic analysis methods including ordinary kriging, simple cokriging, ordinary cokriging, standardized ordinary kriging, moving average using inverse distance with powers of 1 to 5 were applied for spatial analysis of annual, monthly and 24 hourly maximum rainfall data in Hajighoshan watershed located in northeast of Iran. For this reason, rainfall data were fitted to different methods and compared using cross validation by removes rainfall values of each station, one at a time, and predicts the associated data value. The results of geostatistic analysis showed that ordinary kriging is the best method with MBE=34.26 for annual rainfall while moving average using inverse distance with power of 5 is the best method for monthly and 24 hourly maximum rainfall. According to the results obtained through analysis of variogram model, gaussian model are supposed as the best models for annual, monthly and 24 hourly maximum rainfall data.

Successive drought events as one of the most important environmental crises, along with population growth and uncontrolled water extraction, have led to an increase in the depth of groundwater, especially in arid and semi-arid regions. The purpose of this study is to investigate the Geostatistical relationship between groundwater depth data and groundwater depth based on precipitation data in three observation wells located in Fars province. These wells were selected based on the PSO clustering technique. Thus, the three observation wells that were closest to the center of the calculated clusters were selected as the representative of the clusters. These wells are located in Karsia, Dolatabad, and Fatehabad regions for clusters 1 to 3, respectively. Monthly groundwater depth data has been used from 2003 to 2017. Kriging and cokriging methods were performed in the GS+ environment. In this research, precipitation data was used as an auxiliary variable. Furthermore, the models were selected based on the lowest RSS values and the nearest R2 values, and the spatial structure ratio (C / C0 + C) to one. Accordingly, the selected models for the main variable (groundwater depth) in the first to third clusters are spherical, power, and linear, respectively, and for crossvariogram models (precipitation-groundwater depth) are all spherical. The results showed that in the validation and test stage, the Cokriging method has higher accuracy than the Kriging method. The test stage in kriging and cokriging methods for RMSE index are (0. 92 and 0. 41), (0. 54 and 0. 52), and (1. 25 and 0. 95) in 1, 2, and 3 clusters, respectively.

To model the spatial variability of groundwater chemical characteristics, our research was performed using Geostatistic and deterministic methods. In our study, Na+, CI-, HCO3-2, total Cations, TH, SAR, EC and TDS from ground water characteristics were selected. At first, normality of data tested using Kolmogorov-Smirnov test, then we transformed EC, total Cations and TDS using logarithmic transformation. Variography and interaction variogram of data calculated. The result of estimated and expected amount using MAE and MBE were presented. Result showed significance of Geostatistical methods in comparison to deterministic methods and Cokriging increased result's precision. Cokriging is the best method for modeling of Cl-, total Cations and TH. Disjunctive Kriging is the suitable methods for modeling of HCO3-2 and Na+. Universal Kriging resulted best model for TDS. On the other hand ordinary Kriging is the best method for SAR modeling.

The spatial and temporal distributions of ecosystem characteristics are required for sustainable management and optimum exploitation of the resources. Soil quality preservation is one of the most important factors in sustainable ecosystem management. Therefore, knowing the spatial distribution of soil characteristics is very important. In the present study, Kriging and IDW methods were used for prediction of spatial distribution of salinity, Pb, Cu, Zn, Mn, CEC; and percentage of OM and clay in soils of Akhtarabad region. After data normalization, the variogram was developed. For selecting the best model for competing on experimental variogram, the lower RMSE value was used. The best model for interpretative was selected by means of cross validation and error evaluation methods, such as RMSE method. The results showed that Kriging method is better than IDW method for prediction of soil properties spatial distribution due to strong spatial structure. Finally, the soil characteristics maps were prepared using the best interpolation method in GIS environment.

Analysis of the spatial variability of soil properties is important to interpret ecosystems and to improve modeling. Soil is a heterogeneous environment that its properties have spatial and temporal changes. Soil and vegetation have reciprocal relationship and influence each other. Then investigation of spatial variability of soil properties with other environmental change is essential. In order to analysis of spatial variability of soil properties in Reineh rangelands in Mazandaran Province, 300 soil samples from 0-30 cm depth were gathered and transported to laboratory. Soil properties included: pH, CaCo3, Bulk density, Particle density, total Phosphorus, total Nitrogen, absorbed Potassium, Organic Matter, Saturation Moisture, Soil Texture, Field Capacity, permanent Wilting Point, available Water Capacity and Water Holding Capacity were measured in laboratory. Afterwards, data normalization was performed statistical analysis for description of soil properties and Geostatistical analysis for indication spatial analysis correlation between these properties. Finally using Kriging methods and ELWIS Software were made maps of spatial distribution of soil properties. Results indicated that in the study area has had spatial correlation between researched factors and pH and potassium had highest and lowest spatial correlation respectively.

Salinity is one of the most destructive processes in soils, particularly in arid and semi-arid areas. In order to use and exploitation of such soils, the soil monitoring and mapping are necessary. In this study, in order to zoning and mapping of soils, sampling was collected based on network method from Bolagh (Saveh) saline lands and the electrical conductivity of saturated soil extract was determined. Then the data had been transferred to the ArcGIS 10 software and soil mapping had been drawn. The exponential model of Semivariogram showed the best cross-validation and efficiency than the other models (spherical, linear and gussian). Also, the amount of nugget effect to the threshold was 84/43% which indicates that the medium spatial correlation for soil EC amounts in the study area. Also, the variogram effect range was calculated about 261 meters. Assessment of the resultant index indicates that the Geostatistical has been able to soil salinity mapping with moderate accuracy and precision. The results showed that among five soil salinity classes, the soils of study area classifying in four Classes (including non-salinity, low salinity, medium salinity and high salinity) which highest quantities are related to middle southern regions. These results show that soil salinity in this area has high variability.

Geostatistical methods are one of the most advanced techniques for monitoring of groundwater quality. In this research, we compare efficiency of three interpolation techniques namely IDW, kriging, and cokriging for predicting a few groundwater quality indices such as: Na+, TH, EC, SAR, Cl-, Ca2+, Mg2+ and SO4. Data were gathered from 75 wells in Darab district, of Fars province. After normalizing the data, variograms were computed. A suitable model of fitness on experimental variogram was selected which was based on least RMSE value. Then the best method for interpolation was selected, using cross-validation and RMSE. Results showed that for all groundwater quality indices, cokriging performed better than other methods in simulating groundwater quality indices. Finally, using cokriging method, maps of Groundwater quality were prepared in GIS environment.

The present study was carried out to evaluate three interpolation methods including weighted moving average (WMA) with the power of 2 and 3, Kriging and Cokriging methods. Data of 23 wells in Mazandaran province were collected in fall and spring 2006. Seven parameters including electrical conductivity (EC), pH, total dissolved solids (TDS), sodium adsorption ratio (SAR), total hardness (TH), chloride concentration (Cl-) and sulphate concentration (SO42-) have been chosen as groundwater quality indices in the study area. Variogram analysis and extracting the spatial distribution maps of groundwater quality parameters were done using Geostatistics extension program in GIS environment. All interpolation methods have been evaluated based on mean bias error (MBE) and mean absolute error (MAE) criteria. The spherical model for semi-variograms had the less value of RSS (residual sum of square) for Cl-, EC, pH, SAR and SO42- parameters. TDS and TH parameters followed a Gaussian model.All semi-variograms and cross variograms had high confident level due to little values of nugget effects (Co) relative to sill. The covariance matrix demonstrated that magnesium concentration (Mg2+), sodium concentration (Na+), Total anions, Cl-, EC and TDS parameters have been the best covariate for estimating TH, SO42-, Cl-, PH, TDS and EC parameters, respectively. Co-Kriging was the best method for estimating all parameters far apart TH for which Kriging method was the best. Spatial distribution maps of groundwater quality indices demonstrated that the groundwater in the study area is slightly basic and the values of EC exceeded the permeable limit in more than 40% of the study area. Also there was sodium hazard and high concentration of TDS in the north-east part. Therefore, further studies are needed to recognize the pollution sources in order to reclaim the polluted part in the study area.