This paper compares the evaluation of three geostatistical interpolation methods including ordinary kriging, residual kriging and cokriging for the interpolation of long-term monthly and yearly reference crop potential evapotranspiration (ETo). This study has been conducted in a region including Fars, Booshehr, Hormozgan, and Kohgilooye-Boyrahmad provinces. Long-term mean values of monthly and yearly ETo were computed from recorded meteorological variables at 119 weather stations using the Hargreaves-Samani method. ETo estimates and estimation errors were evaluated at 19 validation stations. In general, estimates were in good agreement with observed values for residual kriging and cokriging methods. Based on mean absolute error (MAE), mean square error (MSE), mean error percent (MEP) and root mean square interpolation error (RMSIE), the best method for Farvardin (April) is kriging and for Khordad (June), Tir (July), Aban (November), and Azar (December) is cokriging. For other months and for mean annual ETo the best method is residual kriging. It should also be noted that MAE, MSE, and MEP for Mordad (August), Mehr (October), Dey (January), and Bahman (February) are very similar for cokriging and residual kriging. With the exception of Farvardin (April), Ordibehesht (May), and Shahrivar (September), for the other months and for annual ETo, the deviation of cokriging estimations from a 1:1 line is less than kriging and residual kriging. In other words, the points from these methods are more spread out around the 1:1 line, but the band of the deviation in cokriging is less than the two other methods. Therefore, the best method for estimation of monthly and yearly ETo is cokriging, except in Farvardin (April), Ordibehesht (May) and Shahrivar (September).

In order to investigate on the spatial structure and estimation of forest growing stock in the Caspian region using geostatistical approach, this study was carried out in the Educational and Research Forest Station of Tehran University, Kheyroodkenar- Noshahr. Field sampling was performed, based on a 150m by 200m systematic rectangular grids. Since geostatistical techniques basically, rely on good estimates of spatial auto-correlation, particularly at short distances, four sample plots were taken 50m away, from central sample plots in the W-E and N-S directions. Each sample plot contained two concentric circles with areas of 300m2 and 700m2. Overall, 721 sample plots were inventoried in total area of 502 hectares. Then experimental variogram was calculated and plotted using the geo- referenced inventoried sample plots. The variogram revealed more than 80% Nugget effect, implying weak spatial auto- correlation between samples, even in 50m distances. Estimation was performed by ordinary block (100×100 m) Kriging using spherical model. Cross- validation results indicated that all the estimations are biased because of the large Nugget effect in the experimental variogram. Therefore, Kriging couldn’t make a precise estimation due to large variability in short distances and the weak spatial structure of forest growing stock in this heterogeneous and uneven-aged forest.

In this study to assess and identify the characteristics of the basin drought Hendijan-Jarahi is used statistics a climatic period (30years). To determine the best indicator of drought in a correlation matrix using Pearson correlation coefficient values of PN, DI, SPI, SZI, CZI, MCZI with a confidence level of 99% and 95% review and were compared. Indices SPI, SZI, CZI together had a strong correlation more than 0. 9. the SPI drought index among them have ability to better identify the start and end time of drought, and based on the drought division into 4 groups: mild, moderate, severe and extreme. based on SPI index five characteristics of the drought were extracted; many with years of drought, the longest continuity, number of events, the years and the frequency of extreme events. In order to normalize the data of the method was applied Cox box. Among the deterministic and geostatistical interpolation methods according to the spatial dependence data Ordinary kriging was used. Then, to examine the spatial correlation between measurement data and assessment methods of estimation and modeling, drawing and analysis of semi-variograms were used Based on different methods, spherical, exponential and Gaussian features vario gram on the basis of Nagget and Sill, the variance structured to non-structured Proportion, the Mean, RMS, ASE RMSS, a suitable method was chosen for zoning. The results based on the five characteristics of the study due to the large difference topography and variety of terrain and other natural and climatic diversity, characteristics of drought in the basin does not follow of a certain order. But overall abundant number of years with the drought and the highest occurrence of severe drought are more than half of its eastern extreme in the West basin that most have occurred in recent decades.

There are numerous methods for data filling in hydrology. Most, however, are based on correlations with nearby stations in a general scheme of regionalization. These methods, though robust, fail to function when and where all the near stations are missed-data too. The Mashhad synoptic station has annual rainfall data over a 50 year period from 1951 to 2000 and historic rainfall data from 1893 to 1940, just before World War II. This time series has about 15 years of missed data which cannot be filled by usual methods. So, the techniques of Geostatistics and kriging were adapted to this long-term time series as an alternative. The data showed a poor correlation at every time lag, showing that, while all the semi-variogram models performed nearly equal, there was a high correlation among each of the others. The results included with polynomial regression fits to different moving average orders, nailed at some reasonable estimates for missed rainfall values.

The aim of the study is determination of the correlation between factors affecting in the wheat yield and preparing of yield mapping of wheat in north of Darab city. In order to determine the relationship between biological and grain yield with some of the important agronomic traits 60 samples in the north of Darab city was investigated. Parameters such as plant height, seed weight, harvest index, tiller number, latitude and longitude for each of the samples was measured. The results show that grain weight has highest correlation with the biological yield (0. 97**). In this study, also using the Kriging (Gaussian models, spherical, circular and exponential models) and average inverse distance (IDW) maps of the biological yield and grain weight was determined. The results of the interpolation showed that kriging method (Gaussian model) with a minimum error (RMSE=0. 98 for biologic yield and RMSE=0. 97 for grain weight) was the best model for preparation of these parameters in the study area. Also the results of biologic yield map showed that areas locating in the North West of the study area had the highest yield.

Facies modeling is an essential part of reservoir characterization. The connectivity of facies model is very critical for the dynamic modeling of reservoirs. Carbonate reservoirs are so heterogeneous that variogram‐based methods like sequential indicator simulation are not very useful for facies modeling. In this paper, multiple point Geostatistics (MPS) is used for facies modeling in one of the oil fields in the southwest of Iran. MPS uses spatial correlation of multiple points at the same time to characterize the relationships between the facies. A small part of the oil field, in the vicinity of the simulation grid, is used as a training image, in which there is 25 well data for creating suitable training image by the principal component analysis (PCA) method. In this study, MPS is successfully applied to facies modeling and the spatial continuity of facies is reasonably reproduced. The facies model verifies the reproduction of facies proportion in training image and wells. Also, five wells are used for the cross correlation of the facies model. The results indicate that the facies model shows a strong correlation with the facies of these five wells. Additional hard data, which is extracted from high confidence seismic data, is so useful for the improvement of the facies model.

At present about 90% of Mashhad water consumption is supplied by deep wells. This high level of consumption indicates the importance for monitoring groundwater quality in this area. There is a need for a dense network to be able to extend the point data to unpaged locations. The adequacy; of Mashhad water supply deep well network for monitoring nitrate and electrical conductivity (EC) has been investigated in this research by kriging which is an optimal interpolation technique based on spatial structure of data. An exponential model of semivariogram was fitted to nitrate data (after removing its trend by a second order equation) while EC data showed a linear-sill one. On the whole nitrate was more variable than EC with higher error of estimate. However the error maps showed that the variation of error was not so great in the study area for both parameters. Three new well locations were proposed for decreasing the maximum error of estimates. These locations were around the boundaries of the study and reduced the maximum error by less than 3%. Such a reduction is quite insignificant; illustrating that based on the available data the performance of the present network cannot be improved. Despite this the need for an optimum: network with a better spatial and temporal distribution is felt

Soil Cation Exchange Capacity (CEC) is an important vital indicator of soil fertility and as well, of pollutant sequestration capacity. Throughout the present study, spatial variability of soil CEC was investigated Through Kriging and corking with the principal components derived from soil physico-chemical properties including texture, (clay, sand, and silt content), organic carbon, electrical conductivity as well as pH. To follow the purpose, 247 soil samples were collected from central areas of Guilan province. Seventy five percent of the soil samples were used for training and 25% for testing. The first two Principal Components (PC1 and PC2) together explained 68.54% of the total variance of soil physico-chemical properties. PC1 explained the highest significantly positive correlation with CEC (r=0.81, P<0.01), whereas there was no significant correlation observed between CEC and PC2 (r=-0.19). PC1 was then used as an auxiliary variable in cokriging method for the prediction of soil CEC. Root mean square error of kriging for the test dataset was found 0.159 and that of cokriging for the dataset amounted to 0.118. The cross-validation determination coefficient (R2) for the test dataset was recorded 0.49 for kriging while 0.71 for cokring at a 0.01 level. The results show that interpolation through cokriging, with an auxiliary variable PC1 derived from soil physico-chemical properties, proves more reliable than through kriging. In addition, the principal components that bear the highest positive significant correlation with the dependent variable are of the most potential for prediction through cokriging.

The importance of spatial distribution in sampling weed populations, modeling population dynamics, and long-term weed management has been particularly important for methods to describe and analyze the spatial and temporal distribution of weeds. In year 2002, in a field located at Mashhad, weeds were identified and counted at 171 points of a corn field (1 ha) based on a 7 (m) by 7 (m) grid in 0.15 m2 quadrates, 3 times within the season including prior to post emergence management, after post emergence management, and before harvest. Geostatistical techniques were used to analyze the spatial structure of weeds and dynamics of patches. Fifteen weed species were observed across the field. Semivariogram analysis indicated 3.5 to 236.5m as the range of influence (patch size) which depends on weed species and sampling time (stage of growth). The semivariogram analysis also indicated that 51 to 85 % of the variation of sample density was due to spatial dependence, which suggests that most of the species were patchy. Semivariogram parameters did not change significantly over time for field bindweed which indicated the relative stability patches of this weed. Barnyardgrass was not treated with herbicide, thus patches have rapidly spread. For other weed species, the range of influence decreased (patches were smaller), but spatial structure was more stable over time which results in consistent patch position. The maps also showed elongated patches (anisotropy) along the field which may be in response to direction of tillage, irrigation and all other management practices. The results of this study showed that spatial distribution monitoring allows prediction of weed behavior and thus can be a valuable tool for management decisions and increases our understanding of the dynamics of weed