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 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.

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.