Many hydrological models require high resolution rainfall data. The aim of this paper was to interpolate annual and monthly rainfall in Golestan province from sparse point data. To do this the methods, which make use of secondary variables (e.g. a digital elevation model, DEM) for rainfall estimation were compared with those, which do not make use of such information in estimation. The methods applied included univariate interpolation algorithms such as inverse square distance and ordinary kiriging and MULTIVARIATE geostatistical algorithms such as cokriging, kriging with an external drift and simple kriging with varying local means. The performance of each interpolator was assessed through examination of mapped estimates of rainfall and crossvalidation. It was concluded that cokriging provides the most accurate estimates of rainfall for May to October except June which was best estimated using kiriging with an external drift judging by the cross-validation estimation error summary statistics. For other periods ordinary kriging yielded more accurate rainfall predictions than other interpolators. The worst algorithm was inverse square distance that ignores both the elevation and rainfall records at neighboring stations. Relative nugget effect of semivariograms and correlation between rainfall and elevation affected the performance of different methods. For instance, ordinary kriging outperformed other technique when the correlation between rainfall and elevation was less than 0.5.

Soil pollution by heavy metals is an important environment issue throughout the world. Heavy metals’ origin, accumulation, and distribution in soil have been the focus of much attention by many researchers. The objective of this study was to recognize the sources of some heavy metals in surface soils in Zob-Ahan industrial district, Isfahan province, using MULTIVARIATE geostatistical techniques. A total of 202 surface (0–30 cm) soil samples were collected. Total lead (Pb), zinc (Zn), manganese (Mn), iron (Fe), copper (Cu), nickel (Ni), cobalt (Co) and chromium (Cr) contents of the samples were determined. A MULTIVARIATE geostatistical analysis was performed to identify the common source of heavy metals. The results of principal component analysis led to the identification of three components. So, these components were explained 31, 27, and 16 % of total variance of heavy metal concentration, respectively. The distribution of scores of each components were shown that the quantities of Fe, Mn, Pb and Zn were found to be associated with anthropogenic activities, corresponding to the first factor was termed the “anthropogenic component”. The quantities of Co were found to be associated with parent rocks, corresponding to the second factor was termed the “lithologic component”. Also, the third factor was mainly attributed to Cu, Ni and Cr which also comprised the first and third factors, indicating a mixed source both from lithologic and anthropogenic inputs.

Introduction Precipitation is an atmospheric factor, its quantity and distribution vary considerably in different parts of the planet, and is one of the most influential climatic elements that has always been influenced by the climate. Its amount changes in time and place continuously. Knowing the temporal and spatial distribution of rainfall is a useful tool for understanding how non-uniform distribution of water resources and vegetation in each region. Precipitation occurs when the wet weather and the climb factor exist both in the region. In other words, the wet air must rise to a certain height so that it can reach the saturation point due to the subsequent cooling down, and in the next, the cloud produces precipitation. The absence of any of these two factors prevents the occurrence of precipitation. Rainfall variation is considered as a key factor in the structure and functioning of ecosystems, but its impact on scale and magnitude is much less than its spatial variation. The climatic element, especially precipitation, has significant changes in time periods. Therefore, the recognition of the element of precipitation as one of the two elements of the climate and its changes in different times and places allows the optimal utilization of the natural environment. The amount and spatial distribution of rainfall is a fundamental factor for decision making, design and evaluation of hydrological models as well as water management and planning. Temporal spatial variations have diverse and varied impacts on the management and planning of water resources along a water basin and nationally. Climate change is one of the factors affecting the change of water resources. Precipitation, as a highly variable element, has always been a concern for climatologists and waterologists as a fundamental factor in the blue balance. The extreme variability of rainfall along the time-space has a variety of study approaches. The purpose of this research is to identify the conditions of rainfall in the Mazandaran province. Therefore, the location of rainfall in this province was investigated. In this regard, identification of the effective factors of the occurrence of these rainfall in different seasons and their role in the province has been addressed and its results will be available as a scientific and practical solution.Materials In this study, for the purpose of identifying the rainfall in the province of Mazandaran, five years rainfall from 2006-2010 has been used from a total of 12 synoptic stations. Using extracted data from precipitation graphs, rainfall of more than 10 mm was extracted in the studied area. Then the data were categorized into four parts: spring, summer, autumn, winter and year; to create the database, they entered the SPSS and ARC GIS10 software. In the spatial analysis of the data, the semi-modification of these models has been used, which was calculated using ARC GIS10 software. The methods used in the zoning of Kriging and IDW models for fitting include: IDW with three potentials of 1, 2, 3, and the Kriging method with spherical, circular, exponential, Gaussian, and spherical models, which is performed with conventional Kriging technique. Also, for statistical comparison of models, root mean square error of RMSE, MAE, RMSE and their correlation coefficient were used. Then, optimal mapping based on MULTIVARIATE regression was fitted based on the simulation method and the recursive method of six variables in rainfall generation including latitude and longitude, number of rainfall days, elevation, relative humidity and dew point temperature. The effects of these factors on rainfall in the province will be evaluated in different seasons and annual.Results& Discussion The results of the spring survey show that there were 5 stations out of 12 stations without rainy rainfall. These stations are located in the plain and in the mountain range of the region. The analysis showed that the correlation coefficient between variables is R^2=967, which indicates a strong relationship between the set of independent variables and the dependent variable.85.8% of rainfall in the spring season in Mazandaran province depends on these variables. In the summer, only 2 stations in the province did not experience rainfall ranges, both of which were at high altitudes and include the station Alasht and Kyasar. Variables show a very strong relationship in summer with a correlation coefficientofR2=0.995.Which is 0.99% of rainfall in the Mazandaran province depends on these six variables. The fall season is one of the high seasons in the province of Mazandaran province. Only one station (siahbisheh) has been registered from 12 storm rainfall stations. Estimates show that the six variables analyzed in this chapter with a correlation coefficient of R2=0.983 represent a strong correlation. The results of the winter season show that all stations in Mazandaran province have rainfall, although it includes fewer days than the autumn season. All stations experience at least one day at Alasht Station for up to 7 days in Ramsar. The results of the analysis show that in winter, the correlation coefficient is R2=0.996.Conclusion The method used in the zoning kriging and IDW models for fitting include: IDW with three possible 1, 2, 3, kriging with spherical model is a model of, circular, exponential, Gaussian and spherical - is the ordinary kriging technique was conducted to assess the accuracy of each map generated by determining the best model calculated health. Also, statistical models for comparing the square root error RMS, MAE, RMSE and correlation coefficient was used for the best model for zonation model IDW and ordinary kriging with the 1.3 was a circle. After extracting the optimal plan based on MULTIVARIATE regression models and ENTER precipitation method Backward method retrograded create six variables, including the length and breadth of geography, number of days of rainfall, altitude, relative humidity and dew point temperature were fitted. Results show that the six-variable correlation of 0.97 in spring, 0.99 in summer, 0.98 in autumn, winter is 0.99 and about 0.99 per year., Which indicates a strong relationship between these six variables Showers Mazandaran province.

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.

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.

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.

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