Spatial data analysis methods have many applications in various fields‎, ‎such as agriculture‎, ‎mining engineering‎, ‎and meteorology‎. ‎In this study‎, ‎ordinary Kriging and indicator Kriging are considered to predict alumina grade in the Jajarm mine in Iran‎, ‎and the precision of the methods is computed‎. ‎A conditional simulation is carried out based on the data set for a more general comparison of ordinary and indicator Kriging to interpolate Alumina grade in the mine‎. ‎In the case of monitoring possible variation related to sample size and type of variogram model‎, ‎simulations are performed with various sample sizes and different types of variogram models‎. ‎Then ordinary and indicator Kriging methods are applied for every set of simulated data (concerning different sample sizes and types of variogram models)‎, ‎and root of standardized mean square error prediction is considered as a cross-validation criterion to compare the Kriging methods‎. ‎The simulation results show that under the assumptions‎, ‎ordinary Kriging has better performance than the indicator Kriging method.

In statistics it is often assumed that sample observations are independent. But sometimes in practice, observations are somehow dependent on each other. Spatiotemporal data are dependent data which their correlation is due to their spatiotemporal locations. Spatiotemporal models arise whenever data are collected across both time and space. Therefore such models have to be analyzed in terms of their spatial and temporal structure. Usually a spatiotemporal random field {Z(s, t) : (s, t) Î D x T} is used for modeling the spatiotemporal data, where D Ì Rd, d ³ 1 is a space region and T Í R is a time region. One of the fundamental subjects in analyzing such data is prediction. In spatial statistics, assuming that the spatiotemporal random field Z(s,.t) is stationary with finite variance at all coordinates (s, t) Î D x T, and spatiotemporal covariance function C(h, u) = cov (Z(s, t)j Z(s + h, t + u)) exists, the unknown value of the random field at a given location (s0, t0) is usually predicted with Kriging as the best linear unbiased predictor. In practice, the spatiotemporal covariance function is unknown and a positive definite function should be fitted to the estimates of the covariance function. To ensure that a valid spatiotemporal covariance model is fitted to the data, one usually considers a parametric family whose members are known to be separable positive definite functions. A separable spatiotemporal covariance function might decompose into sum or product of a purely spatial and a purely temporal covariance function. In this paper the product-sum model introduced by De Iaco et al. (2001) is used to determine the spatiotemporal correlation of the data.In some applied problems, in addition to the values of an attribute of interest Z(0, 0), some additional information is available in each sample location, so the precision of prediction would be improved by their implementation. In this paper, to exploit this additional information in Kriging, two techniques for spatiotemporal Kriging of temperature are compared. The first technique, spatiotemporal ordinary Kriging, is the simplest of the two, and uses only information about temperature. The second technique, spatiotemporal Kriging with external drift, uses also the relationship between temperature and height to aid the interpolation. It is shown that the behavior of the temperature predictions is physically more realistic when using spatiotemporal Kriging with external drift. The implementation of spatiotemporal Kriging with external drift, then, is illustrated in a real problem, consisting of maximum and minimum temperature of 6 provinces in Iran.

Scouring, occurring when the water flow erodes the bed materials around the bridge pier structure, is a serious safety assessment problem for which there are many equations and models available in the literature in order to estimate the approximate scour depth. This research work is aimed to study how the surrogate models estimate the scour depth around circular piers, and compare the results with those of the empirical formulations. To this end, the pier scour depth is estimated in non-cohesive soils based on a sub-critical flow and live bed conditions using the artificial neural networks (ANNs), group method of data handling (GMDH), multivariate adaptive regression splines (MARS), and Gaussian process models (Kriging). A database containing 246 lab data gathered from various studies is formed, and the data is divided into three random parts: 1) training, 2) validation, and 3) testing in order to build the surrogate models. The statistical error criteria such as the coefficient of determination (R2), root mean squared error (RMSE), mean absolute percentage error (MAPE), and absolute maximum percentage error (MPE) of the surrogate models are then found and compared with those of the popular empirical formulations. The results obtained reveal that the surrogate models‘,test data estimations are more accurate than those of the empirical equations,Kriging has better estimations than the other models. In addition, the sensitivity analyses of all the surrogate models show that the pier width‘, s dimensionless expression (b/y) has a greater effect on estimating the normalized scour depth (Ds/y).

Understanding ecological and anthropogenic drivers of fish population dynamics andachieving a sustainable yield requires detailed studies on habitat selection and spatial distribution.The objective of this study was to predict spatial density and distribution of kilka species in thesouthern Caspian sea in relation to satellite-derived sea surface temperature, chlorophyll-aconcentration, turbidity and water depths using ordinary Kriging and co-Kriging geostatisticalmethods and introduction an appropriate potential fishing area according to the present fishing points.Three hundred and fifty fishing surveys were done in two main kilka fishing ports in the southernCaspian Sea (Anzali and Babolsar ports) from 2015 to 2016. The Geostatistical analysis showed thatthe co-Kriging spatial interpolation method provided the best prediction of fish abundance whenchlorophyll-a content was included in model.

In this research, a hybrid wavelet-artificial neural network (WANN) and a geostatistical method were proposed for spatiotemporal prediction of the groundwater level (GWL) for one month ahead. For this purpose, monthly observed time series of GWL were collected from September 2005 to April 2014 in 10 piezometers around Mashhad City in the Northeast of Iran. In temporal forecasting, an artificial neural network (ANN) and a WANN were trained for each piezometer. Kriging was used in spatial estimations. The comparison of the prediction accuracy of these two models illustrated that the WANN was more efficacious in prediction of GWL for one month ahead. Thereafter, in order to predict GWL in desired points in the study area, the Kriging method was used and a Gaussian model was selected as the best variogram model. Ultimately, the WANN with coefficient of determination and root mean square error and mean absolute error, 0.836 and 0.335 and 0.273 respectively, in temporal forecasting and Gaussian model with root mean square, 0.253 as the best fitted model on Kriging method for spatial estimating were suitable choices for spatiotemporal GWL forecasting. The obtained map of groundwater level showed that the groundwater level was higher in the areas of plain located in mountainside areas. This fact can show that outcomes are respectively correct.

Background and Objective: Estimating aboveground carbon (AGC) of forest is a fundamental task for sustainable management of forest ecosystems,therefore, there is a critical need for appropriate approaches for quantifying of AGC. The most commonly used approaches for estimating include global regression models that estimate the target variable over a wide range using cost-effective auxiliary data. Traditional regression models with fixed regression coefficients at all locations do not consider heterogeneity and spatial structure in modeling. The objective of this study is estimating the AGC using Regression Kriging, Geographically Weighted Regression Kriging and Landsat 8 data and compare methods. Material and Methodology: The study was carried out in part of Zagros Forest, in Kohgiluyeh and Boyer-Ahmad Province. Totally, 184 plots (30×30 meters) surveyed and AGC were calculated by allometric equations. 32 variables were extracted from Landsat 8 as auxiliary data in the modeling process. The assessment of accuracies of methods was evaluated by K-fold cross validation via criteria such as coefficient of variation (R2), root mean square error (RMSE). Findings: The results showed that Geographically Weighted Regression Kriging (R 2 = 0. 66, RMSE= 21) had a better performance compared to Regression Kriging. Discussion and Conclusion: Hybrid methods with heterogeneity and spatial correlation can be a good alternative to early regression methods for estimating aboveground carbon (AGC).

Introduction: The map of diseases is usually constructed using the information from diseases incidnce in some regions. Some factors, such as measurment error and rapid variation of diseases rates in different regions make maps so wiggly that their interpretation becomes difficult. Therefore these maps must be smoothed using statisical methods.Methods: Since disease rates of different regions reflect an spatial correlation structure, in this paper the spatial correlation structure of data is specified by fitting a variogram model, then Kriging as a best linear unbiased prediction method is used to make a smooth map of diseases. Results: The tuberculosis incidence rates of 262 counties of Iran are used to demonstrate the application and accuracy of the diseases mapping method presented in this paper. The smoothing map of tuberculosis disease, obtained by Kriging method shows the geographical trend of the disease in Iran. In this map, central and western regions of Iran have minimum incidence rates, and it gradually increases toward the eastern boundaries.Discussion: The object of this article is introducing Kriging method for disease mapping and tuberculosis disease is used to demonstrate the application of this method. There is on dubt that the numerical results of prediction and mapping can be affected by undercount in the smir positive (S+) tuberculosis data, which are gathered by the office for campaigning against diseases. However this method has a wide application in different areas of medical sciences. such as geographical epidemiology of diseases, environmental health and environmental engineering.