• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.573-583
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• 2001

A condition in which the covariances of Matheron's variogram estimators are expressed in a simple form is reviewed. An asymptotic property of the covariances of the variogram estimators is examined, and a sufficient condition that guaranties the finiteness of the asymptotic variance of the normalized variogram estimators is provided.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.547-568
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• 2020

Modeling the statistical autocorrelations in spatial data is often achieved through the estimation of the variograms, where the selection of the appropriate valid variogram model, especially for small samples, is crucial for achieving precise spatial prediction results from kriging interpolations. To estimate such a variogram, we traditionally start by computing the empirical variogram (traditional Matheron or robust Cressie-Hawkins or kernel-based nonparametric approaches). In this article, we conduct numerical studies comparing the performance of these empirical variograms. In most situations, the nonparametric empirical variable nearest-neighbor (VNN) showed better performance than its competitors (Matheron, Cressie-Hawkins, and Nadaraya-Watson). The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with hole effect structure, fitted to the empirical VNN variogram is the most appropriate choice. This selected variogram is used with the ordinary kriging model to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.109-123
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• 2005

Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.609-619
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• 2010

Geostatistical data among spatial data is analyzed in three stages: (1) variogram estimation, (2) model fitting for the estimated variograms and (3) spatial prediction using the fitted variogram model. It is very important to estimate the variograms properly as the first stage(i.e., variogram estimation) affects the next two stages. In general, the variogram is estimated with the moment estimator. To estimate the variogram, we have to decide the 'lag increment' or the 'number of lags'. However, there is no established rule for selecting the number of lags in estimating the variogram. The present paper proposes a method of choosing the optimal number of lags based on the PRESS statistic. To show the usefulness of the proposed method, we perform a small simulation study and show an empirical example with with air pollution data from Korea.

• Journal of Positioning, Navigation, and Timing
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• v.10 no.4
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• pp.271-278
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• 2021

In this paper, a tropospheric delay error was calculated by using meteorological data collect from weather station and Saastamoinen model, and an empirical variogram of the tropospheric delay in the Korean peninsula was estimated. In order to estimate the empirical variogram of the tropospheric delay according to weather condition, sunny day, rainy day, and typhoon day were selected as analysis days. Analysis results show that a maximum correlation range of the empirical variogram on sunny day was about 560 km because there is overall trend of the tropospheric delay. On the other hand, the maximum correlation range of the empirical variogram on rainy was about 150 km because the regional variation was large. Although there is regional variation when the typhoon exists, there is a trend of the tropospheric delay due to a movement of the typhoon. Therefore, the maximum correlation range of the empirical variogram on typhoon day was about 280 km which is between sunny and rainy day.

• Korean Journal of Remote Sensing
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• v.22 no.5
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• pp.357-366
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• 2006

A traditional image analysis or classification method using satellite imagery is mostly based on the spectral information. However, the spatial information is more important according as the resolution is higher and spatial patterns are more complex. In this study, we attempted to compare and analyze the variogram properties of actual high resolution imageries mainly in the urban area. Through the several experiments, we have understood that the variogram is various according to a sensor type, spatial resolution, a location, a feature type, time, season and so on and shows the information related to a feature size. With simple modeling, we confirmed that the unique variogram types were shown unlike the classical variogram in case of small subsets. Based on the grasped variogram characteristics, we made a level index map for determining urban complexity or land-use classification. These results will become more and more important and be widely applied to the various fields of high-resolution imagery such as KOMPSAT-2 and KOMPSAT-3 which is scheduled to be launched.

• Economic and Environmental Geology
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• v.27 no.1
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• pp.81-91
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• 1994

There has been considerable research dealing with the influence of surface roughness along surfaces of rock discontinuities in relation to the peak shear strength of rock masses. Concepts accepted recently for measuring such strength include estimation of a roughness coefficient such as developed by Barton's studies. The method for estimation the Joint Roughness Coefficient (JRC) value of a measured roughness profile is subjective. The aim of this research is to estimate the JRC value of the roughness of a surface profile in a rock mass system using an objective method. The study of roughness of surfaces has included measurement of fractal geometric characteristics. Once the irregularity of the surface has been described by the fractal dimension, the spatial variation of the surface irregularities can be described using variogram and drift analysis. An empirical relationships between the roughness profiles of selected JRC ranges and their fractal dimension with variogram and drift were derived. The application of analyses of fractal dimension, variogram and drift was novel for the analysis of roughness profiles. Also, an empirical equation was applied to experimental data.

• Proceedings of the KSRS Conference
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• v.1
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• pp.413-416
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• 2006

As even small features can be classified as high resolution imagery, urban remote sensing is regarded as one of the important application fields in time of wide use of the commercialized high resolution satellite imageries. In this study, we have analyzed the variogram properties of high resolution imagery, which was obtained in urban area through the simple modeling and applied to the real image. Based on the grasped variogram characteristics, we have tried to decomposed two high-resolution imagery such as IKONOS and QuickBird reducing window size until the unique variogram that urban feature has come out and then been indexed. Modeling results will be used as the fundamental data for variographic analysis in urban area using high resolution imagery later on. Index map also can be used for determining urban complexity or land-use classification, because the index is influenced by the feature size.

• Korean Journal of Soil Science and Fertilizer
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• v.16 no.4
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• pp.305-310
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• 1983

Spatial variability of infiltration rates of 96 samples from Hwadong SiCL was studied by using geostatistical concepts. The measurement was made at the nodes of the regular grid consisting of 12 rows and 8 columns. Sample spacing within rows and columns was 3 and 2 meters, respectively. This study illustrated the use of variogram as a tool to identify the degree of dependency of the infiltration rate on the distance between pairs of measurements and how to take advantage of this dependency. Fractile diagram showed that the distribution of observation was approximately normal. The range of the variogram was about 7.4 meters. The minimum number of samples necessary to reproduce the results similar to the 96 measured values was 8 to 10. Coefficients of theoretical variogram function for computing kriged values and kriged varionces of nuogget effect, slope, and range were 0.444 cm/day, 0.003 cm/day, and 7.4 m, respectively.

• Korean Journal of Soil Science and Fertilizer
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• v.17 no.4
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• pp.319-324
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• 1984

Spatial variability of sand, silt, and clay contents on Hwadong SiCL and Jungdong SL was studied by using geostatistical concept. The measurements were made within a $33{\times}14m^2$ area at the nodes of 2 by 2m grids. The validity of all assumptions (stationarity, variogram models, etc.) was proved by Jack-knifing procedure and frequency distribution performed on the original data grids. The variogram of sand content on Hwadong SiCL was different from the linear model and that of clay content of Jungdong SL the linear and the spherical model in calculation of both kriged values and kriged variances in identification of its choice for simplicity.