• Journal of the Korean Statistical Society
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• 제30권4호
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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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• 제27권5호
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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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• 제34권2호
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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.

• 응용통계연구
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• 제23권3호
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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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• 제10권4호
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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.

• 대한원격탐사학회지
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• 제22권5호
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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.

• 자원환경지질
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• 제27권1호
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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.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2006년도 Proceedings of ISRS 2006 PORSEC Volume I
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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.

• 한국토양비료학회지
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• 제16권4호
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• pp.305-310
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• 1983

화동미사질식양토(華東微砂質埴壤土)의 침투속도(浸透速渡)에 대한 변이성(變異性)이 표준통계학적(標準統計學的) 방법(方法)과 지질통계학적(地質統計學的) 방법(方法)인 Variogram에 의해 연구(硏究)되었다. 지질통계학적(地質統計學的) 개념(槪念)인 지역(地域) 변수(變數) 이론(理論)으로 관측치(觀測値)에 대한 공간변이성(空間變異性)이 기술(記述)되었고 구조분석(構造分析)된 후 Kriging을 위한 최적(最適)의 표본추출수(標本抽出數)와 그 거리(距離)를 결정(決定)할 수 있도록 장방형(長方型)의 $2{\times}3m$ Grid 형태(形態)로 표본추출(標本抽出)하여 수행(遂行)한 결과(結果)는 다음과 같다. 1. 표본(標本)에 대한 산술평균(算術平均)값과 표준편차(標準偏差) 값이 각각(各各) 3.56, 0.67cm/day이었으며 변이계수(變異係數)는 18.93%로서 관측치(觀測値)는 거의 정규분포(正規分布)를 나타내었다. 2. Sill값을 갖는 선형(線型)의 평균(平均) Variogram을 선정(選定)한 결과(結果) Nugget효과(效果)를 보였으며 그 범위(範圍)는 7.4m이었다. 3. Variogram의 구조분석(溝造分析) 결과(結果) 공시지역(供試地域) 표본수(標本數) 96과 같은 결과(結果)를 가져올 수 있고 최적표본수(最適標本數)는 8~10이었다. 4. Kriging값과 Kriging분산(分散)을 계산(計算)하는데 필요(必要)한 이론적(理論的)인 Variogram함수(函數)의 계수(係數)는 Nugget 효과(效果) 0.444cm/day, 선형(線型) Variogram의 기울기 0.003cm/day, 그리고 이웃간 거리(距離) h=7.4m이었다.

• 한국토양비료학회지
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• 제17권4호
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• pp.319-324
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• 1984

지질통계학적(地質統計學的) 개념(槪念)인 지역변수(地域變數) 이론(理論)을 적용(適用)하여 $2{\times}3m$ Grid형태(形態)로 표본추출(標本抽出)된 중동사양토(中東砂壤土)와 화동미질식양토(華東微質埴壤土)의 입경분포(粒徑分布)에 대한 구조분석(構造分析) 결과(結果) 설정(設定)된 Variogram에 기본(基本)을 둔 최량(最良)의 선형불편추정치(線型不偏推定値)(BLUE)인 Kriging값을 계산(計算)하였다. 1. 화동토양(華東土壤)의 모래함량(含量)에 대한 선형(線型) Variogram은 적합(適合)하지 않았으며, 중동토양(中東土壤)의 점토함량(含量)은 선형(線型) 또는 곡면형(曲面型) Variogram에 부적합(不適合)하였다. 2. 공시지역(供試地域)의 Kriging값과 Kriging 분산(分散)이 계산(計算)되었다. 3. 화동토양(華東土壤)에서 Kriging 분산(分散)과 표준오차(標準誤差)의 차(差)는 Nugget효과(效果)와 근사(近似)하였지만 중동토양(中東土壤)의 점토함량은 그 차(差)가 컸다.