• 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.

• 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.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.15-31
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• 2003

In this study, we will construct a statistical model which considered the irregularity of observed time sequence in order to analyze sets of bioindex data gathered from stations in Lake Ontario for a number of years. We fit a linear model to account for the trend and seasonal component in an exploratory way and draw variogram and correlogram for further confirmatory studies.

• 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.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.82-85
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• 2003

강원도 춘천시 신북읍 유포리 연구지역의 지하수의 NO$_3$-N 2차원 공간 분포를 정의하기 위하여 지구통계학적 해석 방법인 sequential Gaussian simulation(SGS)을 이용하였다. 원자료의 공간적 clustering을 제거하기 위하여 cell declustering을 수행한 후 normal score 변환을 거친 후 variogram 분석과 모델링을 수행하였다. Exponential, gaussian, spherical variogram model에 대한 각각의 nugget, range, sill을 정의하여 SGS에 이용하였다. SGS에 의해 도출된 결과들은 모두 동일한 결과를 나타낸다. 또한 관측 자료의 분포와 주 오염원의 분포와 상응하는 모델링 결과를 나타내는 것으로 보아 SGS를 이용한 농촌지역 지하수내 NO$_3$-N의 공간적 오염 분포 영상화가 매우 유용하게 활용될 수 있을 것으로 판단된다.

• Journal of Biosystems Engineering
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• v.39 no.4
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• pp.377-388
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• 2014

Purpose: Determining the spatial structure of data is important in understanding within-field variability for site-specific crop management. An understanding of the spatial structures present in the data may help illuminate interrelationships that are important in subsequent explanatory analyses, especially when site variables are correlated or are a combined response to multiple causative factors. Methods: In this study, correlation, principal component analysis, and single and nested variogram models were applied to soil electrical conductivity and chemical property data of two fields in central Missouri, USA. Results: Some variables that were highly correlated, or were strongly expressed in the same principal component, exhibited similar spatial ranges when fitted with a single variogram model. However, single variogram results were dependent on the active lag distance used, with short distances (30 m) required to fit short-range variability. Longer active lag distances only revealed long-range spatial components. Nested models generally yielded a better fit than single models for sensor-based conductivity data, where multiple scales of spatial structure were apparent. Gaussian-spherical nested models fit well to the data at both short (30 m) and long (300 m) active lag distances, generally capturing both short-range and long-range spatial components. As soil conductivity relates strongly to profile texture, we hypothesize that the short-range components may relate to the scale of erosion processes, while the long-range components are indicative of the scale of landscape morphology. Conclusion: In this study, we investigated the effect of changing active lag distance on the calculation of the range parameter. Future work investigating scale effects on other variogram parameters, including nugget and sill variances, may lead to better model selection and interpretation. Once this is achieved, separation of nested spatial components by factorial kriging may help to better define the correlations existing between spatial datasets.

• Korean Journal of Remote Sensing
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• v.36 no.1
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• pp.83-92
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• 2020

The purpose of this work was to apply geographical information system (GIS) for geostatistical analyzing by selecting a semi-variogram model to quantify the spatial correlation of the population distribution with residential neighborhoods in the both sides of Mosul city. Two hundred and sixty-eight sample sites in 240 ㎢ are adopted. After determining the population distribution with respect to neighborhoods, data were inserted to ArcGIS10.3 software. Afterward, the datasets was subjected to the semi-variogram model using ordinary kriging interpolation. The results obtained from interpolation method showed that among the various models, Spherical model gives best fit of the data by cross-validation. The kriging prediction map obtained by this study, shows a particular spatial dependence of the population distribution with the neighborhoods. The results obtained from interpolation method also indicates an unbalanced population distribution, as there is no balance between the size of the population neighborhoods and their share of the size of the population, where the results showed that the right side is more densely populated because of the small area of residential homes which occupied by more than one family, as well as the right side is concentrated in economic and social activities.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.1
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• pp.91-98
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• 2016

In order to apply Kriging methods for geostatistics of spatial data, an estimation of spatial coherency functions is required priorly based on the spatial distance between measurement points. In the study, the typical coherency functions, such as semi-variogram, homeogram, and covariance function, were estimated using the national geoid model. The test area consisting of 2°×2° and the Unified Control Points (UCPs) within the area were chosen as sampling measurements of the geoid. Based on the distance between the control points, a total of 100 sampling points were grouped into distinct pairs and assigned into a bin. Empirical values, which were calculated with each of the spatial coherency functions, resulted out as a wave model of a semi-variogram for the best quality of fit. Both of homeogram and covariance functions were better fitted into the exponential model. In the future, the methods of various Kriging and the functions of estimated spatial coherency need to be studied to verify the prediction accuracy and to calculate the Mean Squared Prediction Error (MSPE).

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.403-418
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• 2004

Recently space-time model in spatial data analysis is widly used. In this paper we applied this model to analysis of greenhouse whitefly. For handling time component, we used ARMA model and autoregressive error model and for outliers, we adapted Mugglestone's method. We compared space-time models and geostatistic model with MSE and MAPE.