• The Korean Journal of Applied Statistics
• /
• v.14 no.2
• /
• pp.415-427
• /
• 2001

공간통계학에서는 다변량 공간자료에 대한 예측방법으로서 코크리깅 기법을 이용한다. 본 논문에서는 코크리깅을 위한 첫 번째 단계인 교차베리오그램의 추정에 대한 감도분석 대신에 일반통계학적 측면에서 주성분점수를 이용한 감도분석방법을 제안한다. 변수가 2개인 경우, 교차베리오그램에 대한 감조분석의 결과와 제안된 주성분점수를 이용한 감도분석의 결과를 비교해 본다. 모의실험을 통하여 제안한 방법의 타당을 검증하고, 실제 자료를 이용한 사례분석의 결과로써 재확인해 본다.

• Journal of The Geomorphological Association of Korea
• /
• v.19 no.3
• /
• pp.37-49
• /
• 2012

The objective of this paper is to propose a methodology for surface sediments classification in tidal flats that can combine ground survey data with high-resolution remote sensing data by multivariate kriging. Unlike conventional methodologies that have classified remote sensing data by using pre-classified sediment components, a new classification methodology presented in this paper first generates sediment component fraction maps and then classifies the sediments on a final stage. For generating sediment component fractions, regression kriging, as one of multivariate kriging algorithms, is applied to integrate ground survey data and remote sensing data. First, trend components of sand, silt, and clay are derived through regression analysis of ground survey data and spectral information from remote sensing data. Then, residuals at sample locations are computed and interpolated to generate residual components in the study area. Finally, the sediment component fractions are computed by adding the residuals to the trend components and are classified on a final stage. A case study at the Baramarae tidal flats with KOMPSAT-2 imagery is carried out to evaluate the classification capability of the proposed classification methodology. Through the case study, the proposed methodology showed the best classification accuracy, compared with the conventional classification methodologies. Especially, much improvement of classification accuracy for fine-grained sediments were also obtained. Therefore, it is expected that the presented classification methodology would be an effective one for surface sediments classification in tidal flats.

• Spatial Information Research
• /
• v.19 no.4
• /
• pp.81-89
• /
• 2011

This paper presents a multivariate kriging algorithm that integrates categorical data as secondary data for spatial interpolation of sparsely sampled ground survey data. Instead of using constant mean values in each attribute of categorical data, disaggregated local mean values at target grid points are first estimated by area-to-point kriging and then are used as local mean values in simple kriging with local means. This algorithm is illustrated through a case study of spatial interpolation of a geochemical copper element with geological map data. Cross validation results indicates that the presented algorithm leads to significant respective improvement of 15% and 25% in prediction capability, compared with univariate ordinary kriging and conventional simple kriging with constant mean values. It is expected that the multivariate kriging algorithm applied in this study would be effectively applied for spatial interpolation with categorical data.

• Journal of the Korean Geographical Society
• /
• v.43 no.6
• /
• pp.1002-1015
• /
• 2008

We investigate the potential of digital elevation model and multivariate geostatistical kriging in mapping of temperature and rainfall based on sparse weather station observations. By using elevation data which have reasonable correlation with temperature and rainfall, and are exhaustively sampled in the study area, we try to generate spatial distributions of temperature and rainfall which well reflect topographic effects and have less smoothing effects. To illustrate the applicability of this approach, we carried out a case study of Jeju island using observation data acquired in January, April, August, and October, 2005. From the case study results, accounting for elevation via colocated cokriging could reflect detailed topographic characteristics in the study area with less smoothing effects. Colocated cokriging also showed much improved prediction capability, compared to that of traditional univariate ordinary kriging. According to the increase of the magnitude of correlation between temperature or rainfall and elevation, much improved prediction capability could be obtained. The decrease of relative nugget effects also resulted in the improvement of prediction capability.

• Economic and Environmental Geology
• /
• v.55 no.4
• /
• pp.353-366
• /
• 2022

Spatial estimation of geoscience data (geo-data) is challenging due to spatial heterogeneity, data scarcity, and high dimensionality. A novel spatial estimation method is needed to consider the characteristics of geo-data. In this study, we proposed the application of Gaussian Mixture Model (GMM) among machine learning algorithms with multivariate data for robust spatial predictions. The performance of the proposed approach was tested through soil chemical concentration data from a former smelting area. The concentrations of As and Pb determined by ex-situ ICP-AES were the primary variables to be interpolated, while the other metal concentrations by ICP-AES and all data determined by in-situ portable X-ray fluorescence (PXRF) were used as auxiliary variables in GMM and ordinary cokriging (OCK). Among the multidimensional auxiliary variables, important variables were selected using a variable selection method based on the random forest. The results of GMM with important multivariate auxiliary data decreased the root mean-squared error (RMSE) down to 0.11 for As and 0.33 for Pb and increased the correlations (r) up to 0.31 for As and 0.46 for Pb compared to those from ordinary kriging and OCK using univariate or bivariate data. The use of GMM improved the performance of spatial interpretation of anthropogenic metals in soil. The multivariate spatial approach can be applied to understand complex and heterogeneous geological and geochemical features.

• Korean Journal of Remote Sensing
• /
• v.22 no.6
• /
• pp.581-593
• /
• 2006

Various geological thematic maps have been generated by interpolating sparsely sampled ground survey data and geostatistical kriging that can consider spatial correlation between neighboring data has widely been used. This paper applies multi-variate geostatistical algorithms to integrate secondary information with sparsely sampled ground survey data for geological thematic mapping. Simple kriging with local means and kriging with an external drift are applied among several multi-variate geostatistical algorithms. Two case studies for spatial mapping of groundwater level and grain size have been carried out to illustrate the effectiveness of multi-variate geostatistical algorithms. A digital elevation model and IKONOS remote sensing imagery were used as secondary information in two case studies. Two multi-variate geostatistical algorithms, which can account for both spatial correlation of neighboring data and secondary data, showed smaller prediction errors and more local variations than those of ordinary kriging and linear regression. The benefit of applying the multi-variate geostatistical algorithms, however, depends on sampling density, magnitudes of correlation between primary and secondary data, and spatial correlation of primary data. As a result, the experiment for spatial mapping of grain size in which the effects of those factors were dominant showed that the effect of using the secondary data was relatively small than the experiment for spatial mapping of groundwater level.

• Geophysics and Geophysical Exploration
• /
• v.16 no.4
• /
• pp.257-267
• /
• 2013

3-D ore modeling was performed to understand the configuration of ore bodies by integrated analysis of borehole and geophysical data in iron-mine area. Five representative indices of rocks were designated, which were obtained from geological survey and borehole. The five indices of rocks were geostatistically simulated by Sequential Indicator Simulation method to delineate boundary of the ore bodies. And Ordinary Kriging and Sequential Gaussian Simulation was applied to make secondary information using resistivity data from magnetotellurics and DC resistivity survey, and this information was used for simple kriging with local varying means, one of integrated kriging techniques. From the correlation analysis between each properties, it was found that high grade of ore is characterized by increased density, whereas the electrical resistivity decreases. With the integrated results of geophysical and borehole data, it was also found that the real configuration of ore body was similar to the modeled result and information about ore grade in 3-D space was obtained.

• Journal of the Korean Geographical Society
• /
• v.44 no.2
• /
• pp.105-121
• /
• 2009

The accurate official map of air temperature does not exist for the Hawaiian Islands due to the limited number of weather stations on the rugged volcanic landscape. To alleviate the major problem of temperature mapping, satellite-measured land surface temperature (LST) data were used as an additional source of sample points. The Moderate Resolution Imaging Spectroradiometer (MODIS) system provides hypertemperal LST data, and LST pixel values that were frequently observed (${\ge}$14 days during a 32-day composite period) had a strong, consistent correlation with air temperature. Systematic grid points with a spacing of 5km, 10km, and 20km were generated, and LST-derived air temperature estimates were extracted for each of the grid points and used as input to inverse distance weighted (IDW) and cokriging methods. Combining temperature data and digital elevation model (DEM), cokriging significantly improved interpolation accuracy compared to IDW. Although a cokriging method is useful when a primary variable is cross-correlated with elevation, interpolation accuracy was sensitively influenced by the seasonal variations of weather conditions. Since the spatial variations of local air temperature are more variable in the wet season than in the dry season, prediction errors were larger during the wet season than the dry season.

• Economic and Environmental Geology
• /
• v.38 no.4 s.173
• /
• pp.435-450
• /
• 2005

The purpose of the study is to analyze the hydrogeochemical characteristics by multivariate statistical method, to interpret the hydrogeochemical processes for the new variables calculated from principal components analysis (PCA), and to infer the groundwater flow and circulation mechanism by applying the geostatistical methods for each element and principal component. Chloride and nitrate are the most influencing components for groundwater quality, and the contents of $NO_3$ increased by the input of agricultural activities show the largest variation. The results of PCA, a multivariate statistical method, show that the first three principal components explain $73.9\%$ of the total variance. PC1 indicates the increase of dissolved ions, PC2 is related with the dissolution of carbonate minerals and nitrate contamination, and PC3 shows the effect of cation exchange process and silicate mineral dissolution. From the results of experimental semivariogram, the components of groundwater are divided into two groups: one group includes electrical conductivity (EC), Cl, Na, and $NO_3$, and the other includes $HCO_3,\;SiO_2,$ Ca, and Sr. The results for spatial distribution of groundwater components showed that EC, Cl, and Na increased with approaching the coastal line and nitrate has close relationship with the presence of agricultural land. These components are also correlated with the topographic features reflecting the groundwater recharge effect. The kriging analysis by using principal components shows that PC 1 has the different spatial distribution of Cl, Na, and EC, possibly due to the influence of pH, Ca, Sr, and $HCO_3$ for PC1. It was considered that the linear anomaly zone of PC2 in western area was caused by the dissolution of carbonate mineral. Consequently, the application of multivariate and geostatistical methods for groundwater in the study area is very useful for determining the quantitative analysis of water quality data and the characteristics of spatial distribution.