• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.6B
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• pp.525-532
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• 2010

Kriging is widely applied to dealing with the spatial distribution of rainfall, however its prediction results are different according to the selection of variogram type. This study investigated adequate variogram for daily rainfall. The comparative results show that kriging prediction with covariates is better than that without covariates. The Mat$\acute{e}$rn correlation function, which is the most general type variogram, is recommended if adequate variogram is difficult to determine.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2002.09a
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• pp.156-160
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• 2002

실험적 베리오그램의 모델링에 SA(Simulated Annealing)기법을 이용하였다. 최소 자승법의 해를 구하기 위하여 기존의 상용 프로그램에서 많이 이용되고 있는 반복법에 근거한 방법에 비해서 SA 기법은 초기 가정값에 크게 영향을 받지 않고 일정한 모델 인자의 값을 제시하였다. 임의의 초기 가정값을 입력하여도 충분한 반복 계산을 통하여 목적함수의 값이 광역적 최소값으로 수렴하는 것을 확인할 수 있었다. 베리오그램 모델이 일반적으로 비선형 모델이기 때문에 목적함수의 지역적 최소값으로의 수렴이 문제가 되고 이로 인하여 구해지는 인자의 값이 정확하지 않을 수 있지만 SA 기법을 이용하여 최소 자승법의 해를 구하게 되면 정확한 인자의 값을 구할 수 있음을 확인하였다.

• The Korean Journal of Applied Statistics
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• v.12 no.1
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• pp.125-141
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• 1999

서로 다른 위치에서 동시에 관찰된 자료들이 공간적인 변인에 의하여 영향을 받는다면 공간적인 변인의 함수식에 의한 예측모형을 설정하는 것이 타당하다. 본 연구에서는 공간적인 변인으로 거리가 주어졌을 때, 공간자료에 대한 세미베리오그램 모형의 추정과 관측되지 않은 지점에 대한 공간예측기법을 정리하였으며, 또한 공간이상치 탐지를 위한 두가지 방법론으로 분포론적 방법과 p-Deletion 방법을 제시하였다. 방법론의 예시를 위하여 강우강도 자료를 이용하였으며 서로 상관되어 있는 공간데이터에 대한 시뮬레이션을 통하여 두가지 방법을 비교하였다.

• Tunnel and Underground Space
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• v.11 no.2
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• pp.156-166
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• 2001

A stochastic continuum(SC) modeling technique was developed to simulate the groundwater flow pathway in fractured rocks. This model was developed to overcome the disadvantageous points of discrete fracture network(DFN) modes which has the limitation of fracture numbers. Besides, SC model is able to perform probabilistic analysis and to simulate the conductive groundwater pathway as discrete fracture network model. The SC model was formulated based on the discrete fracture network(DFN) model. The spatial distribution of permeability in the stochastic continuum model was defined by the probability distribution and variogram functions defined from the permeabilities of subdivided smaller blocks of the DFN model. The analysis of groundwater travel time was performed to show the consistency between DFN and SC models by the numerical experiment. It was found that the stochastic continuum modes was an appropriate way to provide the probability density distribution of groundwater velocity which is required for the probabilistic safety assessment of a radioactive waste disposal facility.

• Journal of the Korean earth science society
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• v.34 no.1
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• pp.13-27
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• 2013

Quantitative precipitation estimation (QPE) is one of the most important elements in meteorological and hydrological applications. In this study, we adjusted the QPE from an S-band weather radar based on co-kriging method using the geostatistical structure function of error distribution of radar rainrate. In order to estimate the accurate quantitative precipitation, the error of radar rainrate which is a primary variable of co-kriging was determined by the difference of rain rates from rain gauge and radar. Also, the gauge rainfield, a secondary variable of co-kriging is derived from the ordinary kriging based on raingauge network. The error distribution of radar rain rate was produced by co-kriging with the derived theoretical variogram determined by experimental variogram. The error of radar rain rate was then applied to the radar estimated precipitation field. Locally heavy rainfall case during 6-7 July 2009 is chosen to verify this study. Correlation between adjusted one-hour radar rainfall accumulation and rain gauge rainfall accumulation improved from 0.55 to 0.84 when compared to prior adjustment of radar error with the adjustment of root mean square error from 7.45 to 3.93 mm.

• Tunnel and Underground Space
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• v.19 no.5
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• pp.407-420
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• 2009

In this study geostatistical technique using indicator kriging was performed to evaluate the optimal rock mass classification by integrating the various geophysical information such as borehole data and geophysical data. To get the optimal kriging result, it is necessary to devise the suitable technique to integrate the hard (borehole) and soft (geophysical) data effectively. Also, the model parameters of the variogram must be determined as a priori procedure. Iterative non-linear inversion method was implemented to determine the model parameters of theoretical variogram. To verify the algorithm, behaviour of object function and precision of convergence were investigated, revealing that gradient of the range is extremely small. This algorithm for the field data was applied to a mountainous area planned for a large-scale tunneling construction. As for a soft data, resistivity information from AMT survey is incorporated with RMR information from borehole data, a sort of hard data. Finally, RMR profiles were constructed and attempted to be interpreted at the tunnel elevation and the upper 1D level.

• Journal of the Korean earth science society
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• v.32 no.3
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• pp.249-264
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• 2011

A multi-Gaussian kriging approach extended to space-time domain is presented for uncertainty modeling as well as time-series mapping of environmental variables. Within a multi-Gaussian framework, normal score transformed environmental variables are first decomposed into deterministic trend and stochastic residual components. After local temporal trend models are constructed, the parameters of the models are estimated and interpolated in space. Space-time correlation structures of stationary residual components are quantified using a product-sum space-time variogram model. The ccdf is modeled at all grid locations using this space-time variogram model and space-time kriging. Finally, e-type estimates and conditional variances are computed from the ccdf models for spatial mapping and uncertainty analysis, respectively. The proposed approach is illustrated through a case of time-series Particulate Matter 10 ($PM_{10}$) concentration mapping in Incheon Metropolitan city using monthly $PM_{10}$ concentrations at 13 stations for 3 years. It is shown that the proposed approach would generate reliable time-series $PM_{10}$ concentration maps with less mean bias and better prediction capability, compared to conventional spatial-only ordinary kriging. It is also demonstrated that the conditional variances and the probability exceeding a certain thresholding value would be useful information sources for interpretation.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.99-108
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• 2006

대형 할인점 매출 데이터는 G-CRM, 에어기어 마케팅(Area Marketing)에 활용하기 위해 고객의 구매정보와 위치정보를 포함한다. TM중부좌표로 이루어진 고객 위치정보를 이용하여 지점간의 거리를 구할 수 있다. 서로 다른 위치에서 통시에 측정된 자료들이 공간적인 변인에 의하여 영향을 받는다면, 공간적인 변인의 함수식에 의한 예측모형을 설정하는 것이 타당하다. 본 연구에서는 공간적인 변인으로 거리가 주어졌을 때, 대형 할인점 매출 자료에 대한 세미베리오그램(Semi-Variogram)의 모형을 추정하고, 관측되지 않은 지역에 대한 할인점 이용권을 공간예측기법으로 예측하였다. 그리고 공간예측 기법을 통해 예측된 할인점 이용권을 토대로 할인점 이용권 지도를 작성하였다. 또한 매출 데이터의 공간이상치 탐지를 위한 방법을 제시하고 실례로 알아보았다.

• Spatial Information Research
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• v.14 no.1 s.36
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• pp.29-41
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• 2006

Geostatistical data are obtained only at selected sites even though they are potentially available at any location In a continuous surface. Therefore it is necessary to estimate the unknown values at unsampled locations based on observations. In this study we compared the accuracy of 5 spatial interpolation methods: local trend surface, IDW, RBF, ordinary kriging, universal kriging. These interpolation methods were applied to annual rainfall data. As the results of validation tests, universal kriging with gaussian variogram model showed the best accuracy in comparison with other interpolation methods. In the case of kriging, the predicted values were more accurate and within a more narrow range than other methods. In contrast with kriging, local trend surface analysis, IDW and RBF showed the wide range of predicted values and abrupt changes between neighbors.

• Journal of the Korean Society of Groundwater Environment
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• v.7 no.3
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• pp.125-132
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• 2000

pH, EC and TDS are basic components in the investigation of groundwater quality, and are very important to the preliminary assessment of groundwater quality. These three chemical components investigated at the Youngsan and Sumjin river basins in 1998 suggest that the groundwater quality is generally good in these basins. Linear regression analysis shows that TDS versus EC has an linear correlation, but EC versus pH, and TDS versus pH have nearly no correlation. The relation of TDS and EC is 1.0 mg/1=1.52 $mu\textrm{S}$/cm, and it is the quality of natural water. In geostatistical analysis. three kinds of data are stationary random functions and they have exponential variograms. According to the isopleth maps of the groundwater quality, the groundwater quality of the Youngsan river basin is more contaminated than that of the Sumjin river basin. The isopleth maps of TDS and EC show very similar patterns because of the strong correlation between TDS and EC. The minimum and maximum values of the groundwater quality data are not reflected on the isopleth maps because kriging produces smooth distributions with minimum estimation variances.