Journal of the Korean earth science society (한국지구과학회지)

The Korean Earth Science Society (한국지구과학회)
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Selection of Optimal Values in Spatial Estimation of Environmental Variables using Geostatistical Simulation and Loss Functions

  • Park, No-Wook (Department of Geoinformatic Engineering, Inha University)
  • Received : 2010.07.14
  • Accepted : 2010.08.30
  • Published : 2010.09.30
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Abstract

Spatial estimation of environmental variables has been regarded as an important preliminary procedure for decision-making. A minimum variance criterion, which has often been adopted in traditional kriging algorithms, does not always guarantee the optimal estimates for subsequent decision-making processes. In this paper, a geostatistical framework is illustrated that consists of uncertainty modeling via stochastic simulation and risk modeling based on loss functions for the selection of optimal estimates. Loss functions that quantify the impact of choosing any estimate different from the unknown true value are linked to geostatistical simulation. A hybrid loss function is especially presented to account for the different impact of over- and underestimation of different land-use types. The loss function-specific estimates that minimize the expected loss are chosen as optimal estimates. The applicability of the geostatistical framework is demonstrated and discussed through a case study of copper mapping.

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References

  1. Chiles, J.-P. and Delfiner, P., 1999, Geostatistics: Modelling Spatial Uncertainty. Wiley, NY, USA, 695 p.
  2. Cho, H.-L. and Jeong, J.-C., 2009, The distribution analysis of PM10 in Seoul using spatial interpolation methods. Journal of the Korean Society of Environmental Impact Assessment, 18, 31-39. (in Korean)
  3. Da Cruz, P.S., 2000, Reservoir management decision-making in the presence of geological uncertainty. Ph.D. thesis, Stanford University, Stanford, USA, 221 p.
  4. De Bruin, S., Bregt, A., and Van De Ven, M., 2001, Assessing fitness for use: the expected value of spatial data sets. International Journal of Geographical Information Science, 15, 457-471. https://doi.org/10.1080/13658810110053116
  5. Deutsch, C.V., 2002, Geostatistical Reservoir Modeling. Oxford University Press, NY, USA, 376 p.
  6. Deutsch, C.V. and Journel, A.G., 1998, GSLIB: Geostatistical Software Library and User's Guide. 2nd ed., Oxford University Press, NY, USA, 369 p.
  7. Godoy, M.C., Dimitrakopoulos, R., and Costa, J.F., 2001, Economic functions and geostatistical simulation applied to grade control. In Edwards, A.C. (ed.), Mineral Resources and Ore Reserve–The AusIMM Guide to Good Practice. The Australasian Institute of Mining and Metallurgy, Melbourne, Australia, 591-599.
  8. Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation. Oxford University Press, NY, USA, 483 p.
  9. Goovaerts, P., 2001, Geostatistical modeling of uncertainty in soil science. Geoderma, 103, 3-26. https://doi.org/10.1016/S0016-7061(01)00067-2
  10. Journel, A.G., 1983, Non-parametric estimation of spatial distributions. Mathematical Geology, 15, 445-468. https://doi.org/10.1007/BF01031292
  11. Journel, A.G., 1996, Modeling uncertainty and spatial dependence: stochastic imaging. International Journal of Geographical Information Science, 10, 517-522. https://doi.org/10.1080/02693799608902094
  12. Kwon, B.-D. and Oh, S.-H., 2002, Bayesian inversion of gravity and resistivity data: detection of lava tunnel. Journal of the Korean Earth Science Society, 23, 15-29.
  13. Lee, D.-S., 1966, Explanatory Text of the Geological Map of Ogdong Sheet. Geological Survey of Korea, Seoul, Korea, 30 p.
  14. Lee, J.-S., Hong, Y.-K., Kim, S.-Y., Yun, H.-S., Jin, M.-S., and Lee, C.-Y., 1984, Geochemical Maps for Ogdong Sheet in the Taebagsan Mineralized Belt. Korea Institute of Energy and Resources, Daejeon, Korea, 35 p.
  15. Leuangthong, O., Khan, K.D., and Deutsch, C.V., 2008, Solved Problems in Geostatistics. Wiley, NJ, USA, 207p.
  16. Morgan, M.G. and Henrion, M., 1990, Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press, NY, USA, 332 p.
  17. Oh, S.-H., 2005, RMR evaluation by integration of geophysical and borehole data using non-linear indicator transform and 3D kriging. Journal of the Korean Earth Science Society, 26, 429-435. (in Korean)
  18. Oh, S.-H., 2008, Geostatistical inversion of RMR using geophysical data. Journal of the Korean Society for Geosystem Engineering, 45, 620-626. (in Korean)
  19. Park, N.-W., 2009, Comparison of univariate kriging algorithms for GIS-based thematic mapping with ground survey data. Korean Journal of Remote Sensing, 25, 321-338. (in Korean) https://doi.org/10.7780/kjrs.2009.25.4.321
  20. Park, N.-W., Jang, D.-H., and Chi, K.-H., 2009, Integration of IKONOS imagery for geostatistical mapping of sediment grain size at Baramarae beach, Korea. International Journal of Remote Sensing, 30, 5703-5724. https://doi.org/10.1080/01431160902729564
  21. Solow, A.R. and Ratick, S.J., 1994, Condtional simulation and the value of information. In Dimitrakopoulos, R. (ed.), Geostatistics for the Next Century, Springer, NY, USA, 209-217.
  22. Srivastava, R.M., 1987, Minimum variance or maximum profitability? CIM Bulletin, 80, 63-68.