Science China Earth Sciences

, Volume 53, Issue 2, pp 181–188 | Cite as

Estimating spatial attribute means in a GIS environment

Research Paper

Abstract

The estimation of geographical attributes is a crucial matter for many real-world problems, and the issue of accuracy stands out when the estimation is used for between-regions comparison. In this work, our concern is area attribute estimation in a GIS environment. We estimate the area attribute value with a mean Kriging technique, and the probability distribution of the estimate is derived. This is the best linear unbiased observed spatial population mean estimate and can be used in more relaxed situations than the block Kriging technique. Both theoretical analysis and empirical study show that the mean Kriging technique outperforms the ordinary Kriging, spatial random sampling, and simple random sampling techniques in estimating the observable spatial population mean across space.

Keywords

spatial mean mean Kriging spatial dependence GIS 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Christakos G, Bogaert P, Serre, M L. Temporal GIS. Berlin: Springer-Verlag, 2002Google Scholar
  2. 2.
    Christakos G. Modern statistical analysis and optimal estimation of geotechnical data. Eng Geol, 1985, 22: 175–200CrossRefGoogle Scholar
  3. 3.
    Christakos G. Random Field Models in Earth Sciences. San Diego: Academic Press, 1992Google Scholar
  4. 4.
    Arrow K, Dasgupta P, Maler K G. Evaluating projects and assessing sustainable development in imperfect economics. Environ Resour Econ, 2003, 26: 647–685CrossRefGoogle Scholar
  5. 5.
    Olea R A. Geostatistics for Engineers and Earth Scientists. Berlin: Springer, 1999Google Scholar
  6. 6.
    Bayraktar H, Turalioglu F S. A Kriging-based approach for locating a sampling site—in the assessment of air quality. Stochastic Environ Res Risk Assess, 2005, 19: 301–305CrossRefGoogle Scholar
  7. 7.
    Brus D J, Gruijter J J D. Random sampling of geostatistical modeling? choosing between design-based and model-based sampling strategies for soil (with discussion). Geoderma, 1997, 80: 1–44CrossRefGoogle Scholar
  8. 8.
    Cressie N. The origins of Kriging. Math Geol, 1990, 22: 239–252CrossRefGoogle Scholar
  9. 9.
    Haining R. Estimating spatial means with an application to remote sensing data. Comm Stat, 1988, 17: 537–597Google Scholar
  10. 10.
    Saito H, McKenna S A, Zimmerman D A, et al. Geostatistical interpolation of object counts collected from multiple strip transects: Ordinary Kriging versus finite domain Kriging. Stochastic Environ Res Risk Assess, 2005, 19: 71–85CrossRefGoogle Scholar
  11. 11.
    Christakos G. Recursive parameter estimation with applications in earth sciences. Math Geol, 1985, 17: 489–515CrossRefGoogle Scholar
  12. 12.
    Courtier P, Talagrand O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus A, 1990, 42: 531–549CrossRefGoogle Scholar
  13. 13.
    Daley R. Atmospheric Data Analysis. Cambridge: Cambridge University Press, 1991Google Scholar
  14. 14.
    Li X, Yeh A G. Modelling sustainable urban development by the integration of constrained cellular automata and GIS. Int J Geogr Inf Sci, 2000, 14: 131–152CrossRefGoogle Scholar
  15. 15.
    Serre M L, Christakos G. BME studies of stochastic differential equations representing physical laws-Part II. 5th Annual Confer, Intern Assoc for Math Geol, Trondheim, Norway, 1999. 93–98Google Scholar
  16. 16.
    Christakos G. A Bayesian/maximum-entropy view to the spatial estimation problem. Math Geol, 1990, 22: 763–776CrossRefGoogle Scholar
  17. 17.
    Christakos G. Spatiotemporal information systems in soil and environmental sciences. Geoderma, 1998, 85: 141–179CrossRefGoogle Scholar
  18. 18.
    Kolovos A, Christakos G, Serre M L, et al. Computational BME solution of a stochastic advection-reaction equation in the light of site-specific information. Water Resour Res, 2002, 38: 1318–1334CrossRefGoogle Scholar
  19. 19.
    Papantonopoulos G, Modis K.A. BME solution of the stochastic three-dimensional Laplace equation representing a geothermal field subject to site-specific information. Stoch Environ Res and Risk Assess, 2006, 20: 23–32CrossRefGoogle Scholar
  20. 20.
    Courtier P, Derber J, Errico R, et al. Important literature on the adjoint, variational methods and the Kalman filter in meteorology. Tellus A, 1993, 45: 342–357CrossRefGoogle Scholar
  21. 21.
    Derber J C. A variational continuous assimilation technique. Mon Wea Rev, 1989, 117: 2437–2446CrossRefGoogle Scholar
  22. 22.
    Fillion L, Errico R M. Variational assimilation of precipitation data using moist-convective parameterization schemes: A 1D-VAR study. Mon Wea Rev, 1997, 125: 2917–2942CrossRefGoogle Scholar
  23. 23.
    Ott W, Hunt B R, Szunyogh I, et al. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A, 2004, 56: 415–428CrossRefGoogle Scholar
  24. 24.
    Zhang C S, Fay D, McGrath D, et al. Use of trans-Gaussian Kriging for national soil geochemical mapping in Ireland. Geochem-Explor Environ Anal, 2008, 8: 255–265CrossRefGoogle Scholar
  25. 25.
    Christakos G, Kolovos A, Serre M L, et al. Total ozone mapping by integrating data bases from remote sensing instruments and empirical models. IEEE Trans Geosci Remote Sensing, 2004, 42: 991–1008CrossRefGoogle Scholar
  26. 26.
    Goodman J M. Space Weather and Telecommunications. Berlin: Springer, 2005Google Scholar
  27. 27.
    Reddy J N. Energy Principles and Variational Methods in Applied Mechanics. New York: John Wiley & Sons, 2002Google Scholar
  28. 28.
    Zhu A X, Hudson B, Burt J, et al. Soil mapping using GIS, expert knowledge, and fuzzy logic. Soil Sci Soc Am J, 2001, 65: 1463–1472CrossRefGoogle Scholar
  29. 29.
    Cochran W G. Sampling Techniques. New York: John Wiley & Sons, 1997Google Scholar
  30. 30.
    Griffith D A, Haining R, Arbia G. Heterogeneity of attribute sampling error in spatial data sets. Geogr Anal, 1994, 26: 300–320Google Scholar
  31. 31.
    Haining R. Spatial Data Analysis: Theory and Practice. Cambridge: Cambridge University Press, 2003Google Scholar
  32. 32.
    Isaaks E H, Srivastava R M. An Introduction to Applied Geostatistics. Oxford: Oxford University Press, 1989Google Scholar
  33. 33.
    Grimmett G R, Stirzaker D R. Probability and Random Processes. Oxford: Oxford Science Publications, 1992Google Scholar
  34. 34.
    Shi W Z, Tian T. A hybrid interpolation method for the refinement of regular grid digital elevation model. Int J Geogr Inf Sci, 2006, 20: 53–67CrossRefGoogle Scholar
  35. 35.
    Christakos G. Modern Spatiotemporal Geostatistics. Oxford: Oxford University Press, 2000Google Scholar
  36. 36.
    Krejcr P. Development of the Kriging method with application. Appl Math, 2002, 47: 217–230CrossRefGoogle Scholar
  37. 37.
    Pardo-Ig’uzquiza E, Dowd P A. Empirical maximum likelihood Kriging: The general case. Math Geol, 2005, 37: 477–492CrossRefGoogle Scholar
  38. 38.
    Atkinson P M. The effect of spatial resolution on the experimental variogram of airborne MSS imagery. Int J Remote Sensing, 1993, 14: 1005–1011CrossRefGoogle Scholar
  39. 39.
    Brus D J, Gruijter J J D. A method to combine non-probability sample data with probability sample data in estimating spatial means of environmental variables. Environ Monitor Assess, 2002, 83: 303–317CrossRefGoogle Scholar
  40. 40.
    Wang J F, Liu J Y, Zhuang D F, et al. Spatial sampling design for monitoring cultivated land. Int J Remote Sensing, 2002, 23: 263–284CrossRefGoogle Scholar
  41. 41.
    Wang J F, Christakos G, Li L F. Sampling and Kriging spatial means: Efficiency and conditions. Sensors, 2009, 9: 5224–5240CrossRefGoogle Scholar
  42. 42.
    Liu J Y, Zhang Z X, Zhuang D F, et al. Remote Sensing Analysis of Landuse Change in the 1990s (in Chinese). Beijing: Science Press, 2005Google Scholar
  43. 43.
    Wang J F, Christakos G, Hu M G. Modeling spatial means of surfaces with stratified non-homogeneity. IEEE Trans Geosci Remote Sensing, 2009, 47: 4167–4174CrossRefGoogle Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institute of Geographic Sciences & Natural Resources ResearchChinese Academy of SciencesBeijingChina
  2. 2.Department of GeographySan Diego State UniversitySan DiegoUSA

Personalised recommendations