Skip to main content
SpringerLink
Log in

Estimating spatial attribute means in a GIS environment

  • Research Paper
  • Published:
Science China Earth Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Christakos G, Bogaert P, Serre, M L. Temporal GIS. Berlin: Springer-Verlag, 2002

    Google Scholar 

  2. Christakos G. Modern statistical analysis and optimal estimation of geotechnical data. Eng Geol, 1985, 22: 175–200

    Article  Google Scholar 

  3. Christakos G. Random Field Models in Earth Sciences. San Diego: Academic Press, 1992

    Google Scholar 

  4. Arrow K, Dasgupta P, Maler K G. Evaluating projects and assessing sustainable development in imperfect economics. Environ Resour Econ, 2003, 26: 647–685

    Article  Google Scholar 

  5. Olea R A. Geostatistics for Engineers and Earth Scientists. Berlin: Springer, 1999

    Google Scholar 

  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: 301–305

    Article  Google Scholar 

  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: 1–44

    Article  Google Scholar 

  8. Cressie N. The origins of Kriging. Math Geol, 1990, 22: 239–252

    Article  Google Scholar 

  9. Haining R. Estimating spatial means with an application to remote sensing data. Comm Stat, 1988, 17: 537–597

    Google Scholar 

  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: 71–85

    Article  Google Scholar 

  11. Christakos G. Recursive parameter estimation with applications in earth sciences. Math Geol, 1985, 17: 489–515

    Article  Google Scholar 

  12. Courtier P, Talagrand O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus A, 1990, 42: 531–549

    Article  Google Scholar 

  13. Daley R. Atmospheric Data Analysis. Cambridge: Cambridge University Press, 1991

    Google Scholar 

  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: 131–152

    Article  Google Scholar 

  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. 93–98

  16. Christakos G. A Bayesian/maximum-entropy view to the spatial estimation problem. Math Geol, 1990, 22: 763–776

    Article  Google Scholar 

  17. Christakos G. Spatiotemporal information systems in soil and environmental sciences. Geoderma, 1998, 85: 141–179

    Article  Google Scholar 

  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: 1318–1334

    Article  Google Scholar 

  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: 23–32

    Article  Google Scholar 

  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: 342–357

    Article  Google Scholar 

  21. Derber J C. A variational continuous assimilation technique. Mon Wea Rev, 1989, 117: 2437–2446

    Article  Google Scholar 

  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: 2917–2942

    Article  Google Scholar 

  23. Ott W, Hunt B R, Szunyogh I, et al. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A, 2004, 56: 415–428

    Article  Google Scholar 

  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: 255–265

    Article  Google Scholar 

  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: 991–1008

    Article  Google Scholar 

  26. Goodman J M. Space Weather and Telecommunications. Berlin: Springer, 2005

    Google Scholar 

  27. Reddy J N. Energy Principles and Variational Methods in Applied Mechanics. New York: John Wiley & Sons, 2002

    Google Scholar 

  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: 1463–1472

    Article  Google Scholar 

  29. Cochran W G. Sampling Techniques. New York: John Wiley & Sons, 1997

    Google Scholar 

  30. Griffith D A, Haining R, Arbia G. Heterogeneity of attribute sampling error in spatial data sets. Geogr Anal, 1994, 26: 300–320

    Google Scholar 

  31. Haining R. Spatial Data Analysis: Theory and Practice. Cambridge: Cambridge University Press, 2003

    Google Scholar 

  32. Isaaks E H, Srivastava R M. An Introduction to Applied Geostatistics. Oxford: Oxford University Press, 1989

    Google Scholar 

  33. Grimmett G R, Stirzaker D R. Probability and Random Processes. Oxford: Oxford Science Publications, 1992

    Google Scholar 

  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: 53–67

    Article  Google Scholar 

  35. Christakos G. Modern Spatiotemporal Geostatistics. Oxford: Oxford University Press, 2000

    Google Scholar 

  36. Krejcr P. Development of the Kriging method with application. Appl Math, 2002, 47: 217–230

    Article  Google Scholar 

  37. Pardo-Ig’uzquiza E, Dowd P A. Empirical maximum likelihood Kriging: The general case. Math Geol, 2005, 37: 477–492

    Article  Google Scholar 

  38. Atkinson P M. The effect of spatial resolution on the experimental variogram of airborne MSS imagery. Int J Remote Sensing, 1993, 14: 1005–1011

    Article  Google Scholar 

  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: 303–317

    Article  Google Scholar 

  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: 263–284

    Article  Google Scholar 

  41. Wang J F, Christakos G, Li L F. Sampling and Kriging spatial means: Efficiency and conditions. Sensors, 2009, 9: 5224–5240

    Article  Google Scholar 

  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, 2005

    Google Scholar 

  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: 4167–4174

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Geographic Sciences & Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China

    JinFeng Wang & LianFa Li

  2. Department of Geography, San Diego State University, San Diego, CA, 92182-4493, USA

    George Christakos

Authors
  1. JinFeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. LianFa Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George Christakos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JinFeng Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Li, L. & Christakos, G. Estimating spatial attribute means in a GIS environment. Sci. China Earth Sci. 53, 181–188 (2010). https://doi.org/10.1007/s11430-009-0193-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11430-009-0193-x

Keywords

Search

Navigation