Mathematical Geology

, Volume 28, Issue 1, pp 73–86 | Cite as

Comparison of kriging techniques in a space-time context

  • Patrick Bogaert
Article

Abstract

Space-time processes constitute a particular class, requiring suitable tools in order to predict values in time and space, such as a space-time variogram or covariance function. The space-time co-variance function is defined and linked to the Linear Model of Coregionalization under second-order space-time stationarity. Simple and ordinary space-time kriging systems are compared to simple and ordinary cokriging and their differences for unbiasedness conditions are underlined. The ordinary space-time kriging estimation then is applied to simulated data. Prediction variances and prediction errors are compared with those for ordinary kriging and cokriging under different unbiasedness conditions using a cross-validation. The results show that space-time kriging tend to produce lower prediction variances and prediction errors that kriging and cokriging.

Key words

space-time kriging space-time separability linear coregionalization autokrigeability condition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armstrong, M., Chetboun, G., and Hubert, P., 1992, Kriging and rainfall in Lesotho,in Soares, A., ed., Geostatistics, v. 2: Troia, Portugal, p. 661–672.Google Scholar
  2. Bilonick, R. A., 1985, The space-time distribution of sulfate deposition in the northeastern United States: Atmospheric Environment, v. 19, no. 11, p. 1829–1845.CrossRefGoogle Scholar
  3. Christakos, G., 1992, Random fields models in earth sciences: Academic Press, New York, 474 P.Google Scholar
  4. Isaaks, E. H., and Srivastava, R. M., 1989, An introduction to applied geostatistics: Oxford Univ. Press, Oxford, 561 p.Google Scholar
  5. Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatistics: Academic Press, London, 600 P.Google Scholar
  6. Myers, D. E., 1991, Pseudo-cross variograms, positive-definiteness, and cokriging: Math. Geology, v. 23, no. 6, p. 805–816.CrossRefGoogle Scholar
  7. Myers, D. E., and Journel, A., 1990, Variograms with zonal anisotropies and noninvertible kriging systems: Math. Geology, v. 22, no. 7, p. 779–785.CrossRefGoogle Scholar
  8. Papritz, A., and Flühler, H., 1994, Temporal change of spatially autocorrelated soil properties: optimal estimation by kriging: Geoderma, v. 62, p. 29–43.CrossRefGoogle Scholar
  9. Rodriguez-Iturbe, I., and Mejia, J. M., 1974, The design of rainfall networks in time and space: Water Resources Res., v. 10, no. 4, p. 713–728.Google Scholar
  10. Rouhani, S., and Hall, T. J., 1989, Space-time kriging of groundwater data,in Armstrong, M., ed., Geostatistics, v. 2: Avignon, France, p. 639–650.Google Scholar
  11. Rouhani, S., and Myers, D. E., 1990, Problems in space-time kriging of geohydrological data: Math. Geology, v. 22, no. 5, p. 611–623.CrossRefGoogle Scholar
  12. Rouhani, S., and Wackemagel, H., 1990, Multivariate geostatistical approach to space-time data analysis: Water Resources Res., v. 26, no. 4, p. 585–591.CrossRefGoogle Scholar
  13. Searle, S. R., 1982, Matrix algebra useful for statistics: Wiley, New York, 438 p.Google Scholar
  14. Seguret, S., 1993, Analyse krigeante spatio-temporelle appliquée à des données aéromagnétiques: Cahiers de Géostatistique, Fasc.3, ENSMP, Fontainebleau, France, p. 115–138.Google Scholar
  15. Wackernagel, H., 1992, Cours de géostatistique multivariable: Report C-146, Centre de Géostatistique, Fontainebleau, France, 62 p.Google Scholar
  16. Wackernagel, H., 1994, Cokriging versus kriging in regionalized multivariate data analysis: Geoderma, v. 62, p. 83–92.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • Patrick Bogaert
    • 1
  1. 1.Faculté des Sciences AgronomiquesUnité de BiométrieLouvain-la-NeuveBelgium

Personalised recommendations