Sequential kriging and cokriging: Two powerful geostatistical approaches

J. A. Vargas-Guzmán, T. C.Jim Yeh

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

A sequential linear estimator is developed in this study to progressively incorporate new or different spatial data sets into the estimation. It begins with a classical linear estimator (i.e., kriging or cokriging) to estimate means conditioned to a given observed data set. When an additional data set becomes available, the sequential estimator improves the previous estimate by using linearly weighted sums of differences between the new data set and previous estimates at sample locations. Like the classical linear estimator, the weights used in the sequential linear estimator are derived from a system of equations that contains covariances and cross-covariances between sample locations and the location where the estimate is to be made. However, the covariances and cross-covariances are conditioned upon the previous data sets. The sequential estimator is shown to produce the best, unbiased linear estimate, and to provide the same estimates and variances as classic simple kriging or cokriging with the simultaneous use of the entire data set. However, by using data sets sequentially, this new algorithm alleviates numerical difficulties associated with the classical kriging or cokriging techniques when a large amount of data are used. It also provides a new way to incorporate additional information into a previous estimation.

Original languageEnglish (US)
Pages (from-to)416-435
Number of pages20
JournalStochastic Environmental Research and Risk Assessment
Volume13
Issue number6
DOIs
StatePublished - Jan 1 1999

Keywords

  • Conditional covariance
  • Interpolation with large data sets
  • Sequential linear estimator
  • Successive linear estimator

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)

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