On the prediction error variance of three common spatial interpolation schemes

Phaedon C. Kyriakidis, Michael F. Goodchild

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

Three forms of linear interpolation are routinely implemented in geographical information science, by interpolating between measurements made at the endpoints of a line, the vertices of a triangle, and the vertices of a rectangle (bilinear interpolation). Assuming the linear form of interpolation to be correct, we study the propagation of error when measurement error variances and covariances are known for the samples at the vertices of these geometric objects. We derive prediction error variances associated with interpolated values at generic points in the above objects, as well as expected (average) prediction error variances over random locations in these objects. We also place all the three variants of linear interpolation mentioned above within a geostatistical framework, and illustrate that they can be seen as particular cases of Universal Kriging (UK). We demonstrate that different definitions of measurement error in UK lead to different UK variants that, for particular expected profiles or surfaces (drift models), yield weights and predictions identical with the interpolation methods considered above, but produce fundamentally different (yet equally plausible from a pure data standpoint) prediction error variances.

Original languageEnglish (US)
Pages (from-to)823-855
Number of pages33
JournalInternational Journal of Geographical Information Science
Volume20
Issue number8
DOIs
StatePublished - Sep 1 2006
Externally publishedYes

Keywords

  • Bilinear interpolation
  • Error propagation
  • Geostatistics
  • Linear interpolation
  • Spatial accuracy assessment
  • Trend surface models

ASJC Scopus subject areas

  • Information Systems
  • Geography, Planning and Development
  • Library and Information Sciences

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