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AI-GEOSTATS: Summary of effect of variogram parameter uncertainty on OK

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  • Ruben Roa
    Hi all: In intrinsic geostatistics, spatial continuity is described by a model (usually the theoretical variogram). Its parameters are estimated by fitting
    Message 1 of 1 , May 7, 2002
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      Hi all:

      In intrinsic geostatistics, spatial continuity is described by a model
      (usually the 'theoretical' variogram). Its parameters are estimated by
      fitting the model to the moment-based Matheron non-parametric
      ('empirical') variogram (with several methods available for estimation).
      Despite being estimated, the model variogram is treated as known in
      intrinsic geostatistics, i.e. the covariance matrix of variogram
      parameters is ignored. The assumedly known (but actually estimated)
      model is then used in kriging. I asked then what was the feeling of
      people in this list about the effect of model-variogram parameter
      uncertainty on kriging, in particular OK.


      My original question:

      Dear list members:
      Do you expect that the uncertainty related to estimating variogram
      parameters have a strong effect on spatial prediction via ordinary
      kriging? It is my impression that usually the analist disregard this
      source of variance and proceeds as if these parameters from the
      variogram were known. This might be justified since normally the sample
      size (pairs of observations) is quite high when fitting the variogram
      via weighted least squares, for instance. Any opinion on this and/or
      references would be much welcome.
      Ruben Roa

      Additional point raised:

      Dear list members,

      Following Ruben Roa's email, I would like to add that I did not
      find any clear criterion to what is the minimum number of data
      pairs that should be used in each lag and this would certainly
      affect the variogram uncertainty. I know that a minimum of 30 data
      pairs is used frequently but my impression is that this is a "rule
      of thumb". I guess this rule originated from the central limit
      theorem (?). I found that the lack of a clear criterion might have
      a big effect on the estimation of the Variogram especially in cases
      where the data points are non regular and in cases where a non
      parametric variogram might be considered.

      I would gratefully appreciate any comments on this as well.



      Response to point raised by Arie:

      I do not know if it is a rule of thumb. But it also depends on the
      variability of your data values. I think it is quite subjective how much
      pairs you will use.

      But you should also consider some more robust variogram estimators as
      or standardized variograms to see if
      there are no artificial structures or erratic structures caused by
      values or outliers or even trends...

      There is a paper which is quite interesting:

      Srivastava, R.M.; Parker, H.M., 1989:Robust measures of spatial
      continuity. In: Armstrong, M., 1989 (editor):Geostatistics. Vol.I.
      Dordrecht, pp. 295-308.

      Regards, Ulrich

      Response to my original question:

      Ruben -

      The variogram parameters you select will influence the final model. In
      my experience, however, the number of neighboring samples can have a
      greater influence than the variogram parameters. I have attached a
      paper describing the selection of the number of samples to use when
      kriging. This is also described in my book on "Geostatistical Error
      Management". You can also visit my website at http://www.gemdqos.com

      Jeff Myers

      Response to my original question:

      You might want to look at a recent book by M. Stein, Some Theory about
      kriging, Springer Publishers

      Donald E. Myers

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