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AI-GEOSTATS: Number of data points & Variograms

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  • K. Ramanitharan
    Dear AI-GEOSTATiSticians, My research is on heavy metal pollution in water bodies. As a part of the analysis, I am doing kriging with the pollutant data. I
    Message 1 of 2 , May 15, 2001
      Dear AI-GEOSTATiSticians,

      My research is on heavy metal pollution in water bodies.
      As a part of the analysis, I am doing kriging with the pollutant data.
      I have couple of problems in doing this task.

      1. Though I have the data sets for 90 water bodies, most of them (85) have
      data points
      less than 10. As one can expect, this 'environment' gives trouble in
      fitting variograms.
      Two papers, I came across on similar issue haven't help me much in solving
      the problem.

      Is there any consistent tested way to approach such 'not-enough-data'
      situations?

      2. Some data are with 'Hot Spots'. However, when I work with the data sets,
      I have the trouble in fitting the variogram. My questions may be trivial ones.

      How to distinguish Outliers from Hotspots, if there is a lack of
      site-information beyond the data set?
      Could it be possible to effectively fit variograms, when the hot spots are
      present?
      Could a variogram capture the hot spot presence for kriging?
      [ For most of the cases I tried with such suspected hotspot data, my
      results show that
      the linear interpolation works better than the krigged distribution based
      on the 'fitted' variograms]


      I would appreciate if anyone could provide me some suggestions on the above
      difficulties, and relevant
      references for my reading

      Thank you very much.

      Regards,
      -/Ramanitharan, K.

      =====

      Ramanitharan Kandiah
      Graduate Student
      Department of Civil & Environmental Engineering
      Tulane University
      New Orleans, LA 70125
      USA.




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    • Isobel Clark
      ... Hi, some thoughts (your numbering): (1) One of the things I have found successful is the following: construct your semi-variogram using ALL of your data
      Message 2 of 2 , May 15, 2001
        > My research is on heavy metal pollution in water
        > bodies.........

        Hi, some thoughts (your numbering):

        (1) One of the things I have found successful is the
        following:
        construct your semi-variogram using ALL of your
        data but not allowing pairs between samples in
        different water bodies;
        use cross validation on each water body separately
        to see if the 'generic' model works for all of them or
        whether some are more variable or harder to predict
        than others;
        use the generic model for kriging with a
        variance/sill scaled for each water body.

        > Is there any consistent tested way to approach such
        > 'not-enough-data' situations?
        Not really, but I have found this works if the
        'deposition' is similar in the various bodies.

        (2) 'Hot spots' are (a) erratic highs due to
        distribution being skewed or (b) true outliers
        (inhomogeneities). Which? Tackle accordingly. Cross
        validation will pick up outliers but not work properly
        if data is severely skewed.

        > Could it be possible to effectively fit variograms,
        > when the hot spots are present?
        Try calculating semi-variograms with and without 'hot
        spots' and see what happens.

        Kriging is based on an assumption of homogeneity and
        it is a little unfair to expect it to come back and
        say "that's a daft thing to do" ;-)

        > [ For most of the cases I tried with such suspected
        > hotspot data, my results show that
        > the linear interpolation works better than the
        > krigged distribution based on the 'fitted'
        > variograms]
        I find this statement interesting. How do you define
        "better" -- prettier? nicer? easier to interpret? less
        polluted?


        Isobel Clark


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