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AI-GEOSTATS: interpretation/testing robustness of variogram

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  • Juliann Aukema
    Hi, I have a question about interpretation and robustness of a variogram. My variogram rises then plateaus and then rises again. I interpret this as meaning
    Message 1 of 3 , Nov 28, 2001
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      Hi,

      I have a question about interpretation and
      robustness of a variogram. My variogram rises then
      plateaus and then rises again. I interpret this as
      meaning that there are two scales at which there is
      spatial dependence of the values. However, the number
      of pairwise comparisons is quite different for each of
      these stages and I am afraid I may just be seeing an
      artifact of the sampling. I used variowin and when I
      fit a model for just the first rise and plateau, the
      sill was at about 1500 meters. The first point has 70
      pairs and then from right before the plateau (1000 m)
      to the beginning of the second rise, there are 324-396
      pairs and finally the points in the second rise have
      between 512-534 pairs. I have a total of 66 sample
      points, but they are not evenly spaced with two areas
      more heavily sampled than intervening areas.
      Additional sampling is not feasible. Do I have a
      problem? Is there a way to test the robustness of this
      variogram (I don't know how to fit a model to a
      variogram with two rises, so I couldn�t' do cross
      validation)?

      (Additional information - other data and analyzing the
      same data with nested ANOVA, looking at smaller scales
      within the data set, support the first rise. Taking
      the residuals of a correlated variable - elevation -
      removes the second rise but maintains the first rise -
      my interpretation is that there are different
      processes at the two scales).

      I would appreciate any suggestions,

      Thanks a lot,
      Juliann Aukema
      aukema@...


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    • Pierre Goovaerts
      Hi Juliann, This type of feature is frequently observed when the variogram is being computed for lags larger than half the maximum dimension of the study area.
      Message 2 of 3 , Nov 28, 2001
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        Hi Juliann,

        This type of feature is frequently observed when
        the variogram is being computed for lags larger
        than half the maximum dimension of the study area.
        In your case it might also correspond to the
        separation distance between the two most densely sampled
        subareas.

        The most important questions is "What do you want
        to do with this variogram". If the next step is to apply
        kriging and this rise is not spurious (e.g. may
        reflect some trend in the data), the issue is whether you
        need to model this second part of the variogram.
        If the radius of the kriging search window is smaller
        than the lag at which the second rise occurs, I wouldn't
        bother modeling it.

        Pierre
        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        ________ ________
        | \ / | Pierre Goovaerts
        |_ \ / _| Assistant professor
        __|________\/________|__ Dept of Civil & Environmental Engineering
        | | The University of Michigan
        | M I C H I G A N | EWRE Building, Room 117
        |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
        _| |_\ /_| |_
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        Fax: (734) 763-2275
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        On Wed, 28 Nov 2001, Juliann Aukema wrote:

        > Hi,
        >
        > I have a question about interpretation and
        > robustness of a variogram. My variogram rises then
        > plateaus and then rises again. I interpret this as
        > meaning that there are two scales at which there is
        > spatial dependence of the values. However, the number
        > of pairwise comparisons is quite different for each of
        > these stages and I am afraid I may just be seeing an
        > artifact of the sampling. I used variowin and when I
        > fit a model for just the first rise and plateau, the
        > sill was at about 1500 meters. The first point has 70
        > pairs and then from right before the plateau (1000 m)
        > to the beginning of the second rise, there are 324-396
        > pairs and finally the points in the second rise have
        > between 512-534 pairs. I have a total of 66 sample
        > points, but they are not evenly spaced with two areas
        > more heavily sampled than intervening areas.
        > Additional sampling is not feasible. Do I have a
        > problem? Is there a way to test the robustness of this
        > variogram (I don't know how to fit a model to a
        > variogram with two rises, so I couldn’t' do cross
        > validation)?
        >
        > (Additional information - other data and analyzing the
        > same data with nested ANOVA, looking at smaller scales
        > within the data set, support the first rise. Taking
        > the residuals of a correlated variable - elevation -
        > removes the second rise but maintains the first rise -
        > my interpretation is that there are different
        > processes at the two scales).
        >
        > I would appreciate any suggestions,
        >
        > Thanks a lot,
        > Juliann Aukema
        > aukema@...
        >
        >
        > __________________________________________________
        > Do You Yahoo!?
        > Yahoo! GeoCities - quick and easy web site hosting, just $8.95/month.
        > http://geocities.yahoo.com/ps/info1
        >
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        >


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      • Isobel Clark
        Juliann Three obvious possibilities: (1) you have a large scale trend which only shows up when you start taking pairs at larger distances. This would be the
        Message 3 of 3 , Nov 29, 2001
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          Juliann

          Three obvious possibilities:

          (1) you have a large scale trend which only shows up
          when you start taking pairs at larger distances. This
          would be the case if your second 'rise' tends to curve
          upwards rather than flattening.

          (2) you have anisotropy. If you did an
          'omni-directional' semi-variogram, your smaller
          distances will have pairs from all directions and you
          will see an 'average' sort of semi-variogram. When you
          go to larger distances you are getting lots of pairs
          in whatever direction lies between the two clusters
          and not much in any other direction. So your larger
          scale semi-variogram may be the one in that direction
          only.

          (3) you are actually dealing with two different
          population groups within the sampled areas. If they
          have much the same internal structure but differ from
          one another in behaviour, you would get this type of
          behaviour. In geological applications, you would look
          (perhaps) for a fault line or geological boundary
          between the two.

          As Pierre says, you must ask some basic questions.
          Mine would be: why were those two areas so heavily
          sampled with comparatively sparser sampling elsewhere?

          Hope this helps
          Isobel
          http://uk.geocities.com/drisobelclark

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