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[ai-geostats] Understanding variograms

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  • Jose Luis Gomez Dans
    Hi all, I m new to the list, so bear with me :) I m trying to carry out some kriging of some (x,y,v) data set on to a regular grid. I have read some of the
    Message 1 of 4 , Nov 3, 2004
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      Hi all,
      I'm new to the list, so bear with me :)
      I'm trying to carry out some kriging of some (x,y,v)
      data set on to a
      regular grid. I have read some of the literature, and
      I think that
      this would be a good option (I have also examined the
      possibility of
      interpolating using a TIN, but I feel a bit more
      "safe" using a
      statistical approach!).

      In order to do my kriging, I need to have a model
      semi-variogram, and I
      thought about using gstat for this (from the command
      line, no R
      interfaces, my files are just ASCII (x,y,z) triplets).
      Given that my
      data files are huge (of the order of millions of
      points), I selected a
      region of interest, and tried to produce a sample
      semi-variogram, with
      views to fitting a model.

      In gstat, I got something that resembles y=exp(x),
      which looks
      distinctly wrong. The semivariogram value is ever
      increasing, and does
      not reach a sill at all. This is strange, and rather
      unexpected. I have
      tried doing a log transform of the data, but the shape
      of the curve is
      mostly unchanged.

      I would be very grateful if anyone could shed any
      light on what this
      variogram means, how I could make progress modelling
      it and so on.

      Many thanks!
      José

      --
      Jose L Gomez-Dans, Research Assistant
      Bristol Glaciology Centre, Geographical Sciences/CPOM
      University of Bristol, Bristol, UK






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    • Dan Bebber
      It probably means that you have a spatial trend in your data. Remove any trend, then try again. Dan Bebber Department of Plant Sciences University of Oxford
      Message 2 of 4 , Nov 3, 2004
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        It probably means that you have a spatial trend in your data.
        Remove any trend, then try again.

        Dan Bebber

        Department of Plant Sciences
        University of Oxford
        South Parks Road
        Oxford OX1 3RB
        UK
        Tel. 01865 275000



        > -----Original Message-----
        > From: Jose Luis Gomez Dans [mailto:jgomezdans@...]
        > Sent: 03 November 2004 16:19
        > To: ai-geostats@...
        > Subject: [ai-geostats] Understanding variograms
        >
        >
        > Hi all,
        > I'm new to the list, so bear with me :)
        > I'm trying to carry out some kriging of some (x,y,v)
        > data set on to a
        > regular grid. I have read some of the literature, and
        > I think that
        > this would be a good option (I have also examined the possibility of
        > interpolating using a TIN, but I feel a bit more
        > "safe" using a
        > statistical approach!).
        >
        > In order to do my kriging, I need to have a model
        > semi-variogram, and I
        > thought about using gstat for this (from the command
        > line, no R
        > interfaces, my files are just ASCII (x,y,z) triplets).
        > Given that my
        > data files are huge (of the order of millions of
        > points), I selected a
        > region of interest, and tried to produce a sample
        > semi-variogram, with
        > views to fitting a model.
        >
        > In gstat, I got something that resembles y=exp(x),
        > which looks
        > distinctly wrong. The semivariogram value is ever
        > increasing, and does
        > not reach a sill at all. This is strange, and rather
        > unexpected. I have
        > tried doing a log transform of the data, but the shape
        > of the curve is
        > mostly unchanged.
        >
        > I would be very grateful if anyone could shed any
        > light on what this
        > variogram means, how I could make progress modelling
        > it and so on.
        >
        > Many thanks!
        > José
        >
        > --
        > Jose L Gomez-Dans, Research Assistant
        > Bristol Glaciology Centre, Geographical Sciences/CPOM
        > University of Bristol, Bristol, UK
        >
        >
        >
        >
        >
        >
        > ___________________________________________________________ALL
        > -NEW Yahoo! Messenger - all new features - even more fun!
        http://uk.messenger.yahoo.com
      • Dan Bebber
        Detrending is a pretty basic practice in geostatistics. I think you should do some more reading before you plunge into analyses. Dan Bebber ...
        Message 3 of 4 , Nov 3, 2004
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          Detrending is a pretty basic practice in geostatistics. I think you should
          do some more reading before you plunge into analyses.

          Dan Bebber

          > -----Original Message-----
          > From: Jose Luis Gomez Dans [mailto:jgomezdans@...]
          > Sent: 03 November 2004 17:01
          > To: Dan Bebber
          > Subject: Re: [ai-geostats] Understanding variograms
          >
          >
          > Dan and Isobel,
          > Many thanks for your prompt reply!
          >
          > On Wednesday 03 Nov 2004 16:39, you wrote:
          > > It probably means that you have a spatial trend in
          > your data.
          > > Remove any trend, then try again.
          >
          > OK, my data are point heights above the geoid over a
          > large area. While
          > there could well be a trend, how would I go
          > de-trending the data? I
          > have a digital elevation model of this region, and I
          > guess I could
          > subtract the grid value for each point considered, and
          > that should get
          > rid of things like slope effects (in effect, a
          > linear-ish trend).
          >
          > Does this make any sense?
          >
          > Many thanks
          > Jose
          >
          > --
          > Jose L Gomez-Dans, Research Assistant
          > Bristol Glaciology Centre, Geographical Sciences/CPOM
          > University of Bristol, Bristol, UK
          >
          >
          >
          >
          >
          >
          > ___________________________________________________________ALL-NEW
          > Yahoo! Messenger - all new features - even more fun!
          http://uk.messenger.yahoo.com
        • Pierre Goovaerts
          Another explanation for this shape is that Jose is looking at the variogram for short distances. It is well known that for very continuous attributes, such as
          Message 4 of 4 , Nov 3, 2004
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            Another explanation for this shape is that Jose is looking at
            the variogram for short distances. It is well known that for
            very continuous attributes, such as elevation or depth to water table.
            the semivariogram is expected to display a parabolic behaviour at
            the origin, which can be modeled using a Gaussian or cubic model
            for example. If one computes the semivariogram before it reaches
            its sill, then one will look only at a power curve and conclude
            that a trend is present. As always, everything is a matter of scale,
            and what looks like as a trend at a local scale can be modeled as
            part of a stationary process at a more regional scale.

            Cheer,

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

            Dr. Pierre Goovaerts
            President of PGeostat, LLC
            Chief Scientist with Biomedware Inc.
            710 Ridgemont Lane
            Ann Arbor, Michigan, 48103-1535, U.S.A.

            E-mail: goovaert@...
            Phone: (734) 668-9900
            Fax: (734) 668-7788
            http://alumni.engin.umich.edu/~goovaert/

            <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

            On Wed, 3 Nov 2004, Dan Bebber wrote:

            > Detrending is a pretty basic practice in geostatistics. I think you should
            > do some more reading before you plunge into analyses.
            >
            > Dan Bebber
            >
            > > -----Original Message-----
            > > From: Jose Luis Gomez Dans [mailto:jgomezdans@...]
            > > Sent: 03 November 2004 17:01
            > > To: Dan Bebber
            > > Subject: Re: [ai-geostats] Understanding variograms
            > >
            > >
            > > Dan and Isobel,
            > > Many thanks for your prompt reply!
            > >
            > > On Wednesday 03 Nov 2004 16:39, you wrote:
            > > > It probably means that you have a spatial trend in
            > > your data.
            > > > Remove any trend, then try again.
            > >
            > > OK, my data are point heights above the geoid over a
            > > large area. While
            > > there could well be a trend, how would I go
            > > de-trending the data? I
            > > have a digital elevation model of this region, and I
            > > guess I could
            > > subtract the grid value for each point considered, and
            > > that should get
            > > rid of things like slope effects (in effect, a
            > > linear-ish trend).
            > >
            > > Does this make any sense?
            > >
            > > Many thanks
            > > Jose
            > >
            > > --
            > > Jose L Gomez-Dans, Research Assistant
            > > Bristol Glaciology Centre, Geographical Sciences/CPOM
            > > University of Bristol, Bristol, UK
            > >
            > >
            > >
            > >
            > >
            > >
            > > ___________________________________________________________ALL-NEW
            > > Yahoo! Messenger - all new features - even more fun!
            > http://uk.messenger.yahoo.com
            >
            >
            >
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