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[ai-geostats] kriging proportions

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  • Marc-Olivier Gasser
    Hi everyone, Lets say we have measured three soil particule size values for clay, silt and sand, all adding to one. cl + s i + sa = 1 What would be the best
    Message 1 of 3 , Jun 10, 2004
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      Hi everyone,

      Lets say we have measured three soil particule size values for clay, silt and sand, all adding to one.

      cl + s i + sa = 1

      What would be the best way to take into account each particule size, so the interpolated values still add up to one?

      Is there any geostatistical process that can handle this?

      I have tried interpolating parameters caracterising different particle size distribution functions (in the case where there are more than 10 particule sizes) but this adds errors to the modelling and some parameters don't necessarily exhibit spatial correlation.
       
      Maximum autocorrelation factor kriging has been suggested such as in:

      A. J. Desbarats and R. Dimitrakopoulos. Geostatistical Simulation of Regionalized Pore-Size Distributions Using Min/Max Autocorrelation Factors. Mathematical Geology, Vol. 32, No. 8, 2000.

      but I haven't found many statistical packages implementig this procedure.

      What other possibilities are there?

      Best regards,
      Marc-Olivier


    • Pierre Goovaerts
      Hi Marc, You may want to look at the following paper: de Gruijter, J.J., Walvoort, D.J.J., van Gaans, P.F.M., 1997. Continuous soil maps --- a fuzzy set
      Message 2 of 3 , Jun 10, 2004
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        Hi Marc,

        You may want to look at the following paper:
        de Gruijter, J.J., Walvoort, D.J.J., van Gaans, P.F.M., 1997.
        Continuous soil maps --- a fuzzy set approach to bridge the gap
        between aggregation levels of process and distribution models.
        Geoderma 77, 169--195.

        The authors describe compositional kriging to interpolate class
        memberships, and they have incorporated additional constraints into
        the kriging system to ensure that all estimates are positive
        and add up to a constant (1 in this case).

        Cheers,

        Pierre Goovaerts
        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        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 Thu, 10 Jun 2004, Marc-Olivier Gasser wrote:

        > Hi everyone,
        >
        > Lets say we have measured three soil particule size values for clay, silt
        > and sand, all adding to one.
        >
        > cl + s i + sa = 1
        >
        > What would be the best way to take into account each particule size, so the
        > interpolated values still add up to one?
        >
        > Is there any geostatistical process that can handle this?
        >
        > I have tried interpolating parameters caracterising different particle size
        > distribution functions (in the case where there are more than 10 particule
        > sizes) but this adds errors to the modelling and some parameters don't
        > necessarily exhibit spatial correlation.
        >
        > Maximum autocorrelation factor kriging has been suggested such as in:
        >
        > A. J. Desbarats and R. Dimitrakopoulos. Geostatistical Simulation of
        > Regionalized Pore-Size Distributions Using Min/Max Autocorrelation Factors.
        > Mathematical Geology, Vol. 32, No. 8, 2000.
        >
        > but I haven't found many statistical packages implementig this procedure.
        >
        > What other possibilities are there?
        >
        > Best regards,
        > Marc-Olivier
        >
        >
        >
      • Dr Inakwu Odeh
        Marc-Olivier, You can try our recent publication in the Journal Soil Science which compared several geostatistical techniques for simultaneously
        Message 3 of 3 , Jun 10, 2004
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          Marc-Olivier,

          You can try our recent publication in the Journal "Soil Science" which compared several geostatistical techniques for simultaneously interpolating soil particle-size fractions while ensuring summation to a constant. The reference is:

          Odeh IOA Todd AJ and Triantafilis J 2003.  Spatial prediction of particle size fractions as compositional data.  Soil Science 168, 501-515.

          Odeh
          At 01:01 PM 10/06/2004 -0400, Marc-Olivier Gasser wrote:
          Hi everyone,

          Lets say we have measured three soil particule size values for clay, silt and sand, all adding to one.

          cl + s i + sa = 1

          What would be the best way to take into account each particule size, so the interpolated values still add up to one?

          Is there any geostatistical process that can handle this?

          I have tried interpolating parameters caracterising different particle size distribution functions (in the case where there are more than 10 particule sizes) but this adds errors to the modelling and some parameters don't necessarily exhibit spatial correlation.
           
          Maximum autocorrelation factor kriging has been suggested such as in:

          A. J. Desbarats and R. Dimitrakopoulos. Geostatistical Simulation of Regionalized Pore-Size Distributions Using Min/Max Autocorrelation Factors. Mathematical Geology, Vol. 32, No. 8, 2000.

          but I haven't found many statistical packages implementig this procedure.

          What other possibilities are there?

          Best regards,
          Marc-Olivier


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