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GEOSTATS: Theissen Polygons/Voronoi Diagrams

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  • William C. Thayer
    I am interested in using spatial models to estimate exposure point concentrations for soil for use in probabilistic risk assessments. I have experienced some
    Message 1 of 4 , Mar 11, 1998
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      I am interested in using spatial models to estimate exposure point
      concentrations for soil for use in probabilistic risk assessments. I
      have experienced some difficulties using geostatistics due to small
      sample sizes. Therefore, I would like to explore other methods to
      interpolate/contour data. Specifically, I am looking for references on
      using theissen polygons to interpolate/contour pollution concentration
      data. I am also interested in software (preferably free) that uses
      theissen polygons to contour data. Feedback will be greatly
      appreciated.


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    • Gregoire Dubois
      Hello William, freeware and links for computational geometry can be found at http://www.geom.umn.edu/software/cglist/ About the use of Thiessen polygons,
      Message 2 of 4 , Mar 12, 1998
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        Hello William,

        freeware and links for computational geometry can be found at

        http://www.geom.umn.edu/software/cglist/

        About the use of Thiessen polygons, initially used to estimate average
        rainfalls (Thiessen A. H. 1911, "Precipitation average for large areas",
        Month. Weather Review. 39: 1082-1084), I think these may not be appropriate
        if you have isolated and highly variable measures as these will get too
        much weight. The recent papers I have seen about the use of these polygons
        were more for the description of the sampling network rather than for
        interpolation.

        Hope this helps a bit (at least the link should help)

        Best regards

        Gregoire

        William C. Thayer wrote:
        >
        > I am interested in using spatial models to estimate exposure point
        > concentrations for soil for use in probabilistic risk assessments. I
        > have experienced some difficulties using geostatistics due to small
        > sample sizes. Therefore, I would like to explore other methods to
        > interpolate/contour data. Specifically, I am looking for references on
        > using theissen polygons to interpolate/contour pollution concentration
        > data. I am also interested in software (preferably free) that uses
        > theissen polygons to contour data. Feedback will be greatly
        > appreciated.
        >

        --
        Gregoire Dubois Tel. 39-332-78.99.44
        Joint Research Centre Fax. 39-332-78.54.66
        Environment Inst. TP 321 Email: gregoire.dubois@...
        I-21020 Ispra (Va), ITALY URL: http://curie.ei.jrc.it/
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      • Heinz Burger
        ... Hello! It is my point of view that interpolation methods are not always appropriate for risk assessment for contamination. The smoothing effects are well
        Message 3 of 4 , Mar 12, 1998
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          William C. Thayer wrote:
          >
          > I am interested in using spatial models to estimate exposure point
          > concentrations for soil for use in probabilistic risk assessments. I
          > have experienced some difficulties using geostatistics due to small
          > sample sizes. Therefore, I would like to explore other methods to
          > interpolate/contour data. Specifically, I am looking for references on
          > using theissen polygons to interpolate/contour pollution concentration
          > data. I am also interested in software (preferably free) that uses
          > theissen polygons to contour data. Feedback will be greatly
          > appreciated.
          >

          Hello!

          It is my point of view that interpolation methods are not always
          appropriate
          for risk assessment for contamination. The smoothing effects are well
          known:
          high peaks of concentrations are supressed and errors are difficult to
          be
          estimated without geostats.

          I have used Thiessen-polgons in combination with geostatistics in
          such applications (see IAMG-95 Abstracts, p. 19-22, Osaka, 1995).
          The advantage is that data-values, area of influence and estimation
          errors can be analysed and displayed. I'm using the extension variance
          for estimating confidence intervals. The upper confidence limit can be
          compared with tabulated limit values (publ. by nat. environmental
          agencies).

          Virtual data points may be placed in order to estimate the effect
          of error reduction in critical areas because the extension variance does
          not depend on the data values. (This is all elementary geostats.)

          A VB3.0-program is available upon request - (unfortunally display &
          helpfile
          in German language only). It will perhaps be easier to use the
          tesselation
          module in Arc/Info and to write an external module for calculating the
          extension variance for each polygon.

          And a final reference for Thiessen-polygons & interpolation:
          D.F. Watsons textbook 'Contouring' (Pergamon Press, 1992)

          Regards,

          Heinz Burger

          --
          **********************************
          Dr. Heinz Burger
          Freie Universitaet Berlin
          - Geoinformatik -
          Malteserstr. 74-100
          12249 BERLIN, Germany
          e-mail: hburger@...-berlin.de
          **********************************
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        • Michele Scardi
          ... Point your browser to: 1) http://puddle.mit.edu/~glenn/kirill/SAGA/triangul.m 2) http://puddle.mit.edu/~glenn/kirill/SAGA/interptr.m These Matlab programs
          Message 4 of 4 , Mar 12, 1998
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            William C. Thayer wrote:
            > ...
            > I am also interested in software (preferably free) that uses
            > theissen polygons to contour data. Feedback will be greatly
            > appreciated.

            Point your browser to:

            1) http://puddle.mit.edu/~glenn/kirill/SAGA/triangul.m
            2) http://puddle.mit.edu/~glenn/kirill/SAGA/interptr.m

            These Matlab programs are part of a complete toolbox for spatial and
            geometrical analysis by K. Pankratov (see
            http://puddle.mit.edu/~glenn/kirill/saga.html for more info).

            Cheers,

            Michele Scardi


            ------------------------------------------
            Michele Scardi

            Stazione Zoologica "A. Dohrn" di Napoli
            Villa Comunale
            80121 Napoli
            Italy

            tel: +39-81-5833201
            fax: +39-81-7641355
            email: mscardi@...
            home page: http://www.mare-net.com/mscardi
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