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Re: GEOSTATS: Theissen Polygons/Voronoi Diagrams

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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 1 of 4 , Mar 12, 1998
      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 2 of 4 , Mar 12, 1998
        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 3 of 4 , Mar 12, 1998
          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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