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Re: GEOSTATS: Theissen Polygons/Voronoi Diagrams

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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 1 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 2 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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