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GEOSTATS: Why should geostatisticians use GIS ?

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  • Gregoire Dubois
    Greetings again, I m afraid this is going to be a very long mail. I believe it is an interesting topic which could generate some good discussions on the
    Message 1 of 1 , Jan 19, 2005
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      Greetings again,

      I'm afraid this is going to be a very long mail. I believe it is an
      interesting topic which could generate some good discussions on the
      ai-geostats mailing list. It summarises a presentation I'm currently preparing
      for a small GIS workshop. Although GIS have still nowadays a significant lack
      of tools and functions that are required for a proper analysis of
      geostatistical data (the new versions of Idrisi and Arc/Info seem however to
      have finally proper geostatistical modules), GIS users can gain some
      experience in the application of geostatistics by using recently developed
      supplementary software. But the progress made in combining geostatistics to
      GIS seems to have taken a one way road since geostatisticians have not shown
      much interest in the use of GIS. On the other hand, GIS users are looking for
      geostatistical software that could be integrated within their tools without
      justifying clearly the need for such integration besides the benefit of an
      improved convenience of use. The intent of this mail is therefore to identify
      through a step-by-step analysis of a standard geostatistical case study where
      interactions between GIS and geostatistics exist and how these could be used
      efficiently.
      A typical sequence of the work of a geostatistician can be summarised as
      following

      1) Primary analysis of the data in order to make a portrait of the analysed
      variable(s)
      - Univariate statistics
      - Multivariate statistics

      2) Analysis of the coherence in the sampling of the studied phenomena
      - Declustering techniques
      - Thiessen/Voronoi polygons
      - Fractal dimension of the sampling network

      3) Analysis of the coherence in the spatial structure of the studied variable
      - Moving windows statistics: analysis of stationnarity
      - Exploratory variography
      - Modelling of the drift if any and variogram modeling

      4) Estimations/Interpolation
      - Definition of the hypothesis on the basis of the information provided during
      the exploratory analysis
      - Selection of a spatial estimator from the kriging family
      - Estimation/Interpolation

      5) Validation of the selected method
      - Cross-validations
      - Analysis of the errors and residuals
      - Correction of the parameters of the interpolation method
      - New estimations and cross-validations

      So where do GIS operations fit within these steps ? My personal experience,
      gained during the development of an object oriented GIS which integrates a
      Bayesien geostatistical module developed at the university of Klagenfurt
      (Austria) is the following

      1) Primary analysis:
      Before any analysis, GIS will clearly facilitate the projection of the
      geostatistical dataset. GIS functions also allow efficient logical consistency
      checks of the topological information of the data. Soil samples, for example,
      can not be located within a lake or an ocean, measurements provided by a
      national monitoring network are not supposed to be discovered across the
      political borders of the country where the measurements are made. Practically,
      such filtering require the overlay of the digital maps on the geostatistical
      dataset and the selection of points falling within specific polygons, or cells
      in case the geographic data is in a raster format.
      It is also clear that interactive histograms as well as map of proportional
      symbols will help to identify and locate anomalies and trends.

      2) Analysis of the coherence in the sampling of the studied phenomena
      Declustering techniques are usually either based on polygons of influence
      (Thiessen/Voronoi polygons) or on a cell based method. The advantage of the
      polygons is that it doesn't require subjective decisions (a size of the cells
      has to be selected for the second method) and it can allow to take into
      account the geometry of the surface that is analyzed. The last can be done by
      "clipping" the surface generated by Thiessen polygons with the borders of the
      analyzed surface. Doing this also avoids the bias generated by the external
      polygons when taking a simple rectangle or the convex hull. The problem of
      measurements situated on the edges is also still not really solved when using
      fractal techniques.

      3) Analysis of the coherence in the spatial structure of the studied variable

      Variowin has clearly shown the power of interactivity during the analysis of
      the spatial correlation. However, the location on a map (with any additional
      geographical information) of the sample pairs selected on an h-scatterplot
      could in certain cases help to explain certain anomalies. The display of
      additional information should also certainly help to understand certain
      anisotropies.

      4) Estimations/Interpolation

      This is probably where the use of GIS in the analysis of geostatistical data
      becomes more tricky but also where it might show the biggest perspectives. If
      GIS can certainly facilitate the definition of polygons of exclusion used
      during the estimation, it theoretically could also be used to define other
      criteria to select the measurements to be used during the estimation than the
      distance. Such criteria could be the slope, aspect, curvature of a DEM. Or
      more simply all data falling within a buffer created around a polygon, a point
      or a line.
      Around two years ago I asked on the list if any work was made in the use of
      other information in the variogram modelling than the Euclidean distance. I
      suggested as an example to use the so called "cost-path distance", the
      distance one would effectively travel by walking from one point to another one
      when the variable under study is strongly affected by the DEM. If the few
      tests I have made were not convincing but I still believe that better tests
      can still be made since I didn't have a good code to calculate this cost-path
      distance and most probably because I didn't really take much time to think
      about it. Another example could come from studies involving hydrology:
      particles, pollutants, etc. in suspension will have their spatial
      distribution certainly influenced by the shape of the river/lake and most
      probably will show patterns with strong local anisotropies. The lake/river
      could however be somehow "transformed" in order to become in a situation
      where the hypothesis of stationnarity can be considered as true and improve so
      the estimations.
      I suggest the readers to have a look at

      Zoraster Steven, 1996. "Imposing Geologic Interpretations on
      Computer-Generated Contours Using Distance Transformations"
      Mathematical Geology, Vol. 28, No. 8, pp 969-985.

      It uses a different approach, with an interesting potential for GIS users, but
      has the same ideas.

      Bayesian geostatistics is a growing field full of promises. The use of
      additional information to reduce the uncertainty associated to the estimates
      certainly should gain a lot in being combined with GIS. I believe that this is
      the field in geostats that should see its major developments in the near
      future and stimulate the geostatisticians to work more with GIS.

      This was certainly not an exhaustive list on what GIS can bring to
      geostatistics but the first that came to my mind.

      I would more than welcome any references, ideas and comments on all this.

      Sorry for having taken so much of your time.

      Best regards

      Gregoire


      PS: A small comment on the outputs of the estimates: Isaaks and Srivastava
      have in their book clearly underlined the importance of the sample support. So
      why do most GIS directly convert point estimates into a raster (block
      estimates) ? I believe this should be corrected in the future.



      Gregoire Dubois
      Section of Earth Sciences
      Institute of Mineralogy and Petrography
      University of Lausanne
      Switzerland

      Currently detached in Italy

      http://curie.ei.jrc.it/ai-geostats.htm
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