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Re: AI-GEOSTATS: Stationarity in Bathimetric LiDAR Data

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  • Pierre Goovaerts
    Hi Kent, Usually the search strategy can be limited to the definition of the maximum number of observations to be used for kriging, leaving the search radius
    Message 1 of 1 , May 15, 2003
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      Hi Kent,

      Usually the search strategy can be limited to the definition
      of the maximum number of observations to be used for kriging,
      leaving the search radius as big as needed to find the specified
      number of observations. Then, the search window will tend to
      be naturally larger in sparsely sampled areas.

      Two comments regarding the staionarity
      1. It's a property of the model, not of the data.
      2. As illustrated in the following paper, ordinary kriging
      with local search window allows one to account for global trends
      and avoid artifacts (i.e. negative estimates)
      frequently exhibited by surfaces extrapolated using universal kriging.
      Journel and Huijbrets, 1989.
      "When do we need a trend model in kriging?"
      Mathematical Geology, 21(7): 715-739.

      So in summary you could use ordinary kriging with local search windows
      and don't bother about unbounded variograms.


      Regards,

      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, 15 May 2003 kent.todd@... wrote:

      > Dear listerv members,
      >
      > I am currently working on interpolating bathimetric lidar measurements for
      > part of Lake Ontario. The dataset has an extremely high point density and
      > represents the nearshore and offshore areas within 500m of the coastline.
      > Each point represents an X,Y,Z value of elevation (shore and lake bottom)
      >
      > Here are the data specs:
      >
      > point spacing: on-shore (without flightpath overlap) - 7.0 m
      > on-shore (with flightpath overlap) - 0.5 to 2.0m
      > off-shore (water cover) - 0.5m to 75m
      > Percentage of Flightpath Overlap: 25%
      >
      > I have been attempting to perform ordinary kriging on the point returns,
      > but have run into some analytical problems. There is a directional trend
      > in the dataset resulting from the continual drop in elevation
      > perpendicular to the shoreline. A variogram on this data does not
      > reach a sill due this non-stationarity process. When I remove this trend
      > as a 1st order process and evaluate the omnidirectional variogram on the
      > residuals, there is significant improvement (sill is reached). However, a
      > sill is not reached in all the directional variograms (0,45,90,135
      > degrees).
      >
      > Is it possible to argue that the data is stationary when this occurs?
      > If not, how should I evaluate whether I have achieved stationarity?
      >
      > Also, the spatial distribution of the points ranges from very dense
      > on-shore or in areas with shallow water to being more sparse in areas with
      > greater water depth (point distances up to 75m apart).
      > Should this be considered when identifying a resolution for my
      > interpolation?
      > Does anyone have any references on choosing an optimal resolution based on
      > spacing of observations?
      >
      >
      > Thanks in advance for any feedback,
      > Sincerely,
      >
      > Kent
      >
      > ---------------------------------------
      > Kent W. Todd
      > Geomatics Analyst,
      > Ontario Ministry of Natural Resources
      > 5th Floor, North Tower
      > Peterborough, Ontario, Canada
      > K9J 5Z4
      > kent.todd@...
      > ph: (705) 755-5023
      >
      >
      >
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