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1685RE: [ai-geostats] FW: spatial relationships

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  • Glover, Tim
    Sep 2, 2004
      Thisa reminds me of a site where the "failure" of variogram modeling actually told me quite a bit about the problem at hand. It was a large field where dumptruck loads of soil with a contaminant had been dumped randomly and spread. This was unknown until after a gridded set of samples had been taken and a bizarre spotted pattern emerged. The directional variogram showed an unusual hump - increasing variance with distance, then decreasing variance with even more distance. This was the clue that some sort of "spot" activity had occurred. We finally tracked down a retired ex-employee who remembered the dumping activity.

      Sometimes a failed model tells more than one that fits!

      Tim Glover
      Senior Environmental Scientist - Geochemistry
      Geoenvironmental Department
      MACTEC Engineering and Consulting, Inc.
      Kennesaw, Georgia, USA
      Office 770-421-3310
      Fax 770-421-3486
      Email ntglover@...
      Web www.mactec.com
      -----Original Message-----
      From: Gregoire Dubois [mailto:gregoire.dubois@...]
      Sent: Thursday, September 02, 2004 3:53 AM
      To: ai-geostats@...
      Subject: [ai-geostats] FW: spatial relationships

      -----Original Message-----
      From: Gregoire Dubois [mailto:gregoire.dubois@...]
      Sent: 02 September 2004 09:42
      To: mark.dowdall@...
      Cc: drisobelclark@...
      Subject: Re: spatial relationships
      Hi Mark,
      re-reading Isobel's mail, I thought about a proviso on the proviso. I personally do consider that a semivariogram showing a pure trend is decent. Not in a geostatistical point of view, but it does provide you with some useful information. If you have a trend, the variogram becomes incompatible with the intrinsic hypothesis... but you still have a slope in the experimental correlation functions (semivariograms, correlograms, madogram, etc.). Thus you have a structure, that is you "have something" there that may provide you with some useful information about your data set that can be used for estimating values of your variable at unsampled locations. If you have a flat correlation function, that is a pure nugget effect, then certainly you are in troubles.

      Isobel Clark <drisobelclark@...> wrote:
      > Mark
      > I could not agree more with Gregoire (with one
      > proviso, see below).
      > Both geostatistics and any weighted average estimators
      > are based on the same assumptions -- that relationship
      > between values at two locations depends on the
      > distance between them and (possibly) their relative
      > orientation. If you cannot get a decent semi-variogram
      > after trying every type of graph [normal, robust,
      > relative] and every transformation and/or
      > interpretation of your data [logarithm, indicator,
      > rank transforms, Normal scores, mixed populations],
      > you do not have a distance-based relationship. This
      > conclusion also rules out: inverse distance weighting
      > of any kind; Delaunay triangles; Thiessen polygons and
      > so on.
      > My proviso: there are other forms of spatial
      > relationship than pure distance/direction types. The
      > simplest example of this is data with a trend, where
      > the value at a specified point will depend on its
      > absolute position. There may be an added component for
      > the 'residuals' which turns out to be
      > distance/direction based. There are also many examples
      > where, for example, flow characteristics, connectivity
      > and so on play a large part in the structure of your
      > variable.
      > In short: no decent semi-variogram does NOT mean no
      > spatial relationship. It means no simple second-order
      > stationary geostatistical type spatial relationship.
      > Isobel
      > http://geoecosse.bizland.com/whatsnew.htm
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      Gregoire Dubois (Ph.D.)
      JRC - European Commission
      IES - Emissions and Health Unit
      Radioactivity Environmental Monitoring group
      TP 441, Via Fermi 1
      21020 Ispra (VA)
      Tel. +39 (0)332 78 6360
      Fax. +39 (0)332 78 5466
      Email: gregoire.dubois@...
      WWW: http://www.ai-geostats.org
      WWW: http://rem.jrc.cec.eu.int
      "The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission."
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