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[ai-geostats] FW: spatial relationships

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  • Gregoire Dubois
    ... From: Gregoire Dubois [mailto:gregoire.dubois@jrc.it] Sent: 02 September 2004 09:42 To: mark.dowdall@nrpa.no Cc: drisobelclark@yahoo.co.uk Subject: Re:
    Message 1 of 5 , Sep 2, 2004
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      Message
       
      -----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.

      Regards,

      Gregoire


      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
      >
      >
      >      
      >      
      >              
      > ___________________________________________________________ALL-NEW Yahoo! Messenger - all new features - even more fun!  http://uk.messenger.yahoo.com

      >
      >

      > ---------------------------------------------
      >       Attachment: message-footer.txt
      >       MIME Type: text/plain
      > ---------------------------------------------

      __________________________________________
      Gregoire Dubois (Ph.D.)
      JRC - European Commission
      IES - Emissions and Health Unit
      Radioactivity Environmental Monitoring group
      TP 441, Via Fermi 1
      21020 Ispra (VA)
      ITALY
       
      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."

    • Isobel Clark
      Gregoire/Mark Yes, a trend is a spatial structure and can be used for prediction purposes. It just isn t suitable for stationary geostatistical analysis. I
      Message 2 of 5 , Sep 2, 2004
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        Gregoire/Mark

        Yes, a trend is a spatial structure and can be used
        for prediction purposes. It just isn't suitable for
        'stationary' geostatistical analysis.

        I have seen cases where the semi-variogram was almost
        pure nugget effect, but there was a spatial structure.
        Again, just not a straight-forward 'stationary'
        geostatistical analysis. Need to look at all the
        possibilities and at other forms of spatial
        relationship.

        Do not despair, there is a pattern!
        Isobel
        http://www.geostatistics.info





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      • Glover, Tim
        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
        Message 3 of 5 , Sep 2, 2004
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          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.
          Regards,
          Gregoire

          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
          >
          >
          >      
          >      
          >              
          > ___________________________________________________________ALL-NEW Yahoo! Messenger - all new features - even more fun!  http://uk.messenger.yahoo.com
          >
          >
          > ---------------------------------------------
          >       Attachment: message-footer.txt
          >       MIME Type: text/plain
          > ---------------------------------------------
          __________________________________________
          Gregoire Dubois (Ph.D.)
          JRC - European Commission
          IES - Emissions and Health Unit
          Radioactivity Environmental Monitoring group
          TP 441, Via Fermi 1
          21020 Ispra (VA)
          ITALY
           
          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."
        • Pierre Goovaerts
          I would agree with Gregoire s assessment. The presence of a global trend does not prohibit the use of geostatistics. As illustrated in the following paper by
          Message 4 of 5 , Sep 2, 2004
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            I would agree with Gregoire's assessment.
            The presence of a global trend does not prohibit the use of geostatistics.
            As illustrated in the following paper by Journel and Rossi:
            Journel, A.G. and M.E. Rossi. 1989. When do we need a trend model
            in kriging? Mathematical Geology, 21(7):715--739.
            global trends can be easily handled by the use of local search
            windows in kriging, which allows us to rely on the assumption of
            quasi-stationarity.

            Of course if the trend is complex and can be described using
            process-based models (e.g. urban pollution), it is better to use
            this physical model for the trend and use geostatistics to
            interpolate the residuals, provided there is some spatial
            correlation left.

            Cheers,

            Pierre
            <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

            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, 2 Sep 2004, Gregoire Dubois wrote:

            >
            > -----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.
            >
            > Regards,
            >
            > Gregoire
            >
            >
            > 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>
            > http://geoecosse.bizland.com/whatsnew.htm
            > >
            > >
            > >
            > >
            > >
            > > ___________________________________________________________ALL-NEW
            > Yahoo! Messenger - all new features - even more fun!
            > <http://uk.messenger.yahoo.com> http://uk.messenger.yahoo.com
            >
            > >
            > >
            >
            > > ---------------------------------------------
            > > Attachment: message-footer.txt
            > > MIME Type: text/plain
            > > ---------------------------------------------
            >
            > __________________________________________
            > Gregoire Dubois (Ph.D.)
            > JRC - European Commission
            > IES - Emissions and Health Unit
            > Radioactivity Environmental Monitoring group
            > TP 441, Via Fermi 1
            > 21020 Ispra (VA)
            > ITALY
            >
            > Tel. +39 (0)332 78 6360
            > Fax. +39 (0)332 78 5466
            > Email: <mailto:gregoire.dubois@...> gregoire.dubois@...
            > WWW: <http://www.ai-geostats.org> http://www.ai-geostats.org
            > WWW: <http://rem.jrc.cec.eu.int> 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."
            >
            >
          • Ted Harding
            ... Indeed! It s the difference between discovery and measurement. Best wishes, Ted. ... E-Mail: (Ted Harding) Fax-to-email: +44
            Message 5 of 5 , Sep 2, 2004
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              On 02-Sep-04 Glover, Tim wrote:
              > 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!

              Indeed! It's the difference between discovery and measurement.

              Best wishes,
              Ted.


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              Fax-to-email: +44 (0)870 167 1972
              Date: 02-Sep-04 Time: 14:19:37
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