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AI-GEOSTATS: Quick evaluation of geostatistical problem

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  • Koen Hufkens
    Hi list, Sorry for the long mail but I need an opinion on what I ve been up to the last weeks/months. I was asked as a student to look at spatial relations in
    Message 1 of 4 , Apr 4, 2004
    • 0 Attachment
      Hi list,

      Sorry for the long mail but I need an opinion on what I've been up to the last weeks/months.

      I was asked as a student to look at spatial relations in sample data with the intention to optimize the sampling protocol for future field campaignes.

      This is a wrapup of my findings:

      The data I use is the leaf area index of a semi-arid vegetation. The leaf area index is a vegetation parameter so on locations with no vegetation this gives a 0 value. This is an actual measurement.

      To give you an idea of the vegetation and it's very sparse nature:

      http://users.pandora.be/requested/images/vegetation.jpg

      Measurements are made in a 13 point 20x20m grid, called an ESU (elementary sample unit). The picture below gives the exact configuratoin.

      http://users.pandora.be/requested/images/ESU.gif

      37 of such 13 point plots were measured, look at the link below for a figure.

      http://users.pandora.be/requested/images/allplots.gif

      Given the sparse vegetation this results in the following data distribution for all the data points:

      http://users.pandora.be/requested/images/histtot.gif

      The distribution of the seperate ESU plots is therefor also highly skewed.

      To investigate spatial relations I used the Moran's I index. This turned out to be slightly NEGATIVE, wich is rare for ecological data but can be explained based on the desert like nature of the vegetation. But, none of these indexes were significant (under Randomization and Monte Carlo terms).

      Knowing my data is a little to skewed to evaluate using semivariograms I plotted them anyway. Wich gave some strange but to be expected results. No relation is to be detected using all of the 13x37 data points.

      omnidirectional:
      http://users.pandora.be/requested/images/variotot.gif

      directional:
      http://users.pandora.be/requested/images/variodir.gif

      On an ESU level (13 points, 20x20m plot) I did this again to look at it on a smaller scale avoiding some of the exess 0's. The outcome was this:

      http://users.pandora.be/requested/images/varioesu.gif

      So on a small scale it isn't that much better.

      I read an article from the man who made up the this sampling protocol in the first place. He tests the kriging average over the ESU's vs the normal average over the 13 samples. So I fitted a linear model on the last semivariogram and did the same calculation.
      The outcome was the same: No signicant difference between the kriging average and the normal average. (I repeated this for all the useable ESU plots)

      So my conclusions would be:

      1) this is some fucked up data to let a novice in geostatistics work upon
      2) there is no spatial relation to be detected or not significant anyway
      3) you don't gain any information by knowing the location of a sample:
      3.1 it doesn't say anything about the structure of the vegetation
      3.2 because of a lack of spatial relations, random sampling is to be considered = cheaper less work

      Any input on this would be greatly appreciated, I'm a novice so give me hell if I go wrong. I rather learn the hard way then not at all. Tips to put this in a more positive daylight would also be appreciated, I've got to sell this thing to people who started with the believes that some positive relation would be detected.

      Best regards and my excuses for the long post,
      Koen.









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    • Pierre Goovaerts
      Hi Koen, Given the very large proportion of zero values in your dataset, the only meaningful variogram you could get would be an indicator one where all
      Message 2 of 4 , Apr 4, 2004
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        Hi Koen,

        Given the very large proportion of zero values in your dataset,
        the only meaningful variogram you could get
        would be an indicator one where all non-zero values would be
        converted into 1. This variogram should inform on whether
        the patches of vegetation are purely random in space.

        I agree that it's not a too compelling dataset to start with,
        and as I often said I was lucky with my 1st experimental semivariogram.

        Good luck and go drink a good Belgian beer to cheer you up!

        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 Mon, 5 Apr 2004, Koen Hufkens wrote:

        > Hi list,
        >
        > Sorry for the long mail but I need an opinion on what I've been up to the last weeks/months.
        >
        > I was asked as a student to look at spatial relations in sample data with the intention to optimize the sampling protocol for future field campaignes.
        >
        > This is a wrapup of my findings:
        >
        > The data I use is the leaf area index of a semi-arid vegetation. The leaf area index is a vegetation parameter so on locations with no vegetation this gives a 0 value. This is an actual measurement.
        >
        > To give you an idea of the vegetation and it's very sparse nature:
        >
        > http://users.pandora.be/requested/images/vegetation.jpg
        >
        > Measurements are made in a 13 point 20x20m grid, called an ESU (elementary sample unit). The picture below gives the exact configuratoin.
        >
        > http://users.pandora.be/requested/images/ESU.gif
        >
        > 37 of such 13 point plots were measured, look at the link below for a figure.
        >
        > http://users.pandora.be/requested/images/allplots.gif
        >
        > Given the sparse vegetation this results in the following data distribution for all the data points:
        >
        > http://users.pandora.be/requested/images/histtot.gif
        >
        > The distribution of the seperate ESU plots is therefor also highly skewed.
        >
        > To investigate spatial relations I used the Moran's I index. This turned out to be slightly NEGATIVE, wich is rare for ecological data but can be explained based on the desert like nature of the vegetation. But, none of these indexes were significant (under Randomization and Monte Carlo terms).
        >
        > Knowing my data is a little to skewed to evaluate using semivariograms I plotted them anyway. Wich gave some strange but to be expected results. No relation is to be detected using all of the 13x37 data points.
        >
        > omnidirectional:
        > http://users.pandora.be/requested/images/variotot.gif
        >
        > directional:
        > http://users.pandora.be/requested/images/variodir.gif
        >
        > On an ESU level (13 points, 20x20m plot) I did this again to look at it on a smaller scale avoiding some of the exess 0's. The outcome was this:
        >
        > http://users.pandora.be/requested/images/varioesu.gif
        >
        > So on a small scale it isn't that much better.
        >
        > I read an article from the man who made up the this sampling protocol in the first place. He tests the kriging average over the ESU's vs the normal average over the 13 samples. So I fitted a linear model on the last semivariogram and did the same calculation.
        > The outcome was the same: No signicant difference between the kriging average and the normal average. (I repeated this for all the useable ESU plots)
        >
        > So my conclusions would be:
        >
        > 1) this is some fucked up data to let a novice in geostatistics work upon
        > 2) there is no spatial relation to be detected or not significant anyway
        > 3) you don't gain any information by knowing the location of a sample:
        > 3.1 it doesn't say anything about the structure of the vegetation
        > 3.2 because of a lack of spatial relations, random sampling is to be considered = cheaper less work
        >
        > Any input on this would be greatly appreciated, I'm a novice so give me hell if I go wrong. I rather learn the hard way then not at all. Tips to put this in a more positive daylight would also be appreciated, I've got to sell this thing to people who started with the believes that some positive relation would be detected.
        >
        > Best regards and my excuses for the long post,
        > Koen.
        >
        >
        >
        >
        >
        >
        >
        >
        >
        > --
        > * To post a message to the list, send it to ai-geostats@...
        > * As a general service to the users, please remember to post a summary of any useful responses to your questions.
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        >
        >

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        * As a general service to the users, please remember to post a summary of any useful responses to your questions.
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      • mrufino@cmima.csic.es
        Hello Koen, ... So this means that you have 37*13 samples? ... hmmm... According to this I would try two things, 1. Indicator kriging (you do it with binomial
        Message 3 of 4 , Apr 5, 2004
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          Hello Koen,


          > The data I use is the leaf area index of a semi-arid vegetation. The leaf
          > area index is a vegetation parameter so on locations with no vegetation this
          > gives a 0 value. This is an actual measurement.

          > Measurements are made in a 13 point 20x20m grid, called an ESU (elementary
          > sample unit). The picture below gives the exact configuratoin.
          > http://users.pandora.be/requested/images/ESU.gif
          > 37 of such 13 point plots were measured, look at the link below for a
          > figure.
          > http://users.pandora.be/requested/images/allplots.gif
          So this means that you have 37*13 samples?


          > Given the sparse vegetation this results in the following data distribution
          > for all the data points:
          > http://users.pandora.be/requested/images/histtot.gif
          hmmm...
          According to this I would try two things,
          1. Indicator kriging (you do it with binomial variable. So you actully
          reclassify your variable into 1 and 0). You can do this with gstat in R, I
          belive.
          2. Have you tried box.cox transformations? MAybe this might give better results
          (you do this with geoR in R).
          3. remove any outlier (according to a threshhold level) and see what happens.

          I think you have classical type of data for ecology (I have similar problems),
          so it is somehow dificult to see what is happening because the distribution of
          the variable may 'hide' the spatial structure of the variogram. I have
          references that jusify any of those, so if you need them just tell me.
          Anyway, your variograms look very 'weird'. What program did you used?

          Hope this helps,
          Good luck,
          Marta


          -------------------------------------------------
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        • Sanjay Lamsal
          Hi Keon, I am also a kind of new to this field of Geostatistics. Your research is interesting. I think you and me are dealing with similar type of dataset - my
          Message 4 of 4 , Apr 5, 2004
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            Hi Keon,

            I am also a kind of new to this field of Geostatistics. Your research is
            interesting.

            I think you and me are dealing with similar type of dataset - my case is
            with the nitrate-nitrogen distribution in soils at a watershed scale (3585
            Sq km). My data is more skewed than yours, and as Dr Goovaerts suggested-
            Indicator kriging remains as a method of choice.

            It might be useful for you to go through the beauty of indicator thresholds
            (see Isaaks and Srivastava' book - page 417-457). You might explore some
            thresholds, as the change in threshold gives you a different scenario about
            the spatial distribution of 0s and 1s (see some pictures of the exhaustive
            data set from Isaaks and Srivastava's book - page 81-89). Perhaps after
            going through these chapters, another interesting step might be to go
            through the chapters on Dr. Goovaerts book, and some articles from Van
            Meirvienne and Goovaerts might be an asset.

            If these efforts do not work out and seems like the distribution of
            vegetation patches is totally random, it might be interesting to see what is
            the driving force to create these patches to be random (here i might be just
            haunching - however - Imagination is more important than knowledge "A.
            Einstein").

            Good luck. And you seem to be Belgian - thats a great nation - I got my
            Masters from Ghent - wonderful memories.

            Sanjay

            -----------------------------
            Sanjay Lamsal
            GIS Research Lab
            Soil and Water Science Dept.
            University of Florida
            2169 McCarty A
            PO Box 110290
            Gainesville, FL 32611-0290
            Phone: 352-392-1951 ext 233
            Fax: 352-392-3902
            ----- Original Message -----
            From: "Koen Hufkens" <koen.hufkens@...>
            To: "AI-GEOSTATS" <ai-geostats@...>
            Sent: Sunday, April 04, 2004 6:29 PM
            Subject: AI-GEOSTATS: Quick evaluation of geostatistical problem


            Hi list,

            Sorry for the long mail but I need an opinion on what I've been up to the
            last weeks/months.

            I was asked as a student to look at spatial relations in sample data with
            the intention to optimize the sampling protocol for future field campaignes.

            This is a wrapup of my findings:

            The data I use is the leaf area index of a semi-arid vegetation. The leaf
            area index is a vegetation parameter so on locations with no vegetation this
            gives a 0 value. This is an actual measurement.

            To give you an idea of the vegetation and it's very sparse nature:

            http://users.pandora.be/requested/images/vegetation.jpg

            Measurements are made in a 13 point 20x20m grid, called an ESU (elementary
            sample unit). The picture below gives the exact configuratoin.

            http://users.pandora.be/requested/images/ESU.gif

            37 of such 13 point plots were measured, look at the link below for a
            figure.

            http://users.pandora.be/requested/images/allplots.gif

            Given the sparse vegetation this results in the following data distribution
            for all the data points:

            http://users.pandora.be/requested/images/histtot.gif

            The distribution of the seperate ESU plots is therefor also highly skewed.

            To investigate spatial relations I used the Moran's I index. This turned out
            to be slightly NEGATIVE, wich is rare for ecological data but can be
            explained based on the desert like nature of the vegetation. But, none of
            these indexes were significant (under Randomization and Monte Carlo terms).

            Knowing my data is a little to skewed to evaluate using semivariograms I
            plotted them anyway. Wich gave some strange but to be expected results. No
            relation is to be detected using all of the 13x37 data points.

            omnidirectional:
            http://users.pandora.be/requested/images/variotot.gif

            directional:
            http://users.pandora.be/requested/images/variodir.gif

            On an ESU level (13 points, 20x20m plot) I did this again to look at it on a
            smaller scale avoiding some of the exess 0's. The outcome was this:

            http://users.pandora.be/requested/images/varioesu.gif

            So on a small scale it isn't that much better.

            I read an article from the man who made up the this sampling protocol in the
            first place. He tests the kriging average over the ESU's vs the normal
            average over the 13 samples. So I fitted a linear model on the last
            semivariogram and did the same calculation.
            The outcome was the same: No signicant difference between the kriging
            average and the normal average. (I repeated this for all the useable ESU
            plots)

            So my conclusions would be:

            1) this is some fucked up data to let a novice in geostatistics work upon
            2) there is no spatial relation to be detected or not significant anyway
            3) you don't gain any information by knowing the location of a sample:
            3.1 it doesn't say anything about the structure of the vegetation
            3.2 because of a lack of spatial relations, random sampling is to be
            considered = cheaper less work

            Any input on this would be greatly appreciated, I'm a novice so give me hell
            if I go wrong. I rather learn the hard way then not at all. Tips to put this
            in a more positive daylight would also be appreciated, I've got to sell this
            thing to people who started with the believes that some positive relation
            would be detected.

            Best regards and my excuses for the long post,
            Koen.









            --
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            * As a general service to the users, please remember to post a summary of
            any useful responses to your questions.
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            "unsubscribe ai-geostats" followed by "end" on the next line in the message
            body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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