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AI-GEOSTATS: hole effect

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  • FT.Maestre@ua.es
    Dear list, I am working with vegetation data, and I have got some variograms that are characterized by the presence of a “hole effect” that I would like to
    Message 1 of 5 , Jan 25, 2002
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      Dear list,

      I am working with vegetation data, and I have got some variograms
      that are characterized by the presence of a “hole effect” that I
      would like to model. I have found in the manual of GSLIB (2nd
      edition) a model with a periodical component that can be fitted to
      such data, but the authors remark that this model valid only in one
      direction. Since I am working with omnidirectional variograms in a
      two-dimensional grid, I would be very grateful if somebody could give
      me any indication about where I can find conditional negative semi-
      definite (CNSD) models that incorporate a periodic component and that
      are valid for two-dimensional data.

      Many thanks in advance for your attention.

      Best Regards,

      Fernando T. Maestre
      Departamento de Ecología
      Universidad de Alicante
      Apdo correos 99
      03080 Alicante
      SPAIN


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    • Isobel Clark
      Fernando Although the hole effect model is a little ustable mathematically, we have had considerable success in practice by combining it with a spherical
      Message 2 of 5 , Jan 25, 2002
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        Fernando

        Although the hole effect model is a little ustable
        mathematically, we have had considerable success in
        practice by combining it with a spherical component.

        We call this 'model' the Paddington Mix and have used
        it in several field studies where there is a cyclic
        component in addition to the more usual continuity.

        You can see how it works in our kriging game which can
        be freely downloaded from my briefcase at:

        http://uk.geocities.com/drisobelclark/briefcase.html

        Isobel



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      • Colin Daly
        Fernando, I m not sure what variogram you were given that works only in 1d I can think of two -- gamma(h) = 1 -cos(h) and gamma(h)=exp(-ah)*cos(h) The
        Message 3 of 5 , Jan 30, 2002
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          Fernando,

          I'm not sure what variogram you were given that works only in 1d
          I can think of two -- gamma(h) = 1 -cos(h) and gamma(h)=exp(-ah)*cos(h)

          The problem with higher dimensions is that the 'size' of the hole, defined
          as |min(C(h))|/ C(0) which takes the value 1.0 for the first of these
          variograms , has to less dramatic in higher dimensions. The higher the
          number of dimensions, the less important the hole size can be.

          So ideally you would like a variogram that is legitimate in 2d but not in
          3d. I can't remember any of those off hand - although they do exist.

          The next best thing is one that works in 3d (and therefore also in 1d and
          2d). This will have a smaller hole effect size than is theoretically
          possible for 2d data. The one I'm giving you does attain the maximum hole
          size allowed for 3d data. It is

          gamma(h) = 1 - sin(r)/r

          The problem is that it has quadratic behavior at the origin - so you might
          need to add a small spherical or exponential variogram as suggested by
          Isobel to ensure that your resultant random function model is not
          differentiable.

          Bye

          Colin Daly


          ----- Original Message -----
          From: <ft.maestre@...>
          To: <ai-geostats@...>
          Sent: Friday, January 25, 2002 12:29 PM
          Subject: AI-GEOSTATS: hole effect


          Dear list,

          I am working with vegetation data, and I have got some variograms
          that are characterized by the presence of a "hole effect" that I
          would like to model. I have found in the manual of GSLIB (2nd
          edition) a model with a periodical component that can be fitted to
          such data, but the authors remark that this model valid only in one
          direction. Since I am working with omnidirectional variograms in a
          two-dimensional grid, I would be very grateful if somebody could give
          me any indication about where I can find conditional negative semi-
          definite (CNSD) models that incorporate a periodic component and that
          are valid for two-dimensional data.

          Many thanks in advance for your attention.

          Best Regards,

          Fernando T. Maestre
          Departamento de Ecología
          Universidad de Alicante
          Apdo correos 99
          03080 Alicante
          SPAIN


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        • Ercan Yesilirmak
          Dear list members Omnidirectional variogram shows a dip toward the end of lags. As far as I know this is hole effect. Would you tell me how to tackle with it?
          Message 4 of 5 , Apr 24, 2002
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            Dear list members

            Omnidirectional variogram shows a dip toward the end
            of lags. As far as I know this is hole effect.
            Would you tell me how to tackle with it?

            Ercan


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          • Isobel Clark
            ... Ercan What is your maximum lag compared to the size of your study area? If the maximum lag is more than one-half (some people say one-quarter) of the
            Message 5 of 5 , Apr 24, 2002
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              > Omnidirectional variogram shows a dip toward the end
              > of lags. As far as I know this is hole effect.
              > Would you tell me how to tackle with it?
              Ercan

              What is your maximum 'lag' compared to the size of
              your study area? If the maximum lag is more than
              one-half (some people say one-quarter) of the maximum
              distance in your area, you will be getting the common
              artifact caused by diminishing numbers of pairs.

              If it is a real cycle, it may be of such a large
              extent that it is irrelevant to your analysis.

              Isobel
              http://uk.geocities.com/drisobelclark

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