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Re: AI-GEOSTATS: hole effect

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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 1 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 2 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 EcologĂ­a
        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 3 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 4 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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