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Re: AI-GEOSTATS: hole effect

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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 1 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 2 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 3 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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