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524Re: AI-GEOSTATS: hole effect

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  • Colin Daly
    Jan 30, 2002
    • 0 Attachment
      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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