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2458RE: [ai-geostats] kriging without a nugget

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  • Pierre Goovaerts
    Mar 6, 2006
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      Hi Niklas,

      This is a very good question; in fact one of the participants to my last short course
      asked the same question since he was using ARCview with the option
      "nugget effect excluded" and was surprised to see that his observations were
      not honored by the kriging predictions. This is related to the issue
      of how to define the nugget effect. On almost all figures in the literature the semivariogram
      model seems to start on the vertical axis at a value equal to the nugget effect, while
      in fact the value of the model is set to zero for h=0 in the kriging system. This ensure
      that kriging is an exact interpolator, which is usually a desirable property.
      When interpolated nodes correspond to sampled locations, this exactitude
      property can create spikes in the kriged map; in other words these locations
      contrast with the general smoothness of the interpolated map produced by kriging
      and it is one reason why the option to filter the noise, even at the sampled locations
      was introduced (A general presentation of the filtering properties of kriging
      can be found in my book p. 172-174). Another application of the filtering
      method is the use of kriging for finding minimum or maximum in numerical models;
      see paper
      Sasena, M.J., Parkinson, M., Goovaerts, P., Papalambros, P.Y. and M. Reed. 2002. <http://ode.engin.umich.edu/publications/papers/2002/DETC2002_DAC34091.pdf>
      Adaptive experimental design applied to an ergonomics testing procedure. Proceedings of
      DETC'02 ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Montreal, Canada, September 29- October 2, 2002.
      http://ode.engin.umich.edu/publications/papers/2002/DETC2002_DAC34091.pdf

      More generally, the question is whether the nugget effect represents measurement errors
      (variability at the sampled locations) which you might want to filter, or whether it
      represents small-scale variability in the field.
      Note that the discontinuities in the map will disappear if you use a simulation method.

      Hope it helps,

      Pierre

      Pierre Goovaerts
      Chief Scientist at BioMedware
      516 North State Street
      Ann Arbor, MI 48104
      Voice: (734) 913-1098 (ext. 8)
      Fax: (734) 913-2201
      http://home.comcast.net/~goovaerts/

      ________________________________

      From: Törneman Niklas [mailto:Niklas.Torneman@...]
      Sent: Mon 3/6/2006 3:14 PM
      To: ai-geostats@...
      Subject: [ai-geostats] kriging without a nugget


      Hi All,

      I am sort of a beginner within this field and my question might seem a bit simple. Any help would be appreciated however.

      In commercial all purpose software's such as SURFER there is an option to exclude the nugget effect from the kriging interpolation.
      The purpose is to ensure that measured values are honoured at their locations. This seems understandable to me since the absence of a nugget ensures that the variance is zero at a distance of zero from the measured point, i.e. the measured value=interpolated value.

      However, in most projects that I work with (soil pollution problems) there is a significant nugget effect. My question is simply how the interpolation is affected if the nugget effect is excluded when in reality there is a clear nugget present in the data.

      One reason for this question (apart from a personal interest) is that I am trying to motivate the use of other methods (i.e. SGS) and more specialized software such as SGeMS and GS+. One good easily explainable motivation for this would be if the above mentioned methodology of excluding the nugget is inappropriate, which is suspect that it is.


      cheers


      Nicholas
      ________________________________


      <http://www.sweco.se/>
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