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AI-GEOSTATS: Optimal Kriging parameters

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  • Eva Pierce
    Hi. I want to use Ordinary Kriging on an arbitrary dataset of X,Y, and Z values to estimate the Z values on a grid of arbitrary size/density. But I don t know
    Message 1 of 3 , Jul 8, 2002
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      Hi.

      I want to use Ordinary Kriging on an arbitrary dataset of X,Y, and Z
      values to estimate the Z values on a grid of arbitrary size/density. But
      I don't know what length and scale parameters to choose for the
      semivariogram. So I need to answer the following questions. I'm looking
      for guidance and resources, not necessarily definitive answers. When
      answering, please keep in mind that I'm a computer programmer, not a
      statistician, by education and experience. :-)

      1. How does one measure the "goodness" or "badness" of a Kriging
      estimate? E.g. when the bounds of the grid are fairly close to the
      bounds of the dataset, I might expect the estimated surface of Z values
      to have roughly the same number of "bumps" and "valleys" as the original
      dataset (if discernible), and not too many flat regions. How do I
      quantify such characteristics, and are there others I should be looking
      for?
      2. How does one arrive at the "optimal" length and scale parameters
      for the semivariogram when doing ordinary Kriging, given these measures
      of "goodness" and "badness"? (here's where my comp. sci education would
      come in handy, if I knew the answer to #1)

      I'll send out a summary of answers that I receive. Thanks!
      Eva






      [Non-text portions of this message have been removed]
    • Syed Abdul Rahman Shibli
      Variogram modeling is usually a pre-requisite for kriging and/or stochastic simulation. It s not usally something that you d want to automate in some sort of
      Message 2 of 3 , Jul 9, 2002
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        Variogram modeling is usually a pre-requisite for
        kriging and/or stochastic simulation. It's not
        usally something that you'd want to "automate" in some
        sort of computer program. Selection of a model type/range/sill
        will usually be based on available sample points,
        or analagous samples of the same origin as the dataset
        one is looking at, complemented by a qualitative interpretation
        of the spatial model. I guess one can try to "program"
        this whole process from start to finish (exploratory
        data analysis/variogram modeling/kriging) but this is
        not at all recommended. Perhaps in some applications with
        abundant data, yes, but probably not in a geoscience
        setting.

        You haven't told us what your applications are? Will you
        be mapping some geological variable? Interpolating 6 million
        pixels in an image file? Trying to gauge the distribution of a
        certain species of rare tropical flower?

        Syed

        ---- Original message ----
        >Date: Mon, 8 Jul 2002 20:56:15 -0700
        >From: "Eva Pierce" <logicgrrl@...>
        >Subject: AI-GEOSTATS: Optimal Kriging parameters
        >To: <ai-geostats@...>
        >
        >Hi.
        >
        >I want to use Ordinary Kriging on an arbitrary dataset of X,Y, and Z
        >values to estimate the Z values on a grid of arbitrary size/density. But
        >I don't know what length and scale parameters to choose for the
        >semivariogram. So I need to answer the following questions. I'm looking
        >for guidance and resources, not necessarily definitive answers. When
        >answering, please keep in mind that I'm a computer programmer, not a
        >statistician, by education and experience. :-)
        >
        >1. How does one measure the "goodness" or "badness" of a Kriging
        >estimate? E.g. when the bounds of the grid are fairly close to the
        >bounds of the dataset, I might expect the estimated surface of Z values
        >to have roughly the same number of "bumps" and "valleys" as the original
        >dataset (if discernible), and not too many flat regions. How do I
        >quantify such characteristics, and are there others I should be looking
        >for?
        >2. How does one arrive at the "optimal" length and scale parameters
        >for the semivariogram when doing ordinary Kriging, given these measures
        >of "goodness" and "badness"? (here's where my comp. sci education would
        >come in handy, if I knew the answer to #1)
        >
        >I'll send out a summary of answers that I receive. Thanks!
        >Eva
        >
        >
        >
        >

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      • Isobel Clark
        Hi Eva You have your questions the wrong way round. Once you find the semi-variogram model for your particular application, the kriging system should povide
        Message 3 of 3 , Jul 9, 2002
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          Hi Eva

          You have your questions the wrong way round. Once you
          find the semi-variogram model for your particular
          application, the kriging system should povide you with
          a measure of 'goodness' of the estimator. It is
          usually called the 'kriging standard error' or
          sometimes software provides the kriging variance.

          Please feel free to download a free copy of my (old)
          book at
          http://uk.geocities.com/drisobelclark/practica.html

          It is only 125 A5 pages long and you can skip a lot of
          that to get what you need. Alternatively download my
          RSMA article which says much the same thing in 500
          words. Find this on
          http://uk.geocities.com/drisobelclark/resume/Publications.html

          Mind the capital P on Publications ;-)

          Hope this helps
          Isobel Clark

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