Loading ...
Sorry, an error occurred while loading the content.
 

AI-GEOSTATS: Experimental variograms.

Expand Messages
  • Digby Millikan
    Hello, When one calculates an experimental variogram used for spatial modelling one averages the semivariogram values at each distance. This value is just an
    Message 1 of 5 , Jan 12, 2003
      Hello,
      When one calculates an experimental variogram used for spatial
      modelling one averages the semivariogram values at each distance.
      This value is just an average with a certain variance and coefficient
      of variation which we assume to represent the true underlying
      variogram as we only have samples of the entire population. To this
      effect can anyone suggest any literature that which discusses
      individual variogram variances and the effect of these assumptions,
      and smoothing it may cause in our modelling, or is that our averaged
      estimates of the variogram are accurate represenations as in many
      cases they do produce smooth curves.

      Thanks in advance.

      Regards Digby Millikan B.Eng

      Geolite Mining Systems
      U4/16 First Ave.,
      Payneham South SA 5070
      Australia.
      Ph: +61 8 84312974

      digbym@...
      http://www.users.on.net/digbym


      --
      * To post a message to the list, send it to ai-geostats@...
      * As a general service to the users, please remember to post a summary of any useful responses to your questions.
      * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
      * Support to the list is provided at http://www.ai-geostats.org
    • Digby Millikan
      Hello, Further information regarding my previous email, I illustrate by means of an example. e.g a variogram may be computed from data; Lag(m) SemiVariogram
      Message 2 of 5 , Jan 13, 2003
        Hello,

        Further information regarding my previous email, I illustrate by means
        of an example.

        e.g a variogram may be computed from data;

        Lag(m) SemiVariogram Number of values Coefficient of Variation
        2 20 100
        5%
        4 40 200
        3%
        6 60 200
        5%
        8 60 200
        7%

        Another variogram may be calculated within a different region;

        Lag(m) SemiVariogram Number of values Coefficient of Variation
        2 20 100
        25%
        4 40 200
        30%
        6 60 200
        28%
        8 60 200
        30%


        In both cases a well shaped variogram has been computed to which a
        spherical model could be fitted.
        However the coefficient of variation is much different for the variogram
        points for the two cases.
        In the first case the coefficient of variation for each sample point is
        fairly low, so we could assume that the variogram is a good
        representation of the underlying dataset considering that we have taken
        a few random samples from an underlying large population.
        In the second case however the Coefficient of Variation is considerably
        higher so we would wonder how much any spatial model produced from
        this variogram is smoothed using a model fitted to such a variogram.
        My question was I was wondering if anyone has comments or can
        suggest any research or literature on the effects of the C.V., S.D. or
        variance of variogram values, and their effect on producing smoothed
        models.

        Regards Digby Millikan B.Eng

        Geolite Mining Systems
        U4/16 First Ave.,
        Payneham South SA 5070
        Australia.
        Ph: +61 8 84312974

        digbym@...
        http://www.users.on.net/digbym


        --
        * To post a message to the list, send it to ai-geostats@...
        * As a general service to the users, please remember to post a summary of any useful responses to your questions.
        * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
        * Support to the list is provided at http://www.ai-geostats.org
      • Tom Mueller
        Hi Digby: In a paper (Mueller, T.G., F.J. Pierce, O. Schabenberger, and D.D. Warncke. 2001. Map quality for site-specific management. Soil Sci. Soc. Am. J. 65:
        Message 3 of 5 , Jan 13, 2003
          Hi Digby:

          In a paper (Mueller, T.G., F.J. Pierce, O. Schabenberger, and D.D. Warncke. 2001. Map quality for site-specific management. Soil Sci. Soc. Am. J. 65: 1547-1558), I suggest that the variance of the semivariogram at each lag may explain why map quality was poorer than expected in this study. I also suggest that this variance, particularly at earlier lags may be a good indicator of map quality. Bottom line is that semivariogram models are still just field average models of spatial autocorrelation. Since its not a Gaussian distribution (more like a Chi square distribution) it may not be appropriate to use CV’s do describe the semivariogram cloud. Something I’ve been looking at recently is Hawkins and Cressie’s robust estimator. It transforms the semivariogram distribution into a normal distribution to calculate the semivariogram and then rescales it back. I’ve found RMSE values are smaller with this approach more often than not with jack-knife analysis.

          Tom


          -----Original Message-----
          From: "Digby Millikan" <digbym@...>
          To: "ai-geostats" <ai-geostats@...>
          Date: Mon, 13 Jan 2003 15:35:40 +1030
          Subject: AI-GEOSTATS: Experimental variograms.

          Hello,
          When one calculates an experimental variogram used for spatial
          modelling one averages the semivariogram values at each distance.
          This value is just an average with a certain variance and coefficient
          of variation which we assume to represent the true underlying
          variogram as we only have samples of the entire population. To this
          effect can anyone suggest any literature that which discusses
          individual variogram variances and the effect of these assumptions,
          and smoothing it may cause in our modelling, or is that our averaged
          estimates of the variogram are accurate represenations as in many
          cases they do produce smooth curves.

          Thanks in advance.

          Regards Digby Millikan B.Eng

          Geolite Mining Systems
          U4/16 First Ave.,
          Payneham South SA 5070
          Australia.
          Ph: +61 8 84312974

          digbym@...
          http://www.users.on.net/digbym


          --
          * To post a message to the list, send it to ai-geostats@...
          * As a general service to the users, please remember to post a summary of any useful responses to your questions.
          * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
          * Support to the list is provided at http://www.ai-geostats.org


          Tom Mueller
          Assistant Professor of Agronomy
          University of Kentucky
          Lexington, Ky 40546-0091
          859-257-8887
          mueller@...
          www.uky.edu/~mueller

          phone 859-257-8887
          cell 859-608-2215

          --
          * To post a message to the list, send it to ai-geostats@...
          * As a general service to the users, please remember to post a summary of any useful responses to your questions.
          * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
          * Support to the list is provided at http://www.ai-geostats.org
        • Tom Mueller
          Hi Digby: In a paper (Mueller, T.G., F.J. Pierce, O. Schabenberger, and D.D. Warncke. 2001. Map quality for site-specific management. Soil Sci. Soc. Am. J. 65:
          Message 4 of 5 , Jan 13, 2003
            Hi Digby:

            In a paper (Mueller, T.G., F.J. Pierce, O. Schabenberger, and D.D. Warncke. 2001. Map quality for site-specific management. Soil Sci. Soc. Am. J. 65: 1547-1558), I suggest that the variance of the semivariogram at each lag may explain why map quality was poorer than expected in this study. I also suggest that this variance, particularly at earlier lags may be a good indicator of map quality. Bottom line is that semivariogram models are still just field average models of spatial autocorrelation. Since its not a Gaussian distribution (more like a Chi square distribution) it may not be appropriate to use CV’s do describe the semivariogram cloud. Something I’ve been looking at recently is Hawkins and Cressie’s robust estimator. It transforms the semivariogram distribution into a normal distribution to calculate the semivariogram and then rescales it back. I’ve found RMSE values are smaller with this approach more often than not with jack-knife analysis.

            Tom


            -----Original Message-----
            From: "Digby Millikan" <digbym@...>
            To: "ai-geostats" <ai-geostats@...>
            Date: Mon, 13 Jan 2003 15:35:40 +1030
            Subject: AI-GEOSTATS: Experimental variograms.

            Hello,
            When one calculates an experimental variogram used for spatial
            modelling one averages the semivariogram values at each distance.
            This value is just an average with a certain variance and coefficient
            of variation which we assume to represent the true underlying
            variogram as we only have samples of the entire population. To this
            effect can anyone suggest any literature that which discusses
            individual variogram variances and the effect of these assumptions,
            and smoothing it may cause in our modelling, or is that our averaged
            estimates of the variogram are accurate represenations as in many
            cases they do produce smooth curves.

            Thanks in advance.

            Regards Digby Millikan B.Eng

            Geolite Mining Systems
            U4/16 First Ave.,
            Payneham South SA 5070
            Australia.
            Ph: +61 8 84312974

            digbym@...
            http://www.users.on.net/digbym


            --
            * To post a message to the list, send it to ai-geostats@...
            * As a general service to the users, please remember to post a summary of any useful responses to your questions.
            * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
            * Support to the list is provided at http://www.ai-geostats.org


            Tom Mueller
            Assistant Professor of Agronomy
            University of Kentucky
            Lexington, Ky 40546-0091
            859-257-8887
            mueller@...
            www.uky.edu/~mueller

            phone 859-257-8887
            cell 859-608-2215

            --
            * To post a message to the list, send it to ai-geostats@...
            * As a general service to the users, please remember to post a summary of any useful responses to your questions.
            * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
            * Support to the list is provided at http://www.ai-geostats.org
          • Digby Millikan
            Hello, Continuing my discussion that we calculate each point on the variogram by averaging variogram values can anyone give examples of standard deviations of
            Message 5 of 5 , Jan 13, 2003
              Hello,
              Continuing my discussion that we calculate each point on the variogram
              by averaging variogram values can anyone give examples of standard
              deviations of variogram values for depositional type. It would be
              interesting
              to compare a sedimentary deposition to a highly skewed, high nugget effect,
              transgressive gold deposit.

              Regards Digby Millikan
              digbym@...
              http://www.users.on.net/digbym


              --
              * To post a message to the list, send it to ai-geostats@...
              * As a general service to the users, please remember to post a summary of any useful responses to your questions.
              * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
              * Support to the list is provided at http://www.ai-geostats.org
            Your message has been successfully submitted and would be delivered to recipients shortly.