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Thread: Cokriging equation

  1. #1
    qi xp
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    Default Cokriging equation

    Could someone tell me what is the Arcgis cokriging equation? I can only find the simple equation which is:
    Z1(s) = µ1 + ε1(s)
    Z2(s) = µ2 + ε2(s)

    When I use SAS to do the cokriging analysis, it's more accurate than using Arcgis. So I want to compare the difference between each equation.

    Many thanks,
    Xiaopeng

  2. #2
    Eric Krause

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    Default Re: Cokriging equation

    The cokriging equations are well-known, and you can reference them in Cressie (1993), for example. Any differences between SAS and Geostatistical Analyst are almost certainly due to different variogram parameters, different search neighborhoods, and/or different preprocessing techniques (transformations, detrending, declustering, for example).

    What criteria are you using to say that SAS is more accurate? Are you using the default model and comparing crossvalidation results?
    Eric Krause
    Geostatistical Analyst Product Engineer

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    qi xp
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    Default Re: Cokriging equation

    I compared the performance of geostatistical models to estimate average temperature in each month using weather station temperature and elevation. Monthly estimates were validated for 30% split-sample of stations with ordinary cokriging in ArcGIS and universal kriging in SAS Proc Mixed. They were produced with elevation as a covariate using ordinary cokriging in ArcGIS and universal kriging in SAS. Performance of models was assessed by comparing adjusted R2, mean squared error, root mean squared error. Accuracy and precision were higher for universal kriging estimates in SAS. In arcgis, I use Histograms, Normal QQ Plots and trend analyses and select the proper parameter to do the cokriging. But in SAS, there are not many parameters needed to be adjusted. For what I know is that SAS uses the restricted maximum likelihood method to estimate variance and covariance of the models and Arcgis builds semivariograms and computs corresponding semivariogram parameters. I select exponencial model in both Arcgis and SAS. I use split validation not cross validation.

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    Eric Krause
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    Default Re: Cokriging equation

    If you're comparing ordinary cokriging to universal kriging, you aren't getting a fair comparison. You need to compare the predictions using the same type of kriging.

    Restricted maximum likelihood is the most accurate method for determining variography parameters; however, it doesn't scale well. For large datasets, the method quickly becomes computationally infeasible. I don't know what algorithm SAS uses, but if they really are using REML, it will take an incredibly long time to process when there are thousands or millions of points. Our weighted least-squares algorithm, however, is able to efficiently handle datasets into the billions.
    Eric Krause
    Geostatistical Analyst Product Engineer

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    qi xp
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    Smile Re: Cokriging equation

    Many thanks. You are absolutely correct. SAS took more than 8 hours in computing 5000 points, while Arcgis only took several seconds. By the way, I still cannot find this book 'Cressie (1993)' in China. Could you send me relative equations? My email address: caroline_qi@163.com

    Best regards

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    Eric Krause

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    Default Re: Cokriging equation

    You can see the cokriging equations on page 271 (Appendix A):

    http://dusk.geo.orst.edu/gis/geostat_analyst.pdf

    To see them in more detail, you're going to have to go to a geostatistics textbook. Again, "Statistics for Spatial Data" by Cressie (1993) is the classic text, and all the cokriging equations are in there.
    Eric Krause
    Geostatistical Analyst Product Engineer

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    qi xp
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    Smile Re: Cokriging equation

    It's very helpful. I appreciate it.

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