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[ai-geostats] Interpolation of climatic data thorugh space and time.

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  • Dave Miller
    Dear all, Please bear with me on this. A first submission to the list from a perplexed and increasingly stressed research assistant (I m sure you ve all been
    Message 1 of 3 , Mar 2, 2005
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      Dear all,

      Please bear with me on this. A first submission to the list from a
      perplexed and increasingly stressed research assistant (I'm sure you've
      all been there once upon a time, or here)! My queries relate principally
      to the comparison of interpolation methods.

      I have a dataset of 25 locations across the UK of empirically derived
      values based on cloud cover. Each station has a varying length of record
      between 10 years and 42 years between the years 1952 - 2000.

      To test which was the most appropriate technique to use for
      interpolation between locations for the mean value for each site, I have
      tested a variety of functions available in ArcGIS Geostatistical Analyst
      (version 8.3) including Inverse Distance Weighting, the five radial
      basis functions (completely regularised spline, spline with tension,
      thin plate spline, multiquadratic, inverse multiquadratic) and ordinary
      kriging (spherical semivariogram, no nugget, search neighbourhood
      equalling the range of the variogram). Because of the limited number of
      locations for which data was available, I have used cross-validation to
      generate RMSE, MAE, MSE and G-measures for each interpolation method. My
      first question is: Is the surface with the lowest resulting error
      measures, be they RMSE, MAE or MSE necessarily a feasible way to select
      the best interpolation method? If so the Inverse Multiqudratic function
      appears to yield the best surface.

      Secondly, since data is available on a year-to-year basis, I'd like to
      be able to analyse the variability between years. The problem is that
      data isn't necessarily available for each year for each site! As a
      result the 'best' interpolation method (as measured by RMSE at least)
      varies between years. Nice. By ranking the methods for each year and
      summing the ranks for each interpolation method, it seems that overall
      the Inverse Multiquadratic function marginally outperforms the spline
      with tension.

      If you've got this far then thanks for reading, and if anyone can
      suggest any tips on where I might go from here with my analysis (or
      where I need to go back to!) I'd be very happy to hear from you.

      Regards,

      Dave Miller

      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      Dave Miller
      Research Assistant
      GIS & Remote Sensing
      The Macaulay Institute
      Craigiebuckler
      Aberdeen
      AB15 8QH

      tel: +44 (0) 1224 498200 (switchboard) ext. 2261
      fax +44 (0) 1224 311556
      e-mail: dave.miller@...
      websites: http://www.macaulay.ac.uk
      http://www.macaulay.ac.uk/LADSS/ladss.shtml
    • Chaosheng Zhang
      Hi Dave, My concern is that the 25 locations may not be enough to capture the spatial structure of the parameter (which climatic data?) across the UK. As
      Message 2 of 3 , Mar 3, 2005
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        Hi Dave,
         
        My concern is that the 25 locations may not be enough to capture the spatial structure of the parameter (which climatic data?) across the UK. As discussed earlier in this list, you need to perform analyses on spatial correlation. If your data is lack of spatial (auto)correlation, any spatial interpolation is questionable.
         
        Meanwhile, there should be some models in climate. Some time ago, I had to produce a long-term average climate map (precipitation) of Ireland, and I found that it is helpful to use the knowledge of experts in climate, not based on pure mathematical methods, even though they are very attractive. Well, the model itself is still mathematical: precipitation is a function of coordinates (second order) and elevation. Such a model may not be applicable everywhere, but UK should be similar to Ireland, or you may try to find other models. This may also give you an idea of using co-kriging, but there should be a good relationship between your parameter and e.g., elevation. The fact of "rain shadow" obviously destroys such a relationship. What I did was to perform an interpolation on the residuals, and put the residuals back to the modelled results.
         
        Hope this is helpful for you to think about your problem.
         
        Cheers,
         
        Chaosheng
        --------------------------------------------------------------------------
        Dr. Chaosheng Zhang
        Lecturer in GIS
        Department of Geography
        National University of Ireland, Galway
        IRELAND
        Tel: +353-91-524411 x 2375
        Direct Tel: +353-91-49 2375
        Fax: +353-91-525700
        E-mail:
        Chaosheng.Zhang@...
        Web 1: www.nuigalway.ie/geography/zhang.html
        Web 2: www.nuigalway.ie/geography/gis
        ----------------------------------------------------------------------------
         
         
        ----- Original Message -----
        From: "Dave Miller" <Dave.Miller@...>
        Sent: Wednesday, March 02, 2005 5:06 PM
        Subject: [ai-geostats] Interpolation of climatic data thorugh space and time.

        >
        > Dear all,
        >
        > Please bear with me on this. A
        first submission to the list from a
        > perplexed and increasingly stressed
        research assistant (I'm sure you've
        > all been there once upon a time, or
        here)! My queries relate principally
        > to the comparison of interpolation
        methods.
        >
        > I have a dataset of 25 locations across the UK of
        empirically derived
        > values based on cloud cover. Each station has a
        varying length of record
        > between 10 years and 42 years between the years
        1952 - 2000.
        >
        > To test which was the most appropriate technique
        to use for
        > interpolation between locations for the mean value for each
        site, I have
        > tested a variety of functions available in ArcGIS
        Geostatistical Analyst
        > (version 8.3) including Inverse Distance
        Weighting, the five radial
        > basis functions (completely regularised
        spline, spline with tension,
        > thin plate spline, multiquadratic, inverse
        multiquadratic) and ordinary
        > kriging (spherical semivariogram, no
        nugget, search neighbourhood
        > equalling the range of the variogram).
        Because of the limited number of
        > locations for which data was available,
        I have used cross-validation to
        > generate RMSE, MAE, MSE and G-measures
        for each interpolation method. My
        > first question is: Is the surface with
        the lowest resulting error
        > measures, be they RMSE, MAE or MSE
        necessarily a feasible way to select
        > the best interpolation method? If
        so the Inverse Multiqudratic function
        > appears to yield the best
        surface.
        >
        > Secondly, since data is available on a year-to-year
        basis, I'd like to
        > be able to analyse the variability between years. The
        problem is that
        > data isn't necessarily available for each year for each
        site! As a
        > result the 'best' interpolation method (as measured by RMSE
        at least)
        > varies between years. Nice. By ranking the methods for each
        year and
        > summing the ranks for each interpolation method, it seems that
        overall
        > the Inverse Multiquadratic function marginally outperforms the
        spline
        > with tension.
        >
        > If you've got this far then
        thanks for reading, and if anyone can
        > suggest any tips on where I might
        go from here with my analysis (or
        > where I need to go back to!) I'd be
        very happy to hear from you.
        >
        > Regards,
        >
        > Dave
        Miller
        >
        > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        > Dave
        Miller
        > Research Assistant
        > GIS & Remote Sensing
        > The
        Macaulay Institute
        > Craigiebuckler
        > Aberdeen
        > AB15
        8QH
        >
        > tel: +44 (0) 1224 498200 (switchboard) ext. 2261
        >
        fax +44 (0) 1224 311556
        > e-mail:
        href="mailto:dave.miller@...">dave.miller@...
        > websites: http://www.macaulay.ac.uk
        > http://www.macaulay.ac.uk/LADSS/ladss.shtml
        >
        >


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      • Mahdi Osman
        As an addition to my previous messge............. VarioWin, Vesper etc are easy tools for variography. Variowin offers a simple interactive variogram modelling
        Message 3 of 3 , Mar 4, 2005
        • 0 Attachment
          As an addition to my previous messge.............


          VarioWin, Vesper etc are easy tools for variography. Variowin offers a
          simple interactive variogram modelling interface. Vesper, developed by
          Australian centre of precision agriclture is very interesting, it is based
          on ml iteration methods. Try for more information. I have been doing
          variography using ARCMAM (8.3). It was not interactive at all, but plenty of
          colours, mate.

          Please check also R packages such as sgeostat, geoR, MASS, etc

          Cheers

          Mahdi

          >

          > Dear all,
          >
          > Please bear with me on this. A first submission to the list from a
          > perplexed and increasingly stressed research assistant (I'm sure you've
          > all been there once upon a time, or here)! My queries relate principally
          > to the comparison of interpolation methods.
          >
          > I have a dataset of 25 locations across the UK of empirically derived
          > values based on cloud cover. Each station has a varying length of record
          > between 10 years and 42 years between the years 1952 - 2000.
          >
          > To test which was the most appropriate technique to use for
          > interpolation between locations for the mean value for each site, I have
          > tested a variety of functions available in ArcGIS Geostatistical Analyst
          > (version 8.3) including Inverse Distance Weighting, the five radial
          > basis functions (completely regularised spline, spline with tension,
          > thin plate spline, multiquadratic, inverse multiquadratic) and ordinary
          > kriging (spherical semivariogram, no nugget, search neighbourhood
          > equalling the range of the variogram). Because of the limited number of
          > locations for which data was available, I have used cross-validation to
          > generate RMSE, MAE, MSE and G-measures for each interpolation method. My
          > first question is: Is the surface with the lowest resulting error
          > measures, be they RMSE, MAE or MSE necessarily a feasible way to select
          > the best interpolation method? If so the Inverse Multiqudratic function
          > appears to yield the best surface.
          >
          > Secondly, since data is available on a year-to-year basis, I'd like to
          > be able to analyse the variability between years. The problem is that
          > data isn't necessarily available for each year for each site! As a
          > result the 'best' interpolation method (as measured by RMSE at least)
          > varies between years. Nice. By ranking the methods for each year and
          > summing the ranks for each interpolation method, it seems that overall
          > the Inverse Multiquadratic function marginally outperforms the spline
          > with tension.
          >
          > If you've got this far then thanks for reading, and if anyone can
          > suggest any tips on where I might go from here with my analysis (or
          > where I need to go back to!) I'd be very happy to hear from you.
          >
          > Regards,
          >
          > Dave Miller
          >
          > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
          > Dave Miller
          > Research Assistant
          > GIS & Remote Sensing
          > The Macaulay Institute
          > Craigiebuckler
          > Aberdeen
          > AB15 8QH
          >
          > tel: +44 (0) 1224 498200 (switchboard) ext. 2261
          > fax +44 (0) 1224 311556
          > e-mail: dave.miller@...
          > websites: http://www.macaulay.ac.uk
          > http://www.macaulay.ac.uk/LADSS/ladss.shtml
          >
          >

          --
          -----------------------------------
          Mahdi Osman (PhD)
          E-mail: m_osm@...
          -----------------------------------

          DSL Komplett von GMX +++ Superg´┐Żnstig und stressfrei einsteigen!
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