12 Replies Latest reply on Aug 10, 2012 8:06 AM by slynch-esristaff

    Best interpolation methods

    maya3m
      How can one fix the different parameters in the  geostatistical analyst tool for various interpolation techniques? such as power for IDW, Smoothening parameters for RBF, range ,sill and nugget for kriging.
      Is there any range for these parameters? Should trend, transformations necessary to be considered?
        • Re: Best interpolation methods
          EKrause-esristaff
          Most parameters apply only for that particular interpolator.  The Power in IDW, for example, has no analogous parameter in any other interpolators.

          Global Polynomial Interpolation, Local Polynomial Interpolation, and Kernel Smoothing are all based on polynomials, so the Order of Polynomial means the same thing in each tool.  Additionally, LPI and KS share Kernel types because they're based on local kernels.

          The only parameters that are shared across the board are related to the searching neighborhood (except when you introduce barriers).

          The domain of each parameter depends on what the parameter does (for example, the range in kriging has to be greater than 0).  These domains are all documented, and if you try to use a value outside that domain, the software will throw an error telling you that it is outside the parameter domain.

          You should always consider trend removal and transformations, but that doesn't mean you have to use them.  Only use them if they help create a better model (which you can judge with crossvalidation statistics).
          • Re: Best interpolation methods
            maya3m
            Thank you

            I would like to know whether there is any specific range for RBF interpolations?
            Because when i did my work, i obtained a default parameter as 30.262 for completely regularised spline, 43.588 for spline with tension and 1E20 for tension spline. Can i continue my work with these default parameters? Is this the right way?

            To find the best interpolation methods, is it the way  that i change the parameters for one type of interpolation method and find the best model from it and again find best models for other methods by changing their corresponding parameters.

            For my work , is it necessary to create test data and training data and then do the analysis to get the best model?
            • Re: Best interpolation methods
              EKrause-esristaff
              The default Kernel Parameter in RBF is calculated such that it minimizes the Root-Mean-Square error (RMS) during crossvalidation.  Comparing the RMS values from different models is the most common method of deciding which model is better.  Comparing crossvalidation statistics between models can get complicated, but the rule-of-thumb is to use the model with the lowest RMS. All interpolation methods will calculate RMS during crossvalidation, and it has the same meaning for all interpolators, so it can be compared across the board to decide which interpolation method (and which parameters) to use.

              Theoretically, the kernel parameter can take any real number, but computer limitations keep the possible range between +/- 1.79769 x 10^308.
              • Re: Best interpolation methods
                maya3m
                Thank You So Much


                While i did ESDA, with the temperature data , in the Histogram tool i observed that my data is not normally distributed and when i did transformations I couldnt  find any change. Why is it like that?
                Was my data normally distributed? But it didnt show a bell shaped graph that appear for a normal distribution. I am attaching the  screen shots of histogram and QQ plot result please check and help me
                • Re: Best interpolation methods
                  EKrause-esristaff
                  From that Word doc, it doesn't look like a Log transformation is a good choice.  Instead, try a Normal Score Transformation. In the Geostatistical Wizard, use Kriging, then on the second page, use "Simple" as the kriging type.  The default transformation will be "Normal Score."  Click Next.  On this screen, change "Type" to Gaussian Kernels.  See if the default fit seems to fit your histogram.  You may need to try changing the number of kernels if the default fit doesn't look good.  If you find a transformation that fits your histogram, the software will automatically do the back-transformation for you, so the result of the kriging will be in the original units (not transformed units).

                  The Normal Score transformation is the most powerful and functional transformation, but it's only available for Simple, Probability, and Disjunctive kriging.
                  • Re: Best interpolation methods
                    maya3m
                    Thank you

                    But if i want to any do any other kriging other than simple and disjunctive , can i assume the histogram data as normal as obtained  in the word-Will there be any wrong with this? Is this assumption correct?
                    • Re: Best interpolation methods
                      EKrause-esristaff
                      The histogram and QQ plot look pretty good without a transformation; you'll probably be fine without one.  That being said, I would still try Simple Kriging with a Normal Score Transformation.
                      • Re: Best interpolation methods
                        maya3m
                        Thank you so much for the reply
                        • Re: Best interpolation methods
                          maya3m
                          What is the real difference between Completely regularized spline, spline with tension and thin plate spline?

                          How can we say that in RBF, the point Surface created must go through each measured sample value and also it predicts values above the maximum and below the minimum measured values
                          • Re: Best interpolation methods
                            slynch-esristaff
                            Have you looked in the help?
                            http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//00310000002p000000.htm

                            If you want additional information on splines I would suggest doing a literature search.

                            Regards
                            Steve
                            • Re: Best interpolation methods
                              maya3m
                              Respected sir,

                              Even though i read ESRI help regarding RBF functions: Completely regularized spline, spline with tension and thin plate spline- i couldnot make out the differences between the three.  Can you please help me with this ?  I read that all these provide similar output surfaces- then how can the user define these?
                              • Re: Best interpolation methods
                                slynch-esristaff
                                While doing a search did you find
                                http://resources.arcgis.com/en/help/main/10.1/index.html#//009z00000078000000 ?

                                Have you looked at the 2 references ?

                                Regards
                                Steve