Creating maps using Radial Basis Functions

Available with Geostatistical Analyst license.

Radial Basis Functions (RBF) are exact interpolators that create smooth surfaces. They produce good results for gently varying attributes. Because predictions are exact, RBFs can be locally sensitive to outliers (that is the surfaces will contain locally high or low values in order to pass through a extreme measured values).

1. Click the point layer in the ArcMap table of contents that contains the attributes you are interested in.

   Alternatively, go directly to Step 2 and browse to the dataset you are interested in on the first page of the Geostatistical Wizard.

2. Start the Geostatistical Wizard
3. Under the Methods section, choose Radial Basis Functions, which is located under Deterministic Methods.

   The lower portion of the Geostatistical Wizard shows information about Radial Basis Functions. There is also a link that will take you directly to more detailed information on Radial Basis Functions in the main help system.

4. Under the Input Data section, you should see that Source Dataset has been set to the layer you clicked on in the ArcMap table of contents. Under Data Field, select the attribute that you want to interpolate.
5. Click Next.
6. Select a Kernel Function, a Kernel Parameter value and specify the Search Neighborhood.

   Step 2 of the Geostatistical Wizard is where the parameter values for this method must be defined. For Radial Basis Functions, parameters that you can change are the Kernel Function, Kernel Parameter and Search Neighborhood. You can investigate the effects of changing these parameters by examining the preview surface, and by evaluating the goodness of fit of the model on the next page of the Geostatistical Wizard.

   There is an option to optimize the Kernel Parameter value by clicking on the Optimize button . The optimization process will evaluate several models and choose the Kernel Parameter value, for the selected kernel function, that gives the model with the lowest Root Mean Square error (see Step 9 for more information on cross validation and error statistics). Note that the kernel function and search neighborhood will not be changed during the optimization process. Choosing a different kernel function and adjusting the search neighborhood may lead to a better model, and should be investigated before deciding on a final model to use.

7. Adjust the Search neighborhood options (refer to Altering the search neighborhood by changing its size and shape and Altering the search neighborhood by changing the number of neighbors) to see how to modify the number of neighbors and the shape of the search neighborhood. Anisotropy (directional influences present in the phenomenon that the data represents) can be accounted for at this stage by modifying the Major semiaxis, Minor semiaxis and Angle parameters.

   When using the Inverse Multiquadric kernel,Neighborhood type can be changed from Standard to Smooth. In this case, Maximum neighbors, Minimum neighbors and Sector type are replaced by a Smoothing factor, and the method will produce a smoother surface. Refer to smooth interpolation for more details. The other kernel types do not support smooth interpolation.

8. Click Next.
9. Assess the goodness of fit of the model using the Predicted and Error graphs, the summary information on Prediction Errors, and by examining particular pairs of measured and predicted values in the table on the left hand side.
10. Once you are satisfied with the model, click Finish.
11. A Method Report window will appear. Click OK to produce the surface.

    The Method Report window contains a summary showing the dataset, attribute, interpolation method and parameter values used to create the surface. This information can be retrieved for any geostatistical layer by right-clicking on it in the ArcMap table of contents, choosing Properties from the menu and then clicking on the Method Summary tab.

The result is a surface generated by interpolating attribute values using a particular Radial Basis Function. The surface is added directly to the ArcMap table of contents, and is displayed using a default color scheme and class breaks, which can be changed by accessing the layer's properties.