Creating maps using global polynomial interpolation

Global polynomial interpolation (GPI) is best suited to fit a surface to attribute values that vary slowly over the area of interest. It is also useful when examining the data for the presence of global trends (trend surface analysis). The surface that GPI produces is sensitive to outliers, especially along the edges of the area of interest.

Steps:

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 Global Polynomial Interpolation, which is located under Deterministic Methods.

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

   Under the Input Data section, Source Dataset is set to the layer you clicked in the ArcMap table of contents.

4. Under Data Field, choose the attribute that you want to interpolate.
5. Click Next.
6. Modify the Order of Polynomial value, which can vary between 1 and 10.

   For global polynomial interpolation, the only parameter that you can change is Order of Polynomial. You can investigate the effects of changing this parameter by examining the preview surface on the left-hand side and by evaluating the goodness of fit of the model on the next page of Geostatistical Wizard.

7. Click Next.
8. Assess the goodness of fit of the model by using the Predicted and Error graphs, using the summary information on prediction errors, and examining particular pairs of measured and predicted values in the table on the left-hand side.

   For more information on how to assess the goodness of fit of a model, refer to Performing cross-validation and validation.

9. Once you are satisfied with the model, click Finish. A Method Report window appears.
10. 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 its name in the ArcMap table of contents, choosing Properties from the menu, then clicking the Method Summary tab.

The result is a surface generated by interpolating attribute values using global polynomial interpolation. 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.