Creating a Surface Model Using the Spline Interpolation Method

Spline is a deterministic interpolation method where the predicted values are estimated using a function that minimizes the total curvature of the surface. The result is a smooth surface that passes precisely through all of the measured data points. Like IDW, the Spline interpolation is available as a stand-alone tool. However, deterministic methods like IDW and Spline do not provide a standardized measure of uncertainty. Just as with IDW, the Geostatistical Analyst extension within the ArcGIS software can provide some measure of uncertainty, even among deterministic methods through the use of cross-validation. From the Geostatistical Analyst toolbar, select Geostatistical Wizard from the drop-down menu.  Under the Methods section, choose Radial Basis Functions, which is located under Deterministic Methods. For the Data Field option, select altitude and click Next.

An image of the Geostatistical Wizard Spline step 1

Maximize the Geostatistical Wizard window to view the results. You should now see a colored preview of your surface model along with a few model settings on the right.

An image of the Geostatistical Wizard Spline step 2
This image shows the method properties window. Your results will appear different than this image. Click to view in a larger size.

Take a moment to explore the data. As before, you will record the default settings and RMSE onto an Excel table. However, the settings here are slightly different. Instead of Power and Neighborhood Type, you have Kernal Function and Kernel Parameter. An example table is shown below.

Default Spline Optimized Spline
Kernel Function Completely Regularized Spline  ?
Kernel Parameter 61.26578  ?
Maximum Neighbors 15  ?
Minimum Neighbors 10  ?
Sector Type  1 Sector  ?
Angle  0  ?
Major semiaxis  76.54706  ?
Minor Semi Axis  76.54706  ?
Root Mean Square Error (RMSE) 2.47245  ?

Your values may be different than the example above.

Now you will attempt to optimize the Spline interpolation. On step 2 in the Geostatistical Wizard, spend about 5 minutes experimenting with the Spline settings mentioned above in order to try to improve the RMSE value. A good place to start is to click the Optimize Kernal Parameter button to the right of the Kernal Parameter setting. You may also want to compare regularized spline with other types of spline functions, such as the tension spline located under the Kernal Function Settings. While you are experimenting, occasionally return to step 3 in the Geostatistical Wizard to check on the RMSE value. Once you are satisfied, record the results in your Excel table. Save your excel file in your final folder for later use. Once you have recorded the optimized RMSE value, return to ArcMap. In the Geostatistical Wizard, click Finish and then click OK.

An image of the Geostatistical Wizard Spline step 2 optimized
In this example, I have optimized the settings by changing the kernel function, the kernel parameter, the maximum neighbors, the minimum neighbors, the sector type, the major semiaxis, and the minor semiaxis. I kept the angle at 0 because I knew the values in this dataset tended to be similar in a north-south direction. You may need to use different settings to optimize your dataset. Click to view a larger image.

A temporary geostatistical layer should now be added to your Table of Contents. Next, you will create a surface modeling using the Kriging method.

An image of the Spline Prediction Map Results in ArcMap
The results of the Geostatistical Wizard are only temporary and will not exist outside of the map document.