Creating a Surface Model Using the Kriging Interpolation Method
Kriging refers to a group of geostatistical interpolation techniques that can provide a standardized measure of uncertainty in their predictions. Like some of the deterministic interpolation methods, it is based on the assumption that things that are closer together are more alike than those farther away. There are numerous options to choose from when using the Kriging method, most of which are beyond the scope of this course. Instead, will primarily rely on the default settings and use cross-validation to compare the results. Unlike deterministic interpolation methods, prediction points are estimated by modeling the statistical correlation between pairs of known points. This relationship between the values of data points and the distance between them is known as spatial autocorrelation. In this step, you will explore the use of a geostatistical interpolation method to compare with your two previous deterministic interpolation methods. The number of options available through the different Kriging methods can be overwhelming. The method we will use in this lesson will be Ordinary Kriging, which has only a limited number of options from which to choose. From the Geostatistical Analyst toolbar, select Geostatistical Wizard from the drop-down menu. Under the Methods section, choose Kriging/CoKriging, which is located under Geostatistical Methods. For the Data Field option, select altitude. Leave Dataset 2, Dataset 3, and Dataset 4 alone. These are used for cokriging, and we will not be using them for this lesson. Click Next.
On step 2 of the Geostatistical Wizard, you have the option to choose from a variety of Kriging types. From the list on the left, under Kriging Type, select Ordinary. Beneath that list, you will see some other options under Output Surface Type. On this list choose Prediction. Click Next.
Step 3 of the Geostatistical Wizard displays a graph called a semivariogram. In this semivariogram, each waypoint in the dataset gets paired with every other waypoint. The Geostatistical Analyst records the difference in elevation value between each paired data point along with the distance between them. The expectation is that there will be small differences in elevation values between pairs that are close together. Pairs that have greater distances between them are expected to have more substantial differences in elevation values. The Geostatistical Analyst plots each of these pairs, represented by the red dots, on a graph which makes up the semivariogram. It defines the surface model by finding the best fit through the points in the semivariogram. At this time, you will accept the default settings. In step three of the Geostatistical Wizard window click Next.
Step 4 and step 5 of the Geostatistical Wizard should look familiar based on the previous work with IDW and Spline interpolation. 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. You may notice that the setting, Copy from Variogram, is set to True. This option means that many of the settings here will be determined by the settings in the semivariogram on step 3 of the Geostatistical Wizard. While you are trying to optimize the model, you will go back and forth between step 3 and step 4. You can check the RMSE values on step 5 of the Geostatistical Wizard. For now, record the default values. An example table is shown below.
|Default Ordinary Kriging||Optimized Ordinary Kriging|
|Sector Type||4 Sectors with 45 offset|
|Root Mean Square Error (RMSE)||2.486262|
Your values may be different than the example above.
As mentioned before, Kriging interpolation can have an overwhelming number of options. The mathematics behind these options are beyond the scope of this course. However, experimenting with a few options may improve your surface model. Spend about five minutes to try to improve the RMSE value. A good place to start your optimization is to try the different model types. You can locate this parameter back on Step 3 of the Geostatistical Wizard. By default, it should be set to Stable. 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. A temporary geostatistical layer should now be added to your Table of Contents. This layer is a temporary representation of your surface model. In the next step, you will choose the best interpolation method from which to base your digital elevation model.