Example: Creating a terrain surface with sample points

ArcGIS™ Spatial Analyst makes it easy to interpolate any type of surface from a set of sample points. Interpolation methods such as Inverse Distance Weighted (IDW) depend on good, quality sample point sets to function properly. For ths reason, you should pay attention to spacing and density when assembling a set of sample points.

Take a look at an area on the southern tip of the Shivwits Plateau in Arizona.

Left: A 7.5' Travertine Rapids topographic map of the Shivwits Plateau. Contours help represent the features and characteristics of the landscape. Right: A surface, 30-meter digital elevation model (DEM) for the same quadrangle. At this scale, you can just see the 30-meter square cells of the raster surface.

For this example, suppose the digital elevation model above does not exist and it's your job to produce it. The only tools you have to create it are your ArcGIS™ software and this digital raster graphic (DRG) of the Travertine Rapids topographic map (left). Lucky for you, that's enough to interpolate a point layer.

First, you need to create enough points to make interpolation worthwhile. Using the contours on the topographic map as a guide, you digitize points and record the elevation values for each location. As you digitize, you make sure to distribute the sample points as evenly as possible throughout the area, placing fewer points on the plateau where it's fairly level, and putting more points in places where the contour lines are closer together.

Once you have created an initial set of sample points, you use the IDW function to interpolate the surface.

Left: The black dots on the topographic map are the initial sample point set. Based on the elevation values assigned to each sample point, the IDW function will estimate the elevation values between the points. Right: In this case, the resulting surface is a continuous raster with 30-meter cell size.

IDW does a good job of estimating the surface with only a limited number of sample points, but when compared to the topographical map, you can see that there is detail missing. You need more sample points.

Using the same method as before, you supplement the sample point set with more points, then run IDW again.

More sample points help the IDW function refine the surface estimation.

Now the plateau, steep cliffs, and variations in the terrain are more apparent. Encouraged by these developments, you continue building the density of sample points and run IDW again.

Left: Notice that this dense set of sample points is made up of clusters of evenly spaced points. Right: In the resulting surface, features such as the plateau, the cliff faces, and the steeply sloping landscape are distinguished from each other.

You notice that the more sample points you add, the more accurately the digital surface represents the actual terrain. Remember that the elevation values for each point must be derived from somewhere (e.g., contour lines or field observations). If you had the data and the time, you could create a sample point set for this area from thousands of points at regularly spaced intervals. But you don't have either, so this surface will have to do for now.

From this example, you can see that a surface interpolation function like IDW depends heavily on the quality of the sample point set. The quality increases as the point set becomes sufficiently dense to capture subtle and dramatic changes in the surface.