Digital Terrain Models

Introduction

After completion of the data collection the next task was to display the points collected as a digital terrain model (DTM)Using ArcMap and ArcScene five different DTMs were created to represent the terrain. Five different forms of interpolation were used to discover which interpolation best represented the snow model that was created in the planter box.

Methodology

Using the data we had five three-dimensional DTMs were created using ArcMap and ArcScene. First the Excel spreadsheet was imported as a layer into ArcMap then the data was displayed using the "Display X,Y data" tool which created a grid showing the 420 points we collected. No projection was used because the points were collected using a custom coordinate system. Below in figure 1 you can see how the points are displayed in ArcMap a program used for mapping data. The points line up perfectly with each other with no missing points inbetween meaning that data collection was accurate as far as the x and y axes go.

Figure 1. data points displayed in ArcMap. There is no projection used with the data points because this is just a model; not a real life interpretation of a landscape.

The file was then exported as a "shapefile" so that it could be used as reference for the other tools which were used to create the DTMs. The five different types of DTMs created were Natural Neighbors, Kriging, Spline, Triangularted Irregular Network (TIN), and Inverse distance weighted (IDW). Each of these surfaces interpolated the data from each of the points to fill in the gaps between the points creating continuous surfaces with no gaps representing the terrain of the snow model that was created earlier.

Natural Neighbors

The algorithm used by the Natural Neighbors interpolation tool finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value. What this means is that it calculates what the height between the points should be by estimating the slope from point to point and those that surround it. Below is the surface created by the Natural Neighbors tool. This method produced a very natural looking surface with smooth elevation transitions.

Figure 2. Natural Neighbors DTM. This method produced a smooth looking surface with prominent peaks in the data. These peaks are created from the interpolation method and do not accurately represent the model.

Kriging

The next surface was created using the Kriging method. Kriging is based on statistical models that include autocorrelation—that is, the statistical relationships among the measured points. What this means is that it uses the surrounding points to determine the height and does not use weights in this determination. Figure 3 shows the surface created using the kriging method. Notice how there seems to be erroneous data around each of the points. This is caused from the way kriging interpolates data. For the amount of points used and how dynamic the landscape was kriging is not the best method for this.

Figure 3. Kriging DTM. The features appear well on the model but closer inspection shows that each original data point can be seen resulting in a very odd looking high resolution model.

Spline

The spline algorithm makes sure that the surface generated goes through each of the original points and smooths the surface by minimizing the amount of curvature of the created surface. This means that the resulting surface may not as accurately represent sharp changes in elevation. Figure 4 shows the model created from the spline technique. Peaks are smoothed over but not as generalized as kriging. The steepness of the ridges and peaks is not as drastic as in the natural neighbors method. Spline is by far the best representation for this data set resulting in an accurate representation of the model created in the snow.

Figure 4. Spline DTM. This method created the most accurate model for all five of the interpolation methods. 

Tin

A triangulated irregular network is pretty much exactly what the name implies. By using a set of points with elevation the tool creates triangles with each point being the corner of a triangle with no overlapping triangles. Since the points were collected in a normal array the tin looks a little odd but is still functional to represent the elevation. With a tin sharp changes in elevation are a little awkward to read. Figure 5 displays the TIN DTM. The triangles are fairly apparent in the overhead view with changes in elevation being overgeneralized. This over-generalization is because of how the triangles do not overlap.

Figure 5. TIN DTM show sharp changes in elevation and an over-generalization of the landscape. Since the interpolation relied on triangles that do not overlap there is a lot of error associated with this model for the terrain it is describing.

IDW

IDW determines cell values using a linearly weighted combination of a set of sample points. The resulting DTM appears very spiky showing that this method assumes that the variable being mapped decreases in influence with distance from its sampled location. This method resulted in a very inaccurate model. Figure 6 shows that each data point stands out considerably more than the interpolated data. In areas where there should be level surfaces between points there are drops in elevation.

Figure 6. IDW DTM. This DTM is the worst representation of the data that has been created. The data points should not be as apparent as they are in the model.

Discussion

Out of all of the surfaces I would suggest not using IDW, TIN, or Kriging because of the way they displayed the data. It was very easy to see each of the data points on the DTMs created by those methods. I prefer the spline method the most for this type of terrain analysis because of how smooth the final product looked. Natural Neighbors looked great visually but upon further inspection there were some places of inaccuracy (too sharp of elevation changes) that may have been improved upon by performing a second collection of data.

Conclusion

Creating the DTMs required no work between members of the group compared to collecting the data. Using the tools in ArcMap to create the surfaces was very simple and required no assistance from the help files as to how to run the tools. ArcScene allowed the DTMs to be displayed in a 3-D environment to better show the elevation of the surface which was very beneficial in examining the accuracy of the surface. It would be interesting to see how a recollection of data at a higher frequency would benefit (or harm) the resulting DTMs.