Lab 1: Benchmarks, DEM Generation, and Landscape Modeling

Introduction: Digital Elevation Model (DEM) generation, landscape modeling, and benchmarks are all vital to field surveying. Benchmarks are set elevation markers and are used to determine the Z-coordinate in the X-Y-Z coordinate system. People like topographic surveyors utilize benchmarks to measure the elevation of the land, to generate DEMs. DEMs are a form of rasterized landscape modeling that represents a surface of a given area. Within each raster cell contains elevation points.

Problem/Statement: In this lab, the process of interpolating elevation data points will be addressed to see which interpolation method is the most accurate, both in the 2-D and the 3-D realm.

Data Collection: For this lab, an aerial DEM of the lower Chippewa River Valley was used. Using the DEM, a raster clip function was performed in ArcMap in order to delineate a smaller study area within the lower Chippewa Valley.

Data Processing: Using the DEM as a study area, the fishnet tool was used in ArcMap. Fishnets produce a grid within the DEM, with points inside the grid as highlighted in Figure 1. After the fishnet was created, the “extract values to points” tool was used that extracted the elevation values of the DEM into the fishnet points. Once the elevation values were extracted into the fishnet points, multiple interpolation methods were used to model the new landscapes. The interpolation methods used were Inverted Distance Weighted (IDW), Kriging, Natural Neighbors, Spline, and Triangular Irregular Networks (TIN).

Figure 1. A created fishnet

Results: The results varied depending on the interpolation. Most out the outputs were blurry, however one can still see differences within each interpolation method. Figure 2 represents the original DEM; Figure 3 represents the Natural Neighbors interpolation method; Figure 4 represents the Kriging interpolation method; Figure 5 represents the IDW interpolation method; Figure 6 represents the Spline interpolation method, all in the 2-D realm.

Figure 2. DEM of the study area. 

Figure 3. Natural neighbors interpolation method

Figure 4. Kriging Interpolation Method

Figure 5. IDW Interpolation Method

Figure 6. Spline Interpolation Method

In analyzing the outputs, it seems that the IDW, the spline, and nearest neighbors interpolation methods produced the most accurate 2-D outputs, or Figure 3, Figure 5 and Figure 6. In comparing the outputs with the white features in the DEM (Figure 2), Figure 3, Figure 5 and Figure 6 seem to most accurately represent the white features. The spline interpolation method (Figure 4) seemed to generalize the features too much, as evident by its representation of the white features in the DEM.

For 3-D representations, Figure 7 represents the DEM; Figure 8 represents the TIN; Figure 9 represents the Natural Neighbor interpolation method; Figure 10 represents the Kriging interpolation method; Figure 11 represents the IDW interpolation method; Figure 12 represents the Spline interpolation method.

Figure 7. 3-D DEM of the study area. 

Figure 8. 3-D TIN of the study area. 

Figure 9. 3-D Natural Neighbors interpolation method

Figure 10. 3-D Kriging interpolation method.  

Figure 11. 3-D IDW Interpolation Method

Figure 12. 3-D Spline Interpolation method

It seems that Spline and Natural Neighbors (Figure 9 and Figure 12) exhibit the most accurate representations of the DEM. The IDW model (Figure 11) seemed to also present an accurate model, however the terrain seems rougher compared to the DEM. The TIN (Figure 8) seemed to also produce an accurate model, however it didn’t seem to represent the river valleys well compared to the other interpolation models.

Discussion: Comparing the interpolation methods, it seems the Spline and the Natural Neighbor produced the most accurate representations of the DEM. The Natural Neighbor method uses an algorithm to determine the closest set of sample points and applies weight to them based on proportionate areas to interpolate a value (Scott Nesbit Blog, 2015). The missing data is then averaged with data around it to give the representation a natural flow, which produces an accurate representation of the DEM.

Spline interpolation estimates values using math, which reduce overall surface curvature and produces a smooth surface (Scott Nesbit Blog, 2015). This method also produces an accurate representation of the DEM because, like the Natural Neighbors, the surfaces are smooth.

The IDW models produces an okay representation of the DEM, however there are golf-ball like bumps throughout the image, which lead to inaccuracies. Inverse distance weighted interpolation uses linearly weighted combination of multiple sample points with in an area to determine cell values.  This method gives more weight to points closer to the cell center and points further away from the center are given less weight (Scott Nesbit Blog, 2015). Because it gives more weight to cells closer it the center, that seems to cause the golf-ball like appearances throughout the interpolation, which leads in inaccuracies.

The Kriging interpolation method uses an advanced geostatistical model to generate an approximate surface from a scattered set of points with height (Scott Nesbit Blog, 2015). Using the averages, it seemed to average out the points too much to the point of inaccurate representations. The features look too rounded, compared to the rougher terrain of the lower Chippewa Valley.

The TIN method was created by triangulating a set of vertices with vector data (Scott Nesbit, 2015). The vertices are then connected to create a network of triangles, which produced a somewhat accurate representation of the terrain. The TINS gloss over the smaller tributaries of the rivers, however the elevation seemed accurate.