Sandbox Survey 2: Visualizing and Refining your Terrain Survey

Introduction

As a followup activity to the Sandbox Survey back in September, the class imported the data they collected using a surveying method for their sandbox terrain and then create a series of DEMs (Digital Elevation Models). Recall in the first activity, the class broke up into groups and created a unique terrain in a 115 cm x 115 cm sandbox. Selecting a sampling method - in this case, systematic point sampling - the groups decided on an arbitrary sea level and measured the terrain's elevation. Many groups utilized at grid system to accomplish accurate systematic measurements. This group constructed a grid with 10 cm x 10 cm cells and measured the elevation at the northwestern corner of the cells using the grid as sea level (Figure 1).

Figure 1: The grid stretched over the sandbox terrain.

Before the collected data could be imported into ArcMap, it had to be recorded and normalized in an Excel sheet. This activity involved x and y values from the grid and z measurements that were the elevation at a point. Therefore, all the x values were in their own column labeled "x," all the y values in their own column labeled "y," and all the z measurements in their own column labeled "z." If read horizontally, the x and y values would indicate the point from the grid that had an elevation of the z value in the row (Figure 2). This is normalized data. Data normalization is (Wenzel, 2017)

Figure 2: A sample of the normalized data in an Excel sheet.

Since the sampling scheme was a systematic point method, all the data points are distributed in an equal distance from each other when laid out spatially by it's coordinates. Interpolation procedures will essentially fill in information between the data points by various methods that will create a complete picture of the survey area. It's accuracy depends on the interpolation method, sampling method, and type of survey. Using a selection of interpolation methods, the sampling frame will be rendered in a 2-D and 3-D scene, visualizing the data in a DEM.

Methods

The normalized data of the survey was imported into the geodatabase for the DEMs. From the imported table, a feature class was created, the x,y, and z values rendering a spatial extent of points.
The following five interpolation methods were used to visualize the data from the created feature class as DEMs:

IDW stands for Inverse Distance Weighted. IDW estimates cell values by averaging the values of the sample data points in the neighborhood of each processing cell. A sample points have more influence in the averaging process the closer they are to the center of the cell being averaged (ESRI, 2016).

Natural Neighbors

Natural Neighbors use an algorithm that finds the closest subset of input samples to a point and applies weights to them based on proportionate areas to interpolate values. Interpolated heights are within the range of the samples used. Therefore, peaks, pits, ridges, and valleys will not be rendered unless they are already represented by sampled points. Voronoi polygons are initially constructed around sample points. Then during interpolation, Moroni polygons are constructed around interpolation points. Therefore, the sampled point's polygon is weighted more in the interpolation process when it takes up the most area in the interpolation point's polygon (ESRI, 2016).

Kriging

Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z values. This tool involves the investigation of the spatial behavior represented by the z values before selecting the best estimation method. Unlike other methods,
Kriging uses statistical models to predict surfaces and provide a measure of accuracy. It assumes distance and direction between sample points reflect a spatial correlation that can be used to explain variation in the surface (ESRI, 2016).

Spline

Spline estimates values by a mathematical function that minimizes the overall surface curvature. The created surface passes smoothly through sample points. Spline is ideal for gradually varying surfaces, like elevation, water table heights, and pollution concentration (ESRI, 2016).

TIN stand for Triangular Irregular Network. The sampled points in a TIN model are connected to each other through a series of triangles that represent a surface's morphology. TINs can represent ridges and streams lines readily. Tins can vary in their resolution based on the features it's meant to represent, increasing resolution for peaks and ridges and decreasing resolution for flat plains. The model's units are in feet or meters. TINs are typically used for modeling smaller areas with high-precision purposes. However, TIN models can be more expensive than raster models (ESRI, 2016).

Each Interpolation raster was visualized as a 3-D model in ArcScene and exported in a 2-D format and incorporated into map of the raster. If a person were to stand before the 3-D model as if they were facing the surveyed terrain, they would be facing north. This is the orientation depicted in the maps. A scale was edited into the maps to show the extent of sampling frame, which was a 115 cm x 115 cm sandbox.

Discussion

The IDW interpolation method created numerous peaks and dips at the sample points that simply weren't present in the actual terrain (Figure 3). This is caused by how the interpolation methods works, so IDW doesn't seem like an ideal method to represent elevation collected systematically. Perhaps a stratified sampling method would avoid creating unnatural peaks and dips in a IDW DEM. A gully at the bottom left of the sandbox failed to appear in this DEM, and the ridges that do appear sport peaks that look like a mountain range which severely misrepresents the data.

Figure 3: Map of the IDW Interpolation method of the sandbox terrain.

The numerous peaks and dips are gone with the Kriging method, but the sharpness of ridges and elevation changes aren't accurately represented (Figure 4). They seemed to have been buffered down too much. The ridge in the bottom left corner appear more subtle in the DEM than in reality. The rough texture generated by the Kriging method is reminiscent of the sloppy sculpting of sand, though this is due to the Kriging method, not a representation of a sandy terrain.

Figure 4: Map of the Natural Neighbor Interpolation method of the sandbox terrain.

The Natural Neighbor interpolation output created a more seemly transition between elevation changes while generating the sharpness of the ridges and gullies (Figure 5). However, the representation is very angular and kind of disrupts the direction of some of the ridges and valleys. This might have been fixed by having more sample points along highly variable areas on the terrain.

Figure 5: Map of the Kriging Interpolation method of the sandbox terrain.

Like it's model description, the Spline interpolation methods generated a smooth, continuous surface of the elevation (Figure 6). The pesky valley in the bottom left corner of the DEM is represented much better with Spline. The rides and slopes are nicely captured, though they might have been smooth down slightly too much. The Spline method appears to have best represented the terrain.

Figure 6: Map of the Spline Interpolation method of the sandbox terrain.

While not the most pleasing to look at and not technically interpolation, the major land features are represented; though, they are rather over-simplified and don't reflect slopes that make up real terrain (Figure 7). The triangles make it difficult to make out anything in the 2-D map. The 3-D DEM is needed to be able to recognize the features of the terrain.

Figure 7: Map of the TIN Interpolation method of the sandbox terrain.

It would have been interesting to see how a combination of a systematic point sampling and stratified point sampling method would represent the terrain. The systematic sampling method is ideal because it guarantees data points are dispersed equally across the sampling frame. A stratified sampling method would give highly variable land areas accurate representation and prevent the underrepresentation that tends to result from the systematic method. Since the study area is extremely small in this case, smaller cell sizes in the grid would be practical and beneficial for generating DEMs.

Conclusion

This survey is similar to other elevation field survey, except on a much smaller scale. For larger land areas, a grid system for sampling wouldn't be practical. Depending on the terrain, a surveyor might have to choose a completely different sampling method, one that takes time, cost, measurements, and nature into consideration. In addition, while the Spline interpolation provided the most accurate DEM, that won't be the case for every survey. Besides elevation, interpolation can be utilized for data like microclimates, the pH or mineral content of the soil, or land use.

Sources

ESRI. (2016). How IDW Works. Retrieved December 3, 2017, from ArcGIS for Desktop: http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-idw-works.htm

ESRI. (2016). How Kriging Works. Retrieved December 3, 2017, from ArcGIS for Desktop: http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-kriging-works.htm

ESRI. (2016). How Natural Neighbor Works. Retrieved December 3, 2017, from ArcGIS for Desktop: http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-natural-neighbor-works.htm

ESRI. (2016). How Spline Works. Retrieved December 3, 2017, from ArcGIS for Desktop: http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-spline-works.htm

ESRI. (2016). What is a TIN Surface? Retrieved December 4, 2017, from ArcGIS For Desktop: http://desktop.arcgis.com/en/arcmap/10.3/manage-data/tin/fundamentals-of-tin-surfaces.htm

Wenzel, K. (2017). Database Normalization Explained in Simple English. Retrieved December 1, 2017, from EssentialSQL: https://www.essentialsql.com/get-ready-to-learn-sql-database-normalization-explained-in-simple-english/

UW - Eau Claire Geography 336 Geo-spatial Field Methods

Monday, December 4, 2017