Sandbox Survey (part 2): Visualizing and Refining the Terrain Survey

Introduction: 

In the previous lab, students were assigned to groups of three and asked to construct and survey an elevation model featuring a ridge, hill, depression, valley, and plain using the terrain in an approximate square meter sandbox. Each group was supplied with tape, string, thumb tacks and some meter sticks in order to construct a grid system pattern and survey the terrain. Groups used various tactics of sampling in order to collect elevation data points from their terrain. The data points collected were then normalized by entering the coordinate points into an Excel document as individual x-, y-, and z-value attributes.

Data normalization is the process of organizing data into a table, with each column representing one attribute of the data presented. In this case, normalizing the data meant that for the table produced in Excel, each x-value needed to be entered into one continuous column labeled 'X-Values,' all y-values entered into a continuous column marked 'Y-Values,' and so on so forth so that each row was comprised of four columns (the OID, x-, y-, and z-values). When looked at as a whole, each row within the excel file would make up one coordinate point (this group had 400 coordinate points, therefore 400 rows of data points).

When done correctly, the X,Y (and Z) coordinates of an Excel file may be uploaded as data points into ArcMap as a grid system. From here, students would be able utilize tools in ArcMap to manipulate the data points and illustrate various 2D files of 3D projections of the terrain, which could then be transported into ArcScene to ultimately generate the 3D digital models of the terrain created in the sandbox during the previous lab.

Methods:

Once the data has been normalized in Excel, the file containing these points is ready to be uploaded into the geodatabase stationed in ArcMap using the 'add XY data' tool option. After the table has been imported, it can be converted into a point feature class, which will reveal the grid-like pattern students previously constructed in their sandboxes onto the map. These points can be symbolized to represent individual values from each data point collected, but the image does not provide a good visual as to the varying gradations between each data point value.

To obtain the 3D visual, one can use the tools under the 3D Analysis option in ArcToolbox, where a variety of interpolation methods can be selected from to provide the 2D output of the image desired. This image is stored in the geodatabase in raster format, and can be uploaded into ArcScene to be viewed in 3D with an option to rotate it to view various angles. For the purposes of this lab, all 3D models utilized were oriented so that they would be viewed in the same direction as the sandbox landscape was while being constructed in the field.

Once the models had been generated, the symbology and orientation set, these 3D images could then be exported in 3D format as a .png file to be returned to ArcMap as raster features for mapping and scaling. Since the files re-added to ArcMap were raster features, scale could not be automatically inputted into the maps as is traditionally done. Instead, scale was reflected using the 'drawing' toolbar in ArcMap to illustrate the general size of the actual sandbox being mapped (1 x 1 meter).

Students were to explore 3D analysis using the following five interpolation methods:

1. IDW (Inverse Distance Weighted)-

The IDW interpolation method uses the assumption of Tobler's First Law of Geography (things that are nearer are more similar to one another than things at a further distance away) to fill in the gaps between the sampled data points. The points collected in the field are weighted with the greatest amount of influence and diminished directly with distance from there. The resulting 3D model, then, resembles a somewhat "lumpy" image, the collected weighted points at the peak of the lump as seen in figure one below. This method tends to only be useful if the data being modeled has minimal variations in the range between the points collected, but is normally not the "go-to" method in 3D modeling.

2. Natural Neighbors-

Also known as "area-stealing" interpolation, the natural neighbors interpolation method uses the same weighted distribution technique as in the previous method, but generally tends to do a better job of smoothing out its transitions between the weighted data points, generating a less "lumpy" as can be seen in figure two.

3. Kriging-

The kriging interpolation model is constructed using the weighted average of all nearby collected data points to fill in the unsampled points within the grid using a specific formula. This method is ideal in many instances since it prioritizes smooth transitions between sampled data points, while still providing the best unbiased prediction of the values inbetween. An example of the sandbox terrain using the Kriging interpolation model is pictured in figure three below. 

4.  Spline-

Like the previous kriging method, spline interpolation uses a mathematical formula that ultimately aims to reduce the overall curvature of the surface within the area sampled. As illustrated in figure four, this again results in a much smoother surface in the transition between collected data points.

5. TIN (Triangular Irregular Networks)-

The last interpolation method, TIN interpolation, creates a series of edges connecting various collected data points to form a network of triangles and reveal a general outline of the sampled surface. In areas where the surface varies more drastically, TIN is able to provide a higher resolution than it does in areas with little variance in values. A drawback to this technique, however, is its limited popularity as a result of its costs to build and process. 

Results:

The first interpolation method used, the IDW interpolation, illustrated a "lumpy" 3D image shown in Figure One, as promised in its description under the methods section. The 400 data points which were collected during the original surveying can somewhat be seen at the peaks and troughs created by the weighted points. This method, though it may be beneficial in some instances to be able to see that original data beneath the created surface, is not the most visually appealing, nor accurate in predicting the unsampled data between the sampled data points, and is therefore not a commonly selected option in 3D mapping.

Figure 1: IDW Interpolation Model

The natural neighbors interpolation method illustrated in Figure Two generates a much more likely option between the first two methods. The weighted distribution at collected data points is still visible, but the transition between data points illustrates a much smoother surface than the first option had provided.

Figure 2: Natural Neighbors Interpolation

Figure Three reveals the kriging interpolation method in use. Here, again, the surface is generally smooth. This option is supposed to be the least biased in generating values for its unsampled points. Perhaps this is why this option seems to reveal the least amount of color variance from the surface beginning its lowest points, to the depths of the area. 

Figure 3: Kriging Interpolation

The fourth figure utilizes the Spline interpolation method. As stated in its description, this interpolation type provides the smoothest outcome of all five methods. It limits the curvature of the surface, but still somehow manages to create the most uniform surface. Some errors can be seen in the image produced, however, in both hill areas on the surveyed display. The etched blending in the side of the hills may indicate error in measurements performed while in the field. In a follow up survey, these measurements could be taken with more care for accuracy and a smaller rounding value than the quarter inch that this group had decided upon. 

Figure 4: Spline Interpolation

The last interpolation method, TIN, is the most distinct of the five method options. The method utilizes edges and resolution to illustrate the surface model. The triangular network pattern that results from these edges connecting the data points can be clearly seen in Figure Five below, and is especially evident in the caldera-looking feature at the lower left corner of the sampled area. 

Figure 5: TIN Interpolation

Conclusion:

Interpolation can be used for a multitude of purposes. Some of these include mapping of rainfall, watertables, chemical concentrations, noise frequencies, and soil-type distribution. There are also many more options of interpolation methods to choose from in addition to the five options previewed for lab this week. Some other types include PointInterp, Trend, and Density. 

The last few weeks of lab allowed students to familiarize themselves with the practice of field sampling, data normalization, and 3D modeling with Interpolation. 

Sources:

http://www.spatialanalysisonline.com/HTML/index.html?kriging_interpolation.htm

http://pro.arcgis.com/en/pro-app/help/analysis/geostatistical-analyst/how-inverse-distance-weighted-interpolation-works.htm

http://resources.arcgis.com/en/help/main/10.1/index.html#//005v00000027000000