Assignment 10: Sandbox Survey part 2: Visualizing and refining your terrain survey.

Introduction:

In this assignment students will be continuing a Sandbox Survey that started earlier in the semester. The goals for that assignment were to create a ridges, hills, depression, and valleys in the sand. Then construct a 115 by 115 centimeter grid with 5 centimeter intervals for each X and Y value. A Z field was also needed to be measured in order to obtain elevation from the datum. The data was later normalized in Microsoft Excel.Now that all the data has been collected, it is time to make maps and 3-D models out if it. Different Spatial Interpolation methods will use the  X, Y, and Z field in order to achieve the final products.  By using ArcMap and ArcScene  2-D and 3-D maps will be creating using these specific Interpolation tools:

• IDW
• Kriging
• Natural Neighbor
• Spline
• TIN

Methods: 

To begin, bring in the X, Y, and Z data recordings in to arc map through and X, Y, and Z field shown in Figure 1 below.

Figure 1. Add XY Data Window

Once the XYZ grid is brought in, a 2-D dotted grid will appear, with all the data that was manually entered in a Microsoft Excel document.

Figure 2. XY Grid

After you create the layer, export it as a feature class. From there you can use different interpolation tools in order to show the data from X, Y, and Z fields.

The first tool used was the IDW tool. To get to this tool, navigate through the arctoolbox to 3-D analysist tools --> Raster Interpolation --> and then IDW. This tool interpolates a raster image from given coordinates using an inverse distance weighted (IDW) method.The farther a sample point is from the cell being evaluated, the less weight it has in the calculation of the cell's value (ESRI, 2017).

The second tool utilized was the Kriging tool. This interpolation method weighs out the collected values to create a predicted value for an unmeasured location according to distance between each point, the prediction locations, and the spatial arrangement among the measured points. This technique is different from the other techniques in that it is an easy method for characterizing the variance of predictions (ESRI, 2017).

The next tool used was the Natural Neighbor tool. This interpolation technique is for multivariate data in a Delaunay triangulation. Weighted values of the nearest surrounding points in the triangulation help estimate the value for each interpolation point. The points then connect to the closest "natural neighbor" when inserted into the triangulation (ESRI, 2017).

Then try the Spline method. This interpolation tool takes estimated cell values derived from a mathematical function that minimizes overall surface curvature allowing it to create a smooth surface that directly passes through the input points (ESRI, 2017).

The last tool used is the TIN tool. It is still an interpolation method, but is not listed under the Raster Interpolation tools like the rest. This is because it is a vector data structure. It partitions geographic space into contiguous triangles that do not overlap. All vertices for every triangle get sampled data points via x-, y-, and z-values. The points are then connected by lines forming Delaunay triangles. TINs not only store surface models, but they also display them (ESRI, 2017).

Results/Discussion:

Note for each of the following figures, displaying examples of each tool, the vertical exaggeration is doubled compared to the original making it easier to visualize the differences in elevation from the highest to lowest points.

IDW (Figure 3):

Figure 3. IDW Method.

The IDW interpolation method was a solid to show the surface elevation, but the changes from each individual dot on the image is based on the actual measurement. In other words, it doesn't do the best job of smoothing out the in between from each spot.

Kriging (Figure 4):

Figure 4. Kriging Technique.

The Kriging Interpolation did a great job of smoothing out the unmeasured area from each measured point. However, it makes it harder to see the elevation difference for both the peaks and the depressions.

Natural Neighbor (Figure 5):

Figure 5. Natural Neighbor Method.

The natural neighbor map does an excellent job at showing the elevation differences, but it as you can see the surface is more jagged and pointy rather than smooth.

Spline (Figure 6):

Figure 6. Spline Technique

The spline method definitely appears to be the smoothest interpolation method so far. The accuracy of the elevation change minimizes distortion creating an image nearly identical to the original model.

TIN (Figure 7):

Figure 7. TIN Method.

The TIN method aesthetics are rather interesting, but that is not important when it comes to making an accurate visual representation of the Sandbox design. The triangles make the surface too rough, and unrealistic. 

Summary/Conclusions:

In conclusion, Spatial Interpolation is a very useful and interesting tool. The IDW method was probably the least effective method due to its bubbly surface. The TIN and Nearest Neighbor methods accurately represents the elevation, but they're surfaces are too rough. The Kriging method makes a very smooth surface, but lacks in showing proper elevation changes. The Spline method, however, does a great job of showing both a smooth surface and an accurate representation of the elevation change. For that reasons, I have concluded that the Spline method is the most accurate method, and looks the most like the original Sandbox design.


Sources:

https://support.esri.com/en/other-resources/gis-dictionary