Exercise 2: Sandbox Survey

Part 1: Introduction

• Discuss what you did in the previous lab.
• In the previous lab, an elevation surface of a terrain was constructed in a square meter sandbox. The profile had to include a ridge, hill, depression, valley, and a plain. Finally, the group will be able to map out the elevated surface using original survey technique.
• For the lab, our group chose to create a grid that allowed for 20 points on the X-axis and 20 points on the Y-axis. The grid consisted of 400 squares, where we measured a point in the top-right corner to achieve our 400 data samples.
• Discuss what the term 'Data Normalization' means, and how that relates to this lab
• Data normalization is the process of organizing data into tables in such a way that the results can be used in a database to create points that can then be used to be manipulated further. 
• The data points of x, y, z were normalized into three columns in an excel data sheet. The points were then projected into ArcMap into a grid that presented the grid that was created on the sandbox. By doing this, then a 3D model can be created of the profile by using ArcScene. 
• Discuss your data points, and how the interpolation procedure in today’s lab will help to visualize that data. 
• After perfecting the data to create the grid that turned out really well, the next processes was to interpolate. This will allow for a 3D model of our Sandbox Terrain to be implemented. By using different interpolation methods, we will then decide which best presents the sand profile. 

Part 2: Methods
You were shown how to bring your data into 3D scene. You were also shown how to export that scene for use in a map layout.

• After the data was normalized into 3 columns of X, Y, and Z, the XY data was added into ArcMap. A grid was created of the X and Y values, which is shown in Figure 1. 

Figure 1. The origional grid, before any interpolations. 

• From there, we experimented with a few different interpolation methods such as IDW, Kriging, Natural Neighbors, Spline and TIN.
• "In most GIS literature, areal interpolation specifically means the reaggregation of data from one set of polygons (the source polygons) to another set of polygons (the target polygons). Predictions and standard errors can be made for all points within and between the input polygons, and predictions (along with standard errors) can then be reaggregated back to a new set of polygons." (ESRI 2016)
• "IDW (inverse distance weighted) interpolation determines cell values using a linearly weighted combination of a set of sample points." (ESRI 2016)
• "Kriging is based on statistical models that include autocorrelation. Kriging assumes that the distance or direction between sample points reflects a spatial correlation that can be used to explain variation in the surface." (ESRI 2016)
• "Natural Neighbor 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" (ESRI 2016).
• "Spline uses an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points." (ESRI 2016)
• "TIN (triangular irregular networks) have been used by the GIS community for many years and are a digital means to represent surface morphology. TINs are a form of vector-based digital geographic data and are constructed by triangulating a set of vertices (points). The vertices are connected with a series of edges to form a network of triangles." (ESRI 2016)
• In what format did you export your 3D scene image?
• From ArcScene, I exported my 3D image as a JPEG, so that it would be easier to show the clarity and availability of the data model. 
• What orientation did you decide upon?
• For the orientation, I chose a tilted side view of the 3D scene image that is viewed from a corner and shows elevation as well as some of the areal view of the image. 
• How did you decide to reflect scale? Why does one need to place scale and orientation in these exports?
• The measurements of the grid was 114 x 114 cm. On the model, I drew in a line that showed how each side was 114 cm. 

Part 3: Results/Discussion 1

• Discuss the results of each method in detail, and refer to the figure, noting where there are issues with the output.
• Revisit your previous lab and make sure you do a detailed job of combining what you did previously with this lab to have what you did carefully documented.
• Discuss with your group what you could do differently in a follow up survey

For the IDW method, every 6 cm our group measured an elevation point (z). In Figure , you can see there there is a small hill or bump that was created where each point was taken and a slight depression where there was an absence in data. The Hill and Valley that our group created were not well mapped to scale with this method. 

 Figure 2. IDW Interpolation Method

When the Kriging Interpolation was used, the profile was smoothed out more than the IDW. However, Figure 3 demonstrates that there is still areas where a few points were exemplified or depressions were formed because of no measurements being taken in that specific spot. 

Figure 3. Kriging Interpolation Method 

The Natural Neighbors Interpolation provided an output that had some inconsistencies in it as well. The 3D image created unaccurate depressions and hills that surround the data points like the Kriging and IDW interpolation. In Figure 4, there almost seems to be a square shape to the layout of the landscape. 

 Figure 4. Natural Neighbors Interpolation Method

Figure 5 demonstrates an interpolation method that provides a smooth and representative sample landscape of the sandbox. The Spline method smooths out the areas that lack the measurements and connects them to the adjacent points. In this figure, the hill, valley, plain, ridge, and depression are easily seen. 

Figure 5. Spline Interpolation Method

The last interpolation method that was looked at was the TIN. The TIN does no use a smoothing technique or show an accurate idea of what the landscape of the sandbox was supposed to look like (Figure 6). TIN uses a series of triangles that connect other interpolation points together from the defined measured points from the data. The series of triangles then make up a sample of the landscape. 

Figure 6. TIN Method

Part 4: Revisit your survey (optional)
Evaluate your best interpolation method and assess where you have data that is lacking.

• If your survey was bad, remake up your terrain to the best of your ability to match your previous terrain.
• Now redo your survey, taking note of where your survey previously lacked detail.
• Perform an interpolation using only the ONE best interpolation method you decided upon
• Discuss the results of this 'redo', and relate the quality of the output to your previous survey.

After 5 methods were gone through, the lab was revisited with the interpolation method that I thought was the most representative of my sandbox terrain. Using the Spline with Barriers Interpolation Method, I redid my terrain with the grid points added as an overlay layer to the 3D scene imagery (Figure 7). I also added an areal image to compare the the overlay of the points with the image that is tilted towards its side. Not much of the terrain did change after I redid it. North of the Hill, there was supposed to be a depression that I attempted to adjust the measurements, but it still did not show. I assume this is either due to an error in the measurements or the tool smooths out the area so much that the depression begins to not be as prominent. 

Figure 7. Spline with Barriers Interpolation Method with the Grid of Points

Part 5: Summary/Conclusions

• How does this survey relate to other field based surveys? How is the concept the same? How is it different?
• These surveys can be used a reference point to demonstrate topography of the area of study. There will also be times where measuring a particular terrain could have impacts on knowing what the slope is, for example, a hill or depression. Knowing the slope can have an impact on providing evidence for how acknowledge a particular land use for a given area. 
• Is it always realistic to perform such a detailed grid based survey?
• No, depending on the size of the study area or study site it would be impractical to have that many data points due to time or too large of an area. 
• Can interpolation methods be used for data other than elevation? How so? Provide examples?
• Interpolation methods could also be used for any other data that contains intervals, such as weather maps or temperature maps. This could establish boundaries of areas that are projected to receive more snow or rain, or collectively show what areas experience the highest or lowest temperatures at any given length of time. 

References

ESRI. 2016. How IDW Works. Accessed February 12, 2017.      http://desktop.arcgis.com/en/arcmap/latest/tools/3d-analyst-toolbox/how-idw-works.htm.

ESRI. 2016. What is a TIN surface? Accessed February 12, 2017.  http://desktop.arcgis.com/en/arcmap/latest/manage-data/tin/fundamentals-of-tin-surfaces.htm.