Field Activity #5: Sandbox Survey Digital Elevation Surface

Introduction

Students were assigned groups of three for this two-week field activity. Group 2, objectively the most amiable group, was comprised of Jesse, Amanda, and Zach (who was absent for a field trip during data collection but returned just in time for the indoor part).  Jesse and Amanda built a landscape in a provided 1x1 meter sandbox. The landscape contained a number of specified features (Fig.1) and a few additional ones just to spice things up. The objective was to collect elevation data in order to create a Digital Elevation Surface (DES) using ESRI software. They chose to use a stratified systematic sampling technique to collect data because it allowed them to collect more data points in area of higher relief without having to increase overall point density in areas of low relief.

Figure 1   The landscape is entitled: Voyage to the Land of the Llama king and his Happily Subservient Peasant-People. The viewer is allowed to guess which features were required and which were not.

 Methods

In order to bring the normalized excel table of data (seen in the previous blog post) into ArcMap 10.4.1, the columns needed to be formatted as numeric data. Excel’s “general” designation has caused problems with ArcMap in the past. A geodatabase had to be created in the student folder designated “Senger.” Then the excel file could be imported and the X,Y data used to create the “Data_Points” point feature class. Since the study area is so small –only a 1x1 meter sandbox— and the data does not need to be anchored to a larger area map, no coordinate system was necessary, but in order to mitigate complications the Northern Wisconsin 1973 HARN PCS in meters was assigned. The next step was interpolation of the data.

Interpolation

Elevation, temperature, and precipitation levels, are examples of data that can be represented by surfaces. Surfaces are continuous, meaning data points can be inferred or predicted mathematically with a high degree of certainty if a point next to it is a known value. This process is known as interpolation; the insertion of data between fixed points. Because obtaining a measurement for every value is impractical, sampling methods are used to collect data points which serve as a source of data through which the rest of the points in the surface can be calculated using raster tools in ArcMap. These tools rely on interpolation methods which dictate the way that values are mathematically assigned to the points in between the known data points. 
When a user chooses a raster tool to work with, they must also choose the interpolation method the tool will use. The common interpolation methods are below. Each has strengths and weaknesses associated with it. More information about interpolation can be found here. 

Inverse Distance Weighted (IDW) assigns values using a linear-weighted combination set of sample points. The weight of each point is assigned as a function of the distance of an input point from the output point cell location. IDW is the choice method when the set of input points is very dense, but may not be impressive in small, conservative data sets like our sandbox data for our little llama-themed landscape.

Spline estimates values based on a function that minimizes surface curvature. The output is a smooth surface that passes exactly through the input points. Spline is the best choice for smoothly varying surfaces such as temperature, but may underestimate the elevation differences in an elevation surface unless the input data measured every breakline.

Kriging fits a function to a specialized number of points to determine the output value for each location. This assumes that the distance or direction between input points can be used to infer a spatial correlation that reflects variation in the surface. Kriging is most useful when any spatial or directional bias in the data is known and is often used for applications in geology, soil science, and pollution modelling. Kriging reflects concentration gradients well, but may add extra “phantom texture” to a landscape when used to interpolate elevation data.

Natural Neighbor uses local coordinates to define the amount of influence that a scatter point till have on output cells. Natural neighbor works well for clustered scatter points and large datasets, but not necessarily for small datasets like ours.

Triangulated Irregular Network (TIN) Unlike the other interpolation methods, a TIN is actually its own vector data structure used to display surface models. This was designed by ESRI in order to provide a more efficient way to represent geographic space and shapes associated with mapping landscapes and features. In a TIN, each data point is connected by edges of a triangle that form a continuous, non-overlapping surface to represent the terrain.

Figure 2

After interpolation the files were saved to the “sandbox” geodatabase and opened one at a time using the program ArcScene (which has a built-in ArcCatalogue window just like ArcMap does). I then opened Layer Properties> Base Heights and checked “Floating on a custom surface” in the elevation from surfaces window. The file source for each interpolation raster I was working on had to be found separately in this window and selected in order to have the best results.
If the result looked like the model below (Fig.2) then the Scene Properties window had to be opened and General>Calculate from Extent selected. Then the image would display the proper elevations.Then different views of each 3D scene made using the five different interpolation techniques was exported as a jpeg and brought into ArcMap again to make maps showing off the results of each technique.

Discussion

Each interpolation technique illuminated the data in a different way. Some of the techniques were better at representing the actual terrain accurately. The TIN and Natural Neighbor methods created a detailed enough digital surface model for our terrain to be recognizable. Spline and Natural Neighbor, however, did not capture the relief well. Note that scale on the maps is expressed through text that says 1x1 meter; the dimensions of the sandbox. It is important to have some sort of scale so the viewer can understand the spatial of the images upon which they are gazing.

Figure 3 IDW requires a dense set of data points. We did not have enough sample points; notice that the points form small islands or pock-marks.

Figure 4 The Spline method tends to smooth and oversimplify landscapes, but in this case it also created unnecessary hills.

Figure 5 Notice the "phantom texture" added to the landscape. The Kriging method distorts narrow features, such as the river valley.

Figure 6 The Natural Neighbor method represented all of the features to the extent that they can be recognized, but it also simplified the landscape. Note that there is little texture outside of the large features.

The TIN method captured the landscape the best. Notice that all of the features are present and recognizable. Even the llama is visible if one looks close enough; it’s in on top of the flat hill-like shrine which the peasants of the plateau village built in its honor.

Figure 7 The TIN is the clear choice for most effective interpolation of the data. This digital elevation surface represents both the large and small features clearly.  

Conclusions

This two-week project of researching and choosing a sampling technique, making a fun landscape in a sandbox, conducting an elevation survey to record X,Y,and Z points, and then mapping the elevation of said landscape was an excellent case study for real-world geographic practices. This survey is different in scale than most geography projects, of course; It is very rare to find a mountain range and a river valley that will fit into a sandbox that’s only a meter squared. Our project and analysis has many implications for the real world of full-sized landscape features, however, since what we built could pass for a scale model. Geographers are responsible for using similar sampling methods to measure elevation points of landscapes anywhere and everywhere around the globe and these interpolation methods can be used to make maps of landscapes with as much certainty as the data will allow.
That being said, it if not always realistic to do a detailed grid-based survey like was done here, unless the geographer was in possession of an extremely large yardstick and a very pliable landscape that was in need of some additional trenches carved into it. Remote sensing tools and LiDAR analysis, however are making strides in the technological world and are making it more and more possible to map elevation on larger scales and with more accuracy than was ever dreamed of during the cartographic history of mankind. But always the cost of time and effort form constraints on data collection and must be weighed carefully.

Sources

Childs, C. (2004, July). Interpolating Surfaces in ArcGIS Spatial Analyst. Retrieved October 18, 2016, from https://www.esri.com/news/arcuser/0704/files/interpolating.pdf