Creation of a Digital Elevation Surface - Week 2

Introduction

In the previous week, a 45"x45" (114x114 cm) sandbox terrain of the students design was surveyed where x, y, and z data points were collected in order to translate the physical terrain into a digital elevation surface map. A grid was constructed on top of the sandbox that allowed sample points to be taken every 5 centimeters along the x and y axes. These points were then entered directly into an Excel spreadsheet that could then be imported into a geodatabase and used as a shapefile in ArcMap.

Data normalization is the process of organizing data in a uniform way for ease of use, and in this case the x,y, and z columns were saved in a numerical format in Excel where each value featured one decimal place.

Over 500 data points (533) were recorded that consisted of an x, y, and z value which represented its position on the terrain. The interpolation procedure used in ArcMap takes these points and runs them through an algorithm that will then create a surface map where each map will differ from each other based on the type of interpolation method being used.


Methods

Five different interpolation methods were used to create the surface maps including:

1. IDW (Inverse Distance Weighted): The IDW tool "estimates cell values by averaging the values of sample data points in the neighborhood of each processing cell. The closer a point is to the center of the cell being estimated, the more influence, or weight, it has in the averaging process." (Comparing Interpolation Methods). This method produces the best results when sampling is dense in areas of variation but the average cannot be higher than the highest input or lower than the lowest input.
2. Natural Neighbors: This interpolation method "finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value (Sibson, 1981)." (Comparing Interpolation Methods). 
3. Kriging: The kriging interpolation method "is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values." (Comparing Interpolation Methods). Kriging is a processor-intensive method where the input dataset will affect the speed of execution.
4. Spline: The spline method "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." (Comparing Interpolation Methods). The spline method produces a very smooth surface.
5. TIN (Triangular Irregular Network): In ArcMap, "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...The edges of TINs form contiguous, nonoverlapping triangular facets and can be used to capture the position of linear features that play an important role in a surface, such as ridgelines or stream courses." (About TIN Surfaces, 2008). TINs can have a higher resolution in more highly variable areas and lower resolution in areas that are less variable and capture features such as mountain peaks well but tend to be more expensive to build and process.

After the surface maps were created in ArcMap using the previously mentioned interpolation methods, each map was then brought into ArcScene in order to render a 3D image. After each 3D image was rendered, it was then exported as a JPEG image to be used in a final map layout in ArcMap.



Results/Discussion

The results of each interpolation along with its 3D rendered image can be found below (figures 2-6) and a picture of the actual sandbox terrain has been placed below (figure 1) as a reference to compare how the results match up with the surveyed terrain.

Figure 1: Sandbox terrain

IDW: This appears to be one of the worst results with the surface resembling an "egg carton" pattern where many little hills and depressions cover the entire surface that do not reflect the true nature of the surveyed terrain. In reality, the terrain is much smoother.

Figure 2: IDW interpolation method

Kriging: This appears to be the best result out of the five interpolation methods that were used. The features are captured well and flow into each other smoothly, it isn't bumpy like IDW, nor is it edgy unlike the TIN.

Figure 3: Kriging interpolation method

Natural: Although the Natural method looks good, it doesn't capture the depth of the depression in the lower left hand corner well enough and the surface as a whole appears "grid-like" in a way that resembles the actual grid that was constructed over the top of the terrain and provided the sample points.

Figure 4: Natural Neighbors interpolation method

Spline: This method provided one of the best results of the terrain where features flow smoothly into one another and the ridge peaks and low valley points are captured well. However, the surface as a whole has a somewhat "bubbly" appearance to it whereas the actual terrain was more smoothed out.

Figure 5: Spline interpolation method

TIN: While the TIN captures ridge peaks and valleys well, it's too "edgy" in comparison to the actual terrain and the elevation differences do not flow well into each other.

Figure 6: TIN interpolation method

In a future survey, although 5 cm increments were already a fairly dense sample spread, tighter sample points could be collected in areas of extreme relief. Also, having a flatter, more solid surface underneath the terrain would help provide more accurate elevation measurements if the same method for measuring the elevation that was used in this lab is to be deployed in the future. 


Conclusions

This survey relates to any other field-based survey that collects sample points to represent a whole population (or in this case surface) where the sample points in this exercise were elevations points along a grid on an x-y plane. Depending on the scale, it is not always going to be realistic to perform a terrain survey as detailed as the one in this exercise (5 cm increments). Increment values would have to be based on the size and scope of the particular survey. For example, if the sandbox had been twice as large, the 5 cm increments may have become 10 cm increments instead. Terrain with varying amounts of relief may require denser sample points while terrain with little relief may not require nearly as many sample points. Interpolation methods can also be used in remote sensing applications to determine surface composition, for example, if there is any missing data within the area of interest.  


Sources:

Comparing Interpolation Methods: http://pro.arcgis.com/en/pro-app/tool-reference/3d-analyst/comparing-interpolation-methods.htm#ESRI_SECTION1_6A0EECC499AA4BB191961A99AFA9352F 

About TIN Surfaces: http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=About_TIN_surfaces