Terrain Interpolation

Introduction:

The first weeks lab was designed to teach the student how to create a grid and collect data from their selected area. The data was then put into a Microsoft Excel spreadsheet to be used in this weeks task. This weeks lab was an extension of the first relating to terrain analysis. Before any of the data was converted into a terrain model, the class met to discuss different grid sampling techniques. This allowed for groups to express what worked well, what they would have done differently and suggest tips for other students in the class.

Study Area:

This week our group decided to change our study area. Originally we created our terrain on the floodplain of the Chippewa River. This week we decided to create our terrain in the volleyball courts behind a residence hall on campus. This allowed for the group to easily create a terrain with the sandy soil without having to deal with the vegetation that was present on the floodplain. The sand was damp and allowed for the structures created to hold their shape throughout the duration of the sampling.

Methods:

The survey method that our group first came up with was a straight grid system. We broke up our sandbox into 210 different sections, each grid square measured 8 cm by 8 cm. Originally, this seemed like a good decision to get a representation of the surfaces that were created. Measurements were taken in the bottom right corner of each grid square to keep the measuring technique as consistent as possible. The figure below (Figure 1) depicts how we took our measurements.

Figure 1. Shows how we collected our measurements
during the first round of data collection.

String was laid across the sandbox at 8 cm intervals and then taped to either side. This allowed for easy and consistent measurements to be taken. Although it provided an easy way to measure out grid, it created a very generalized representation of our terrain and did not catch steep inclines or declines of our features.








Once we collected all of our data it then had to be added into an Excel spreadsheet and normalized. The spreadsheet had a column for the X, Y and Z values that were collected in the field. Since the data was normalized in this way, it allowed each group to upload their data into ArcMap and view their points. In order to create a raster image of the points collected, ESRI Spatial Analyst extension had to utilized within ArcMap. Within the Spatial Analyst extension, the students utilized the interpolation tools to get an image of their terrain. For the purpose of introducing the tool, an IDW raster was created and showed the terrain. ArcMap shows raster images in 2D, so it is hard to see if it accurately reflects the points each group collected. In order to get around this, the IDW raster image was then opened within ArcScene which allows for images to be viewed in 3D. The figure below (Figure 2) is the results of opening the IDW raster image in ArcScene.

Figure 2. This image is the IDW raster image of the first terrain created by our group.
It is an inverted image of the actual terrain 

Our group found that the IDW interpolation made a fairly accurate representation of our features that were created. There were two flaws in the output. The first was that the image was inverted compared to what was actually created. This was due to how the data was collected in the field. The point of origin should have been in the southwest corner but when in the field, data was recorded as the northwest corner as the point of origin. This cause all the features to be created correctly, but flipped on the image. The second flaw was that the features did not appear to be as smooth as they were in the field. It was a lumpy representation of the features our group created.

After looking at our results, we decided to change our technique for sampling our sandbox. Instead of going with a straight grid sample, we decided to go with a  systematic stratified grid sampling technique. This technique allowed up to collect more points in certain areas of our sandbox, hopefully creating a more accurate representation of the features we created. Along with more sampling points, each group tested multiple interpolation techniques in order to find one that most accurately represented their created terrain. As mentioned earlier, the data was normalized in an Excel spreadsheet, added into ArcMap and then manipulated with different interpolation tools.


The first interpolation tool we used was IDW or inverse distance weighted interpolation. IDW determines cell values using a linear-weighted combination set of sample points (p. 34, Childs). This means that it takes the values of nearby cells and comes up with an average. The greater the distance a cell is from a sample point, the less of an impact the sample point will have on that value. The more sample points that are used will typically result in a more accurate model. Figure 3 (shown below) is the result of IDW interpolation for our terrain.

Figure 3. This is the IDW terrain of our second terrain that was created. The feautres
are not shown accurately, but not exactly how they looked during data collection in the field. 

The second interpolation method used was Spline interpolation. The surface of this technique must go through all of the sample points. Since it goes through all of the sample points, spline interpolation generally produces a smooth representation of a particular study area. The figure shown below (Figure 4) is the Spline interpolation for our study area.

Figure 4. This is the Spline interpolation of our study area. This interpolation method
was the most accurately representative of our study area.

The third technique used was Kriging interpolation. This method assumes that there is a spatial correlation between the sample points and the distance and direction between them. This assumption is what allows the interpolation to create the variation of the surface. The Kriging method generates its values from a weighted average technique. This method is best used when there is a spatially correlation between distance and direction within the data. Figure 5 is the Kriging interpolation for our study area.

Figure 5. This is the Kriging interpolation method. This method was the least
representative of our study area. 

The next method used was Natural Neighbor interpolation. Like IDW, this method is also based on weighted averages of the data. This method applies weights to each input based upon proportionate values surrounding the input. Figure 6 shows Natural Neighbor interpolation.

Figure 6. This is the Natural Neighbor interpolation technique. 

The last interpolation technique used was creating a TIN or Triangular Irregular Networks. TINs are vector based data and constructed by using a set of vertices. These vertices are then connected by different edges creating a network of many triangles. The more data points used, the more accurate of a representation this method will create. Figure 7 shows the TIN for our study area.

Figure 7. This is the TIN or Triangular Irregular Networks. 

Discussion:

Each interpolation method had its strengths and weaknesses. Each method is designed for interpolating different types of data, so it made sense that not all methods would accurately represent our terrain. IDW interpolation did represent our features accurately, but did not show them exactly how they looked in the field. It was a very bumpy surface which was not consistent with the data that was collected. Spline interpolation did a great at representing our features. The changes in elevation were gradual, and there were no irregular spikes in the representation of the data. Kriging interpolation did not do an accurate job of representing our terrain. Although the change in elevation was gradual, it was poorly represented. The elevation changes were layered, rather than having a smooth slope. Natural Neighbor interpolation was the second best at representing our terrain. It was very similar to the Spline interpolation, but not quite as smooth. There were a few spikes on the hill and ridge that should not have been there. The TIN that was created represented our features fairly well, but was not quite as accurate as Spline interpolation. There were not apparent flaws with the result of this technique, but it was not as representative of our study area.

Conclusion:

This exercise allowed for the students to learn about the different interpolation methods used spatially. It also allowed the student to further the development of their critical thinking skills. Group members had to work together in order to find out the most effective and efficient method of surveying their particular terrain. Learning different interpolation techniques as well as survey techniques will allow me to better structure data collection projects in the future.

Works Cited:

Interpolating Surfaces in ArcGIS Spatial Analyst.
http://www.esri.com/news/arcuser/0704/files/interpolating.pdf

What is a TIN surface?
http://resources.arcgis.com/EN/HELP/MAIN/10.1/index.html#//006000000001000000

Elevation Terrain Analysis

Introduction:

The class was presented with the assignment of creating an elevation surface of their choosing. This assignment had multiple objectives.  These objectives included teaching the students how to collect their own data and import it into the computer as well as how to complete an assignment with limited direction. The students were divided into groups of three and equipped with string, meter sticks, marking flags and a homemade sandbox. The sandbox was used as the study area where the terrain analysis was conducted. Each group had to come up with their own coordinate system that they felt would accurately represent the terrain they had created.

Study Area:

The study area for this assignment was in Eau Claire, WI, specifically on the University of Wisconsin - Eau Claire Campus. The Chippewa River flows through campus and a sandy flood plain is located on the north side of the river under the student walking bridge. This flood plain is where each group created their specific terrain within the sandbox.

Methods:

The first objective each team needed to complete was choosing a site on the sandy flood plain of the Chippewa River. Once a site was selected, each group made their own terrain within the sandbox. The only landscape features needed within the sandbox were a ridge, valley, hill, plain and depression. After the terrain was made, our group had to decide how to effectively show all of our terrain features.

The sandbox used was not a perfect square.  Our group modified the inside of the sandbox to allow for an even grid, to hopefully create a more accurate model. The inside measured 112 cm wide by 120 cm long. A grid square was created every 8 cm. Figure 1 (shown below) shows the grid lines dividing the sandbox.

Figure 1. This shows the grid lines across the study area. Each grid line was spaced out 8 cm apart from one another. 

One obstacle each group had to over come was deciding where to create their base height. Our group decided that the top side of the sandbox was going to be measured as the base height, or the point of zero elevation. The next step was to measure the height of each grid square. Figure 2 (shown below) shows how the group measured the elevation. In order to keep data consistency, we collected heights from the southeast corner of each grid square. This allowed for for even spacing between measurements.

Figure 2. This shows the method of measurement that was used to determine the height of each grid. 

Once all the heights were recorded, our group transferred the data onto an excel spreadsheet. There were 210 points all together. Since none of our terrain features were taller than the sandbox edges, we recorded all negative values. In order to convert our values to positive numbers, or to show an actual representation of our terrain, 18.4 cm were added to each height value. 18.4 cm needed to be added to each height because it was the height of the sandbox. The table below (table 1) show the results of the conversion.

Table 1. This table is showing each height that was recorded for each grid. Negative values represent features that went below  the base of the sandbox. 

Discussion:

The surveying method we chose was fairly efficient and and allowed for the amount of error to be minimized. There may have been a quicker method to measure the heights, but creating a grid allowed for consistent and accurate data to be collected. I believe that the model that we create will accurately reflect the terrain features that we created.

Conclusion: 

The skills that were learned in this lab are applicable to real life situations. Critical thinking is a very important skill to have when presented with an ambiguous task. Having limited directions forced the students to collaborate with their group members to come up with an efficient way to complete the assignment.