INTRODUCTION
In this lab, a sandbox was used that contained several geographic features with the goal of creating a model of the surface. Since elevation is continuous, it was unfeasible to collect an elevation measurement at every possible point on the surface. This meant the sampling had to be employed. Sampling involves collecting a subset of sample measurements throughout a study area to create a model of the whole. For example, collecting measurements set distances from each other creates a grid of known surface height, which can be used to create a model of what the surface was. Of course, a model is only a simplified representation of reality, so there is a loss of information involved in creating a model.
There were two options for sampling methods. Systematic sampling involved taking measurements every set distance to create a constant distribution of measurements. This would create a grid. The drawback of this method is that finer details of the surface may be missed, such as edges of cliffs, and there bay be unnecessarily high measurement density over low detail features like plains. This could be combated with the other sampling method: stratified sampling. This involves non-constant measurements across the surface. This means taking a higher number of measurements over high detail areas such as cliffs, and lowering the density of measurements over areas of low detail such as plains. The drawback of this method is that gathering the samples and processing the data afterwards is more complicated since a non-continuous distribution of data is created.
The objectives for this lab were to create an interesting layout for the sandbox including certain geographic features: a hill, a ridge, a depression, a valley, and a plain. A sampling method had be developed to take enough measurements of the surface to create a model of it. The data had to be detailed enough that it created a good representation of the surface of the sandbox while not too detailed that it could not be carried out in the time frame given. The actual model will be created in a subsequent lab; this lab only involves procuring the data.
METHODS
Before any data collection, the choice had to be made between systematic and stratified sampling. Systematic sampling was chosen because stratified sampling is more complicated to process, and added complications adds room for error. The decision was made that a straightforward sampling process would minimize potential error.
The area of study was a square sandbox with wooden sides. This sandbox was on the university grounds, East of Phillips Hall, for the purpose of using in this lab.
The materials used for this lab included thumb-tacks, string, and a ruler. The thumb-tacks were pressed into the wooden sides of the sandbox frame with string stretching from one side to the other to create a grid, as shown below.
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| Pushpins were pushed into the frame to support strings |
The sandbox dimensions were 114 x 114 cm. This evenly divided into a grid spacing of 6 cm. This meant the grid was composed of 19 columns by 19 rows. A vertical view of the grid setup is shown below.
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| Grid setup for sandbox |
To measure, a ruler was lowered into the sandbox at each coordinate and value that crossed the strings was measured to the nearest tenth of a centimeter. This meant zero elevation, or sea level, was at the strings and all measurements taken describe height below the strings. To ease in processing, the lowest elevation may be subtracted from all elevations taken to set the zero elevation point at the lowest elevation measured. For the measuring process, there was one group member holding the ruler, one member reading off the measurement, and one member recording the measurement. A picture showing the measuring process is shown below.
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| A ruler was lowered into the sandbox and the value that crossed the strings was recorded |
The measurements were recorded as Cartesian coordinates with XYZ values, with the origin at the lower left side of the sandbox.
RESULTS
This entire process resulted in 400 points (0 - 19 for x by 0 - 19 for y). The minimum value recorded was -11.0 cm (11 cm below sea level), the maximum was -0.8 cm, the average value was -5.2 cm, and the standard deviation was 2.0 cm.
This sampling method proved to be efficient and effective. The data appears to have captured most of the details present in the sandbox, although that will not be know for certain until the DTM is created. If the data proves to not be detailed enough, that means the grid should have been created with shorter spacing or stratified sampling should have been used.
The sampling method stayed constant throughout the survey; no changes were made once it began.
A few problems were encountered and overcome during the survey. First, the strings creating the grid started loosening up and having slack in them as the survey progressed. They were checked several times and pulled taught. Slack in the strings would have impacted measurements by making the sea level appear to be closer to the surface and lowered the elevation values, especially closer to the center of the sandbox where slack would be the most aggressive. The second problem encountered was caused by the size of the base of the ruler. When lowered to the surface, the ruler could contact the surface at a point that is not directly under the grid, for example on a slope. This was remedied by pushing the ruler into the surface when necessary to make sure the measurement was being taken at the point directly under the grid.
CONCLUSION
The systematic sampling method used was a fairly straightforward use of sampling. Sampling involves collecting a subset of samples to make a model of the whole, and collecting sample points across a grid to create a model of the surface fits this definition well. This was not the only viable method out there, but it worked well in this instance.
Sampling is used in spatial situations because creating a perfect representation of real life would be impossible, as it would require an infinite amount of measurements across a continuous surface. Because of this, sampling must be used where a finite amount of measurements are taken to create a simplified model of a surface.
While the sandbox is a small area, the process translates directly to larger survey areas. In larger areas, sample measurements still have to be taken to create a model of the surface. The change in scale would not affect the idea much, although a systematic approach may be more difficult as there may be obstacles in a larger scale, such as a building, that would prevent measurements from being taken every x distance.
The survey appears to have captured the detail that was expected. Since the surface formed letters, the detail needs to be high enough for those letters to be recognizable as well as the features that were used to create them. If the detail is not sufficient, then some stratified sampling should have been used at the edges of the letters to create a better outline of them and to better describe the changes in elevation.
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