Creation of a Digital Elevation Surface - Week 1

Introduction

Sampling is a shortcut method that involves gathering data on just part of a whole population and using that data to represent the whole population. Spatially speaking, and for this exercise specifically, sample points were measured and recorded along a grid for the elevation of a sandbox terrain in order to create a digital elevation surface representative of the actual sandbox terrain. The sampling technique that was employed was a systematic point sampling method where elevation points where measured and recorded along a grid at the grid intersections. The objectives for this exercise include:

• Using critical thinking skills to devise an improvised survey technique for mapping out a sandbox terrain with x, y, and z fields
• Transfer the recorded terrain points into ArcMap and create a digital elevation surface map

Methods

For this exercise, a systematic point sampling technique was used to record the points of the terrain using a grid where intersecting points were measured and recorded (figure 1 shows how the grid was set up where each intersection of string indicated where elevation was measured, including where the string met the wood sides). This method was chosen because it provided a neat and organized grid across the terrain that allowed for unbiased and consistent measurements along the x and y planes. Measurements could have been taken in the middle of each grid square but this would have resulted in less accurate measurements due to having to "eyeball" the exact middle of each square.

Figure 1: Terrain with grid and measuring tools

The sandbox was set up outside of Phillips Hall across the street in a patch of lawn. The 45"x45" (114x114 cm) box (inner square) was then filled with sand. From here, each group developed their own terrain that was to include the following features (refer to figure 2):

• Ridge - surrounding the hill in the middle in a circular pattern
• Hill - in the middle
• Depression - lower left corner
• Valley - lower right corner
• Plain - upper right corner

Figure 2: Terrain with developed features

A variety of tools were used to set up the grid and make and record the elevation measurements including:

• Meter stick - measuring out 5 cm increments on top of the wooden box to insert push pins and for measuring the straight wire when elevation measurements were taken
• Collapsible ruler - used as a place holder when taking elevation measurements on the grid
• Push pins - inserted every 5 cm along the top of the wooden box for weaving string around
• String - weaved around the pins along the x and y axes to create the grid
• Thin straight wire - used to capture depth of elevation of terrain along the grid intersections
• Laptop - recording x, y, and z values of terrain

For setting up the grid, 5 cm increments were measured from the origin (near the student's foot in figure 2) along the x and y axes and the push pins were inserted at these increments. After the pins were inserted, string was woven around them in a parallel fashion starting in one corner and going from one side to the other, then when one axis was done the string was woven perpendicularly again in a parallel fashion and going from one side to the other until the grid was complete (refer to figure 1). Once this was complete, the measurements and subsequent recording of measurements began starting at the origin (which was right up against the corner of the wooden box). A thin straight wire was used to push straight down into the sand until it hit the ground, then marked at where it met the top of the sand, and pulled out and measured with the meter stick from the marked location to the bottom of the wire where it touched the ground underneath the sand (see figure 3).

Figure 3: Measuring elevation with straight wire and meter stick

 After each recording, a collapsible ruler that stretched across and over on each side of the wooden box, was moved to the next grid line as a placeholder for keeping track of which point was to be measured next. The ground acted as the chosen "sea level" in this exercise. This avoided negative numbers in the z field. The top of the wooden box could have been chosen as sea level, but would have led to negative values and error in spots where the ridge and hill rose above the box which could cause inaccurate z values due to the grid points lying above the plane of the top of the box. The data was entered into a spreadsheet on a laptop by one student while the other two students conducted the measurements. Recording the data in the laptop was done as a way to be more time effective. If the data had been recorded in a notebook, then it would've have needed to be transferred into a spreadsheet regardless. Entering the data into the spreadsheet on the laptop directly avoided this extra step.


Results/Discussion

The final number of recorded points totaled 533. The sample values are as follows:

• Minimum value: 6.6
• Maximum value: 23.2
• Mean: 14.6
• Median: 14.4
• Standard Deviation: 2.57

There was a 16.6 cm difference between the highest and lowest elevation points. The median, at 14.4 cm, falls almost directly between the maximum and minimum values. The average value is just slightly above the median value at 14.6 cm. 

The sampling related to the chosen method quite well. Hundreds of elevation points were collected that represented the terrain well. The sampling technique did not change from how it was originally planned out. It was even discussed before the survey that only every other point along the grid in the "plain" area of the terrain would be measured due to consistent elevation values and that is exactly what occurred. The only thing that was improved upon was using the collapsible ruler as a placeholder for measuring the points. The resulting data is what was expected where there was an elevation measured and recorded at every point on the grid except for a few rows in the "plain" area where only every other point was measured. Some problems (and subsequent solutions) that occurred during sampling included:

1. Hitting hard objects with the wire in the sand on the way down to the ground or hitting soft ground with the wire and it going through the ground, giving an inaccurate elevation measurement. Solution: The wire was pushed hard through the objects in the sand and lightly pushed against the ground when it reached that point.
2. Losing track of which point or row was being measured. Solution: The collapsible ruler was used to mark the column that was being measured but did not mark the row. For this, the color of the pin in the wood on that row was used to mark the row being measured. 
3. The laptop ran out of battery with about three rows remaining. Solution: The remaining data points were recorded in a notebook and transferred over into the spreadsheet after the computer was reconnected to a power source. 

Conclusion

The sampling technique used in this exercise, which involved measuring and recording points along a grid that covered a surface area, relates the definition of sampling at the beginning of the introduction where a small part of the data was recorded that was then used to represent the whole population (terrain). Using sampling, in this situation, provided a less time consuming method for gathering elevation data points on the terrain as opposed to if every single elevation point was measured at every possible location (this would be an extremely tedious and time consuming effort). With over 500 points collected, the number of data points adequately sampled the extent of the terrain. If the survey were to be refined to accommodate the desired sampling density, it would be by measuring areas of higher relief more closely (every 2.5 cm as opposed to 5 cm) and the areas with lower relief less closely (every 7.5 cm as opposed to 5 cm).