Creating a Digital Elevation Model

Introduction
     Sampling is a shortcut method of measuring the whole of a population or, in this case, an area. A small portion of the whole data is collected to make inquires and informed decisions on the entire population.
     There are three main techniques of sampling, Random, Systematic and Stratified. Random sampling grabs data from the entire population at random. Meaning that there is no bias with the sample collection. Systematic sampling is using a systematic approach to gather data in evenly or regularly throughout a data set. Finally there is the Stratified which breaks the population down into separate known groups and then data points are collected with in each group.
     The objective of this lab is to create a landscape containing various different features, collect elevation samples form the landscape, which will then be turned into a digital elevation model by means of ESRI.

Methods
     For this project a stratified sampling method was chosen because it gave more flexibility to where more on where larger amounts of samples could be taken. For instance, in the landscape created there was a plane and a mountain ridge. The plain stretched for quite a ways and the elevation did not change, so few samples were need in this area. However, the mountain ridge had drastic changes in elevation so many points in a relatively small area were needed to capture the shape of the ridge. This same flexibility is not possible in the random sample and systematic approaches. With the random sample it is possible that only one point could be taken on the ridge while dozens were taken on the plains. This would have distorted the shape of the mountain ridge greatly. A similar problem occurs with the systematic approach where in the areas of the landscape may be skipped and the land formations will not look as they did in real life.
     The landscape was created in a sandbox where in certain features were required, the feature were: a ridge, hill, depression, valley, and a plain. The materials that were used to create the landscape and measure the elevation were sand, tacks, string, a yard stick, a ruler, and a notebook and pen. The sand was used to create the features in the landscape, the tacks were used to create a the groups need to preform the stratified sampling, the string was used to as a way to maintain "sea level" in the middle of the landscape, the yard stick and rulers were used to measure the elevation, and the notebook and pen were for recording the elevation samples. Image 1 shows the landscape that will be used to create the digital elevation model.

(Image 1: The landscape)

     The sampling schema was set up in the following way. First the sandbox was measure so that evenly spaced grids could be created. The sandbox was used was a square that was about 111 cm by 111 cm. So a tack was pushed into the sandbox container at every 11 cm, to create a 10 by 10 grid over the sandbox. Unfortunately, the sampling process took so long that a proper collection was not possible for every grin. The decision was made to get rid of the 10th row of the Y axis. This areas was part of the plains meaning that there was little elevation change. The loss of this row was deemed acceptable.
     Elevation was chosen to be at the top edge of the sandbox. This elevation was chosen purely for convenience. Having the elevation be below the ridge of the sandbox would have been a nightmare to try and measure. Instead the group decided that if the sea level needed to be lower in the future a simple, equal subtraction of all of the elevations to the new sea level would be easier. Image 2 shows the string method in use. Image 3 shows the yard stick in use to measure the elevation.

(Image 2: Using a string to measure at sea level in middle of the sandbox.)

(Image 3: Yard stick in play.)

     To record the data the origin point was determined and every cell to the right and up from that point would be numbered up by 1, until the Y-axis was 9 and the X-axis was 10. Certain areas in each cell needed more data points collected than others. These points were labelled in the following way, (3.1, 1), (3.2,1), and (3.3,1). This would allow for large elevation changes that were directed east and west. The process could be switched so that the Y value and the .1, .2, .3, which would indicate elevation change going north to south. To actually measure these points a string was stretched tightly across the sandbox and a yardstick was used to measure all elevation below sea level, which were recorded as negative numbers. For the elevation above sea level the ruler was used to give a flat surface from the elevation level above sea level so that the yard stick could measure it. These were measure as positive numbers. This method was chosen simply because it seemed like the easiest.

Results
   The sample size ended up being 145 different elevation points spread out across the landscape. The lowest point for the landscape was -15 cm, the max was 16 cm, the standard deviation was 6.13 cm and the average elevation was -3.05 cm. The range from the highest to the lowest was 31 cm. However, the sea level may be changed and all elevation will be subtracted by 3. This sampling seemed to work the best due to the fact that it was the best way to focus higher amounts of data collection in one area over another, which was a necessity for this assignment. The sampling technique remained the same throughout the sampling process. The two problems that were encountered during the sampling problem were the sea level issue, which was discussed in detail earlier, and the second issue was touched on briefly earlier, which was the switching of the .1, .2, .3 from Y to X axis depending on the direction that the change in elevation occurred. The latter was solved by going back and double checking the areas that had the more in-depth collections. Figure 1 shows a portion of the table containing the elevation points that were collected during this assignment.

(Figure 1 Elevation Table)

Conclusion
     How does your sampling relate to the definition of sampling and the sampling methods out there?
     The sampling method used was the stratified sampling method. The way that it was employed for this assignment fits perfectly with the definition of sampling.
    Why use sampling in spatial situation?
     It took a small portion of the total amount of elevation and will, hopefully, allow for the creation of digital elevation model. To allow for the study of very large areas in shorter amounts of time. It is the same reason why media companies use samples of larger population to create political polls.
    How does this activity relate to sampling spatial data over larger areas?
    Similar methods described above could be used to collect data points on a significantly larger scale.
     Using the numbers you gathered, did your survey perform an adequate job of sampling the area you were tasked to sample? How might you refine your survey to accommodate the sampling density desired.
     Yes, the sample size was large enough to create an accurate model of the actual terrain. The sampling method used was hopefully accurate and will lead to well detailed digital elevation model.