Cartographic Fundamentals

INTRODUCTION

The goal of this lab was to learn the fundamentals of properly displaying data. This includes attaching the proper information to the data for it to have context and be useful. The sandbox data from the previous labs will be revisited and displayed in a more useful way. Following that, several maps were created of Hadleyville Cemetary in Eleva, Wisconsin to display several different variables.


METHODS

Arcmap was used to create all maps in this lab. The sandbox map had some supplemental work done in Adobe Illustrator to put in the scale bar and the origin points. For the cemetery maps, symbology tools were used to display the various features.


RESULTS

Displayed below (Figure 1) is the revised sandbox map. This was created using the spline method from the previous lab. Added to this map was a title, location map, north arrow, scale bar, and map information. These additions add context to the map to make interpreting it easier. On the right side of the map, four different three-dimensional views. The origin point on the 3D views allows the viewer to more easily see where the orientation is being viewed from.

Figure 1: Map of sandbox data created using the spline method

Next are the maps of Hadleyville Cemetery. These also have the same necessary cartographic features added. First (Figure 2) is a map showing year of deaths (YOD) in the cemetery. This method of displaying the year of each grave is good for checking individual dates with good accuracy, but it is difficult to see general trends.

Figure 2: YOD displayed individually

The next map (Figure 3) shows the same information, YOD, displayed in a different way. This map displays the information as graduated circles, with larger circles representing later years, as it shows on the legend. This method of display more easily shows general trends in the data, but if you wanted to know the exact year of a grave, this map would not be suitable. As you can see from the map, newer graves tend to be grouped together and closer to the outside of the cemetery.

Figure 3: YOD displayed by graduated symbols

The next map (Figure 4) shows last names on graves in the cemetery. This is displayed similar to Figure 2, in that each grave has its information individually displayed with no need for a legend. Unlike Figure 2, the information provided in this map is not numeric so the option so symbolize the data using other methods is not viable. There is too much of a variety of last names at the cemetery for them to be cleanly symbolized by type.

Figure 4: Last names displayed indivudually

Lastly, Figure 5 shows a map showing the condition of each grave. Since there are only three options: standing, not standing, or unknown, this is easily symbolized by different color symbols. Notice there are only a few graves that are not standing. There are also many graves that had null values in grave condition, so they are represented as having an unknown condition.

Figure 5: Grave conditions

CONCLUSION

Without metadata, most maps are rendered useless. This data provides context for the viewer to interpret the map, such as location, orientation, what the map is showing, and where the data is from. These map elements will be used in all subsequent labs.

Visualizing and Refining the Sandbox Survey

INTRODUCTION

In the previous lab, a survey of a sandbox was conducted using systematic sampling. A grid was created over the sandbox and measurements were taken at set distances on the grid. In this lab, the data will be visualized using a variety of interpolation methods.

Using the measurements taken in the previous lab will rely on data normalization, which is the process of organizing data into a usable format of columns and rows. This is important for the software to read the data, and also helps find any possible redundancies or missing points. The measurements taken were organized into XYZ points in an Excel spreadsheet, a sample of which is shown below.

Survey measurements organized in Excel

The data in this stage was just a list of numbers, which is difficult to visually analyze. Using interpolation methods, continuous raster images were created from these points. These rasters are models of the data, giving a visual representation of the measurements taken. There are not an infinite amount of points in the area, rather points representing a grid of measurements. Since this leaves room between the points that the elevation is unknown, various methods are available that estimate the values between these points. This is what will be explored in this lab.


METHODS

The first step in the lab was creating a work space. This involved creating a new folder to work in, followed by creating a geodatabse for the lab. The Excel file containing the coordinates was then added as a table to ArcMap. This table was added as XY coordinates into the map. This created a two-dimensional grid of all measurements taken, ready to be used for interpolation. The interpolation methods were found in the ArcToolbox. These five methods are discussed below.

• IDW, or Inverse Distance Weighting, uses distance to weight calculated averages. This means the closer a cell is to a point, the more influence that point will have on it. This works well for surveys where the measurement density is high, but on lower densities, such as this sandbox survey, this method creates the appearance of bumps from weighted calculations.

• Natural Neighrbors is similar to IDW, in that it weights influence based on distance. This method tends to work better on systematic sampling methods as the bumps will be less pronounced, creating a smoother surface.

• Kriging is a computationally intensive geostatistical method. Kriging uses the assumption that the distance between the points is correlated to the difference in variation on the surface. This is a much more complicated method that the others, but creates a fairly accurate representation where certainty for each calculation can be given. The result of this method in lower density surveys such as this one creates ring-like shapes around points, giving the surface a false texture.

• Spline uses mathematical functions to create a surface that minimizes curvature. This creates a smooth surface that works well for low density surveys.

• TIN, or Triangulated Irregular Network, is a vector-based model that creates a surface by connecting all points, or vertices, with triangles. The result has edges instead of a smooth surface.

After the data had gone through interpolation, each method was brought into ArcScene to display it in 3D. From there, it was manipulated to a view that best showed the features and captured as a PNG file.



RESULTS

The least successful method was IDW. The results are shown below in both a bird's eye view and a 3D view. Since the sampling density was not very high for this survey, IDW created false bumps on the model from there measurements were taken. This creates an unrealistic portrayal of the surface of the sandbox.

IDW

The next method was natural neighbors. This method created spikes where measurements were taken, again from a relatively low sampling density. Although these were less pronounced than those in IDW, it still is not a good representation of the surface. This method would be more effective at a higher sampling density.

Nearest Neighbor

Next was kriging. This method created rings around measurements, creating a false texture on the surface of the model. The depiction of the surface seems to be fairly accurate if the texture is overlooked, but this is still not the best method for this sampling density.

Kriging

The next method was spline. This created the most realistic representation of the surface. The curvature is relatively accurate with no unwanted texture or bumps. For lower sampling densities, this seems to create the best estimations for elevation, between the measurements.

Spline

The last method was TIN. This stands apart from the other method, as it is vector based. This is obvious in that there are sharp angles from nodes and vertices rather than the smooth, continuous raster surface of the other methods. Because of these angles, it is not a very accurate representation of the actual surface, however it does have some positives. The model that is created is visually pleasing, as well as giving the viewer an estimate of the confidence in the precision of the survey, as you can see exactly where the measurement locations are. For a survey using stratified sampling, areas with a higher sampling density would be clearly shown by having smaller triangles.

TIN

The survey could be improved if it was performed again. The best way to improve the data would be to up the sampling density and lower the distance between each measurement. This would be a larger time commitment, and it's important to remember that an increase in the number of X and Y measurements would be a squared amount of additional measurements total, so the extra time necessary would add up quickly. Alternatively, stratified sampling could have been used around the edges of features to more clearly show them. This would not drastically raise the time necessary to complete the survey, but it would add complexity and make more room for error. Doing either of these would improve the results for all interpolation methods. Obviously, there is a cost-benefit angle that must be considered, and the results from this survey did a fairly good job of representing the original surface without taking an exorbitant amount of time to procure.


CONCLUSION

While sandboxes do not often need to be mapped in real-world situations, the methods used to do this are similar for larger-scale, practical surveys. The procedure would just have to be scaled up. Instead of being on the order of centimeters for measurement distance, it would be meters. There would also need to be different measurement equipment, as measuring with a taught string and ruler is not a practical way to survey a large area.

Because a string grid would not be used on a larger area, the grid method of systematic sampling would be less usable. GPS equipment would be needed, and a lack of a grid would make stratified sampling more appealing.

It is important to note that interpolation methods have uses other than elevation. They can be used to model any continuous data, such as temperature or CO2 levels across an area. The processing would be the same, but the end result would show a more theoretical representation, where higher "elevation" on the surface of the model would represent a higher value in the variable. For example, with CO2 levels, peaks would show areas of high CO2 concentration, while valleys would show areas of low CO2 concentration. Interpolation extends far beyond the use of elevation mapping as it was used in this lab.

Conducting a Survey of a Sandbox

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.

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.

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.

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.