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.