Lab 10: Visualizing Sandbox Survey

Introduction

Lab 10: Visualizing Sandbox Survey builds upon the work that began in Lab 1: Sand Box Lab. Recall that sand in the sand box was shaped to spell out "JOE" with the J a trench and the O and E raised hills, as shown in Figure 1. The area was systematically sampled in cm, with the cross strings raised above it as 0cm. In this lab, the data collected in Lab 1 is normalized and interpolated to create a series of digital elevation models (DEM). This will inform various methods of DEM creation and the accuracy of the sampling method.

Data normalization with regards to geographic data involves the process of organizing, analyzing, cleaning, data so that it can be as efficient as possible (ESRI Definition). It is important that the data collected in Lab 1 is normalized because one incorrect elevation value can greatly alter the values of interpolated cells near it.

Figure 1: Sand Box

Methods

The first step of good data management is creating a folder for the project, in this case named "SandBox," as well as a file geodatabase, also named "SandBox" in this case. I brought the normalized sandbox data into ArcMap with an excel table and added the geographic data with the "add X, Y data" option. This created a shapefile, shown in Figure 6. Using interpolations methods Inverse Distance Weighted (IDW), Natural Neighbors, Kriging, and Spline several digital elevation models were created. I also created a TIN.

Inverse Distance Weighted

According to ESRI, the IDW tool assumes that things in close proximity are more alike than things far away, and weights the closer points more highly. Figure 2 shows seven iterations of IDW with different parameters. I adjusted the power parameter, which reduces the influence distance points have, and the number of points use to create each new point. IDW 10 is the default parameters of power 2 and points 12. IDW 4.2 used parameters power 3 and variable points 8, and I think best represented the sandbox terrain.

Figure 2: IDW Experimentation

Natural Neighbors Interpolation

According to ESRI, the Natural Neighbors Interpolation method uses a defined number of the closest inputs to define a new query point. With this tool there were not many parameters to experiment with, so Natural Neighbors 1 is the default with cell size 0.39, and Natural Neighbors is cell size 0.45, which didn't make much of a difference in appearance.  

Figure 3: Natural Neighbors Experimentation

Kriging Interpolation

According to ESRI, Kriging Interpolation assumes that the distance and direction between sample points creates a spatial correlation. The tool fits a mathematical function to the points based on this relationship to determine the output values for each location. This tool is often used in soil science and geology, especially when there is a spatially correlated distance or directional bias in the data.

Figure 4:  Kriging Interpolation Experiments

Spline Interpolation

According to ESRI, the spline tool creates a surface that passes through the data points (Figure 6: Raw Input Data) exactly and minimizes curvature. It accomplishes this by passing through all sample point, and fitting a mathematical function to a specific number of closest input points for the space in between the points. This method tends to best suit gently varying surfaces like elevation, water tables, or pollution concentrations.

Figure 5: Spline Interpolation Experimentation

TIN

Triangular Irregular Networks (TIN) are made up of vertices that are connected by a series of edges, together forming a network of triangles. ArcMap supports Delaunay Triangulation method of interpolation, which utilizes distance ordering.

Figure 6: Raw Input Data and TIN Model

Results

Displayed are the best products of Inverse Distance Weighted Interpolation, Natural Neighbors, Kriging, Spline, and TIN processing. Surface models were imported to ArcScene and viewed at an oblique angle to visualize elevation in 3D. Images were exported as a 2D EMF file. The scales remain true to measured values: all a negative distance from an arbitrary "0" elevation height above the sand box. High elevations are approximately -7cm, usually displayed with white colors, and low elevations are about -21cm displayed with dark grey and black colors.

Figure 7: IDW with power 3 and 8 variable points.

Figure 8: IDW Oblique view

Figure 8: Natural Neighbor with default inputs. Produces a smoother output than IDW.

Figure 9: Natural Neighbor oblique view.

Figure 10: Kriging Interpolation with settings ordinary, exponential. Seemed a little blurry.

Figure 11: Kriging Interpolation oblique view, image does not seem blurry.

Figure 12: Spline Interpolation with spline type regularized. Well defined letters.

Figure 13: Spline Interpolation Oblique View. Visually pleasing image.

Figure 14: TIN Interpolation with default settings. Challenging to see defined "J".

Summary and Conclusions

The survey conducted in this lab is similar to other field based surveys but on a very fine scale. Both this survey and field surveys depend on an arbitrary "0" elevation level, and require some sort of systematic measurement plan. Equipment for data collection and measurement vary greatly; I would not want to measure the height of a mountain with a meter stick. Additionally, with this survey there were not obstacles such as private property and impassable terrain that could occur when conducting large scale field surveys.

It is not always realistic to perform a grid based survey as detailed as this one. Our survey was conducted on a very fine scale, therefore grid size and data variability were very small and would not be realistic use on any large surface. Additionally, when conducting an elevation survey on a greater scale covering more surface area, time and physical obstacles may prevent measuring data with a fine grid.

These interpolation methods can be used for any continuous raster data such as air or water temperature, water depth, winds speed, geologic unit thickness, depth to bedrock, water table height, aquifer flow rates, and many more.