Lab 5: Visualizing Terrain Survey

Introduction

In Lab #4, a terrain was created in a sandbox and its elevation was assessed using surveying techniques (refer to previous blog post for more details).  

Figure 1: Normalized table

This lab will serve as a follow-up to the survey conducted last week.  Data normalization played a large role in preparing the data that was collected last week for visualization.  According to ESRI, data normalization is "the process of organizing, analyzing and cleaning data to increase efficiency for data use and sharing" (ESRI, 2016).  In this lab, the elevation data that was collected during the survey had to be normalized in Excel before it could be imported to ArcGIS.  This meant making sure all of the columns were properly sorted and changing the data to be set as 'numeric' with proper decimal values.  After this was done, the data could be imported into ArcMap and converted into a point feature class. 

Methods

After importing the data into ArcMap, it was visualized using five different interpolation techniques.  According to ESRI, interpolation is "the estimation of surface values at unsampled points based on known surface of surrounding points" (ESRI, 2016).  Here are the interpolation techniques that were used in this lab, as explained by ArcHelp and ESRI: 

1. Inverse Distance Weighted (IDW)
   Definition: An interpolation technique that determines cell values using a linearly weighted combination of a set of sample points, wherein the weight is a function of inverse distance.
   Advantages: Can control "power parameter" which determines significance of known points; can limit number of points used for interpolation to speed up processing time
   Disadvantages: Quality of interpolation can be limited if points are unevenly distributed
2. Natural Neighbor
   Definition: A deterministic interpolation method for multivariate data in a Delaunay triangulation; value for interpolation point is estimated using weighted values of closest surrounding points in triangulation.
   Advantages: Well-suited for categorical data
   Disadvantages: Interpolated heights are guaranteed to be within range of samples, so it will not display peaks, ridges or valleys that aren't represented by sample points
3. Kriging
   Definition: A geostatistical interpolation technique in which the surrounding measured values are weighted to derive a predicted value for an unmeasured location.
   Advantages:  Can provide insight on precision of predictions; appropriate when there is a spatially correlated distance or directional bias in data; well-suited for soils, geology
   Disadvantages: Z-values must be assessed prior to interpolation to determine if Kriging is appropriate
4. Spline
   Definition: A deterministic interpolation method in which cell values are estimated using a mathematical funcation that minimizes overall surface curvature, resulting in a smooth surface.
   Advantages: Works best for gently varying surfaces
   Disadvantages: Not desirable if smooth surface isn't wanted
5. Triangular Irregular Network (TIN)
   Definition: A vector data structure that is comprised of contiguous, non-overlapping triangles, wherein the vertices of the triangles are sample data points (x, y, z).
   Advantages: Non-redundant data, can use natural features as break lines; can accommodate more or less complex data with varying triangles
   Disadvantages: Less tools available for processing than for raster data

After applying each interpolation method to the data, the resulting surface maps were imported into ArcScene for 3-D visualization.  Then, the resulting 3-D renderings were exported as JPEGs.  

Results & Discussion

The 3-D visualizations of the survey data using all five interpolation techniques are displayed below (Figure 3, Figure 4, Figure 5, Figure 6, Figure 7).  After viewing all of the interpolations somewhat head-on, side views of each were compared as well (Figure 8).  This helped to determine which interpolation was the best fit for the data at hand.  

Figure 2: Sandbox terrain for comparison with 3-D visualizations

IDW:

This 3-D visualization was one of the worst results, owing to its bumpy appearance which distorts the true nature of the terrain elevation (Figure 3).  The terrain was not nearly this uneven in real life.  

Figure 3: 3-D visualization of IDW interpolation

Kriging: In comparison to the other four results, the Kriging visualization turned out to be the best (Figure 4).  This depiction is much smoother than IDW, and shows a more realistic representation of the depressions, ridge and hill in the terrain.  

Figure 4: 3-D visualization of Kriging interpolation

Natural Neighbor: While this visualization provides a rough interpretation of the surveyed terrain, its edges are somewhat rough (Figure 5).  Additionally, the depressions are not as well defined as other representations like Kriging. 

Figure 5: 3-D visualization of Natural Neighbor interpolation

Spline: The Spline visualization offers the smoothest depiction of the terrain, though in places it appears almost too polished (Figure 6).  Despite this, it stands as one of the best representations of the actual terrain.  

Figure 6: 3-D visualization of Spline interpolation

TIN: Although the TIN visualization depicts all of the intracies in elevation data well, it is rather jagged in appearance (Figure 7).  The complexity it portrayed distracts from providing a comprehensive look at the overall terrain.  

Figure 7: 3-D visualization of TIN

Side Views: Comparing the side views of all five representations reaffirms the aforementioned assessments of the results (Figure 8).  Kriging and Spline still appear to be the most effective visualizations for the terrain.  

Figure 8: Side views of all five interpolations

Conclusion

This survey relates to other field based surveys in that it was an exercise in assessing an area based on a sampling of data.  Though the study area for this exercise was small, the same methodology could be applied at a larger scale.  Using surveying techniques can be a way to save time and money, though it is important to use appropriate and effective techniques to survey the area at hand.  For example, in this terrain survey, it made sense to use intervals of 5cm for the survey grid, however, a larger survey area may require larger increments.  After collecting data in the field, a number of interpolation techniques can be applied to assess the study area.  An element of experimentation may be involved in picking the most fitting interpolation method for the data.  For example, in this exercise, the Spline interpolation appeared to be most suitable, but the TIN interpolation might be more suitable for a project in which the surveyors are concerned with expressing the complexity of the elevation changes.  Other terrain surveys may also benefit from supplemental data from remote sensing techniques or drone technology.  While field based surveys are very useful tools, it is always important to remember that such surveys contain elements of error.  It is impossible to survey every single point of a study area, and interpolation and visualization methods also influence results.