Lab 2. Terrain Model Redo

Introduction
The second activity for class was to redo and improve the survey of a terrain surface that was done the previous week.  Each group was to discuss ways to improve our methods, then re-conduct the survey and use the new data to create an elevation surface.  Various interpolation methods would be used and compared, including IDW, Kriging, Natural Neighbor, Spline, and TIN.  

Methodology
Our group went about this project using the same method for surveying the terrain surface as last week, with the exception of taking measurements at every 5x5 cm intersection as opposed to the 10x10 cm measurements that were previously taken.  This was decided because our group wanted to have a more accurate and better model representation of the actual surface.  Over the course of the week, weather factors such as rain, temperatures above freezing, and snow had altered the surface.

Figure 1. Fresh snow on top of terrain surface in planter box.

Therefore, the surface was rebuilt to resemble the surface that was created last week.  The planter box measured approximately 1.2 meters wide, and 2.4 meters long.  The southwest corner of the planter box was designated as the origin, and five centimeter increments were measured along both axes.  String was stretched over the surface along the X-axis to aid in the measuring process.

Figure 2. Measurement of five centimeter increments along X-axis.

Figure 3. Oblique view of terrain surface and strings spanning entire length of planter box.

To measure the Y-axis, two boards were placed on the edges of the planter box and a meter stick was extended between them over the surface.  Measurements were then taken at the intersection of the meter stick and strings.

Figure 4. Measuring the elevation of the terrain surface.

After the surveying was completed, the XYZ data was entered into Excel.  Because the measurements that we took were from the top of the surface to the meter stick that was laid over the planter box, each value was then subtracted from the highest value to ensure all positive elevation numbers.  After the calculations in Excel, the point data was imported into ArcMap and used to create rasters using various interpolation methods.  The rasters were then imported into ArcScene and displayed in 3-D.  

Figure 5. Excerpt of XYZ data.

Discussion
The following images show the terrain surface that we created in 3-D using IDW, Kriging, Natural Neighbor, and Spline interpolation methods.  Some noticeable features of the surface include the plains in the southwest and northeast corners, the L-shaped ridge in the middle of the surface, as well as the low valley that seems to surround the ridge.  It was very interesting to see the difference between the elevation rasters that were created with the various interpolation methods.  The surface that was created using IDW has odd circle shaped bumps at each point where a measurement was taken.  The IDW method estimates cell values by averaging the values of sample points in the neighborhood of each processing cell.

Figure 6. IDW

The next interpolation method used was Kriging.  Kriging is a geostatistical method of interpolation that creates a surface by examining nearby points.

Figure 7. Kriging 

Natural Neighbor is a method that applies weights based on proportionate areas to interpolate a value.

Figure 8. Natural Neighbor

Spline is an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, which results in a smooth looking surface.

Figure 9. Spline

The Kriging and Natural Neighbor surfaces do not contain the odd circle shaped bumps that the IDW has, although the top of the ridge is rather pointed.  I believe that the Spline surface is the most aesthetically pleasing model that was created.  The surface that we created did not have any pointed edges, as the surface was made out of snow.  The top of the ridge is a little more rounded than the previous two interpolation methods, and best models the surface that we created.  A TIN was also generated, but because of its poor aesthetic look and representation of the data, it was not included in this report.

Conclusion
I really enjoyed this activity, and was able to take a lot away from it.  It challenged us to think critically about a method for surveying terrain, as well as what could be done to improve the process.  Completing this project the second time around was a lot easier.  We improved the surveying process by laying a meter stick over the two boards instead of a string that was attached to them.  We also switched from measurements being taken every 10 centimeters to every 5 centimeters.  Our group discussed that the 10x10 cm measurements that were previously done were too coarse for a surface of this size.  The 5x5 measurements took about a half hour longer to complete, but greatly improved accuracy.