Visualizing and Refining Terrain Survey

Introduction:

This exercise was a follow up on the previous elevation survey taken on our miniature terrain. We had constructed and recorded sampling methods for our terrain that minimized error. One person was charged with taking all of the measurements, so that there was only one person interpreting the incoming data. Next, we had to do some study of our data to explore different ways to optimize our surveying methods, and ultimately get a better final product. This involved importing our data into ArcMap and using various raster interpolation tools to interpret our results. Raster interpolation tools create a continuous (or predicted) surface using the z-values of sampled point values. Basically, instead on sampling every single possible point in our miniature terrain (this would be physically impossible), these tools connect the dots using the values of the samples we did take using a number of advanced geostatistical equations. These interpolation methods included: IDW(inverse distance weighted interpolation), Natural Neighbors, Kriging, Spline, and TIN. These methods will be explained in the methods section below.  After experimenting with these various tools, we were to take note of faults in our data and devise a way to re-sample our miniature terrain to accommodate an interpolation method of our choice.

Methods:

The first step was to import our sampled terrain data into ArcMap to create a point feature class.

This is our original (X,Y,Z) points feature class that we imported from our first survey, conducted on 1/30/15

Once it was imported, we were able to start performing interpolation analysis based on this class's Z-values. Next, we experimented with a number of different interpolation methods. For each of the following methods, shown below in separate images, we created 2D raster images in ArcMap before importing them into ArcScene for 3D analysis. I learned a good trick for ArcScene from another student. Putting a black and white model below a colored, but slightly transparent model highlights the model's surface features. Each interpolation method is shown below, after I had performed the interpolation tools, imported them into ArcScene, styled them and normalized their relief based on the points' values.

IDW (Inverse Distance Weighted)- This method estimates cell values by averaging nearby cell values in a weighted manner; cells that are closer to the cell value being calculated have more influence on the averaging process. As you can see, the result looks a little bit choppy, so this method was not my favorite. That points to the fact that more data points are necessary in order to smooth out this model.

Kriging- This interpolation method uses advanced geostatistics to generate an estimated surface
from scattered Z-value points. This method is said to be quite accurate, like other geostatistical
techniques. However, it is said to be most valuable when you know there is a spatial correlation in
distance or directional bias in the data. It also has a relatively high computational cost. This method outputted a relatively smooth model, but circular peaks and geometric inequalities show that more samples are needed.

Natural Neighbor- This method involves the tool using an algorithm to find the closest subset of input samples to each cell, and applies weights to them based on their areas. Since it was slightly choppy, we didn't choose it for use in the next step of the process

Spline- This method estimates values using a mathematical function to minimize curvature, while placing each sample point on this generated surface. This seems to be a good, simple mathematical technique for generating a smooth model, while at the same time maintaining the samples' original values. We ultimately decided that this was the best interpretation of our planter box's terrain and decided to use this interpolation method in the next part of this exercise. 

TIN (Triangular irregular networks)- This is a common digital way to represent topography. This model
triangulates a set of points, and forms connects them into a network of  triangles. The triangles are sized
based on the amount of change within them- therefore, they have higher resolution in areas where more
detail is necessary. They also preserve discrete features, something that other models aren't able to accomplish.
TIN models are usually used to precisely model small areas, as the computational cost and data availability
often restrict their usability in larger datasets.  

After experimenting with various interpolation methods, we decided to focus on the spline method and resample our terrain in order to obtain a more precise dataset. We decided to add precision in the areas with the most dramatic relief changes- on the hill, the valley, and the depression. This involved some conceptualizing, as we had to revise our previous coordinate system to accommodate higher resolution in the desired areas. We decided to split the desired 10cm cells into four quadrants, giving us 5cm by 5cm cells to sample.

This shows the cells that we resampled at a higher resolution. Compare with the 3D models shown above
for reference to surface features.

The next step was to go outside and take our revised samples. We set up a coordinate system in the same way that we did previously, but this time had enough mason line to string it across an entire axis. We laid measuring sticks across the other axis, and sampled in each corner of the cells created. We faced adverse conditions this time, as the temperature was well below freezing and it was late in the day- we were running out of light quickly. After we gathered the required points, we went inside and added them into our excel file.

Next, we added our updated file of (X, Y, Z) values into a point feature class as we did earlier. We then performed the spline interpolation tool to create an updated model.

An updated model generated using the Spline interpolation method.

Discussion:

Like the last exercise, this was a critical thinking challenge to our group. We were required to decide between various raster interpolation techniques, and chose the spline method. This method maintains the original data's values, while providing a smooth model with minimal curvature. We decided to get a more accurate model, we would use a higher resolution on our areas with higher change in relief. Our final model shows what I believe to be some discrepancies in our sampled cell values. On the ridge to the right in the the above updated model there is a dip and two smaller ridges, where in our real relief, they weren't present. If on the second day of sampling, we were gathering values that were lower than those we gathered on the first day, that would account for this dip in the side of the ridge. That could apply to any areas that there are peaks next to dips. Perhaps using a neighborhood interpolation method could have provided a more realistic model, as it wouldn't be required to maintain the original sample values- rather generating them based on nearby cells. 

Conclusion:

This exercise was valuable because it required us to devise methods for expanding upon previous research, something that is very important in performing field work. In modeling, when something isn't representing the real world features it is important to be able to go back and assess the sources of error, and revise methodology.