Previously, the class had set out to create a Digital Elevation Model (DEM) of a 1m X 1m sandbox terrain by gathering elevation data points based on an artificial sea level. This was achieved using a stratified sampling system (more about the sampling system in the previous post). The survey data was then entered into a table and imported into ArcGIS to create a point feature class with X,Y, and Z values. Data normalization was a key aspect to this lab, because organization of the data is required to get accurate models. Data normalization reduces redundancy and improves the accuracy of our data due to human error. Normalization in this aspect was that our data was categorized into 3 columns, "X_Cell", Y_Cell", and "Z_Value." Each point has XYZ values, that correspond to position on the x axis, y axis, and depth above or below "sea level." With this data, it is easy to do different types of interpolation to make the DEM rasters. Interpolation is a method of construction new data points within the range of a discrete set of data points. 5 different types of Interpolation were used in the assignment to determine which was the best fit for the DEM.
Methods:
First, the compiled data was imported into a File Geodatabase in ArcMAP. From there it was used to create a point feature class with XYZ data. The group double checked to make sure the data was in Numeric format, because after a previous minor slip up Dr. Hupy loves to hang that over our heads. Next, Geostatistical Analyst, Spatial Analyst, and 3D Analyst tools were all checked and ready to roll. With these ready our different forms of Interpolation were ready to rumble.
1. Inverse Distance Weighted (IDW) Interpolation
IDW interpolation assumes that each point has a weighted value to predict unmeasured points around it. It makes the assumption that points that are closer together are more alike than points that are further apart. Figure A below, shows that IDW worked well for the group since a stratified approach was used, meaning there were many points that were clustered in groups.
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| Figure A: IDW Interpolation |
2. Natural Neighbor Interpolation
This Interpolation technique applies only values directly next to each point. Areas directly next to the point carry more weight for each point around the surface. This is often referred to as "Area-Stealing" interpolation. Natural Neighbor Technique (Figure B) created a very natural looking DEM and potentially the most realistic.
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| Figure B: Natural Neighbor Interpolation |
Kriging Interpolation is in a completely different ballpark than other Interpolation methods. Kriging uses geostatistical methods that are based on statistical models that include autocorrelation. This gives kriging the ability to predict surfaces but also add to the certainty of the accuracy of the predictions. It assumes the surface has relatively the same pattern all the way across. This method did not do well to capture the sandbox because it gave too much weight to the flat areas and did not show the peaks well. Figure C below.
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| Figure C: Kriging Interpolation |
Spline Interpolation uses a mathematical function to minimize overall surface curvature by having the lines pass directly through each point. There are two kinds of Spline, Regularized method was used, which creates a gradually changing surface that often results in values that are outside of the sample data range. The Spline method (Figure D) was not as useful because it centered too heavily around the areas that were sampled more (due to stratified sampling).
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| Figure D: Spline Interpolation. It became discoloured from the others no matter what I did, so I left its vibrancy. |
TIN was the final method used, it creates triangular networks between the data points by connecting lines between the data points. With 3 lines going between every point collected the result is a 1980's looking arcade game surface model, much like Figure E below. The TIN method, while blocky, worked well for our group because of the stratified data collection.
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| Figure E: TIN Surface Model |
Results/Discussion:
At first Spline seemed to be the best Interpolation method because of how smooth it is, until it is compared to a picture of the sandbox and it is easy to see that the highs are exaggerated far too much. Natural Neighbor is the real winner of Interpolation methods for the sandbox project because it most accurately represented the curvature of the mountainous regions and rolling prairies.
In conclusion, IDW interpolation provided an accurate image of the sandbox terrain; however, it skewed some data points based on the stratified groupings, and made for awkward spikes that were not large elevation changes. This could easily be fixed by sampling more uniformly. As said before Natural Neighbor most accurately portrayed the sample area, it captured the terrain fluidly. The only thing that could improve its accuracy is if more points were sampled. Kirging Interpolation did a poor job of capturing the sample area because it attempted to predict and normalize. Making the mountain more like a plateau and the lower areas just flat. As noted before the Spline Interpolation was not good, it exaggerated the highs and lows too much creating a map that looks more like ski moguls than land. TIN created a great DEM of the sample area, the mountain looks slightly too flat, but that could have been made better by more data points.
Conclusion:
The sampling method chosen turned out to be a success, stratified sampling and Natural Neighbor Interpolation worked well to create a DEM of the sandbox. This survey method was rather archaic in the fact that it used a string/drawn grid and a meter stick rather than survey grade GPS, but it got the job done and the method worked very well. This method is also not used in many situations, it would be difficult to do in a busy downtown area, a crowded building, or on private land. But for this assignment a stratified system with a grid was the best way to accurately sample the sandbox for the best results.
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