First, I used given elevation points with interpolation techniques to create a DEM using the Spatial Analyst toolbar in ArcMap. The two techniques used were the IDW method and the Tension Spline method. I wanted to see the differences between the two methods so I used the Raster Calculator to subtract the values of the DEM spline grid from those from the DEM IDW grid. The map layout is seen below.
The areas in the brightest red shows areas where the results of the IDW technique show an elevation nearly 40 m greater than those of the Spline method, and the brightest green shows where the Spline method is nearly 40 m greater than the results of the IDW method. When looking at the values of the elevation points, which are about 425 m, I can see that some of the differences between the results approach 10% of the total elevation, which definitely should affect the DEM.
In the second part of the lab, I wanted to use various spatial interpolation techniques to determine which worked best on water quality data for Tampa Bay. Technique 1 was a non-spatial technique, where I used the Statistics tool on the data points. Technique 2 is Thiessen interpolation, which assigns each location the same value as the nearest point. In ArcMap I used the Create Thiessen polygons tool, converted it to a raster, and used the Zonal Statistics tool to determine spatial statistics.I wouldn't use this technique in this case as I'm pretty sure water quality in unsampled locations is not necessarily the same as at the sampled locations; the data is not that densely sampled. Technique 3 was IDW and technique 4 was spline interpolation. As IDW estimates cell values by averaging the values of sample points in the neighborhood of each processing cell, this method works better with densely sampled data, and seemed to work well with the water quality data. Spline interpolation minimizes overall curvature and results in a smooth surface passing through the sample points, and this worked fairly well for the water quality data once it was modified. The spline technique originally resulted in abnormally high maximas and minima with negative values. Much of this was due to some data points that were very close in proximity to each other had largely different values, which caused abnormally high and low extremes nearby. Once this data was modified, the spline interpolation worked well. As far as which interpolation technique, to me it would depend partially on if I knew whether or not the maximum and minimum values were included in my sample points. If I knew they were or if the data was densely sampled, I would go with IDW interpolation as it is an exact interpolator and will not result in values outside the sampled maximum and minimum. Spline interpolation is not an exact interpolator, so if I'm not sure the maximum and minimum have been sampled or if the data is not densely sampled, I would consider using spline interpolation.
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