This week's lab assignment was about interpolation. In the first portion of the lab, we worked with DEMs, and in the second portion we used several different interpolation methods to create surface rasters depicting water quality in Tampa Bay. The methods used were Thiessen, inverse distance weighting (IDW), and spline. Spline additionally has two possible techniques, regularized and tension.
Thiessen interpolation first requires Thiessen polygons, which are geometrically calculated "neighborhoods" where each polygon contains one input point and any location within the polygon is closer to that input point that to any other in the dataset. To create a raster from this, each cell is assigned the same value as the input point in its neighborhood. IDW calculates each cell value based on the values of the closest X number of input points, and gives more weight to points that are closer to the cell being calculated. In the spline methods, smooth curves are drawn to connect the input points and cell values are based on the cell's position on the curve. Tension spline is more constrained by the input values than regularized spline, though both methods preserve the input values at their individual locations.
Here is the output of the tension spline interpolation for the Tampa Bay data (with the original sample points classified similarly to the surface raster):
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