Module 8 - Special Topics in GIS - Surface Interpolation

Spline Interpolation with input data points

This week we worked with several different types of interpolation, that process by which new values can be estimated between known values. I could have  devoted several weeks to this topic, to get a good grasp of which types of interpolation are best for various applications and how best to use them.  I felt that this week, I barely scratched the surface, as it were, in understanding this topic.

The map at left is an example of Spline interpolation of elevation (white and purple are highest, turquoise is lowest). Locations of input data are shown as black dots. This is a method which provides a smooth result, and with which it's possible to extrapolate beyond the available data values and study area.  Newly interpolated values can be more liberally influenced by input data in their general neighborhoods.

Legend (relative Elevation)

IDW Interpolation

This map is an example of IDW, or Inverse Distance Weighted interpolation of the same data points.   It is not as smooth as the Spline method, because interpolated values get less and less influence from the input data points with increased distance; that is, less weight is given.  The IDW has a much rougher and spottier aspect because the influence of a single data point rapidly diminishes with distance away from it.  All of the small dots in this map are centered around input data points (not shown in this view) that are isolated enough from other points that their weight is felt only in their immediate vicinities.  The more extensive areas of color are the result of the combined influence of input data that are more densely arrange,  and of similar values.

Both IDW and Spline interpolation honor the input data, that is, the data points retain their original values.