Types of Interpolation

The aggregation or interpolation of spatial data into a prescribed set of polygons falls into two basic groups: point to polygon methods, and polygon to polygon methods.

Non-Volume preserving interpolation

The first group of methods, using point to polygon interpolation, is a traditional approach (Lam, 1983) in which either a grid of points or a set of centroids are assigned values to represent a source zone. The intersection of these source points with a set of target polygons is calculated. One or more points may fall within a target polygon, after which the values for these points are averaged to obtain a target polygon value. This is referred to as Non-Volume preserving interpolation. This approach has been shown to be a less than satisfactory method (Lam, 1983), because the volume or area of source zones is not taken into account during the averaging of source point values. Additionally, the spatial arrangement and density of points chosen to represent source zones may seriously affect the outcome of Non-Volume preserving interpolation.

Volume preserving interpolation

Volume Preserving interpolation uses polygon to polygon relationships to overcome the deficiencies of point to polygon interpolation. Also called area-based areal interpolation (Lam, 1983) this method preserves the volume or area of source zones and target zones, and uses these area values within the interpolation process. The process involves overlaying source zones on target zones to create intersection or union zones. The area of these union zones can then be compared to the areas of either the associated source zone, or the associated target zone.

References

Lam, N.S. 1983.
Spatial Interpolation Methods: A Review. The American Cartographer 10:129-50
Source: Ballard and Schut., 1995