Spatial Interpolation Methods: A Review

Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished. Traditionally, point interpolation is applied to isarithmic, that is, contour mapping and areal interpolation to isopleth mapping. Recently, areal interpolation techniques have been used to obtain data for a set of administrative or political districts from another set of districts whose boundaries do not coincide. For point interpolation, the numerous methods may further be classified into exact and approximate. Exact methods include most distance-weighting methods, Kriging, spline interpolation, interpolating polynomials, and finite-difference methods. Approximate methods include power-series trend models, Fourier models, distance-weighted least-squares, and least-squares fitting with splines. Areal interpolation methods, on the other hand, are classified according to whether they preserve volume. Traditional areal interpolation methods which utilize point interpolation procedures are not volume-preserving, whereas the map overlay and pycnophylactic methods are. It is shown that methods possessing the volume-preserving property generally outperform those that do not.