A Comparative Analysis of Areal Interpolation Methods

Over the years many approaches to areal interpolation have been developed and utilized. They range from the simple 2-D areal weighing method which uses only the spatial Z variable being processed, to more sophisticated approaches which use auxiliary variable(s) to provide more specificity to the results. In the research reported here, four promising approaches are implemented and comparatively tested. These approaches have widely varying conceptual foundations, and different auxiliary variables, if used. The areal weighing reflects many earlier methods which assumes uniform distributions of the spatial Z variable, and does not use any auxiliary variable. Tobler's pycnophylactic method uses a volumetric preservation approach, which assumes spatial Z variable is heterogeneously distributed, but does not use any auxiliary variable. The traditional dasymetric method of Wright is used with remote sensing spectral data of land use. Xie's road network hierarchically weighted interpolation uses the road network as the auxiliary variable, and assumes that population density is related to the class of the road, and to the density of the road network. The research design implemented here uses Census population distributions at different levels in the hierarchy as the source and target variables analyzed. The source zone population is taken at the Census Tract level, and the target zones are specified at the Census Block Group level in the hierarchy. The first two tests use only the Census population Z data, and no auxiliary variables, whereas the next uses remotely sensed land use data as the auxiliary data variable, and the fourth test utilizes the road network hierarchy as the auxiliary variable. The paper reports on the findings from these tests, and then interprets them in a spatial setting in terms of accuracy and effectiveness. This research points to the network method as the most accurate of the areal interpolation methods tested in this research.