Compare methods

	Areal Interpolation	Population Potential Model
Field	Human Geography	Human Geography
Family	Process / pipeline	Process / pipeline
Year of origin	1979	1947
Originator	Waldo Tobler (pycnophylactic) and Michael Goodchild & Nina Lam (areal weighting)	John Q. Stewart
Type	Method for transferring attribute data between incompatible sets of areal units	Social-physics measure of the cumulative influence of population at a location
Seminal source	Tobler, W. R. (1979). Smooth pycnophylactic interpolation for geographical regions. Journal of the American Statistical Association, 74(367), 519–530.	Stewart, J. Q. (1947). Empirical mathematical rules concerning the distribution and equilibrium of population. Geographical Review, 37(3), 461–485.
Aliases	Cross-Areal Estimation, Zone-to-Zone Interpolation, Spatial Data Transfer	Potential of Population, Market Potential Model, Demographic Potential, Stewart Potential
Related	4	4
Summary	Areal interpolation is the family of methods for transferring attribute data — populations, counts, rates — from one set of areal units (the source zones) onto a different, incompatible set (the target zones). The need arises constantly in geography because census tracts, postal zones, electoral districts, and grid cells rarely align, yet analysts must combine data reported on mismatched geographies. The methods range from simple area-proportional weighting through ancillary-informed dasymetric refinement to Waldo Tobler's 1979 volume-preserving pycnophylactic smoothing, each trading simplicity for accuracy.	The population potential model measures the cumulative influence that all of a region's population exerts on a given point, weighting each place's population inversely by its distance. Introduced by the astronomer-turned-social-scientist John Q. Stewart in 1947 as part of his 'social physics', it borrows the gravitational-potential analogy from physics: every population mass contributes potential at a point in proportion to its size and in inverse proportion to its distance. Summed across all places, the result is a smooth potential surface that maps relative accessibility, market reach, and demographic pressure.