A cartographic modeling approach to isopleth mapping

Isopleth maps depict different types of standardized data densities, general ratios/rates, and proportions/percentages. In this study, we describe different paths each type of standardized data takes to construct isoplethic surfaces in a cartographic modeling framework. As suggested in previous research, an area-based pycnophylactic interpolator is preferred to point interpolators in isopleth mapping not only because it preserves the total volume in each aggregation unit but also because it is non-parametric and is able to incorporate ancillary data to increase the accuracy of a surface representation. Here, a general pycnophylactic method is used to generate isopleth maps of density surfaces, but a hybrid approach is proposed to address the small denominator problem that arises when mapping ratio/rate and proportion/percentage surfaces. Finally, we propose a value-by-perspective height mapping procedure to resolve the visual equalization problem associated with ratio/rate and proportion/percentage surfaces that enable one to distinguish among high rate/large denominator, high rate/small denominator, low rate/large denominator, and low rate/small denominator regions of the surface.