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Intelligent dasymetric mapping and its application to areal interpolation.

Article Excerpt
Introduction

There has been much recent research on areal interpolation of population data. Much of this interest has been driven by demand for small-area population estimates for regions in which only relatively coarse resolution population data can readily be obtained. Such data sets are useful in a wide range of applications, such as emergency planning and management (Dobson et al. 2000), public health (Hay et al. 2005), and monitoring global population (Sutton et al. 2001). The increasing volume and availability of remotely sensed imagery, which has been shown to indicate population distribution (Liu 2003; Holt et al. 2004; Wu et al. 2005), has driven much of the recent research in areal interpolation of population.

A prominent method in areal interpolation is dasymetric mapping, defined here generally as the use of an ancillary data set to disaggregate coarse resolution population data to a finer resolution (Eicher and Brewer 2001). Recent research suggests that dasymetric mapping can provide more accurate small-area population estimates than many areal interpolation techniques that do not use ancillary data (Mrozinski and Cromley 1999; Gregory, 2002). However, this research has not identified an optimal methodology for specifying the functional relationship of the ancillary data with population density. In traditional dasymetric mapping approaches, this relationship has been specified subjectively by the analyst (Wright 1936; Eicher and Brewer 2001). More recently, statistical methods have been used to characterize this relationship (Goodchild et al. 1993; Langford et al. 1991).

In previous research, we described the development of an algorithm for dasymetric mapping that relies on sampling the source population data to quantify the population density of individual ancillary data classes (Mennis 2003; Mennis and Hultgren 2005). Here, we extend this previous research to present a new "intelligent" dasymetric mapping (IDM) technique that supports a variety of methods for characterizing the relationship between the ancillary data and underlying statistical surface. We refer to the technique as intelligent because an analyst may: 1) establish this relationship subjectively using their own domain knowledge; 2) extract this relationship from the data using a novel empirical sampling technique; or 3) combine the subjective and empirically based methods. The IDM method is implemented as a geographic information system (GIS) extension that facilitates the parameterization of the technique and returns a set of statistics that summarize the quality of the resulting dasymetric map. As a case study, IDM is used to redistribute U.S. Census tract-level data for four population variables for the Denver, Colorado, region to sub-tract units using ancillary land cover data. U.S. Census block-level data for the same region are used to analyze the accuracy of the derived dasymetric map. Different parameterizations of IDM are compared with other, conventional areal interpolation methods.

Previous Research in Dasymetric Mapping and Areal Interpolation

To our knowledge, the earliest reference to dasymetric mapping is the 1922 population map of European Russia by Russian cartographer Semenov Tian-Shansky (for discussion, see Fabrikant's (2003) and Bielecka's (2005) readings of the work of Preobrazenski (1954) and (1956), respectively). J.K. Wright (1936) popularized dasymetric mapping in the U.S. and is often incorrectly cited as its inventor, though he noted the Russian origin of the term "dasymetric" (Wright 1936, p. 104). Modern cartography textbooks define a dasymetric map as one that displays statistical surface data by exhaustively partitioning space into zones that reflect the underlying statistical surface variation (e.g., Dent 1999; Slocum et al. 2003). Ideally, the zones in a dasymetric map should be as near to homogeneous in character as possible, having near constant values within, and having boundaries coincident with, the surface's steepest escarpments.

Dasymetric mapping as a procedure is applied to data sets for which the underlying statistical surface is unknown, but for which aggregated data already exist, though the zones of aggregation are not derived from the variation in the underlying statistical surface but are rather the result of some convenience of enumeration. The process of dasymetric mapping is thus the transformation of data from the arbitrary zones of data aggregation to a dasymetric map in order to recover and depict the underlying statistical surface. In dasymetric mapping, the transformation of data from the arbitrary zones of the original source data to the meaningful zones of the dasymetric map incorporates the use of an ancillary data set that is separate from, but related to, the variation in the statistical surface (Eicher and Brewer 2001). Dasymetric mapping therefore has a close relationship to areal interpolation--the transformation of data from a set of source zones to a set of target zones with different geometry (Goodchild and Lam 1980).

Recent research in dasymetric mapping has been subsumed in large measure under the topic of areal interpolation. Mrozinski and Cromley (1999) provide a helpful typology of areal interpolation within which dasymetric mapping may be placed. The typology delineates methods for combining choropleth and area-class maps; in the latter case, zone boundaries demark regions of relatively homogeneous character (Mark and Csillig 1989). Mrozinski and Cromley (1999) distinguish between the "alternate geography" problem, in which areal interpolation is used to transform data from the choropleth map source zones to the area-class map target zones, and the "polygon overlay" problem, in which the target zones are formed by the intersection of the choropleth and area-class maps.

The most basic method for areal interpolation is areal weighting, in which a homogeneous distribution of the data throughout each source zone is assumed. Each source zone therefore contributes to the target zone a portion of its data proportional to the percentage of its area that the target zone occupies. In the case of the alternate geography problem, if we denote a choropleth source zone s and an area-class map zone z, then the target zone t = z. The estimation of the count for the target zone is:

[[??].sub.t] = [n.summation over (s=1)][y.sub.s][A.sub.s[intersection]z]/[A.sub.s] (1)

where:

[[??].sub.t] = the estimated count of the target zone;

[y.sub.s] = the count of the source zone;

[A.sub.s[intersection]z] = the area of the intersection between the source and target zone;

[A.sub.s] = the area of the source zone; and

n = the number of source zones with which z overlaps (Goodchild and Lam 1980).

In the polygon overlay problem, where t = s[intersection]z and each target zone intersects one and only one source zone, Equation (1) may be simplified to read:

[[??].sub.t] = [y.sub.s][A.sub.t]/[A.sub.s] (2)

where [A.sub.t] is the area of the target zone.

Dasymetric mapping can be considered an approach to the polygon overlay areal interpolation problem which seeks to improve on areal weighting by establishing a relationship between the underlying statistical surface and the different classes contained within the area-class map. Dasymetric areal interpolation techniques can be distinguished from other areal interpolation approaches that either do not make use of ancillary data or do not incorporate information regarding the different ancillary classes, such as areal weighting, distance-weighted interpolation of areal data mapped to point locations (Martin 1989), and smooth pycnophylactic interpolation (Tobler 1979).

Perhaps the most common dasymetric mapping method is the traditional binary method, in which ancillary data classes are regarded as either populated or unpopulated (Eicher and Brewer 2001). Other traditional dasymetric methods include the class percent and limiting variable methods (Wright 1936; McCleary 1969; Eicher and Brewer 2001). These traditional methods have been adapted for use with remotely sensed imagery (Mennis 2003; Holt et al. 2004) and, more recently, for road network data (Hawley and Moellering 2005; Reibel and Bufalino 2005). Other researchers have specified the relationship between the underlying statistical surface and the ancillary data classes using regression (Langford et. al. 1991; Goodchild et al. 1993; Yuan et al. 1997), the expectation/maximization (EM; Dempster et al. 1977) algorithm (Flowerdew et al. 1991; Bloom et al. 1996), and the use of maximum likelihood estimation in a spatial interaction model (Mrozinski and Cromley 1999).

Research...

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