Techniques for modeling population related raster databases
D. Martin and I. Bracken
    The techniques used for modeling population using raster databases are based on previous concepts introduced by Bracken and Martin (1989). This article focuses more on the technique for generating such raster models by using point data such as census enumeration centroids, unit postal code locations, or user defined data points. Bracken and Martin note that although the locations of these summary points are not necessarily determined by precise methods, surface estimation algorithms are required for the fuzzy nature of the input data. The approach to the model involves the redistribution of population counts from the input data points into the cells of an output grid. This is done by positioning a window over each data point in turn; the size of the widow varies according to the local densities of the points in order to provide an estimate of the size of the areal unit represented by the current point. The count associated with the current point is then distributed into the cells falling within the window according to weightings derived from a distance-decay function.

    Two types of errors arise from this model, locational errors and attribute estimation errors. Locational errors arise from the incorrect estimation of the spatial extent of populated areas that could be due to a lack of detail in the input data which may cause small settlements to be missed. In addition, the over specification or under specification of window size will cause the population associated with a data point to be spread too far or not far enough. Attribute estimation errors arise from the assignment of incorrect population counts to individual cells from the lack of detail of input data, or the specification of an inappropriate distance decay function.

Towards Improved Visualization of Socio-Economic Data
I. Bracken
    The goal of this paper is to create a surface model from the combination of transformed zone-based census data and point-based address data into a data structure that represents population distribution as a continuous surface. Using a kernel-based analysis, a plausible distribution according to the local density of a given set of point data locations can be generated using the Bracken and Martin methodology. Where population information is not directly captured in raster form, which is often the case, the data can be aggregated and made available in irregular reporting units. Maps of large areas can simply use the centroid of each zone as a locating point for each displayed datum. However, as the scale becomes more local, representation of the spatial distribution begins to break down. Interpretations of resulting displays are therefore highly dependent on scale of visualization in relation to the zonal structure of the data.

Generating and mapping population density surfaces within a geographical information system
M. Langford & D. Unwin
    Conventional Choropleth - Langford and Unwin outline the limitations of traditional choropleth maps, first being the size of areal zones. Larger areas will produce lower population densities, while smaller areas will produce greater population densities. The zones used to represent density act as filters on the data, smoothing out lows and highs, in effect removing data specialization. And finally, the boundaries of the zones are arbitrary, and do not actually represent borders of the data’s significance.

    Dasymetric Alternative - This approach takes into account additional geographical information in order to provide a more realistic view of the world. An example of this is adjusting the size of choropleth zones with the use of satellite imagery. The remotely sensed data may contain information regarding the location of residential housing. This would remove areas in which no people are present. A problem with this method in particular is that the variance between housing types if difficult to decipher. Displaying data in this manner in 1994 would have produced different results than if it was done in 2003; often technological changes create varying methodologies over time.

   Population Density as a Surface - The advantage to mapping population density as a surface is that “population density is a continuous function even though population itself is discrete.” Instead of calculating population density in a region, it is more reasonable to calculate population density at a point based on a moving area centered at that point. This gives a value based on a search radius from that point. Just as zonal size varies the representation of data on choropleth maps, the search radius varies the representation of population density when displayed as a surface. As a surface, however, the data is represented at individual points, and not for a series of points.

Linkage of the 1981 and 1991 UK Censuses using surface modeling concepts
I. Bracken and D. Martin
    Bracken and Martin use surface modeling as an approach to integrating 1981 and 1991 UK census data. Originally the task seemed rather challenging due to changes in the census geography and definitions, the administration of the census, and the format and nature of the data. By applying surface model techniques however, the two data sets were converted into a single consistent geographic database independent of the two original and inconsistent zonal structures (379).     The 1981 and 1991 census information uses population weighted enumeration district data as geographic referencing for each zone. These centroids are “assumed to represent local summary locations for the distribution of the population and its characteristics” (382). The centroids location is then used by a surface generation technique to assign the population associated with each enumeration district into cells of a regular grid. The population in essence, is redistributed from the centroid locations back to the originally derived location.

    This can be achieved by applying a moving window algorithm which passes over each centroid, performing an analysis of the specific centroids local density and calculating an appropriate distance function for the local redistribution. This results in the creation of a matrix of cells each of which contain a population estimate and provide a detailed, unique, geographic model of population distribution which does not have the traditional limits imposed by zonal boundaries.

Defining and delineating the central areas of towns for statistical monitoring using continuous surface representations
M. Thurstain-Goodwin and D. Unwin
   The aim of Goodwin and Unwin in this article is to develop a method in order to generate consistent statistical areas of town centre activity using GIS and existing government data to facilitate the recognition and delineation of town centers using socio-economic data represented by continuous density surfaces. Their method is based on using density information based on the presence of pedestrian gateways, relative lack of residential population, visitor attractions, activities and facilities component, and commercial offices to calculate what they call the Intensity of Town Centeredness (ITC). Unit Postal Codes (UPC) were chosen as the basis for data geo-referencing because it is possible to gain an immediate impression of both the distribution and actual density of the phenomenon being studied. In addition the spatial resolution of UPC’s are much higher than that achieved using Enumeration Districts (ED). The methodology uses kernel density estimation to create continuous surface representations from the Bracken and Martin model. By analyzing the peaks of the surface, the geographic extent of town centers can be delineated.

Policy-relevant Surfaced Data on Population Distribution and Characteristics
M. Coombes and S. Raybould
Coombes and Raybould discuss the surface modeling method known as a constrained moving window method. If a city is further divided by its districts a window can be moved over each specific area. Each district can thus become the “center of its own window” (335). Overlaps will result between the various districts windows. The final values for the district can simply be recalculated by using the raw values throughout the window. This new smoothed value not only emphasizes the information contained in the raw data values but also of “the more immediately relevant areas in its window” (335).

    A number of weaknesses lie in using this method and are identified by the authors. The parameters in the study are judgment based. The values in the data set are more unreliably estimated, and an additional step in analysis is introduced. The strengths of this method include: the creation of overlapping rather than fixed zones, producing less cliff edges, and the generation of more discrete values for each district.

Population Density Surface: A New Approach to an Old Problem
Z. Moon and F. Farmer
    This article focuses on the combination of geospatial data with Census data in order to determine human settlement patterns. A population density surface is applied. This method of representing population as a surface phenomenon has a number of significant advantages. It provides spatial detail that is more complex than that which is provided by zonal or boundary data. An area of analysis can be “based on theoretical considerations without the limitations of Census geographical hierarchy” (40). The researcher can thus draw boundaries without restrictions. In addition, new analysis which could not have been achieved with traditional zonal data becomes possible. This includes measures of contiguity, distance, and spatial differentiation (40). By utilizing a population density surface, a greater degree of spatial differentiation is observed a as well as a greater deal of local specificity.

    The method Moon And Farmer suggest for creating a population surface density model involve using an algorithm to allocate population density distribution data from blocks and existing residential structures. Centroids are allocated to the polygons which represent blocks. The residential structures are assigned to their respective blocks. The population is then assigned “to the centroids of the blocks inside incorporated place boundaries, to centroids of those blocks that have a nonzero population but no residential structure, and to the residential structures in blocks outside incorporated places “(44).

Annotated Bibliography: Continuous Surface Model . Remotely Sensed Imagery . Population Distribution
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