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Exploring the hidden potential of common spatial data models to visualize uncertainty.

Article Excerpt
Introduction

Before visualization, spatial data are stored as text or numbers. Decisionmakers viewing raw data must perform their own mental visualization if they wish to discover relationships or patterns in the data. Geographic visualization (or geovisualization--MacEachren 1995) is visualization of geographic or raw spatial data, stored digitally, which becomes a geo-visual representation (Andrienko et al. 2000). While visualization of information can provide different ways to express data there are also different ways for storing spatial data. Spatial data models (SDMs) such as raster or vector are usually used to store and retrieve spatial data. Depending on how a SDM is used, different visualizations may be possible. Therefore, SDMs can have an influence on how spatial data are visualized.

An underlying objective of the research reported here was to determine how different SDMs--the vector, raster, and quadtree SDMs--store and display information. Of interest here is whether there is a relationship between how an SDM stores spatial data and displays their visualizations. If there is such a relationship, one needs to examine the available protocols for visualizing specific SDMs and how a given protocol impacts the storing and visualization of spatial data.

We examined how a trustree may use the quadtree SDM in a hitherto unexplored mode. Comparisons were made with other SDMs under quasi similarity conditions to determine whether divergence from a traditional use of an SDM would change the quasi similarity measure. The research concept we followed is illustrated in Figure 1, where the question marks represent a different Tp for each SDM. Additionally, the quadtree SDM was changed to use the trustree rules and then the Tp was reassessed checking for transformation differences between the SDMs.

[FIGURE 1 OMITTED]

The remainder of this paper is organized as follows. We begin with a general discussion of uncertainty and its visualization and then briefly outline the concept of using a trustree to express attribute and choropleth spatial boundary uncertainty. In the following section, we examine the models currently available for visualizing uncertainty, discuss techniques for establishing uncertainty, and look at the transformation processes different SDMs use for storage and display. An analysis of the results is followed by conclusions and recommendations for further research.

Uncertainty

GIScience is commonly defined as the "difference between the actual geographical world data in real time and their modeled visualization in a geographical information system (GIS) (Goodchild 1992; Hunter and Beard 1992; Hunter and Goodchild 1997). Three main uncertainties are noted when modeling phenomena in GIS--attribute, spatial, and temporal uncertainty. Attribute uncertainty is the difference between the actual characteristic of a feature and the corresponding attribute data stored for GIS use. Spatial uncertainty is the difference between an actual point, line, or area of interest and its location in a GIS model. Temporal uncertainty is defined as the time difference between when original data are collected for spatial use and the current date (not considered in this research).

A new visualization of attribute and choropleth spatial boundary uncertainty was developed, based on Kardos et al. (2005). To provide an explanation of the new representation method, let us now consider the quadtree SDM (as defined by Samet 1990). Assuming the quadtree, which is typically used for storing and retrieving spatial data, were to be used outside of its traditional context, would this affect the protocol by which we traditionally prepare and view quadtrees? For example, could the quadtree be used to recursively decompose a raster spatial image into areal units, rather than the traditional quadrants? Normally, the quadtree SDM would divide if an area within its bounding box is non-homogenous. However, the quadtree could be divided using a different set of basic rules and assumptions, and this division would be driven by the attribute uncertainty data associated with each areal unit in a study area.

We modeled attribute uncertainty using Monte Carlo (MC) statistical methods (Hammersley and Handscomb 1964). The research was conducted using data from the 2001 New Zealand census; post enumeration data were obtained as well to validate information for the areal units. A detailed description of modeling attribute uncertainty can be found in Kardos et al. (2005).

Spatial uncertainty in the context of this research dealt with the subjectivity associated with choropleth spatial boundaries (referred to as spatial uncertainty for the remainder of this paper). Spatial uncertainty in choropleth maps (see Dent 1993 for an overview of choropleth mapping) can arise due to:

* Unrealistic breaks between areal unit boundaries;

* Unrealistic breaks between class values; and

* Choropleth generalization of a single value or value range for areal units.

Trustree

As mentioned above, MC simulations were conducted to obtain attribute uncertainty values...

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