This thesis defines a novel and intuitive method to visually represent attribute uncertainty, and spatial boundary uncertainty generated from choropleth maps. Like all data, it is not possible to know exactly how far from the truth spatial data used for choropleth mapping is. When spatial data is used in a decision-making context a visual representation of data correctness may become a valuable addition. As an example, the visualisation of uncertainty is illustrated using choropleth mapping techniques superimposed on New Zealand 2001 census data, but other spatial datasets could have been employed. Both attribute and spatial uncertainty are considered, with Monte Carlo statistical simulations being used to model attribute uncertainty. A visualisation technique to manage certain choropleth spatial boundary issues (i.e. the modifiable areal unit problem - MAUP) and uncertainty in attribute data is introduced, especially catering for attribute and choropleth spatial boundary uncertainty simultaneously. The new uncertainty visualisation method uses the quadtree spatial data model (SDM) in a novel manner. It is shown that by adapting the quadtree SDM to divide according to uncertainty levels possessed by attributes (associated with areal units), rather than divide on the basis of homogeneous regions (as the original quadtree design was intended), a measure of attribute and choropleth spatial boundary uncertainty can be exhibited. The variable cell size of the structure expresses uncertainty, with larger cell size indicating large uncertainty, and vice versa. The new quadtree SDM was termed the trustree. A software suite called TRUST v1.0 (The Representation of Uncertainty using Scale-unspecific Tessellations) was developed to create square trustree visualisations. The visual appeal and representational accuracy of the trustree was investigated. Representative accuracy and visual appeal increased when using hexagonal tessellations instead of the quadtree�s traditional square tessellation. In particular, the Hexagonal or Rhombus (HoR) quadtree designed by Bell et al. (1989) was used to programme TRUST v1.1. Using the HoR quadtree in rhombic mode (TRUST v1.1.1) produced Orbison�s optical illusion, so it was disregarded. However, the HoR trustree (the hexagonal tessellation produced by TRUST v1.1.2) was adopted for further research and user assessment. When assessed using an Internet survey, the HoR trustree adequately displayed choropleth spatial boundary uncertainty, but not attribute uncertainty. New trustree visualisations, the value-by-area (VBA) trustree and adjacent HoR trustree were developed to help increase the expression of attribute uncertainty. Upon reassessment, the new trustree visualisations were deemed usable to express attribute uncertainty and choropleth spatial boundary uncertainty at a modest 58% usable (HoR trustree), 80% usable (VBA trustree) and 85% usable (adjacent HoR trustree). A usability test (where participants were asked to spot different levels of uncertainty) validated these results, whereby the HoR trustree achieved a 65% accuracy level and the VBA trustree achieved an 80% accuracy level. The user assessments helped to highlight that the trustree could be used in two ways, to express detail within or clutter over areal units. The HoR trustree showed (1) a level of detail (or resolution) metaphor, where more detail represented more accuracy and/or the reverse, (2) a metaphor of clutter, where the data structure output was sufficiently dense as to cover spatial information, in effect hiding uncertain areas. Further Internet survey testing showed the trustree tessellation works better when representing a metaphor of detail. Attribute and spatial uncertainty can be effectively expressed depending on the tessellation level used. Overall, the new TRUST suite visualisations compare favourably with existing uncertainty visualisation techniques. Some uncertainty visualisation methods consistently performed better than the TRUST visualisations such as blinking areas, adjacent value and non-continuous cartograms. Other methods like colour saturation, image sharpness and a three-dimensional surface frequently performed with less usability. Therefore, the TRUST visualisations have found their place amongst other uncertainty visualisation methods. However, survey results showed that TRUST is a viable option for visualising two forms of uncertainty - attribute and spatial uncertainty. No other visualisation method has these capabilities. Further research could include a laboratory assessment of TRUST and also incorporating vagueness and temporal uncertainty concepts. Additionally, end-user testing could provide a valuable insight into uncertainty visualisation for everyday use. Adopting uncertainty methods to uncertainty, such as the technique presented here, into the mainstream decision making environment could be considered a fundamental objective for future investigation in spatial studies.

This thesis defines a novel and intuitive method to visually represent attribute uncertainty, and spatial boundary uncertainty generated from choropleth maps. Like all data, it is not possible to know exactly how far from the truth spatial data used for choropleth mapping is. When spatial data is used in a decision-making context a visual representation of data correctness may become a valuable addition. As an example, the visualisation of uncertainty is illustrated using choropleth mapping techniques superimposed on New Zealand 2001 census data, but other spatial datasets could have been employed. Both attribute and spatial uncertainty are considered, with Monte Carlo statistical simulations being used to model attribute uncertainty. A visualisation technique to manage certain choropleth spatial boundary issues (i.e. the modifiable areal unit problem - MAUP) and uncertainty in attribute data is introduced, especially catering for attribute and choropleth spatial boundary uncertainty simultaneously. The new uncertainty visualisation method uses the quadtree spatial data model (SDM) in a novel manner. It is shown that by adapting the quadtree SDM to divide according to uncertainty levels possessed by attributes (associated with areal units), rather than divide on the basis of homogeneous regions (as the original quadtree design was intended), a measure of attribute and choropleth spatial boundary uncertainty can be exhibited. The variable cell size of the structure expresses uncertainty, with larger cell size indicating large uncertainty, and vice versa. The new quadtree SDM was termed the trustree. A software suite called TRUST v1.0 (The Representation of Uncertainty using Scale-unspecific Tessellations) was developed to create square trustree visualisations. The visual appeal and representational accuracy of the trustree was investigated. Representative accuracy and visual appeal increased when using hexagonal tessellations instead of the quadtree�s traditional square tessellation. In particular, the Hexagonal or Rhombus (HoR) quadtree designed by Bell et al. (1989) was used to programme TRUST v1.1. Using the HoR quadtree in rhombic mode (TRUST v1.1.1) produced Orbison�s optical illusion, so it was disregarded. However, the HoR trustree (the hexagonal tessellation produced by TRUST v1.1.2) was adopted for further research and user assessment. When assessed using an Internet survey, the HoR trustree adequately displayed choropleth spatial boundary uncertainty, but not attribute uncertainty. New trustree visualisations, the value-by-area (VBA) trustree and adjacent HoR trustree were developed to help increase the expression of attribute uncertainty. Upon reassessment, the new trustree visualisations were deemed usable to express attribute uncertainty and choropleth spatial boundary uncertainty at a modest 58% usable (HoR trustree), 80% usable (VBA trustree) and 85% usable (adjacent HoR trustree). A usability test (where participants were asked to spot different levels of uncertainty) validated these results, whereby the HoR trustree achieved a 65% accuracy level and the VBA trustree achieved an 80% accuracy level. The user assessments helped to highlight that the trustree could be used in two ways, to express detail within or clutter over areal units. The HoR trustree showed (1) a level of detail (or resolution) metaphor, where more detail represented more accuracy and/or the reverse, (2) a metaphor of clutter, where the data structure output was sufficiently dense as to cover spatial information, in effect hiding uncertain areas. Further Internet survey testing showed the trustree tessellation works better when representing a metaphor of detail. Attribute and spatial uncertainty can be effectively expressed depending on the tessellation level used. Overall, the new TRUST suite visualisations compare favourably with existing uncertainty visualisation techniques. Some uncertainty visualisation methods consistently performed better than the TRUST visualisations such as blinking areas, adjacent value and non-continuous cartograms. Other methods like colour saturation, image sharpness and a three-dimensional surface frequently performed with less usability. Therefore, the TRUST visualisations have found their place amongst other uncertainty visualisation methods. However, survey results showed that TRUST is a viable option for visualising two forms of uncertainty - attribute and spatial uncertainty. No other visualisation method has these capabilities. Further research could include a laboratory assessment of TRUST and also incorporating vagueness and temporal uncertainty concepts. Additionally, end-user testing could provide a valuable insight into uncertainty visualisation for everyday use. Adopting uncertainty methods to uncertainty, such as the technique presented here, into the mainstream decision making environment could be considered a fundamental objective for future investigation in spatial studies.