1) Although our case study deals specifically with reliability, we feel that many of the principles discussed in this paper can be applied to other types of metadata. Metadata is a broad term that typically encompasses and "data about data." In this paper we will most often be referring specifically to reliability estimates when we use the term metadata.
2) Marr (1985, p. 111) defines a representation as "a formal system for making explicit certain entities or types of information, together with the specification of how the system does this."
3) The Alexandria project (an effort directed to development of a theoretical basis for creating digital spatial libraries) is one example of a system in which an effort is being made to follow the abstract worlds model (Buttenfield and Beard 1994). A goal of this system is to support queries of the sort, "what impact did the 1993 flooding of the Mississippi have on agriculture?".
4) These data were made available by the National Center for Geographic Information and Analysis through their Visualization of Data Quality Challenge. We would like to thank them and the EPA for facilitating access to this information.
5) The report completed by the Chesapeake Bay Program (CBP) project team gives details on the interpolation procedure that they used to estimate DIN both horizontally and vertically throughout the Bay (CBP 1992). The procedure began by dividing the Bay into a 1-km by 1-km grid horizontally and dividing each grid zone into 1-meter cells vertically to arrive at a set of shallow but broad volumetric cells filling the Bay. A two-stage interpolation method was applied. The first stage involved linear interpolation to estimate values for a sequence of depths at each sample location. Once these estimates were obtained, a simple inverse distance-squared weighting of the nearest four samples was used horizontally to generate a grid of values at each depth.
6) For discussion of error/reliability estimation methods related to continuous geographic phenomena see Cressie (1991); Heuvelink (1993), and Hootsmans (1996).
7) IDL is a data manipulation language that was created by IMSL. It is now owned and distributed by Research Systems, Inc. For further information about IDL see Research Systems’ World Wide Web page at http://www.rsinc.com.
8) See MacEachren (1995) for a more complete discussion of the role of mental schemata in map design and interpretation.
9) Although Schweizer and Goodchild (1992) did not find this scheme particularly effective, they mistakenly assumed that value (rather than saturation) produces a logical match to uncertainty. In addition, their maps used 15 steps of both value and saturation. Most map differences on this 225 category map, therefore, were impossible to see. Brown and van Elzakker (1993) contend that up to four saturation steps can work on bivariate maps.
10) An updated version of IDL does allow true volume representation and therefore three-dimensional interpolation is possible.
11) Such collaboration between cartographers and others in the broader field of scientific visualization are being facilitated by the International Cartography Association's Commission on Visualization. This Commission has just initiated a 4-year collaboration with the American Computer Machinery’s SIGGRAPH Special interest group to explore how viewpoints and techniques from the computer graphics community can be effectively applied to cartographic and spatial data sets.