With these analytical map questions in mind, consider the standard representation used in spatial analysis. With some exceptions (to be noted later), the "standard model" consists of an isotropic plane containing points representing geographic objects. Lines, areas and surfaces are sometimes used in spatial statistics (e.g., Getis and Boots 1978). However, it is rare for these objects to be "mixed" so that each geographic object class is appropriately represented; instead, a single representation is usually imposed on all geographic objects. Relationships among these objects typically reduce to a single dimension, namely, distance or some function of distance (time, cost).
Since geographic representations condition the answers we can obtain from analytical map questions, a critical research question is the extent to which geographic representations in spatial analysis have affected our understanding of spatial phenomena and our prescriptive solutions to geographic problems.
Some precedents for a geospatial analysis exist in the spatial analysis literature, particularly within the fuzzy boundary between spatial analysis and GISci. These include the following:
Geographic Space. Terrain can substantially influence the locations of facilities and transportation routes as well as human and physical interactions across space. Goodchild (1977), Goodchild and Lee (1989) and Lombard and Church (1993) develop facility location and routing models that exploit terrain information in digital elevation models. Land use/land cover can have similar effects. Werner (1968) formulates a computational procedure for capturing the "refracting" effect of cost polygons that reflect physical characteristics on transportation routes. Golledge et al. (1969) and Tobler (1976) develop formal representations of perceived/experienced space; these can greatly enhance the analysis of human spatial behavior (see also Egenhofer and Mark 1995). Spatial analysis at regional, national and international scales requires an explicit treatment of the Earth as a sphere. Love, Morris and Wesolowsky (1988) discuss facility location on a sphere while Raskin (1994) discusses more general spatial analytical techniques (including interpolation) on a sphere. Time is also tightly interlinked with geographical space and individuals' perceptions and actions (Egenhofer and Mark 1995; Hägerstrand 1970). Some recent efforts have been directed at implementing space-time frameworks within spatial analysis (Kwan 1998; Miller, 1991, 1998)
Geographic Objects. Miller (1996) discusses expanding location models to include other spatial objects besides points to represent facilities and clients. Okabe and Saddahiro (1994) and Okabe et al (1995) develop spatial statistical procedures that relate points to surfaces and points to networks, respectively. Okabe and Miller (1996) provide support for mixing spatial objects in spatial analysis by developing computational procedures for measuring average, minimum and maximum distances among all possible pairings of points, lines and polygons. Several researchers have developed shape measures (e.g., Boyce and Clark 1964; Massam and Goodchild 1971; Moellering and Rayner 1981; Tobler 1978) for describing and comparing complex geographic objects. Fractals have been used to describe morphology and processes in both physical and human geographic phenomena (see MacLennan et al. 1991).
Geographic Relationships. Other factors besides distance can affect geographic relationships, either independently or in conjunction. For example, both distance and direction can influence knowledge of an environment (e.g., Moore 1970). Peuqeut and Xiang (1987) develop a procedure for computing directional relationships between planar-embedded polygons. Humans often use toplogical relationships among spatial objects as their primary information about geography, with distance and shape information being secondary (Egenhofer and Mark 1995). Formalisms for capturing topological relationships have been developed (e.g., Egenhofer and Franzosa 1995; Egenhofer, Mark and Herring 1994). Boundaries (physical, built, administrative also condition geographic relationships, e.g., the geometry of boundaries can strongly influence spatial interaction models (Griffith 1982). The geographic scale at which behavior occurs can condition all of the relationships mentioned above, at least with respect to human behavior (Gale and Golledge 1982).
The ordering principle for examining spatial analytical problems should be "What is the best way to represent geography?" based on the empirical nature of the geographic space, geographic objects and geographic relationships in the problem domain. After classifying problem domains based on best representations, the current "state-of-the-practice" within each domain should be assessed, i.e., how is geography represented in practice? Systematic differences between the best and current representations must be assessed carefully. Note that this approach treats the best representations as the "gold standard" and views current practice as deviations from that standard.
After determining best representations and typical deviations used in practice, the next questions concern the costs of these deviations and the benefits of achieving more realistic geographies within each problem domain. Is it worth improving geographic representation in the particular problem domain? What is achieved with respect to theoretical insights and improved prescriptive modeling? These questions must be answered in light of the state-of-the-art in GISci and GIS software.
Egenhofer, M. J. and Franzosa, R. D. (1995) "On the equivalence of topological relations," International Journal of Geographical Information Systems, 9, 133-152.
Egenhofer, M. J. and Mark, D. M. (1995) Naïve Geography. National Center for Geographic Information and Analysis, Technical Report 95-8.
Egenhofer, M. J., Mark, D. M. and Herring, J. (1994) The 9-Intersection: Formalism and its Use tor Natural-Language Spatial Predicates. National Center for Geographic Information and Analysis, Technical Report 94-1.
Gale, N. and Golledge, R. G. (1982) "On the subjective partitioning of space," Annals of the Association of American Geographers, 72, 60-67.
Getis, A. and Boots, B. (1978) Models of Spatial Processes: An Approach to the Study of Point, Line and Area Patterns, Cambridge: Cambridge University Press.
Golledge, R. G., Briggs, R. and Demko D. (1969) "The configurations of distances in intra-urban space," Annals of the Association of American Geographers, 85, 134-158.
Goodchild, M. F. (1977) "An evaluation of lattice solutions to the problem of corridor location," Environment and Planning A, 9, 727-738.
Goodchild, M. F. and Lee, J. (1989) "Coverage problems and visibility regions on topographic surfaces," Annals of Operations Research, 18, 175-186.
Griffith, D. A. (1982) "Geometry and spatial interaction," Annals of the Association of American Geographers, 72, 332-346.
Kwan, M. (1998) "Space-time and integral measures of individual accessibility: A comparative analysis using a point-based framework," Geographical Analysis, 30, 191-216.
Lombard, K. and Church, R. L. (1993) "The gateway shortest path problem: Generating alternative routes for a corridor location problem," Geographical Systems, 1, 25-45.
MacLennan, M, Fotheringham, A. S., Batty, M. and Longley, P. A. Fractal Geometry and Spatial Phenomena. National Center for Geographic Information and Analysis Technical Report 91-1.
Massam, B. H. and Goodchild, M. F. (1971) "Temporal trends in the spatial organization of a service agency," Canadian Geographer, 15, 193-206.
Miller, H. J. (1991) "Modeling accessibility using space-time prism concepts within geographical information systems,” International Journal of Geographical Information Systems, 5, 287-301
Miller, H. J. (1996) "GIS and geometric representation in facility location problems," International Journal of Geographical Information Systems, 10, 791-816.
Miller, H. J. (1998) "Measuring space-time accessibility benefits within transportation networks: Basic theory and computational methods," Geographical Analysis, in press.
Moellering, H. and Rayner, J. N. (1981) "The harmonic analysis of spatial shapes using dual axis Fourier shape analysis (DAFSA)," Geographical Analysis, 13, 64-77.
Moore, E. G. (1970) "Some spatial properties of urban contact fields," Geographical Analysis, 2, 376-386.
Nyerges, T. L. (1991) "Analytical map use," Cartography and Geographic Information Systems, 18, 11-22.
Okabe, A. and Miller, H.J. (1996) "Exact computational methods for calculating distances between objects in a cartographic database," Cartography and Geographic Information Systems, 23, 180-195.
Okabe, A. and Sadahiro, Y. (1994) "A statistical method for analyzing the spatial relationship between the distribution of activity points and the distribution of activity," Geographical Analysis, 26 152-167.
Okabe, A., Yomono, H. and Kitamura, M. (1995) "Statistical analysis of the distribution of points on a network," Geographical Analysis, 27, 152-175.
Peuquet, D. J. and Xiang, Z. (1987) "An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane," Pattern Recognition, 20, 65-74.
Raskin, R. G. (1994) Spatial Analysis on the Sphere: A Review, National Center for Geographic Information and Analysis, Technical Report 94-7.
Tobler, W. R. (1976) "The geometry of mental maps," in R. G. Golledge and G. Ruhston (eds.) Spatial Choice and Spatial Behavior, Columbus, OH: Ohio State University Press, 69-82.
Tobler, W. R. (1978) "Comparison of plane forms," Geographical Analysis, 10, 154-162.
Werner, C. (1968) "The law of refraction in transportation geography: Its multivariate extension," Canadian Geographer, 7, 28-40.
Harvey's research and teaching interests include the interface between spatial analysis and geographic information science, particularly with respect to theory and modeling in transportation and locational analysis. A continuing theme in Harvey's research is the use of computational techniques for building more realistic representations of geographical space, spatial relations and spatial behaviors in transportation and locational analysis. These theoretical concerns are closely linked to application-oriented interests in the use of geographic information science for decision support, specifically with respect to GIS design for visualization and querying of complex results from spatial analytical modeling.
Harvey is a recent recipient of the Geoffrey J.D. Hewings Award for Outstanding Young Scholar from the North American Regional Science Council (1997). He has also received the Springer-Verlag Award from the Western Regional Science Association (1996) and the ESRI Award for Best Scientific Contribution to GIS from the American Society for Photogrammetry and Remote Sensing (1996; with J. Lowry and G. Hepner).
Harvey serves on the editorial boards of Geographical Analysis, Journal
of Regional Science, International Journal of Geographical Information
Science and Transportation. He is the Chair of the Mathematical Modeling/Quantitative
Methods Specialty Group of the Association of American Geographers.
Harvey is also an active member of the University Consortium for Geographic
Information Science, having served on the Education Committee and currently
participating in the Model GIS Curriculum Working Group.
1996. Harvey J. Miller and John D. Storm, "GIS design for network equilibrium-based travel demand models," Transportation Research C, 4C, 373-389.
1996. Harvey J. Miller, "GIS and geometric representation in facility location problems," International Journal of Geographical Information Systems, 10, 791-816.
1996. Atsuyuki Okabe and Harvey J. Miller, "Exact computational methods for calculating distances between objects in a cartographic database," Cartography and Geographic Information Systems, 23, 180-195.
1995. John H. Lowry, Harvey J. Miller and George F. Hepner, "A GIS-based sensitivity analysis of community vulnerability to hazardous contaminants on the Mexico/U.S. border," Photogrammetric Engineering and Remote Sensing (Special GIS Issue), 61, 1347-1359
1991. Harvey J. Miller, "Modeling accessibility using space-time prism
concepts within geographical information systems,” International Journal
of Geographical Information Systems, 5, 287-301.