Model

Definition: A model is a representation of some place, process, or set of interactions.  A model may be physical, quantitative, or conceptual.  Models specify the boundaries of a system of interest in time and space, indicate what the components of the system are, and define how the components can interact with one another.  Finally, a model specifies the nature of the changes or any limits to change that the system can undergo.  Models are based on assumptions that reflect the choices of what is included and left out of the model, and how the relationships are structured. 

Examples: A map is a model of the spatial relationships deemed important in a spatial system.  Roadmaps, maps of historically important sites, or a depiction of subway stops are examples of maps as models.  Models may also exist in the form of equations such as those that describe the dynamics and limitations of biological populations or of interacting populations or predators and prey.  Models may be physical, as in the case of an architectural balsa wood and cardboard model of a building or neighborhood, or an experimental setup to examine how the conditions in a stream channel influence biological foodwebs.

Figure 1. An example of a conceptual model of interactions.  Based on the pulse-press model template for coupled natural-human systems (Collins et al. 2011), this specific example shows expected relationships between riparian structures and functions, ecosystem services, and human actions.  See Cadenasso et al. (2008) for further explanation of the relationships involved in this particular case.

 

δ φ/δt = D(δ² φ/δx²)

 

Figure 2.  Fick’s second law of diffusion.  This model, in the form of an equation, describes the change in concentration (φ) of a substance over time (t). D = the diffusion coefficient and x is the position along the diffusion path.

Figure 3.  Brian McGrath (L) and Victoria Marshall (R), working with M.L. Cadenasso and Phanat Xanamane (not pictured) to construct a model of urban land cover integrating the cover and type of surfaces, vegetation, and buildings.  The resulting model has been called a “periodic table” of urban land cover.  See Cadenasso et al. (2007) for details of the components of the model.

 

Why important: All disciplines and practices use models.  However, how those models are used and constructed differs between disciplines.  In urban systems models range from the informal pictures of a neighborhood by its residents, to the policies employed by different levels of government or different jurisdictions.  Models of urban systems can emphasize the social, the economic, or environmental aspects of the metropolis, and may have different spatial limits.  Models can assume that the structures and processes within their boundaries are aggregated and uniform, or the models may account for the differences among institutional agents or spatial patches.  Many models of urban systems are beginning to treat them as complex systems capable of self organizations, in contrast to classical models of top down control by a narrow function, such as economy or law.

For more information: 

• Band, L.E., C.L. Tague, S.E. Brun, D.E. Tennenbaum, and R.A. Fernandes. 2000. Modeling watersheds as spatial object hierarchies: structure and dynamics. Transactions in Geographic Information Systems 4 181-196.
• Batty, M. 1995. New ways of looking at cities. Nature 377:574.
• Shane, D.G. 2005. Recombinant urbanism: conceptual modeling in architecture, urban design, and city theory. John Wiley & Sons, Hoboken.
• McGrath, B.P. 2008. Digital modelling for urban design. Wiley, London.
• Cadenasso, M.L., S.T.A. Pickett, and K. Schwarz.  2007.  Spatial heterogeneity in urban ecosystems: Reconceptualizing land cover and a framework for classification. Frontiers in Ecology and Evolution 5: 80-88.
• Kennedy, C., J. Cuddihy, and J. Engel-Yan. 2007. The changing metabolism of cities. Journal of Industrial Ecology 11:43-59.
• Cadenasso, M.L., S.T.A. Pickett, P.M. Groffman, G.S. Brush, M.F. Galvin, J.M. Grove, G. Hagar, V. Marshall, B.P. McGrath, J. O’Neil-Dunne, W.P. Stack, A.R. Troy.  2008.  Exchanges across land-water-scape boundaries in urban systems: Strategies for reducing nitrate pollution.  Annals of the New York Academy of Sciences 1134: 213-232.
• Collins, S. L., S. R. Carpenter, S. M. Swinton, D. E. Orenstein, D. L. Childers, T. L. Gragson, N. B. Grimm, J. M. Grove, S. L. Harlan, J. P. Kaye, A. K. Knapp, G. P. Kofinas, J. J. Magnuson, W. H. McDowell, J. M. Melack, L. A. Ogden, G. P. Robertson, M. D. Smith, and A. C. Whitmer. 2011. An integrated conceptual framework for long-term social-ecological research. Frontiers in Ecology and Environment 9:351-357.