Three Presentations on Geographical Analysis and Modeling: Non- Isotropic Geographic Modeling; Speculations on the Geometry of Geography; and Global Spatial Analysis (93-1)

Abstract

Five of the most important and useful theoretical models in the study of geography are, in historical order: the Von Thunen model of agricultural land use; Weber's model of industrial location; Walter Christaller's central place formulation; the gravity model of spatial interaction; and Hagerstrand's model of the geographical spread of innovation.All of these models are of fundamental importance in understanding the world around us.They also have in common the fact that they simplify reality by invoking an isotropic geographic space.Of course they do this to varying degree, and some then relax this assumption.Most of them are also computationally explicit models, again to varying degrees.Both of these aspects of the models are the subject of my discussion.Current Geographic Information Systems have the potential of overcoming the isotropic plane assumption, even though the elegant pedagogic simplicity of models using this assumption will always obtain.Consider first the Von Thunen model.Here agricultural land use patterns are derived as a function of market price, transport cost to market, and agricultural production costs.Under the isotropic assumption, and a single market, the geographic arrangment of crops and land uses takes the concentric form.Years ago, for an Economic Geography class near Detroit, I wrote a simple computer program to demonstrate this, with five commodities, including strawberries, wheat, other foodstuffs, and Cadillacs.Given the other inputs I could demonstrate computer printouts of circularly arranged optimal land uses, and could even run the program with multiple market places to get mixtures of partially concentric patterns, and could include a climatic gradient to get non-circular patterns.All this was done off-line, in a batch environment (circa 1965).My computer program could not incorporate positional variations in transportation cost, even though Von Thunen himself gave such a demonstration introducing a river into the geographic space (Figure I).Several GISs can now provide more realistic calculations.One of our graduate students, R. Dodson, has implemented the Von Thunen model within the IDRISI system, and has done some work on an implementation of the Weber model.This system allows variable transportation costs to be included.However he still uses synthetic landscapes.But this need not be the case.To see how this can be improved upon, I would like to contrast the situation with a popular computer pastime.What I have in mind is the "Flight Simulator" in which one can pretend to be an airplane pilot.The geographically interesting part is that one can purchase a variety of landscapes, and "fly" around these.Each of these "landscapes" or airport vicinities, can be purchased separately.Imagine having the same thing for the USA, or the world, and running Von Thunen, Weber, Christaller, or Hagerstand models on real landscapes.For, say $20, you might purchase "The Los Angeles Region" as a backdrop for your "spread of AIDS" model, or whatever model excites you.I envision the day when we can purchase alternate geographic landscapes for such geographical simulations.These would contain real geographic data (soils, transportation, population, etc., depending on the class of model), for a particular place, region, nation, or continent (or even time period).Indeed, I propose that we consider the development of such a library of modules.The trend is clearly in this direction, and a few prototypes already exist, the Digital Elevation Models and Digital Line Graphs of the US Geological Survey, and the TIGER files of the US Bureau of the Census being two primitive (but useful) examples of proto-modules.

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