Our understanding of some systems may be improved by introducing the spatial dimensions in an explicit manner, especially if the fundamental principles operate at a cellular level. The region is typically subdivided into a cellular grid pattern, and the flows between adjacent cells are simulated based on the fundamental principles. The end result may be a spatially organized model that teaches us more than what we would learn from a model of a single cell. For example, Sancar and Allenstein (1989) argue that an explicit spatial dimension would enhance the usefulness of system dynamics to environmental and city planners. They implemented a dynamic model using a general programming language to permit variable resolution in cell size. Their pedagogic example reveals the power to communicate with graphic displays, but it also revealed a substantial programming challenge given the software available in the late 1980s. More recently, Hannon and Ruth (1997) provide a pedagogic example dealing with predator-prey populations. They used Stella to simulate births, deaths and predation within each cell of a 2x2 grid pattern. The insights from the spatial model emerge when the animals are given the opportunity to migrate between cells. This freedom may change the stability of the spatial system from what one would expect from a conventional predator-prey model.
System Dynamics and GIS
Cell by cell modeling may be implemented with any of the
stock and flow software. The information in the dynamic model may be exchanged
with a spreadsheet or with a geographic information system (GIS) to improve
communication and interpretation. By combining system dynamics and GIS,
researchers may enhance the two approaches. Dynamic models may now deal
with spatially explicit information while allowing fundamental laws to be
expressed at the cellular level. This may build confidence in the model,
especially if the fundamental laws are well understood and the spatial simulations
may be checked against a GIS. The power of GIS is enhanced as well. When
linked to a system dynamics model, a GIS provides a dynamic perspective
as well as a spatial perspective.
| extra note: Appendix I summarizes four examples of a GIS combined with a dynamic model. | Click here for an illustration of a combining a GIS with the dynamic model of Mono Lake in chapter 4. |
The purpose of this appendix is to illustrate how the spatial
dimensions may be simulated within the system dynamics framework using the
Stella software. Huggett's (1993) model of nitrogen flows in a catchment
has been selected for the illustrative example. His model is well documented
and easy to visualize. His work also provides a point of comparison in case
you wish to compare the relative effort required (with and without Stella).
The appendix concludes by demonstrating that the key finding from the nitrogen
model may be approximated by a model without spatial detail. Such approximations
can be useful as part of a larger modeling system that would be unduly encumbered
by a spatial model.