CAs are a well-known class of models that embody the principles of complex system modeling where macro-scale patterns emerge from microscale decisions. The CA model framework has the ability to incorporate both spatial and nonspatial data for simulating a broad range of physical and social system processes within discrete entities in space. The CA modeling approach has been around since the 1950s, but was not widely applied until the processing power of desktop computers was able to efficiently deal with the computational demands of complex models. CA models can be used to explore relationships among system elements and the landscape patterns that emerge from modeled processes. In terms of land-use management, a CA model could simulate potential outcomes of alternative policy scenarios.
CA models utilize a tessellation of grid cells that represent discrete units in space and extend over a specified spatial extent. The cell size is user defined and based on data availability and the intent of the model application. A CA model is driven by four classes of parameters: (1) the spatial extent, (2) the initial condition, (3) the neighborhood boundary conditions, and (4) the set of rules to direct cell state transformation over time. Spatial extent is determined by the process being modeled and the flexibility of CA modeling makes it relatively easy to alter spatial extents (assuming data availability). The initial state is defined by summarizing biophysical and socioeconomic landscape characteristics by grid cell. The neighborhood definition identifies the set of adjacent cells that exert influence over the cell in question. The cells of the neighborhood do not necessarily require a congruent edge with the transition cell; rather their inclusion is explicitly defined in the model specification. The set of transition rules is expressed using mathematical or logical (e.g., IF x THEN y ELSE z) statements, and together the state of cell i and its neighbors at time t determine the state of cell i at time t + 1.
Exogenous factors may be included to serve as proxies for macrolevel conditions that affect the entire model surface or serve as boundary conditions for model processes. These conditions can be used to specify policy or functional constraints that limit the trajectory of the model state. Self-modifying behavior can be included to alter the transition rules based on threshold levels for specific conditions, such as the relationship between population density and zoning restrictions. One example of this type of CA model is the Clarke Urban Growth Model (UGM), developed at the University of California, Santa Barbara. Clarke's UGM has successfully been employed to model land-use patterns in central California, and was more recently coupled with a land-cover model to produce the land-use model
SLEUTH (Slope, Land Cover, Exclusion, Urbanization, Transportation, and Hillshade), which has been applied in a number of major metropolitan areas worldwide.
Finally, recent advances in the development of GIS software have greatly benefited CA modeling. GIS is well-suited to process and manage raster data which serve as model inputs, and model outputs can easily be imported to a GIS for visual display with other ancillary data sets such as roads, boundaries, or topography. While several GIS software packages feature simulation modeling capabilities, IDRISI offers a tighter coupling of the data processing and modeling environments by including a suite of CA-based land-use modeling and policy simulation tools.
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