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One example of a landscape process that is commonly represented by cellular modeling is wildfire propagation. Wildfire is commonly modeled as a spatial stochastic process (Pyne, 1984), including representations as coupled differential equations (Fried and Fried, 1996), embedding of known fire models within a cellular context (Bevins, 1999), and explicitly through CA rules (Clarke et al., 1994). All of the models cited here have the common idea that the likelihood of ignition of a section of vegetation is partially a function of how and how much of the surrounding area is burning. For data sets of high resolution and small unit areas (a few square meters), it is common to include explicit terms and actions representing physical processes in fire burning (such as heat flux, dessication, etc.) to represent transmission of heat from one cell to another. With coarser spatial data (tens of meters), the direct effects of fire from one cell to another are confounded with other processes, weakening the predictive power of many of the physical process models. In these cases, it is more common to approach transmission of flame from one cell to another through a cellular stochastic processes.
In this section the design of an elementary wildfire propagation model will be presented. The model design here is part of a pilot simulation for a fire ecology project at Utah State University. It has not yet been formally published, but some information is available from the project web page (Box, 1999). The details presented here are to illustrate the applicability of the modeling technique described here to wildfire, as they are considered particularly illustrative of the modeling concepts described in section 1.
An under-riding concern for creation of this model was to have every cell in the landscape act with relative independence, accepting inputs from neighbors as required but otherwise an entity unto itself. A cellular model is a logical way to implement this, with many precedents in the fire modeling literature. However, an additional concern was to accommodate any level of heterogeneity within the landscape, allowing each cell to act by its own rules with little concern for the internal details of its neighbors. In the landscape, a stand of trees, a meadow, a building, and an agricultural field will have distinctly different characteristics of how each reacts to a burn, and each will follow a different set of rules as to its burn characteristics. The desired effect was to have each cell have not just a customized set of parameters, but rather each cell embed its own model of how it burns, which can be radically different for various landcover types.
Some aspects of this pilot model were determined by data availability. The simulation was created with vegetation and landcover inputs from the Utah GAP Analysis (Edwards et al., 1995), and topographic information from the USGS Digital Elevation Models (DEMs) (U. S. Geological Survey, 1979). Since both of these data sources are in latticed (grid) format at 30m resolution, this was selected as the base grid cell size for the simulation. At this resolution, it was not considered practical to attempt a model of propagation based on first-order physics, as many of the crucial processes such as heat flux are acting at a much more localized scale. Additionally, other factors, such as ignition by flying embers (known as spotting), can be modeled entirely as physical processes, but for practical reasons are modeled according to probabilistic or stochastic processes. For these reasons, it was decided to model wildfire as a cellular stochastic process.