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A New Perspective on Modeling Forest Fires

In this study, we use numerical simulations to heuristically explore the spread of forest fires. Our numerical studies are based on a “bottom-up" framework in which we start with a model with no spatial information on how forest vegetation is distributed (the Mean Field model (MF)). The MF is then replaced by a more detailed model which explores the effects of local, spatial interactions between vegetation and fire (the Pair-Approximation model (PA)). In this detailed study, the MF model serves as our “null" model because of its disconnection from actual biological processes (i.e. the absence of spatial interactions between vegetation and fire and how it affects fire spread). The most developed model in our framework is a Cellular Automata (CA) model. The stochastic and spatially explicit features of the CA model make it ideal for exploring the effects of distance and random behavior on the spread of fire. With the CA model, we gain insight that is directly applicable to actual forest fire management. For each model, we compare and contrast the dynamics of fire spread using a single and two layered (connected) lattice to measure the effect of including differential behavior of fire between the understory and canopy. From each of the models we observe thresholds (when available) for the stability of the fire-free equilibrium (FFE). We also utilize sensitivity analysis to determine the relationships between parameters in the MF and PA model and the basic ignition number, a measure for the average number of new trees that should catch on fire when a single source of fire is introduced into a forest. Results indicate that for all three models, the rate of fire spread (α), the rate at which an occupied burning state returns to a non-burning occupied state (β), and the rate at which a burning occupied state becomes an empty site (γ) determines the stability or instability of a forest fire. In the case of the two-layered lattice versions of the models, we find that fire controls are best focused on the understory level.

  • Poster session award recipient at the 2010 National SACNAS Convention in Anaheim, CA
  • Poster session award recipient at the 2011 Richard Tapia Celebration of Diversity in Computing Conference

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José Leonel Larios-Ferrer, Universidad Autónoma del Estado de Hidalgo
Justin Peterson, Northwestern College
Arturo Vargas, University of California Irvine
Leon Arriola, University of Wisconsin Whitewater
Michael Golinski, Arizona State University
Benjamin Morin, Arizona State University