# Prometheus and Fire Spread

Prometheus is a spatially explicit, deterministic fire growth simulation model that provides operational and strategic assessments of fire behavior potential. Fire management agencies across Canada are supporting the development of this state-of-the-art, national decision support tool. The foundation of the Prometheus model is the Fire Behavior Prediction Sub-system of the Canadian Forest Fire Danger Rating System(CFFDRS) (Forestry Canada Fire Danger Working Group 1992), and the wave propagation algorithms (marker method) developed by Richards (1990, 1993, 1995, 1999). The application of Huygens' principle of wave propagation to propagate fire frontswas first documented in 1975 (Sanderlin and Sunderson 1975). Since then, two operational wave propagation fire growth simulations models have been developed: FARSITE in the United States and Prometheus in Canada. These models use the same approach: the fire front is composed of an ordered list of vertices or markers. Each vertex on the fire perimeter grows as a firelet (i.e., elliptical wavelet). The vertices move at discreet time steps based on the fire environment information at that location, and the relative location of its neighboring vertices. Collectively, the propagated firelets produce fire perimeters at specific instances in time.

Richards' Model and Prometheus: The Prometheus fire growth model is a deterministic simulator based on the numerical solution of a set of differential equations derived by Richards in 1990. The model uses Huygens' principle which states that each point on the fire front at time t is an ignition point for a small fire that burns out an elliptical region in a finite time interval dt. Each ellipse is parameterized by: the wind direction Î¸; the radius in wind direction a; the radius orthogonal to the wind direction b; and the offset in the wind direction c. These parameters vary spatially and temporally. The firefront at thenext instant of time is the envelope of small ellipses generated during the intervening time by each point of the current front. The coordinates of the fire front at time t are given by (x(s, t),y(s, t)), where 0 â‰¤ s â‰¤ S and S is the length of the entire fire-front. We denote the normal to the fire front as n := (ys,âˆ’xs),where the index denotes partial differentiation. With the definitions of

and the fire front equations of Richards can be written as a system of differential equations

(1)The numerical method to solve these equations goes by anumber of names, including the marker method. A collection of nodes are selected to represent the fire front at time t. A timestep Î”t is selected and each point is moved by a finite difference scheme. The front at time t+Î”t is then given by apath passing through these new nodes. At each time step, and at each spatial location, the a, b and c parameters are evaluated; the FBP System relates these parameters to local rates of spread which in turn are related to fuel type and continuity, moisture content, wind velocity and variability, and topography.The FBP relations are based on data collected from natural and controlled fires with continuous uniform fuels at constant wind velocity, moisture content and slope. The Prometheus approach has achieved excellent results to date. However, there is stillroom for improvement.

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