Calculation of fire spread rates across random landscapes

An approach is presented for approximating the expected spread rate of fires that burn across 2-dimensional landscapes with random fuel patterns. The method calculates a harmonic mean spread rate across a small 2-dimensional grid that allows the fire to move forward and laterally. Within this sample grid, all possible spatial fuel arrangements are enumerated and the spread rate of an elliptical fire moving through the cells is found by searching for the minimum travel time. More columns in the sample grid are required for accurately calculating expected spread rates where very slow-burning fuels are present, because the fire must be allowed to move farther laterally around slow patches. This calculation can be used to estimate fire spread rates across spatial fuel mixtures provided that the fire shape was determined from wind and slope. Results suggest that fire spread rates on random landscapes should increase with fire size and that random locations of fuel treatments would be inefficient in changing overall fire growth rates.

[1]  Range Experiment Station,et al.  Fire Behavior in Nonuniform Fuels , 2018 .

[2]  E. A. Catchpole,et al.  Intensity of fire at its perimeter. , 1982 .

[3]  Francis Fujioka.  Estimating Wildland Fire Rate of Spread in a Spatially Nonuniform Environment , 1985 .

[4]  M. Finney.  Design of Regular Landscape Fuel Treatment Patterns for Modifying Fire Growth and Behavior , 2001, Forest Science.

[5]  G. Richards.  An elliptical growth model of forest fire fronts and its numerical solution , 1990 .

[6]  J. Fried,et al.  CFES--California Fire Economics Simulator: A Computerized System for Wildland Fire Protection Planning , 1987 .

[7]  P. Andrews.  BEHAVE : Fire Behavior Prediction and Fuel Modeling System - BURN Subsystem, Part 1 , 1986 .

[8]  Monica G. Turner,et al.  Predicting the spread of disturbance across heterogeneous landscapes , 1989 .

[9]  M. Finney.  Fire growth using minimum travel time methods , 2002 .

[10]  G. Richards.  A General Mathematical Framework for Modeling Two-Dimensional Wildland Fire Spread , 1995 .

[11]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

[12]  J. Agee.  The landscape ecology of western forest fire regimes , 1998 .

[13]  Leigh House,et al.  Minimum traveltime calculation in 3-D graph theory , 1996 .

[14]  Ross Taplin.  Sources of variation for fire spread rate in non-homogeneous fuel , 1993 .

[15]  G. Richards,et al.  The mathematical modelling and computer simulation of wildland fire perimeter growth over a 3-dimensional surface , 1999 .

[16]  K. Kalabokidis,et al.  Quadrat Analysis of Wildland Fuel Spatial Variability , 1992 .

[17]  E. A. Catchpole,et al.  Modelling the spread of grass fires , 1982, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[18]  T. Hatton,et al.  Fire spread through nonhomogeneous fuel modelled as a Markov process , 1989 .

[19]  C. E. Van Wagner,et al.  A Simple Fire-Growth Model , 1969 .

[20]  James K. Brown.  Bulk densities of nonuniform surface fuels and their application to fire modeling , 1981 .

[21]  L. A. Salazar.  Sensitivity of fire behavior simulations to fuel model variations , 1985 .

[22]  Rc Rothermel.  Predicting Behavior of the 1988 Yellowstone Fires: Projections versus Reality , 1991 .

[23]  M. Finney.  FARSITE : Fire Area Simulator : model development and evaluation , 1998 .

[24]  Gary A. Morris,et al.  Rate of Spread of Free-Burning Fires in Woody Fuels in a Wind Tunnel , 1998 .

[25]  H. Anderson.  Aids to Determining Fuel Models for Estimating Fire Behavior , 1982 .