Register      Login
International Journal of Wildland Fire International Journal of Wildland Fire Society
Journal of the International Association of Wildland Fire
RESEARCH ARTICLE

Physical modelling of forest fire spreading through heterogeneous fuel beds

Albert Simeoni A D , Pierre Salinesi B and Frédéric Morandini C
+ Author Affiliations
- Author Affiliations

A Department of Fire Protection Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA.

B Fire Department of South Corsica, BP 552, F-20189 Ajaccio cedex 2, France.

C Unité Mixte de Recherche (UMR) CNRS (Centre National de la Recherche Scientifique) 6134 – Sciences Pour l’Environnement (SPE), University of Corsica, BP 52, F-20250 Corte, France.

D Corresponding author. Email: asimeoni@wpi.edu

International Journal of Wildland Fire 20(5) 625-632 https://doi.org/10.1071/WF09006
Submitted: 17 January 2009  Accepted: 11 November 2010   Published: 8 August 2011

Abstract

Vegetation cover is a heterogeneous medium composed of different kinds of fuels and non-combustible parts. Some properties of real fires arise from this heterogeneity. Creating heterogeneous fuel areas may be useful both in land management and in firefighting by reducing fire intensity and fire rate of spread. The spreading of a fire through a heterogeneous medium was studied with a two-dimensional reaction–diffusion physical model of fire spread. Randomly distributed combustible and non-combustible square elements constituted the heterogeneous fuel. Two main characteristics of the fire were directly computed by the model: the size of the zone influenced by the heat transferred from the fire front and the ignition condition of vegetation. The model was able to provide rate of fire spread, temperature distribution and energy transfers. The influence on the fire properties of the ratio between the amount of combustible elements and the total amount of elements was studied. The results provided the same critical fire behaviour as described in both percolation theory and laboratory experiments but the results were quantitatively different because the neighbourhood computed by the model varied in time and space with the geometry of the fire front. The simulations also qualitatively reproduced fire behaviour for heterogeneous fuel layers as observed in field experiments. This study shows that physical models can be used to study fire spreading through heterogeneous fuels, and some potential applications are proposed about the use of heterogeneity as a complementary tool for fuel management and firefighting.

Additional keywords: fire critical behaviour, non-combustible zones, reaction–diffusion model, surface fire spread.


References

Baker T (1989) Effect of scale and spatial heterogeneity on fire-interval distributions. Canadian Journal of Forest Research 19, 700–706.
Effect of scale and spatial heterogeneity on fire-interval distributions.Crossref | GoogleScholarGoogle Scholar |

Balbi JH, Santoni PA, Dupuy JL (1999) Dynamic modelling of fire spread across a fuel bed. International Journal of Wildland Fire 9, 275–284.
Dynamic modelling of fire spread across a fuel bed.Crossref | GoogleScholarGoogle Scholar |

Beer T, Enting IG (1990) Fire spread and percolation modelling. Mathematical and Computer Modelling 13, 77–96.
Fire spread and percolation modelling.Crossref | GoogleScholarGoogle Scholar |

Berjak SG, Hearne JW (2002) An improved cellular automaton model for simulating fire in a spatially heterogeneous savanna system. Ecological Modelling 148, 133–151.
An improved cellular automaton model for simulating fire in a spatially heterogeneous savanna system.Crossref | GoogleScholarGoogle Scholar |

Bradstock RA, Gill AM (1993) Fire in semi-arid, mallee shrublands: size of flames from discrete fuel arrays and their role in the spread of fire. International Journal of Wildland Fire 3, 3–12.
Fire in semi-arid, mallee shrublands: size of flames from discrete fuel arrays and their role in the spread of fire.Crossref | GoogleScholarGoogle Scholar |

Brown KB (1982) Fuel and fire behavior prediction in big sagebrush. USDA Forest Service, Intermountain Forest and Range Experiment Station, Research Paper INT-290. (Ogden, UT)

Butcher J (2008) ‘Numerical Methods for Ordinary Differential Equations.’ 2nd edn. (Wiley: Hoboken, NJ)

Caldarelli G, Frondoni R, Gabrielli A, Montuori M, Retzlaff R, Ricotta C (2001) Percolation in real wildfire. Europhysics Letters 56, 510–516.
Percolation in real wildfire.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3MXptVKgu7s%3D&md5=394acdde235a8c284a9e20bcd02e109fCAS |

Cheney NP, Gould JS, Catchpole WR (1993) The influence of fuel, weather and fire shape variables on fire-spread in grasslands. International Journal of Wildland Fire 3, 31–44.
The influence of fuel, weather and fire shape variables on fire-spread in grasslands.Crossref | GoogleScholarGoogle Scholar |

Courant R, Friedrichs K, Lewy H (1928) Über die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen 100, 32–74.
Über die partiellen Differenzengleichungen der mathematischen Physik.Crossref | GoogleScholarGoogle Scholar |

Drossel B, Schwabl F (1992) Self-organized critical forest-fire model. Physical Review Letters 69, 1629–1632.
Self-organized critical forest-fire model.Crossref | GoogleScholarGoogle Scholar |

Duarte JAMS, Carvalho JM, Ruskin HJ (1992) The direction of maximum spread in anisotropic forest fires and its critical properties. Physica A. Statistical and Theoretical Physics 183, 411–421.
The direction of maximum spread in anisotropic forest fires and its critical properties.Crossref | GoogleScholarGoogle Scholar |

Finney MA (2003) Calculation of fire spread rates across random landscapes. International Journal of Wildland Fire 12, 167–174.
Calculation of fire spread rates across random landscapes.Crossref | GoogleScholarGoogle Scholar |

Finney MA, Seli RC, McHugh CW, Ager AA, Bahro B, Agee JK (2007) Simulation of long-term landscape-level fuel treatment effects on large wildfires. International Journal of Wildland Fire 16, 712–727.
Simulation of long-term landscape-level fuel treatment effects on large wildfires.Crossref | GoogleScholarGoogle Scholar |

King KJ, Bradstock RA, Cary GJ, Chapman J, Marsden-Smedley JB (2008) The relative importance of fine-scale fuel mosaics on reducing fire risk in south-west Tasmania, Australia. International Journal of Wildland Fire 17, 421–430.
The relative importance of fine-scale fuel mosaics on reducing fire risk in south-west Tasmania, Australia.Crossref | GoogleScholarGoogle Scholar |

Loehle C (2004) Applying landscape principles to fire hazard reduction. Forest Ecology and Management 198, 261–267.
Applying landscape principles to fire hazard reduction.Crossref | GoogleScholarGoogle Scholar |

Malamud BD, Morein G, Turcotte DL (1998) Forest fires: an example of self-organized critical behavior. Science 281, 1840–1842.
Forest fires: an example of self-organized critical behavior.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK1cXmtVKhsLk%3D&md5=35f173adfd956260cae8a48975911b48CAS |

Marsden-Smedley JB, Catchpole WR, Pyrke A (2001) Fire modelling in Tasmanian buttongrass moorlands. IV. Sustaining versus non-sustaining fires. International Journal of Wildland Fire 10, 255–262.
Fire modelling in Tasmanian buttongrass moorlands. IV. Sustaining versus non-sustaining fires.Crossref | GoogleScholarGoogle Scholar |

Miller C, Urban DL (1999) Interactions between forest heterogeneity and fire regimes in the southern Sierra Nevada. Canadian Journal of Forest Research 29, 202–212.
Interactions between forest heterogeneity and fire regimes in the southern Sierra Nevada.Crossref | GoogleScholarGoogle Scholar |

Morandini F, Santoni PA, Balbi JH (2001) The contribution of radiant heat transfer to laboratory-scale fire spread under the influences of wind and slope. Fire Safety Journal 36, 519–543.
The contribution of radiant heat transfer to laboratory-scale fire spread under the influences of wind and slope.Crossref | GoogleScholarGoogle Scholar |

Morandini F, Santoni PA, Balbi JH, Ventura JM, Mendes-Lopes JM (2002) A two-dimensional model of fire spread across a fuel bed including wind combined with slope conditions. International Journal of Wildland Fire 11, 53–64.
A two-dimensional model of fire spread across a fuel bed including wind combined with slope conditions.Crossref | GoogleScholarGoogle Scholar |

Morandini F, Simeoni A, Santoni PA, Balbi JH (2005) A model for the spread of fire across a fuel bed incorporating the effects of wind and slope. Combustion Science and Technology 177, 1381–1418.
A model for the spread of fire across a fuel bed incorporating the effects of wind and slope.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2MXlvVSmsrc%3D&md5=677ab6a2efa5b5a73cac93377a3489a6CAS |

Nahmias J, Téphany H, Duarte J, Letaconnoux S (2000) Fire spreading experiments on heterogeneous fuel beds. Applications of percolation theory. Canadian Journal of Forest Research 30, 1318–1328.
Fire spreading experiments on heterogeneous fuel beds. Applications of percolation theory.Crossref | GoogleScholarGoogle Scholar |

Ohtsuki T, Keyes T (1986) Biased percolation forest fires with wind. Journal of Physics. A. Mathematical Nuclear and General 19, 281–287.
Biased percolation forest fires with wind.Crossref | GoogleScholarGoogle Scholar |

Pastor E, Zarate L, Planas E, Arnaldos J (2003) Mathematical models and calculation systems for the study of wildland fire behaviour. Progress in Energy and Combustion Science 29, 139–153.
Mathematical models and calculation systems for the study of wildland fire behaviour.Crossref | GoogleScholarGoogle Scholar |

Patankar SV (1980) ‘Numerical Heat Transfer and Fluid Flow.’ (Hemisphere Publishing Corporation: Washington, DC)

Perry GLW (1998) Current approaches to modelling the spread of wildland fire: a review. Progress in Physical Geography 22, 222–245..

Santoni PA, Balbi JH, Dupuy JL (1999) Dynamic modelling of upslope fire growth. International Journal of Wildland Fire 9, 285–292.
Dynamic modelling of upslope fire growth.Crossref | GoogleScholarGoogle Scholar |

Santoni PA, Simeoni A, Rossi JL, Bosseur F, Morandini F, Silvani X, Balbi JH, Cancelieri D, Rossi L (2006) Instrumentation of wildland fire: characterisation of a fire spreading through a Mediterranean shrub. Fire Safety Journal 41, 171–184.
Instrumentation of wildland fire: characterisation of a fire spreading through a Mediterranean shrub.Crossref | GoogleScholarGoogle Scholar |

Sibony M, Mardon JC (1988) ‘Approximations et Équations Différentielles.’ (Hermann: Paris)

Simeoni A, Santoni PA, Larini M, Balbi JH (2003) Reduction of a multiphase formulation to include a simplified flow in a semi-physical model of fire spread across a fuel bed. International Journal of Thermal Sciences 42, 95–105.
Reduction of a multiphase formulation to include a simplified flow in a semi-physical model of fire spread across a fuel bed.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3sXotlCgsA%3D%3D&md5=c0fb2b910f6919d27db96510eb7002d2CAS |

Spyratos V, Bourgeon PS, Ghil M (2007) Development at the wildland–urban interface and the mitigation of forest-fire risk. Proceedings of the National Academy of Sciences of the United States of America 104, 14272–14276.
Development at the wildland–urban interface and the mitigation of forest-fire risk.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2sXhtVGhtLzK&md5=e5f16e032b77c356535b0b9524591eb1CAS |

Stauffer D (1985) ‘Introduction to Percolation Theory.’ (Taylor and Francis: London)

Sullivan AL (2009) Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models. International Journal of Wildland Fire 18, 387–403.
Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models.Crossref | GoogleScholarGoogle Scholar |

Téphany H, Nahmias J (2002) Comment on ‘Percolation in real wildfires’ by G. Caldarelli et al. Europhysics Letters 59, 155–156.
Comment on ‘Percolation in real wildfires’ by G. Caldarelli et al.Crossref | GoogleScholarGoogle Scholar |

Téphany H, Nahmias J, Duarte JAMS (1997) Combustion on heterogeneous media. A critical phenomenon. Physica A 242, 57–69.
Combustion on heterogeneous media. A critical phenomenon.Crossref | GoogleScholarGoogle Scholar |

Von Niessen W, Blumen A (1986) Dynamics of forest fires as a directed percolation model. Journal of Physics. A. Mathematical Nuclear and General 19, 289–293.
Dynamics of forest fires as a directed percolation model.Crossref | GoogleScholarGoogle Scholar |

Weber RO (1990) A model for fire propagation in arrays. Mathematical and Computer Modelling 13, 95–102.
A model for fire propagation in arrays.Crossref | GoogleScholarGoogle Scholar |

Weise DR, Zhou X, Sun L, Mahalingam S (2005) Fire spread in chaparral – ‘go or no go?’ International Journal of Wildland Fire 14, 99–106.
Fire spread in chaparral – ‘go or no go?’Crossref | GoogleScholarGoogle Scholar |

Zekri N, Porterie B, Clerc JP, Loraud JC (2005) Propagation in a two-dimensional weighted local small-world network. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 71, 046121
Propagation in a two-dimensional weighted local small-world network.Crossref | GoogleScholarGoogle Scholar |