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

Curvature effects in the dynamic propagation of wildfires

J. E. Hilton A D , C. Miller A , J. J. Sharples B and A. L. Sullivan C
+ Author Affiliations
- Author Affiliations

A CSIRO Data61, Private Bag 10, Clayton South, Vic. 3169, Australia.

B University of New South Wales, UNSW Canberra, PO Box 9716, Canberra BC 2610, Australia.

C CSIRO Land and Water, GPO Box 1700, Canberra, ACT 2601, Australia.

D Corresponding author. Email: james.hilton@csiro.au

International Journal of Wildland Fire 25(12) 1238-1251 https://doi.org/10.1071/WF16070
Submitted: 26 April 2016  Accepted: 22 August 2016   Published: 18 October 2016

Abstract

The behaviour and spread of a wildfire are driven by a range of processes including convection, radiation and the transport of burning material. The combination of these processes and their interactions with environmental conditions govern the evolution of a fire’s perimeter, which can include dynamic variation in the shape and the rate of spread of the fire. It is difficult to fully parametrise the complex interactions between these processes in order to predict a fire’s behaviour. We investigate whether the local curvature of a fire perimeter, defined as the interface between burnt and unburnt regions, can be used to model the dynamic evolution of a wildfire’s progression. We find that incorporation of curvature dependence in an empirical fire propagation model provides closer agreement with the observed evolution of field-based experimental fires than without curvature dependence. The local curvature parameter may represent compounded radiation and convective effects near the flame zone of a fire. Our findings provide a means to incorporate these effects in a computationally efficient way and may lead to improved prediction capability for empirical models of rate of spread and other fire behaviour characteristics.

Additional keywords: level set method, wildfire modelling, wind-driven fires.


References

Anderson DH, Catchpole EA, de Mestre NJ, Parkes T (1982) Modelling the spread of grass fires. Journal of the Australian Mathematical Society B: Applied Mathematics 23, 451–466.
Modelling the spread of grass fires.Crossref | GoogleScholarGoogle Scholar |

Anderson H, Rothermel R (1965) Influence of moisture and wind upon the characteristics of free-burning fires Symposium (International) on Combustion 10, 1009–1019.

Anderson HE (1969) Heat transfer and fire spread. USDA Forest Service, Intermountain Forest and Range Experiment Station, Research Paper INT-69. (Ogden, UT)

Anderson WR, Cruz MG, Fernandes PM, McCaw L, Vega JA, Bradstock RA, Fogarty L, Gould J, McCarthy G, Marsden-Smedley JB, Matthews S, Mattingley G, Pearce HG, van Wilgen BW (2015) A generic, empirical-based model for predicting rate of fire spread in shrublands. International Journal of Wildland Fire 24, 443–460.
A generic, empirical-based model for predicting rate of fire spread in shrublands.Crossref | GoogleScholarGoogle Scholar |

Balbi J, Santoni P, Dupuy J (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 |

Bose C, Bryce R, Dueck G (2009) Untangling the Prometheus nightmare. In ‘18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation’, 13–17 July 2009, Cairns, Qld. (Eds RS Anderssen, RD Braddock, LTH Newham) Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, pp. 240–246. Available at http://www.mssanz.org.au/modsim09/A4/bose.pdf [Verified 3 October 2016]

Bradski G (2000) The OpenCV library. Doctor Dobbs Journal 25, 120–126.

Butler B, Finney M, Andrews P, Albini F (2004) A radiation-driven model for crown fire spread. Canadian Journal of Forest Research 34, 1588–1599.
A radiation-driven model for crown fire spread.Crossref | GoogleScholarGoogle Scholar |

Cheney NP, Bary GAV (1969) The propagation of mass conflagrations in a standing eucalypt forest by the spotting process. In ‘Mass Fire Symposium: collected papers’, 10–12 February 1969, Canberra. Vol. 1, Paper A6. (Commonwealth of Australia, Defence Standards Laboratory: Melbourne)

Cheney NP, Gould JS (1995) Fire growth in grassland fuels. International Journal of Wildland Fire 5, 237–247.
Fire growth in grassland fuels.Crossref | GoogleScholarGoogle Scholar |

Cheney NP, Gould JS (1997) Fire growth and acceleration. International Journal of Wildland Fire 7, 1–5.
Fire growth and acceleration.Crossref | GoogleScholarGoogle Scholar |

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 |

Cheney NP, Gould JS, Catchpole WR (1998) Prediction of fire spread in grasslands. International Journal of Wildland Fire 8, 1–13.
Prediction of fire spread in grasslands.Crossref | GoogleScholarGoogle Scholar |

Cheney P, Gould J, McCaw L (2001) The dead-man zone – a neglected area of firefighter safety. Australian Forestry 64, 45–50.
The dead-man zone – a neglected area of firefighter safety.Crossref | GoogleScholarGoogle Scholar |

Cheney NP, Gould JS, McCaw WL, Anderson WR (2012) Predicting fire behaviour in dry eucalypt forest in southern Australia. Forest Ecology and Management 280, 120–131.
Predicting fire behaviour in dry eucalypt forest in southern Australia.Crossref | GoogleScholarGoogle Scholar |

Clark TL, Jenkins MA, Coen JL, Packham DR (1996) A coupled atmosphere–fire model: role of the convective Froude number and dynamic fingering at the fireline. International Journal of Wildland Fire 6, 177–190.
A coupled atmosphere–fire model: role of the convective Froude number and dynamic fingering at the fireline.Crossref | GoogleScholarGoogle Scholar |

Countryman CM (1966) The concept of the fire environment. Fire Control Notes 27, 8–10.

Cruz MG, Gould JS, Alexander ME, Sullivan AL, McCaw WL, Matthews S (2015a) Empirical-based models for predicting head-fire rate of spread in Australian fuel types. Australian Forestry 78, 118–158.
Empirical-based models for predicting head-fire rate of spread in Australian fuel types.Crossref | GoogleScholarGoogle Scholar |

Cruz MG, Gould JS, Kidnie S, Bessell R, Nichols D, Slijepcevic A (2015b) Effects of curing on grassfires: II. Effect of grass senescence on the rate of fire spread. International Journal of Wildland Fire 24, 838–848.
Effects of curing on grassfires: II. Effect of grass senescence on the rate of fire spread.Crossref | GoogleScholarGoogle Scholar |

CWFGM Steering Committee (2004) ‘Prometheus user manual v. 3.0.1.’ (Canadian Forest Service: Ottawa)

Dupuy J, Larini M (1999) Fire spread through a porous forest fuel bed: a radiative and convective model including fire-induced flow effects. International Journal of Wildland Fire 9, 155–172.
Fire spread through a porous forest fuel bed: a radiative and convective model including fire-induced flow effects.Crossref | GoogleScholarGoogle Scholar |

Fendell FE, Wolff MF (2001) Wind-aided fire spread. In ‘Forest fires: behaviour and ecological effects’, 1st edn. (Eds E Johnson, K Miyanishi) Ch. 6, pp. 171–223. (Academic Press: San Diego, CA).

Finney MA (2004) FARSITE: Fire Area Simulator – model development and evaluation. USDA, Forest Service, Rocky Mountain Research Station, Research Paper RMRS-RP-4. (Ogden, UT)

Finney MA, Cohen JD, Forthofer JM, McAllister SS, Gollner MJ, Gorham DJ, Saito K, Akafuah NK, Adam BA, English JD (2015) Role of buoyant flame dynamics in wildfire spread. Proceedings of the National Academy of Sciences of the United States of America 112, 9833–9838.
Role of buoyant flame dynamics in wildfire spread.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC2MXhtFOksbnM&md5=8bce922e49fb2496b7c2fdbca1e16d7fCAS | 26183227PubMed |

Forestry Canada Fire Danger Group (1992) Development and structure of the Canadian Forest Fire Behavior Prediction System. Forestry Canada Science and Sustainable Development Directorate, Information Report ST- X-3. (Ottawa, ON)

Frankman D, Webb BW, Butler BW (2010) Time-resolved radiation and convection heat transfer in combusting discontinuous fuel beds. Combustion Science and Technology 182, 1391–1412.
Time-resolved radiation and convection heat transfer in combusting discontinuous fuel beds.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXht1Gjs77K&md5=17fa5d010ea77ce0071f5435c074f90fCAS |

Frankman D, Webb BW, Butler BW, Jimenez D, Forthofer JM, Sopko P, Shannon KS, Hiers JK, Ottmar RD (2013) Measurements of convective and radiative heating in wildland fires. International Journal of Wildland Fire 22, 157–167.
Measurements of convective and radiative heating in wildland fires.Crossref | GoogleScholarGoogle Scholar |

Green DG, Gill AM, Noble IR (1983) Fire shapes and the adequacy of fire-spread models. Ecological Modelling 20, 33–45.
Fire shapes and the adequacy of fire-spread models.Crossref | GoogleScholarGoogle Scholar |

Hilton JE, Miller C, Sullivan AL, Rucinski C (2015) Effects of spatial and temporal variation in environmental conditions on simulation of wildfire spread. Environmental Modelling & Software 67, 118–127.
Effects of spatial and temporal variation in environmental conditions on simulation of wildfire spread.Crossref | GoogleScholarGoogle Scholar |

Johnston P, Kelso J, Milne GJ (2008) Efficient simulation of wildfire spread on an irregular grid. International Journal of Wildland Fire 17, 614–627.
Efficient simulation of wildfire spread on an irregular grid.Crossref | GoogleScholarGoogle Scholar |

Kidnie S, Cruz MG, Gould J, Nichols D, Anderson W, Bessell R (2015) Effects of curing on grassfires: I. Fuel dynamics in a senescing grassland. International Journal of Wildland Fire 24, 828–837.
Effects of curing on grassfires: I. Fuel dynamics in a senescing grassland.Crossref | GoogleScholarGoogle Scholar |

Knight I, Dando M (1989) Radiation above bushfires: report to State Electricity Commission of Victoria and Electricity Trust of South Australia. Client report, National Bushfire Research Unit. (Canberra, ACT)

Loncaric S (1998) A survey of shape analysis techniques. Pattern Recognition 31, 983–1001.
A survey of shape analysis techniques.Crossref | GoogleScholarGoogle Scholar |

Luke RH, McArthur AG (1978) ‘Bushfires in Australia.’ (Australian Government Publishing Service: Canberra)

Mallet V, Keyes D, Fendell F (2009) Modeling wildland fire propagation with level set methods. Computers & Mathematics with Applications 57, 1089–1101.
Modeling wildland fire propagation with level set methods.Crossref | GoogleScholarGoogle Scholar |

Mandel J, Beezley JD, Kochanski AK (2011) Coupled atmosphere–wildland fire modeling with WRF 3.3 and SFIRE 2011. Geoscientific Model Development 4, 591–610.
Coupled atmosphere–wildland fire modeling with WRF 3.3 and SFIRE 2011.Crossref | GoogleScholarGoogle Scholar |

McAlpine R, Wakimoto R (1991) The acceleration of fire from point source to equilibrium spread. Forest Science 37, 1314–1337.

McArthur AG (1967) Fire behaviour in eucalypt forests. Forestry and Timber Bureau Leaflet 107. (Commonwealth Department of National Development: Canberra)

Miller C, Hilton J, Sullivan A, Prakash M (2015) SPARK – A bushfire spread prediction tool. In ‘Proceedings, Environmental software systems. Infrastructures, services and applications: 11th IFIP WG 5.11 International Symposium, ISESS 2015’, Melbourne, Vic., 25–27 March 2015. (Eds R Denzer, RM Argent, G Schimak, J Hřebíček) pp. 262–271 (Springer International Publishing: Cham, Switzerland)

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 |

Newnham G, Blanchi R, Opie K, Leonard J, Siggins A (2015) Incorporating vegetation attenuation in radiant heat flux modelling. International Journal of Wildland Fire 24, 640–649.
Incorporating vegetation attenuation in radiant heat flux modelling.Crossref | GoogleScholarGoogle Scholar |

Packham DR, Pompe A (1971) Radiation temperatures of forest fires. Australian Forest Research 5, 1–8.

Pitts WM (1991) Wind effects on fires. Progress in Energy and Combustion Science 17, 83–134.
Wind effects on fires.Crossref | GoogleScholarGoogle Scholar |

Richards GD (1990) An elliptical growth model of forest fire fronts and its numerical solution. International Journal for Numerical Methods in Engineering 30, 1163–1179.
An elliptical growth model of forest fire fronts and its numerical solution.Crossref | GoogleScholarGoogle Scholar |

Rothermel RC (1972) A mathematical model for predicting fire spread in wildland fuels. USDA Forest Service, Intermountain Forest and Range Experimental Station, Research Paper INT-115. (Odgen UT)

Sethian J (2001) Evolution, implementation, and application of level set and fast marching methods for advancing fronts. Journal of Computational Physics 169, 503–555.
Evolution, implementation, and application of level set and fast marching methods for advancing fronts.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3MXktlOjs7g%3D&md5=ab7c7612a1a87c76ad58e3163524c585CAS |

Sethian JA (1999) ‘Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science.’ (Cambridge University Press: Cambridge, UK)

Sharples JJ, Towers IN, Wheeler GE, Wheeler VM, McCoy JA (2013) Modelling fire line merging using plane curvature flow. In ‘20th International Congress on Modelling and Simulation’, 1–6 December 2013, Adelaide, SA. (Eds J Piantadosi, RS Anderssen, J Boland) pp. 256–262. (Modelling and Simulation Society of Australia and New Zealand)

Silvani X, Morandini F (2009) Fire spread experiments in the field: temperature and heat flux measurements. Fire Safety Journal 44, 279–285.
Fire spread experiments in the field: temperature and heat flux measurements.Crossref | GoogleScholarGoogle Scholar |

Simeoni A, Santoni P, Larini M, Balbi J (2001) On the wind advection influence on the fire spread across a fuel bed: modelling by a semi-physical approach and testing with experiments. Fire Safety Journal 36, 491–513.
On the wind advection influence on the fire spread across a fuel bed: modelling by a semi-physical approach and testing with experiments.Crossref | GoogleScholarGoogle Scholar |

Simpson CC, Sharples JJ, Evans JP, McCabe MF (2013) Large-eddy simulation of atypical wildland fire spread on leeward slopes. International Journal of Wildland Fire 22, 599–614.
Large-eddy simulation of atypical wildland fire spread on leeward slopes.Crossref | GoogleScholarGoogle Scholar |

Smereka P (2003) Semi-implicit level set methods for curvature and surface diffusion motion. Journal of Scientific Computing 19, 439–456.
Semi-implicit level set methods for curvature and surface diffusion motion.Crossref | GoogleScholarGoogle Scholar |

Sullivan AL (2009a) Improving operational models of fire behaviour. In ‘18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation’, 13–17 July 2009, Cairns, Australia. (Eds RS Anderssen, RD Braddock, LTH Newham) pp. 282–288. (Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation)

Sullivan AL (2009b) Wildland surface fire spread modelling, 1990–2007. 1: Physical and quasi-physical models. International Journal of Wildland Fire 18, 349–368.
Wildland surface fire spread modelling, 1990–2007. 1: Physical and quasi-physical models.Crossref | GoogleScholarGoogle Scholar |

Sullivan AL (2009c) Wildland surface fire spread modelling, 1990–2007. 2: Empirical and quasi-empirical models. International Journal of Wildland Fire 18, 369–386.
Wildland surface fire spread modelling, 1990–2007. 2: Empirical and quasi-empirical models.Crossref | GoogleScholarGoogle Scholar |

Sullivan AL (2009d) 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 |

Sullivan AL, Cruz MG (2015) Small-scale flame dynamics provide limited insight into wildfire behavior. Proceedings of the National Academy of Sciences of the United States of America 112, E4164
Small-scale flame dynamics provide limited insight into wildfire behavior.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC2MXht1OmtrnF&md5=4227abff81894756b8a9b56450c82270CAS | 26183231PubMed |

Sullivan AL, Ellis PF, Knight IK (2003) A review of the use of radiant heat flux models in bushfire applications. International Journal of Wildland Fire 12, 101–110.
A review of the use of radiant heat flux models in bushfire applications.Crossref | GoogleScholarGoogle Scholar |

Sullivan AL, Cruz MG, Gould JS, Ellis PF, Plucinski MP, Hurley R, Koul V (2013a) Fire development, transitions and suppression: final report. Client Report EP1312986, CSIRO Ecosystem Sciences and CSIRO Climate Adaptation Flagship. (Canberra, ACT)

Sullivan AL, Knight IK, Hurley R, Webber C (2013b) A contractionless, low-turbulence wind tunnel for the study of free-burning fires. Experimental Thermal and Fluid Science 44, 264–274.
A contractionless, low-turbulence wind tunnel for the study of free-burning fires.Crossref | GoogleScholarGoogle Scholar |

Tolhurst K, Shields B, Chong D (2008) Phoenix: development and application of a bushfire risk-management tool. Australian Journal of Emergency Management 23, 47–54.

Viegas DX, Raposo JR, Davim DA, Rossa CG (2012) Study of the jump fire produced by the interaction of two oblique fire fronts. Part 1. Analytical model and validation with no-slope laboratory experiments. International Journal of Wildland Fire 21, 843–856.
Study of the jump fire produced by the interaction of two oblique fire fronts. Part 1. Analytical model and validation with no-slope laboratory experiments.Crossref | GoogleScholarGoogle Scholar |

Weber RO (1989) Analytical models of fire spread due to radiation. Combustion and Flame 78, 398–408.
Analytical models of fire spread due to radiation.Crossref | GoogleScholarGoogle Scholar |

Wheeler VM, McCoy JA, Wheeler GE, Sharples JJ (2013) Curvature flows and barriers in fire front modelling. In ‘20th International Congress on Modelling and Simulation’, 1–6 December 2013, Adelaide. (Eds J Piantadosi, RS Anderssen, J Boland) pp. 297–303. (Modelling and Simulation Society of Australia and New Zealand)

Wotton B, McAlpine R, Hobbs M (1999) The effect of fire front width on surface fire behaviour. International Journal of Wildland Fire 9, 247–253.
The effect of fire front width on surface fire behaviour.Crossref | GoogleScholarGoogle Scholar |