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Forest Fire Spreading

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Handbook of Geomathematics

Abstract

Due to climate changes, more and more woodlands will be endangered by forest fires in the future. Because of this observation, it is very important to obtain information about how forest fires expand. In this contribution, we are interested in the interacting factors which influence forest fires. Our particular interest is the use of physical models, which consider heat and mass transfer mechanisms. As a result, we are led to a convection-diffusion-reaction problem which is nonstationary and nonlinear. Furthermore, we have a look at the different parameters, which are involved in these equations, especially at the meteorological and fuel data. Finally, we discuss some approaches to solve fire expansion numerically. Moreover, we give some simulations of forest fire spreading.

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References

  • Albini FA, Baughman RG (1979) Estimating windspeeds for predicting wildland fire behaviour. Research paper INT–221, USDA Forest Service, Intermountain Forest and Range Experiment Station

    Google Scholar 

  • Albini FA (1986) Wildland fire spread by radiation – a model including fuel cooling by natural convection. Combust Sci Technol 45:101–113

    Article  Google Scholar 

  • Allgöer B, Schöning R (n.y.) Forest fire modelling with GIS in the Swiss National Park. http://www.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/allgower_britta/allgower.html, 29 Jan 2013

  • Anderson HE (1969) Heat transfer and fire spread. Research paper INT–69, USDA Forest Service, Intermountain Forest and Range Experiment Station

    Google Scholar 

  • Anderson HE (1982) USDA forest services, intermountain forest and range experiment station. General technical report INT-122

    Google Scholar 

  • Anderson HE (1983) Predicting wind-driven wildland fire size and shape.Research paper INT-305

    Google Scholar 

  • Ansorge R, Sonar T (2009) Mathematical models of fluid dynamics.Wiley-VCH, Berlin

    Book  Google Scholar 

  • Archer D, Rahmstorf S (2010) The climate crisis. An introductory guide to climate change. Cambridge University Press, Cambridge

    Google Scholar 

  • Asensio I and Ferragut L (2002) On a wildland fire model with radiation. Int J Numer Methods Eng 54:137–157

    Article  MathSciNet  MATH  Google Scholar 

  • Asensio I, Ferragut L, and Simon J (2001) Modelling of convective phenomena in forest fire. Rev. R. Acad. Cien. 95(1): 13–27

    MATH  Google Scholar 

  • Asensio I, Ferragut L, and Simon J (2005) A convection model for fire spread simulation. Appl Math Lett 18(6):673–677. Elsevier

    Article  MathSciNet  MATH  Google Scholar 

  • Baehr HD, Stephan K (2010) Wärme- und Stoffübertragung.Springer

    Book  Google Scholar 

  • Burmann E, Ern A (2005) Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. Math Comput 74:1637–1652

    Article  MathSciNet  MATH  Google Scholar 

  • Burrows ND (1999) Fire behaviour in jarrah forest fuels. Part 1. Laboratory experiments. CALMScience 3:31–56

    Google Scholar 

  • Burrows ND, Ward B, Robinson A (1991) Fire behaviour in spinifex fuels on the Gibson desert nature reserve, Western Australia. J Arid Environ 20:189–204

    Google Scholar 

  • Camia A, Amatulli G, San-Miguel-Ayanz J (2008) Past and future trends of forest fire danger in Europe (JRC 46533, EUR 23427 EN). European Commission, Joint Research Centre

    Google Scholar 

  • Carvalho AC, Carvalho A, Martins M, Marques C, Rocha A, Borrego C, Viegas DX, Miranda AI (2011) Fire weather risk assessment under climate change using a dynamical downscaling approach. Environ Modell Softw 26:1123–1133

    Article  Google Scholar 

  • Catchpole WR, Catchpole EA (1994) Short course on wildland fire modelling: Kursunterlagen. Coimbra

    Google Scholar 

  • Catchpole WR, Catchpole EA, Rothermel RC, Morris GA, Butler BW, Latham DJ (1998) Rate of spread of free-burning fires in woody fuels in a wind tunel. Combust Sci Technol 131:1–37

    Article  Google Scholar 

  • Cekirge HM (1978) Propagation of fire fronts in forest. Comput Math Appl 1978.4:325–32

    Article  Google Scholar 

  • Chandler C, Thomas P, Trabaud L, and Williams D (1983) Fire in forestry. Wiley, New York

    Google Scholar 

  • Cheney NP, Gould JS, Catchpole WR (1998) Prediction of fire spread in grasslands. Int J Wildland Fire 8(1):1–13

    Article  Google Scholar 

  • Croba D, Lalas D, Papadopoulos C, Tryfonopoulos D (1994) Numerical simulation of forest fire propagation in complex terrain. In: Viegas DX (ed) Proceedings of the second international conference on forest fire research, Coimbra, vol. 1275. University of Coimbra, Portugal, pp 491–500

    Google Scholar 

  • Cumming SG (2001) Forest type and wildfire in the Alberta boreal mixedwood: What do fires burn? Ecol Appl 11:97–110

    Article  Google Scholar 

  • Cui J, Freeden W, and Witte B (1992) Gleichmäßige Approximation mittels sphärischer Finite Elemente und ihre Anwendung in der Geodäsie. Zeitschrift für Vermessungswesen (ZfV), (117): 266–278

    Google Scholar 

  • De Mestre NJ, Catchpole EA, Anderson DH and Rothermel RC (1989) Uniform propagation of a planar fire front without wind. Combust Sci Technol 65(4–6):231–244

    Article  Google Scholar 

  • Diez JI, Vrabie I (1994) Existence for reaction diffusion systems. A compactness method approach. J Math Anal Appl 188:521–540

    Article  MATH  Google Scholar 

  • Dupuy JL (1997) Mieux comprendre et predire la propagation des feux de forets:experimentation,test et propagationdemode les. PhD thesis, Université Claude Bernard, Lyon I, Centre National de la Recherche Scientifique, Villeurbanne

    Google Scholar 

  • Eberle S (2013) Modeling and simulation of forest fire spreading. Mathematics of planet earth. Proceedings of the 15th annual conference of the international association for mathematical geosciences. Madrid, pp 811–814

    Google Scholar 

  • Eberle S (2015) Forest fire determination: theory and numerical aspects. PhD-thesis. University of Kaiserslautern, Geomathematics Group

    Google Scholar 

  • Emmons H (1964) Fire in the forest. Fire Res Abs Rev 5:163–178

    Google Scholar 

  • European Environment Agency (2012) Climate change, impacts and vulnerability in Europe 2012. EEA report 12, http://www.eea.europa.eu/publications/climate-impacts-and-vulnerability-2012, 17 Jan 2013. doi:10.2800/66071

  • Eskin GI (1981) Boundary Value Problems for Elliptic Pseudodierential Equations. American Mathematical Society Translation of Mathematical Monograpgs (from Russian original), Vol. 52, American Mathematical Society Providence, R.I.

    Google Scholar 

  • Fengler M, Freeden W (2005) A nonlinear galerkin scheme involving vector and tensor spherical harmonics for solving the incompressible Navier-Stokes equation on the sphere. SIAM J Sci Comput 27:967–994

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandes PM (1998) Fire spread modelling in Portuguese shrubland. In: Viegas DX (ed) Proceedings of the 3rd international conference on forest fire research, University of Coimbra, Luso, pp 61–628

    Google Scholar 

  • Ferragut L, Asensio I (2004) Simulacion de incendios forestales. Bol Soc Esp Mat Apl 27:7–28.

    Google Scholar 

  • Ferragut L, Asensio I, Monedero S (2004) Modelling slop, wind and moisture content effects on fire spread. European congress on computationl methods in applied sciences and engineering. Finnland

    MATH  Google Scholar 

  • Ferragut L, Asensio I, Monedero S (2005) A numerical method for solving convection-reaction-diffusion multivalued equations in fire spread modelling. Adv Eng Softw 38(6):366–371. Elsevier

    Article  MATH  Google Scholar 

  • Finney MA, McHugh CW, Grenfell IC, Riley KL, Short C (2011) A simulation of probabilistic wildfire risk components for the continental United States. Stoch Environ Res Risk Assess 25:973–1000

    Article  Google Scholar 

  • Flannigan MD, Stocks BJ, Wotton BM (2000) Climate change and forest fires. Sci Total Environ 262:221–229

    Article  Google Scholar 

  • Fons WL (1946) Analysis of fire spread in light forest fuels. J Agric Res 72:93–121

    Google Scholar 

  • Forestry Canada Fire Danger Group (1992) Development and structure of the Canadian forest fire behaviour prediction system. Canadian Department of Forestry. Inf Rep ST-X-3

    Google Scholar 

  • Frandsen WH (1971) Fire spread through porous fuels from the conservation of energy. Combust Flame 16:9–16

    Article  Google Scholar 

  • Fujii N, Hasegawa J, Phallop L, Sakawa Y (1980) A nonstationary model of firespreading. Appl Math Model 41:76–180

    Google Scholar 

  • Gerstengarbe FW, Werner PC, Lindner M, Bruschek G (1999) Estimation of future forest fire development in the state of Brandenburg. Int Forest Fire News 21:91–93

    Google Scholar 

  • Griffin GF and Allan GE (1984) Fire behaviour. In: Saxon EC (ed) Anticipating the inevitable: a patch burn strategy for fire management at Uluru (Ayers Rock-Mt. Olga) National Park. CSIRO, Melbourne, pp 55–8

    Google Scholar 

  • Grishin AM (1997) A mathematical model of forest fires and new methods of fighting them. Publishing House of the Tomsk State University, Tomsk

    Google Scholar 

  • Grishin AM, Gruzin AD and Zverev VG (1983) Mathematical modelling of the spreading of high-level forest fires. Sov Phys Dokl 28:328–330

    Google Scholar 

  • Harten A (1983) High resolution schemes for hyperbolic conservation laws. J Comput Phys 49:357–393

    Article  MathSciNet  MATH  Google Scholar 

  • Holsten A, Dominic AR, Costa L, Kropp JP (2013) Evaluation of meterological forest fire indices for German federal states. For Ecol Manag 287:123–131. doi:10.1016/j.foreco.2012.08.035

    Article  Google Scholar 

  • Hottel HC, Williams GC, Kwentus GK (1971) Fuel pre-heating in free-burning fires. 13th international symposium on combustion. Utah, pp 963–970.

    Google Scholar 

  • Huang CC, Xie Y (1984) Flame propagation along matchstick arrays on inclined base boards. Combust Sci Technol 42:1–12

    Article  Google Scholar 

  • IPCC (2007) Climate change 2007: Synthesis report, contribution of working groups I, II and III to the fourth assessment report of the intergovernmental panel on climate change [Core Writing Team, Pachauri, RK, Reisinger, A (eds)], IPCC, Geneva

    Google Scholar 

  • John V, Novo J (2012) On (essentially) non-oscillatory discretization of evolutionary convection-diffusion equations. J Comput Phys 231(4):1570–1586. Elsevier

    Article  MathSciNet  MATH  Google Scholar 

  • Joos F (2006) Thermische Verbrennung. Springer, Heidelberg

    Google Scholar 

  • Klimawandelinformationssystem Rhineland-Palatinate. Klimawandelinformationssystem kwis-rlp für Rheinland-Pfalz. http://www.kwis-rlp.de/klima-witterung.html, 04 Apr 2013

  • Konev EV, Sukhinin AI (1977) The analysis of flame spread through forest fuel. Combust Flame 28:217–223

    Article  Google Scholar 

  • Kuzmin D (2012) A guide to numerical methods for transport equations. Friedrich-Alexander-Universitant. Erlangen-Nürnberg

    Google Scholar 

  • Kuzmin D, Möller M, Turek S (2004) High-resolution FEM-FCT schemes for multidimensional conservation laws. Comput Methods Appl Mech Eng 193(45–47):4915–4946

    Article  MathSciNet  MATH  Google Scholar 

  • Kuzmin D, Löhner H, Turek S (2012) Flux-corrected transport. Scientific Computation. Springer, Berlin/New York

    Book  MATH  Google Scholar 

  • Larini M, Giraud F, Porterie B, Loraud JC (1998) A multiphase formulation for fire propagation in heterogeneous combustible media. Int J Heat Mass Transf 41(6/7):88–97

    MATH  Google Scholar 

  • Lasch-Born P, Gutsch M, Reyer C, Suckow F (2013) Auswirkungen auf den Wald in Deutschland. In: Gerstengarbe F-W, Welzer H (Eds) Zwei Grad mehr in Deutschland. Wie der Klimawandel unseren Alltag verändern wird. Das Szenario 2040, Fischer, pp 99–130

    Google Scholar 

  • Latif M (2012) Globale Erwärmung. Ulmer, Stuttgart, p 119 S

    Google Scholar 

  • Lindner M, Maroschek M, Netherer S, Kremer A, Barbati A, Garcia-Gonzalo J, Seidl R, Delzon S, Corona P, Kolström M, Lexer MJ, Marchetti M (2010) Climate change impacts, adaptive capacity, and vulnerability of European forest ecosystems. For Ecol Manag 259:698–709

    Article  Google Scholar 

  • Linn RR (1997) A transport model for prediction of wildfire behaviour. PhD thesis. New Mexico State University, Department of Mechanical Engineering, Las Cruces, New Mexico

    Google Scholar 

  • Loustau D, Ogée J, Dufrêne E, Déqué M, Dupouey JL, Badeau V, Viovy N, Ciais P, Desprez-Loustau ML, Roques A, Chuine I, Mouillot F (2007) Impacts of climate change on temperate forests and interaction with management. In: Freer-Smith PH, Broadmeadow MSJ, Lynch JM (eds) Forestry & climate change. Cromwell Press Group, Trowbridge, pp 143–150

    Chapter  Google Scholar 

  • Mallet V, Keyes DE, Fendell FE (2009) Modeling wildland fire propagation with level set methods. Comput Math Appl 57(7):1089–1101. Elsevier

    Article  MathSciNet  MATH  Google Scholar 

  • Mandel J, Beezley JD, Bennethum LS, Chakraborty S, Coen JL, Douglas CC, Hatcher J, Kim M, and Vodacek A (2007) A dynamic data driven wildland fire model. In: Computional science – ICCS 2007. Lecture notes in computer sciences, vol 4487. Springer, Berlin/Heidelberg. pp 1042–1049

    Google Scholar 

  • Marsden-Smedley JB, Catchpole WR (1995) Fire behaviour modelling in Tasmanian buttongrass moorlands. II. Fire behaviour. Int J Wildland Fire 5:215–28

    Article  Google Scholar 

  • Margerit J, Sero-Guillaume O (1999) Modelling forest fires. Inflame Internal report

    MATH  Google Scholar 

  • McArther AG (1967) Fire behaviour in eucalyptus forests. Forest Research Institute. Forest and Timber Bureau of Australia. Leaflet No. 107

    Google Scholar 

  • McCaw WL (1998) Predicting fire spread in Western Australia mallee-heath shrubland. PhD thesis. University College UNSW, Canberra

    Google Scholar 

  • Meyn A, Schmidtlein S, Taylor SW, Girardin MP, Thonicke K, Cramer W (2012) Precipitation-driven decrease in wildfires in British Columbia. Reg Environ Change. doi:10.1007/s10113-012-0319-0

    Google Scholar 

  • Möller M (2008) Adaptive high-resolution finite element schemes. PhD-thesis, Technische Universität Dortmund

    Google Scholar 

  • Moss RH, Edmonds JA, Hibbard KA, Manning MR, Rose SK, van Vuuren DP, Carter TR, Emori S, Kainuma M, Kram T, Meehl GA, Mitchell JFB, Nakicenovic N, Riahi K, Smith SJ, Stouffer RJ, Thomson AM, Weyant JP, Wilbanks TJ (2010) The next generation of scenarios for climate change research and assessment. Nature 463:747–756. doi:10.1038/nature08823

    Article  Google Scholar 

  • Pastor M (2003) Mathematical models and calculation system for study of wildland fire behavior. Prog Energy Combust Sci 29:139–153

    Article  Google Scholar 

  • Pagni J, Peterson G (1973) Flame spread through porous fuels. 14th international symposium on combustion. Pennsylvannia, pp 1099–1107.

    Google Scholar 

  • Perminov V (2010) Numerical modeling of forest fire initiation and spread. In: 4th international conference, latest trends on applied mathematics, simulation, modeling. WSEAS Press, pp 242–248

    Google Scholar 

  • Preisler HK, Weise DR (2006) Forest fire models. In: EL Shaarawi AH, Piegrosch W (eds) Encyclopedia of environmetrics, vol 2. Wiley

    Google Scholar 

  • Pyne SJ (2004) Tending fire: coping with America’s wildland fires. Island Press, Washington D.C.

    Google Scholar 

  • Pyne SJ, Andrews PL, Laven RD (1996) Introduction to wildland fire. Wiley, New York

    Google Scholar 

  • Quintiere J (2006) Fundamentals of fire phenomena. Wiley, England

    Book  Google Scholar 

  • Rothermel RC (1972) A mathematical model for predicting fire spread on wildland fuels. USDA forest service research paper INT-115, p 40

    Google Scholar 

  • Santoni PA, Balbi JH (1998) Modelling of two-dimensional flame spread across a sloping fuel bed. Fire Saf J 31(3):201–205

    Article  Google Scholar 

  • Schöning S (2009) Modellierung des potentiellen Waldbrandverhaltens mit einem geographischen Informationssystem. Geo-Processing Reihe

    Google Scholar 

  • Schaffeld H (1988) Finite-Elemente-Methoden und ihre Anwendung zur Erstellung von Digitalen Geländemodellen. PhD-thesis. University of Kaiserslautern. Geomathematics Group.

    Google Scholar 

  • Schumacher S, Bugmann H (2006) The relative importance of climatic effects, wildfires and management for future forest landscape dynamics in the Swiss Alps. Glob Change Biol 12: 1435–1450

    Article  Google Scholar 

  • Sebastián-Lopéz A, Salvador-Civil R, Gonzalo-Jimenéz J,San-Miguel-Ayanz J (2008) Integration of socio-economic and environmental variables for modelling long-term fire danger in Southern Europe. Eur J Forest Res 127:149–163

    Article  Google Scholar 

  • Séro-Guillaime O, Margerit J (2002a) Modelling forest fires. Part I: a complete set of equations derived by extended irreversible thermodynamics. Int J Heat Mass Transf 45: 1705–1722

    Article  MATH  Google Scholar 

  • Séro-Guillaime O, Margerit J (2002b) Modelling forest fires. Part II: reduction to two-dimensional models and simulation of propagation. Int J Heat Mass Transf 45:1723–1737

    Article  Google Scholar 

  • Shu C-W (1997) Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA/CR-97-206253. IACSE report no.97–65

    Google Scholar 

  • Sneeuwjagt RJ, Peet G (1985) Forest fire behaviour tables for western Australia. Australia: Department of Conservation and Land Management

    Google Scholar 

  • Steward FR (1974) Fire Spread through a fuel bed. In: Blackshear PL (ed) Heat transfer in fires: thermophysics, social aspects, economic impact. Scripta, Washington, DC, pp 315–318

    Google Scholar 

  • Telisin HP (1974) Flame radiation as a mechanism of fire spread in forests. Heat transfer in flames. Wiley, New York, pp 441–449

    Google Scholar 

  • Thomas PH (1967) Some aspects of the growth and spread of fires in the open. Forestry 40: 129–164

    Article  Google Scholar 

  • Torero JL, Simeoni A (2010) Heat and mass transfer in fires: scaling laws, ignition of solid fuels and application to forest fire. Open Thermodyn J 4:145–155

    Article  Google Scholar 

  • Van der Linden P, Mitchell JFB (2009) ENSEMBLES: climate change and its impacts: summary of research and results from the ENSEMBLES project. Met Office Hadley Centre, Exeter. http://ensembles-eu.metoffice.com/docs/Ensembles_final_report_Nov09.pdf, 28 Mar 2013

    Google Scholar 

  • Van Wagner CE (1967) Calculations on forest fire spread by flame radiation. Report No.1185, Canadian Department of Forestry

    Google Scholar 

  • Vega JA, Cuinas P, Fontrubel T, Perez-Gorostiaga P, Fernandez C (1998) Predicting fire behaviour in Galicia (NW Spain) shrubland fuel complexes. In: Viegas DX (ed) Proceedings of the third international conference on forest fire research, University of Coimbra, Luso, pp 713–28

    Google Scholar 

  • Viegas DX, Ribeiro PR, Maricato L (1998) An empirical model for the spread of a fireline inclined in relation to the slope gradient or to wind direction. In: Viegas DX (ed) Proceedings of the third international conference on forest fire research, vol 2718, University of Coimbra, Coimbra, pp 325–42

    Google Scholar 

  • Weber RO (1989) Analytical models for fire spread due to radiation. Combust Flame 78:398–408

    Article  Google Scholar 

  • Weber RO (1991) Modelling fire spread through fuel beds. Prog Enery Combust Sci 17:67–82

    Article  Google Scholar 

  • Weber RO, Sidhu HS (2006) A dynamical systems model for fireline growth with suppression. ANZIAM J 47: C462–C474

    MathSciNet  Google Scholar 

  • Weibel P, Elkin C, Reineking B, Conedera M, and Bugmann H (2010) Waldbrandmodellierung – Möglichkeiten und Grenzen. Schweiz Z Forstwes 161 (2010) 11:433–441

    Google Scholar 

  • Wendland H (2005) Scattered data approximation. Cambridge monographs on applied and computational mathematics. Cambridge University Press, Cambridge/New York

    Google Scholar 

  • Wirth C (2005) Fire regime and tree diversity in boreal forests: implications for the carbon cycle. In: Scherer-Lorenzen M, Körner C, Schulze E-D (eds) Forest diversity and function: temperate and boreal systems. Springer, Berlin/Heidelberg, pp 309–344

    Chapter  Google Scholar 

  • Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31(3):335–362. Elsevier

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Sarah Eberle thanks for the support by the Rhineland-Palatinate Center of Excellence for Climate Change Impacts (at the Forest Research Institute for Forest Ecology and Forestry, Trippstadt, Germany) within the scope of the project “Forest Fire Determination: Theory and Numerical Aspects” (P.I. Willi Freeden).

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Eberle, S., Freeden, W., Matthes, U. (2015). Forest Fire Spreading. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_70

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