Modeling wildland fire propagation with level set methods

V. Mallet*, D. E. Keyes, F. E. Fendell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


Level set methods are versatile and extensible techniques for general front tracking problems, including the practically important problem of predicting the advance of a fire front across expanses of surface vegetation. Given a rule, empirical or otherwise, to specify the rate of advance of an infinitesimal segment of fire front arc normal to itself (i.e., given the fire spread rate as a function of known local parameters relating to topography, vegetation, and meteorology), level set methods harness the well developed mathematical machinery of hyperbolic conservation laws on Eulerian grids to evolve the position of the front in time. Topological challenges associated with the swallowing of islands and the merger of fronts are tractable. The principal goals of this paper are to: collect key results from the two largely distinct scientific literatures of level sets and fire spread; demonstrate the practical value of level set methods to wildland fire modeling through numerical experiments; probe and address current limitations; and propose future directions in the simulation of, and the development of, decision-aiding tools to assess countermeasure options for wildland fires. In addition, we introduce a freely available two-dimensional level set code used to produce the numerical results of this paper and designed to be extensible to more complicated configurations.

Original languageEnglish (US)
Pages (from-to)1089-1101
Number of pages13
JournalComputers and Mathematics with Applications
Issue number7
StatePublished - Apr 2009
Externally publishedYes

Bibliographical note

Funding Information:
The support of the National Science Foundation under grant CCF-03-52334 and the US Department of Agriculture Forest Service under grant SFES 03-CA-11272169-33, administered by the Riverside Forest Fire Laboratory, a research facility of the Pacific Southwest Research Station, is gratefully acknowledged. The authors are particularly indebted to Dr. Francis M. Fujioka of Riverside for enhancing the relevance of our research through his technical advice, and for his support for the training of summer students in the computational technology of fire spread and fire imaging.


  • Front propagation
  • Hamilton-Jacobi equations
  • Level set methods
  • Multivac software
  • Wildland fire spread

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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