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Derivation and investigation of mathematical models for spotting in wildland fire

  • Author / Creator
    Martin, Jonathan Michael
  • Spotting in the context of wildland fire refers to the creation of new fires, downwind from an existing fire front, where the new fires result due to the launch, and subsequent fuel bed ignition upon landing, of burning plant ma- terial released from the main front. We will present a new integro-partial differential equation (i-PDE) model which includes both local spread, com- bustion/extinguishment, and non-local spread due to spotting. We will also present a new model for firebrand transport in the atmosphere, which allows us to incorporate existing physical or empirically-based submodels existing in the literature to obtain the spotting distribution. We will use the spottting distri- bution to investigate the problem of fire fronts breaching obstacles to local fire spread, such as a highway or river, and the spotfire distribution appears as a kernel for the integral term in our i-PDE model. We then investigate travelling wave solutions to the i-PDE model, demonstrating that spotting can increase the rate of spread, or cause acceleration of a fire front’s advance.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3P55DT3V
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Hillen, Thomas (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Reuter, Gerhard (Earth and Atmospheric Sciences)
    • Lewis, Mark (Mathematical and Statistical Sciences)
    • DeVries, Gerda (Mathematical and Statistical Sciences)
    • Minev, Peter (Mathematical and Statistical Sciences)
    • Soung-Ryoul, Ryu (Renewable Resources)