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Derivation and investigation of mathematical models for spotting in wildland fire Open Access


Other title
Type of item
Degree grantor
University of Alberta
Author or creator
Martin, Jonathan Michael
Supervisor and department
Hillen, Thomas (Mathematical and Statistical Sciences)
Examining committee member and department
Reuter, Gerhard (Earth and Atmospheric Sciences)
Soung-Ryoul, Ryu (Renewable Resources)
DeVries, Gerda (Mathematical and Statistical Sciences)
Lewis, Mark (Mathematical and Statistical Sciences)
Minev, Peter (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
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