Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Braun, W. John


University of British Columbia Okanagan

2nd Supervisor

Woolford, Douglas G.


3rd Supervisor

Dean, Charmaine B.


University of Waterloo

Joint Supervisor


Wildland fires are natural disturbances that enable the renewal of forests. However, these fires also place public safety and property at risk. Understanding forest fire spread in any region of Canada is critical to promoting forest health, and protecting human life and infrastructure. In 2014, Ontario updated its Wildland Fire Management Strategy, moving away from ``zone-based" decision making to ``appropriate response" decision making. This new strategy calls for an assessment of the risks and benefits of every wildland fire reported in the province. My research places the emphasis on the knowledge and understanding of fire spread rates and their variabilities. To satisfy these needs for a forest fire risk-benefit assessment tool that incorporates the effects of ignition, extinction, and spreading rate, the research herein explores new methods for spread rate estimation with an emphasis on understanding spread rate variability, for use in stochastic forest fire models.

In this research, we develop a novel anisotropic smoothing method for change-point data that uses estimates of the underlying data generating process to inform smoothing. We show that our anisotropic local constant and local linear kernel regression estimators are consistent with convergence rate O(n^(-1/(q+2)). We demonstrate their effectiveness on simulated one- and two-dimensional change-point data that are motivated by fire spread data. We detail the design and experimentation procedure of a micro-fire spread apparatus. We consider these micro-fire experiments a mouse model for wildland fire spread. We apply the anisotropic smoothers as image processors for measured data, and as an estimator for ignition and extinction event times at the pixel resolution. Those event times are then used to estimate instantaneous and average fire spread rates, and residency times for burning cells.