Smoothing and Bootstrapping with Application to Forest Fire Modelling

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Canada's economy relies on forestry, oil and natural gas making it vulnerable to forest wildfires. The 700000 hectare Richardson Backcountry fire in 2011 is indicative of the risk to communities and the economy; evacuations occurred; some extraction operations near Fort McMurray were temporaily shut down. Fire scientists have long studied the evolution of wildfires and when and how to mitigate their effects. Deterministic approaches dominate the literature, but there is a growing awareness that the modelling of uncertainty is an important component of fire management. The main goal of my research is to add statistical rigour to the science of forest fire modelling and management. In turn, the need for improved statistical tools to solve these problems motivates the development of statistical methodology by myself, my students and collaborators, and by the larger community of environmental statisticians. Two fire spread models are under study: the Prometheus Wildland Fire Growth Model, a deterministic simulator developed at Alberta Environmental and Sustainable Resource Development and a lattice spread model developed by a team including myself and individuals at Ontario Ministry of Natural Resources and the Canadian Forest Service. Recently, a student and I discovered an efficient way to model the uncertainty in the burn maps produced by Prometheus. Our method needs further refinement: the existing rate of spread models which were developed from data having a multi-level structure, are to be revised using modern statistical methods. This is important, because we need good estimates, not only of the mean rate of spread, but also the variance, so that the uncertainty is correctly modelled. Because crownfire behaviour is very different from surface fire behaviour, we will develop a new statistical model to distinguish them, as well as a model to distinguish active and passive crowning. Motivated by this kind of problem, new methods are being developed for estimating curves and surfaces that satisfy given properties. These curve-fitting methods will find wide applicability in other areas of quantitaitve science. We also plan to develop models for the forecast errors in the rate of spread and incorporate these into our randomized Prometheus simulator. The lattice spread model needs an accurate calibration method. Data from small experimental fires will be used to refine data extraction methods and parameter estimation methodology. Anisotropic filtering is useful in processing the data; this is inspiring a new class of kernel smoothers which exploit the underlying principal. Additional features of a good fire spread simulator include a model for the duration of a fire (given that wildfires are normally not detected at the time of ignition), and a model for the lofting of dangerous firebrands which start new fires at locations remote from the original fire. Longer term plans include the study of lightning and fire ignitions which uses joint modelling methods. Fire managment problems include the modelling and monitoring of the fire weather index (FWI), an important measure of fire danger. With my students, I have begun developing spatial versions of control charts which can be used to identify FWI hotspots. To do this accurately, spatio-temporal models of FWI are required. My students and I are also studying historical trends in initial attack response time as a way of evaluating fire management effectiveness. This statistical study of wildfire opens up ways to address larger risk management questions which are of use for long range fire management planning; the insurance industry will also benefit from such information.