Smoothing and Bootstrapping with Application to Forest Fire Modelling

加拿大的经济依赖于林业、石油和天然气，这使得它很容易受到森林大火的影响。2011年理查森70万公顷的山火表明了社区和经济面临的风险；疏散发生;麦克默里堡附近的一些提取作业被暂时关闭。火灾科学家长期以来一直在研究野火的演变以及何时以及如何减轻其影响。确定性方法在文献中占主导地位，但越来越多的人意识到不确定性建模是火灾管理的重要组成部分。**我研究的主要目标是为森林火灾建模和管理科学增加统计严谨性。反过来，对改进统计工具来解决这些问题的需求促使我、我的学生和合作者，以及更大的环境统计学家群体发展统计方法。**目前正在研究两种火灾蔓延模型：普罗米修斯野火增长模型，这是阿尔伯塔环境和可持续资源发展部开发的确定性模拟器，以及由我和安大略省自然资源部和加拿大林业局的个人组成的团队开发的晶格蔓延模型。最近，我和一个学生发现了一种有效的方法来模拟普罗米修斯生成的燃烧图中的不确定性。我们的方法需要进一步改进：现有的从具有多层次结构的数据中建立的传播率模型需要用现代统计方法进行修正。这很重要，因为我们不仅需要对平均扩散率，而且需要对方差进行良好的估计，这样才能正确地模拟不确定性。由于顶火行为与地表火灾行为非常不同，我们将开发一个新的统计模型来区分它们，以及一个区分主动和被动顶火的模型。在这类问题的推动下，人们开发了新的方法来估计满足给定性质的曲线和曲面。这些曲线拟合方法将广泛适用于定量科学的其他领域。**我们还计划开发预测传播率误差的模型，并将其纳入我们的随机普罗米修斯模拟器。点阵展开模型需要精确的标定方法。来自小型实验火灾的数据将用于改进数据提取方法和参数估计方法。各向异性滤波在数据处理中很有用；这启发了一类新的利用底层原理的核平滑器。一个好的火灾蔓延模拟器的附加功能包括一个火灾持续时间的模型（考虑到野火通常在点燃时无法检测到），以及一个在远离原始火灾的地方引发新火灾的危险火种的放样模型。长期计划包括使用联合建模方法研究闪电和点火。**火警管理问题包括模拟及监察火警天气指数（火警天气指数是火警危险的重要量度）。与我的学生一起，我已经开始开发空间版本的控制图，可以用来识别wi热点。为了准确地做到这一点，需要FWI的时空模型。我和我的学生也在研究初始攻击响应时间的历史趋势，作为评估火灾管理有效性的一种方式。**这项野火的统计研究开辟了解决长期火灾管理规划中使用的更大风险管理问题的方法；保险业也将从这些信息中受益。

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.