June  5, 2020

Workshop on Forest Fires and Point Processes
May 24-28, 2005(back to home page)


Larry S. Bradshaw, USDA Forest Service, Rocky Mountain Research Station
Missoula Fire Sciences Laboratory

Basics of the National Fire Danger Rating System
The National Fire Danger Rating System (NFDRS) is utilized by most United States federal and state agencies to monitor seasonal fire danger conditions. NFDRS outputs are numeric measures of the potential over a large area for fires to ignite, spread, and require suppression action. The NFDRS processes weather observations and forecasts to estimate daily moisture content of four dead and two live categories of fuel which are integrated with stylized fuel models by the Rothermel fire spread model to produce the systems' basic fire characteristic based indexes. Fire occurrence risk factors can be used to produce indexes of fire occurrence, which are combined with the fire characteristic based indexes to provide an overall fire suppression workload estimate for a fire danger rating area. Application of NFDRS output is generally based on probability of exceeding thresholds of climatic normals that, when combined with historical fire occurrence distributions, provide meaningful measures of fire business for fire management decision support systems. The national system runs on the USDA, Forest Service Weather Information Management System (WIMS) which receives hourly observations from some 1200 automated weather stations and next-day forecasts from the National Weather Service. WIMS interfaces with national databases that facilitate the climatological aspect of interpreting and applying NFDRS outputs.

This talk will cover the history and development and structure of the NFDRS, caveats to consider when working with the outputs, and current work to improve the modeling, validation, and application of the system outputs.

David R. Brillinger, Statistics Department, University of California, Berkeley

Risk Analysis for Two Marked Point Process Data Sets
We consider the analysis of spatial-temporal marked point process data. In one example the marks are ordinal-valued and the data are recently discovered ones concerning damage observed in Spain in consquence of the Great 1755 Lisbon Earthquake. In a second example the marks are fire sizes in acres for wildfires in Federal Lands in Oregon during the period 1989 to 1996. A connecting thread is the development of damageability matrices that may be employed for planning and insurance purposes.

David T. Butry, USDA Forest Service, Southern Research Station

Estimating the Effect Wildfire Management has on Fire Behavior: A Propensity-Score Matching Approach
Florida experiences more than 200,000 acres of wildfire and another 500,000 acres of hazard mitigating prescribed fire a year. Since prescribed fire is targeted to fire prone areas, simply comparing the amount of wildfire in locations with prescribed fire with those without, we find that fire size and intensity is much larger in areas with prescribed fire. Does this imply fuel management is ineffective? Hardly, but it does suggest that using an ordinary least squares framework to model wildfire behavior (size or intensity) as a function of management (fuels treatment/prescribed fire) may underestimate the true effect of management. Fundamentally, the model is biased due to the endogeneity exhibited between wildfire behavior and wildfire management and mitigation. We employ a spatially-explicit propensity-score matching model to evaluate the effectiveness of prescribed fire. The propensity-score matching model is superior to its least squares counterpart, in this case, since it is unbiased, nonparametric, and causal. We find that the returns to prescribed burning, in terms of fire mitigation and damage, are significant.

Steven G. Cumming, Boreal Ecosystems Research
Co-author: Brendan Mackey.

A multivariate regionalisation of Canadian fire regimes.
The Canadian Large Fire Database (LFDB) records the point location, date, final size and cause of all known wildfires larger than 200ha from 1957--1997 (41yr). We used these data to estimate and map fire regime parameters of frequency, size and seasonality over a uniform grid 10,000 km^2 hexagonal cells. We assumed Poisson frequencies (fires/yr) and truncated exponential fire sizes (scaled and shifted as z = log x/200), evaluating goodness-of-fit by Anderson-Darling tests. Seasonality was measured as the expected proportion of annual area burned by summer fires. We used an agglomerative hierarchical clustering procedure to identify sets (n=10 or 20) of cells with similar parameters. This revealed distinct contiguous areas with relatively homogeneous fire regimes. These "fire regions" do not coincide with Ecoregions or larger spatial units of the Canadian Ecological Land Classification. We derived expected annual burn rates from expected fire sizes and frequencies. Only 73/547 boreal or taiga cells (13.3%) had burn rates above 0.01, a value perhaps considered typical of the boreal. The mean and median rates were 0.0043 and 0.0023, respectively. I will conclude by discussing some open problems in the statistical analysis of the LFDB, including size-biased sampling, covariance of the frequency and size processes, and temporal non-homogeneity

Andre Dabrowski, University of Ottawa

Modeling distances between ignitions
Forest fires ignitions by lightning are frequently represented as a point process, and one can adopt a variety of methods to study the characteristics of such a process. Here we look at inter-point distances, $\|X_1-X_2\|$ and the tail index $\alpha$ defined by $$ P[\|X_1-X_2\|\le x]\sim x^\alpha $$ as $x\downarrow 0$. This index is can be estimated using the extreme least order statistics of the inter-point distances, and we illustrate those methods on a sample data set of ignitions.

Sylvia R. Esterby, UBC-Okanagan

Analysis of fire index data
In a variety of contexts, indices are developed to characterize the state and change of state of a system. Fire weather indices are an example. Calculation of such an index may involve weather elements as input to a set of equations, where the equations incorporate scientific knowledge about the process by which these inputs affect measures of fire risk.
A preliminary analysis of the variability of such an index will be discussed with the objective of adding a measure of uncertainty about the index value.

M.J. Fortin, Department of Zoology, University of Toronto,

Deforestation in Québec northern boreal forest due to fire regime
Boreal forest cover in northern Québec changes from a continuous forest stand mosaic in the boreal forest to isolated forests fragments in the forest-tundra biome. This distribution and extent of forest fragments are the direct consequences of fire patterns and repetitive failures of the postfire forest-recovery process, which are still visible and quite active today. To test whether wildfires are sufficient to explain the current deforestation in northern Québec, we developed a spatially explicit model of wildfire and postfire forest regeneration at the biome scale that simulates the spatial dynamics of forest in terms of forest cover and its spatial pattern. The calibration of the model was based on historical fire data of Québec northern boreal forest, ranging from 1920 to 1984. The proportion of remnant forest stands within fires was quantified using aerial photographs. As a surrogate for climatic data not available for this area, latitude and elevation were used. At the biome scale, it is found that the large-scale reduction of the forest cover induces positive feedbacks that exacerbate the climatic differences between the northern and the southern forest-tundra biome, due to enhanced albedo. Results are put into perspective with the tundra-boreal forest ecotone regression south due to change in fire regime.

Marcia Gumpertz, North Carolina State
Co-Authors: David Butry, Marc Genton

Wildfires in Florida -- Preliminary Analysis
Our objectives are to examine the wildfires that occurred in the St. John's River Water management District (SJRWMD) in Florida between 1996 and 2001. We are interested in differences exhibited by large and small wildfire regimes and the effects of ignition and fuel sources, weather, land use and landscape characteristics, and wildland management strategies. For each wildfire that occurred in this period we know the date and cadastral section (a one square mile area) of ignition and the reported area burned, but not the actual perimeter of the fire. We use an auto-Gaussian approach to incorporate previous wildfire and prescribed burning in the section and neighboring sections into our regression models. Using this regression approach we found that the models for wildfires greater than 1000 acres are quite different than those for wildfires smaller than 1000 acres, which might indicate the need for different management strategies. For instance we found that preventive burning reduced wildfire size for the small fires (less than 1000 acres), but not for the larger fires. This finding is the subject of further study.

Gail Ivanoff, University of Ottawa

What is a multiparameter renewal process?
The concept of the renewal property is extended to processes indexed by a multidimensional time (or spatial) parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. A new version of the waiting time paradox is given for multidimensional Poisson processes, and is shown to imply the renewal property. Finally, martingale properties of renewal processes are considered. Under mild conditions, a Poisson limit theorem holds.

A multiparameter renewal process can be used to model the spread of a forest fire under a prevailing wind. Even as an approximate model, the renewal process has the advantage that it is very easy to simulate.

This is joint work with Ely Merzbach.

Edward A. Johnson, Department of Biological Sciences and Kananaskis Field Stations, University of Calgary

A Process Approach to Predicting Tree Mortality in Surface Fires
Traditional methods for predicting post-fire tree mortality employ statistical models which neglect the processes linking fire behavior to tree-level mortality patterns. Here we present an alternative process approach which predicts tree-level mortality using heat transfer theory and tree allometry models. A linefire plume model drives independently validated conduction and lumped capacitance heat transfer analyses to predict time to meristem necrosis in tree stems, branches, and buds. Local stem, branch, and bud meristem necrosis is scaled to tree-level mortality using a sapwood area budget derived from tree allometry models. Thus, our approach provides a predictive, mechanistic model which explains how tree-level mortality patterns are governed by physical fire characteristics (fireline intensity and residence time), tree physiology (water content), and tree morphology (meristem height, bark thickness, branch/bud size, foliage architecture). To illustrate, we predict tree-level mortality for white spruce (Picea glauca (Moench) Voss) and lodgepole pine (Pinus contorta Loudon var. latifolia Engelm.) across a range of fire conditions typical of these communities. Models were parameterized using data collected from subalpine spruce and pine communities in the southern Canadian Rocky Mountains. Foliage effects were quantified using convection correlations obtained in a laminar flow wind tunnel for a Re range of 100 to 2000, typical for branches/buds in a linefire plume. Our results generally agree with empirical observations of tree mortality. However, results also suggest stem meristem necrosis (girdling) as the mechanism of whole tree mortality, challenging statistical model assumptions that crown meristem necrosis is the primary mechanism.

Rafal Kulik, University of Ottawa

Tutorial on point processes
The main idea of my presentation is to introduce to the different aspects of the theory of point processes and especially to point out the possible applications to the various fields (simulation of random processes, empirical processes, stochastic geometry, among others). We concentrate on applied examples, instead of on general theory.

First, I will give an introduction to the theory of point processes on the real line, including the Palm measure approach to stationary point processes and simple compensator theory. Then, limited extensions to point processes on general spaces will be given.

Finally, I want to point out some recent results on point process theory, including long range dependence.

David Martell, University of Toronto

Forest Fire Management - a Systems Modelling Perspective
Forest fire managers must resolve decision-making problems with planning horizons that vary from minutes to decades across distances that can range from meters to hundreds of kilometers and many of their decision-making problems are complicated by uncertainty concerning when and where fires will occur and how they will behave. I will characterize fire management from a systems modelling perspective and describe some of the mathematical models that have been developed and statistical methods that have been used to support the development of decision support systems that can be used by fire and forest managers.

Robert McAlpine, Ministry of Natural Resources

Forest Fire Management in Ontario - a Primer and Manager's perspective.
The forest fire management organization in Ontario is at times large, at others small, and always seemingly changing and adapting to the situation. This talk will provide the audience with a primer of the organization - size and structure, and the basics of how and what we do. The fire management program, like most other emergency operations programs, is based on response decisions; decisions that are often made very quickly to difficult situations. These decisions are made at all levels in the organization, from the front line of the fire, to the provincial management offices, and within a number of areas - operations, logistics, and business management. The back bone information systems and models that support the decision making within that organization will be presented along with some of the current challenges we face.

Farouk Nathoo and Charmaine Dean, Simon Fraser University

Mixture Models for Spatio-Temporal Multi-State Processes
Multi-state models can be useful in longitudinal studies where at any point in time, an individual may be said to occupy one of a discrete set of states and interest centers on determining what influences transitions between states. For example, states may refer to the number of recurrences of an event, or the stages of a disease. Methodology for the analysis of multi-state models is well developed for the health context, where typically, individuals may be considered to be independent. In forestry, statistical methodology for the analysis of this type of longitudinal data needs to recognize the added feature of incorporating spatial correlation. For example, how the rates of transitions over states differ spatially over a region may be of interest. Spatial random effects are considered in a special case: the two-state mover stayer model. Our motivating example is a study of recurrent weevil infestation in British Columbia forests. This seven-year study was conducted by the BC Ministry of Forests. Of primary interest was to describe the pattern of weevil infestation throughout the area over the period of observation.

Haiganoush K. Preisler, Pacific Southwest Research Station

Some Statistical Issues in Predicting Wildland Fire Risk
Wildland fire managers require forecasts of fire hazards at a variety of scales ranging from the total expected area to burn nationally in a given year to the expected area to burn in the remaining hours of a raging fire.
There are data available at all these scales and statistical issues vary accordingly.
In this talk I will discuss some of the stochastic methods that are proving useful for forecasting fire risk and some of the open problems remaining.

Fuensanta Saura, Universitat Jaume 1, Castellon, Spain.
Co-Authors: Pablo Gregori, Pablo Juan and Jorge Mateu

Analysis of forest fires in Comunidad Valenciana (Spain) using a spatial statistics methodology
The study of the process that governs the occurrence of forest fires in particular regions has very much interest in very different places of the planet,since the consequences can be really disastrous everywhere. Because of it, different methodologies have been developed with a common aim: predicting forest fires and determining their possible gravity. A particular example is the methodology exposed in [5] and [4]. In that case, observations of forest fires along time were registered, and different conditional intensity models were fitted, some of them including a component given by a risk index, the BI. Based on a residual analysis, they studied if the fit involving the BI improved the fit without it, trying to determine the goodness of that risk index.

Rick Schoenberg, (Statistics, UCLA)

On the Estimation of Separable Point Processes and Possible Improvements to the Burning Index.
In Los Angeles County, wildfire risk assessments are often made using the Burning Index (BI), a numerical rating issued by the USDA
Department of Forestry. Unfortunately, the BI appears to be a rather poor predictor of wildfires in Los Angeles County. Because so many variables are positively associated with wildfire risk, the construction of models to improve upon the BI is quite a difficult
task. The problem is essentially the familiar "curse of dimensionality," and is greatly alleviated when different components in the process may be estimated separately. Some results will be presented concerning situations where such separability is permitted,
and their use in predicting wildfires in Los Angeles County will be explored.

Dean Slonowsky,University of Manitoba

Set-Indexed Martingales: Tools forMultidimensional Stochastic Modelling and Analysis
This talk presents the notion of set-indexed martingales, which are capable of modelling processes which evolve randomly over time and
over complex regions of space. Some theoretical innovations in this .eld will be discussed, including:(i) central limit theorems, (ii) the set-indexed Ito integral, and (iii) a set-indexed notion of “stopping line”. Results such as these may provide useful tools for practitioners in the stochastic modelling of the space-time dynamics of forest .res and related phenomena.

David Stanford, University of Western Ontario

Co-authors: Douglas G. Woolford(1), Dennis Boychuk(2)
(1) Department of Statistical and Actuarial Sciences, The University of Western Ontario
(2) The Ontario Ministry of Natural Resources, Sault Ste. Marie, Ontario

Fire Perimeter Analyzed as a Fluid Queue
The primary goal when fighting a wildfire is its containment. This is commonly done by ground crews who attempt to obstruct the fire’s growth by removing available fuel from around its perimeter. Once a fire has been completely surrounded by these ‘fire lines’, it is said to be fully contained. In this talk, we examine the potential application of recent theoretical developments in fluid queues to model uncontrolled wildfire perimeter. Specifically, we focus on the probability of containing a fire prior to reaching a randomly distributed, finite time horizon. Transitions to lower nonzero levels are also investigated. A preliminary model is introduced to demonstrate the potential of the application, and numerical results are given for illustrative purposes.

Rolf Turner, University of New Brunswick

Planar Point Pattern Analysis of New Brunswick Forest Fire Data
This talk will consist essentially of a case study in the analysis of forest re data. The data sets to be considered include information on the location (coordinates) of each re, the start and nish time, the cause, and the area burned. These data were very graciously made available to me by the New Brunswick Department of Natural Resources. The data comprise the records of all forest res occurring in New Brunswick from 1987 to 2003, (with the data for 1988 unfortunately being missing at this time). For the most part I shall approach the data from a purely spatial (rather than spatio-temporal) point of view. The data for each year will be viewed as planar point pattern
which is in turn a realization of a planar point process. I have structured the data sets as \point pattern objects" amenable to being analyzed in the R programming environment via the (contributed) package spatstat. The auxiliary information (cause, area burned, etc.) are supplied as data frames, columns of which may be used as marks for the patterns. I will brie y introduce some of the facilities of spatstat and then use these facilities to e ect the analysis. I will begin with some basic graphical displays of the New Brunswick re data, after which I will experiment with exploratory techniques. I will also t a number of basic point pattern models to these data. Finally I will demonstrate some techniques for assessing and evaluating the t of these models. The objective throughout will be to gain some insight into these data and to reveal any non-obvious structure that may exist in them.

.David Vere-Jones, Victoria University of Wellington and Statistical Research Associates Ltd.

Some Models and Procedures for Space-Time Point Processes
In this talk I shall briefly review the background to space-time models defined through conditional intensities, and then examine issues arising from two specific topics which have caused us recent headaches. The first concerns situations where the point process model is regressed onto background variables which are themselves integrated from space-time information. In this case a first approach may be to develop a lattice-based model for both collecting information and preparing forecasts based on that information. However questions arise as to how best to define the lattice structure, the regions from which information should be collected, and the regions to which forecasts should be applied. The other topic relates to the limited progress we have so far made in thinking about the applicability of hidden Markov structures to space-time point process models.

Domingos Xavier Viegas, University of Coimbra, Portugal

A Mathematical Model for Eruptive Fire Behaviour and Related Problems
An overview of the research carried out by the author and his research group on some physical aspects of forest fires is given, covering in particular the following topics:
- Meteorological fire danger index
- Fuel characterization
- Wind and slope effects on fire behaviour
- Dynamic behaviour of a fire.
A mathematical model to predict the eruptive behaviour of a fire is proposed. This phenomenon is known in the American literature as fire blow-up and is related to jump fires and to many fatal accidents in the past. Eruptive fire behaviour is an example of a self exciting process as the convection induced by the fire itself has a feedback on the combustion zone modifying its properties. As a result fire spread may increase dramatically causing loss of control of a fire.

Douglas G. Woolford, University of Western Ontario

Co-authors: W. John Braun and Reg J. Kulperger Department of Statistical and Actuarial Sciences, The University of Western Ontario

Exploring Lightning and Fire Ignition Data Using Data Sharpening Techniques
We present an exploratory analysis of lightning strike and fire ignition data supplied by the Ontario Ministry of Natural Resources. The focus will be on the 'sharpening' of the lightning data to locate 'centres' of lightning activity in both space and time. Data sharpening, developed by Choi and Hall, is an iterative technique in which data is regressed on itself via local constant regression. This reduces the data in the sense that the observations converge to local modes. By varying parameters in the algorithm we reduce noise in an attempt to track the storm centres through time. The identified storm centres provide a possible explanatory variable to explain forest fire ignitions and a means to validate a cluster process model for centres of lightning activity.

Talk 1: CFFDRS

Mike Wotton, Great Lakes Forestry Centre, Canadian Forest Service -Natural Resource Canada

Using and interpreting output from the Canadian Forest Fire Danger Rating System
The Canadian Forest Fire Danger Rating System (CFFDRS) is used universally across Canada and in several other countries to aid fire management agencies in the estimation of daily forest fire potential. Fire management activities, such as the estimation of expected daily fire occurrence, the pre-positioning of suppression resources, the routing of detection flights, and the estimation of fire behaviour of a spreading fire, all rely on information from the system. The CFFDRS is composed of two major sub-systems, the Fire Weather Index (FWI) System and the Fire Behaviour Prediction (FBP) System. The FWI System consists of a set of models tracking moisture in three distinct fuel layers of the forest floor, and a set of relative fire behaviour indices used for the estimation of regional fire danger. The FBP System consists of models predicting fire behaviour (fuel consumption, rate of spread, fire intensity etc.) in a number of the major fuel types across Canada. Both systems rely for the most part on models that have been derived empirically after years of experimental field research.

This talk will cover the history of the development of the (CFFDRS) with emphasis on the application and interpretation of the outputs of the system. Current (and future) plans to improve the capabilities of the system will also be presented.

Talk 2: Fire Occurrence

Mike Wotton, Great Lakes Forestry Centre, Canadian Forest Service -Natural Resource Canada

Methods for the prediction of forest fire occurrence in Ontario
The daily planning and resource deployment procedures of forest fire management agencies rely on estimates of when and where fires are expected to occur each day. As part planning and resource pre-positioning activities fire managers estimate the number of both people- and lightning-caused fire expected in their region each day. Currently, in most operational agencies across Canada, fire occurrence predictions are made based on the local knowledge and expertise of operational personnel. This talk describes recent work carried out using both logistic and Poisson regression to build predictive models of daily forest fire occurrence. Separate models of people and lightning-caused fire occurrence, recently developed for Ontario, will be presented. Their potential application as tools to assist in daily operational fire management activities will be discussed.

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