Workshop on Forest Fires and Point Processes
May 24-28, 2005(back
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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
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
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
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
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
M.J. Fortin, Department of Zoology,
University of Toronto,
Deforestation in Québec northern boreal forest due to fire
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
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
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
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
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
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
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
Fuensanta Saura, Universitat Jaume 1, Castellon,
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  and . 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
Dean Slonowsky,University of Manitoba
Set-Indexed Martingales: Tools forMultidimensional Stochastic Modelling
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
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 fires
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 eect 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
Domingos Xavier Viegas, University of Coimbra,
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
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
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
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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