Forests, Fires and Stochastic Modeling
Charmaine Dean
Statistics & Actuarial Science
Simon Fraser University, Canada
Looking for climate change signals
Challenges in analysis
CCIRC - SFU
J. Cao1, C.B. Dean1, D.L. Martell2 & D.G. Woolford1,2
1. Statistics & Actuarial Science; Simon Fraser University, Canada
2. Faculty of Forestry; University of Toronto, Canada
Photo: Gisela Kraus. http://commons.wikimedia.org/wiki/Image:Blitz_Gewitter_in_den_Bergen.jpg
Overview
Introduction / Motivating Example
Climate Change and Forest Fires
The Data
Modelling Framework
Preliminary Results
Discussion
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Introduction
fires are a significant
disturbance in forested
ecosystems
Photo: Fletcher Quince
Alberta Sustainable Resource Development
there is a need to characterize these regimes
-
the spatial-temporal behaviour of ignitions
-
how fire spreads and is affected by suppression
-
the impact of climate change
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A Motivating Example
The Largest Wildland Urban Interface
Forest Fire in Canadian History...
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The 2003 Okanagan Mountain Park Fire
discovered August 15, 2003
driest summer in 104 years
appox. 30,000 ha burned
50,000 evacuated
238 homes destroyed
$200 million in insurance claims
$400 million fire fighting costs
Kelowna
burned area
Image: NASA/GSFC/MITI/ERSDAC/JAROS, and
U.S./Japan ASTER Science Team and the NASA
Earth Observatory.
Photo: James Moore
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The 2003 Okanagan Mountain Park Fire
discovered August 15, 2003
driest summer in 104 years
appox. 30,000 ha burned
50,000 evacuated
238 homes destroyed
$200 million in insurance claims
Extreme
$400 million fire An
fighting
costs
Kelowna
Event.
Due To Climate Change?
burned area
Image: NASA/GSFC/MITI/ERSDAC/JAROS, and
U.S./Japan ASTER Science Team and the NASA
Earth Observatory.
Photo: James Moore
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Climate Change & Forest Fires
Weber & Stocks (1998):
Increasing temperatures could
increase number of ignitions
extend fire season
increase amount of severe
fire-weather
Thunder Bay Fire # 37 (May 2007).
Ontario Ministry of Natural Resources
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Climate Change & Forest Fires
Thunder Bay Fire # 37 (May 2007).
Ontario Ministry of Natural Resources
Weber & Stocks (1998):
Increasing temperatures could
increase number of ignitions
extend fire season
increase amount of severe
fire-weather
Studies using climate model forecasts suggest increased
severity ratings[1], area burned[2] & ignitions[3]
Quality-control analysis of historical fire records found
changes in variance for ignitions and area burned[4]
[1] Flannigan & Van Wagner (1990)
[3] Wotton et al. (2003)
[2] Flannigan et al. (2005)
[4] Podur et al. (2002)
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The Data
The Ontario Ministry
of Natural Resources
responsible for detection,
suppression, prevention and
forest fire management
record each fire’s:
- date
- location
- cause
- final size
Photo: Mitch Miller
Ontario Ministry of Natural Resources
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The Data (continued)
Some Statistics on Forest Fires in
Ontario, a central province in Canada:
Ontario’ area > 1 million km2
86% of Ontario is forested
Between 1996 – 2005:
~ 13,000 wildfires
~ 1.5 million hectares burned
~ 54% due to lightning
lightning fires accounted for
80% of the total burned area
Photos:
Ontario Ministry of Natural Resources
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Modelling Framework
A Finite Mixture of Generalized Additive Models
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Generalized Additive Models (GAMs)
Extend generalized linear models
incorporate non-linear relationships via smoothers
smoothers = linear combinations of basis functions
K
f ( x ) = ∑ ck φ k ( x )
k =1
where
- the sum is over a finite number of knots k,
partitioning the range of the covariate
- {ck} are a set of coefficients (to be estimated)
for the set of basis functions, {φk(w)}
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Finite Mixture Models
assume the response variable comes from a population
made up of a set of G distinct groups, each of which has a
different distribution:
G
Y ~ ∑ π i fi ( y)
i =1
where the πi are mixing proportions (that sum to 1),
representing the probability that Y comes from the
component density fi(y)
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Mixtures
Many problems where mixtures seem evident
Flexible mixture methods for counting processes: panel
data and on multi-state data, and for zero-heavy data
Heterogeneity: need to accommodate hidden subpopulations; differential effects across sub-groups?
Estimate functional mechanism generating event
recurrence
Several random effects including spatial effects need
handling in a multivariate fashion
Health studies: clustering of disease trends, accounting
for spatial correlation, developing surveillance alarm
functions
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Mixtures
Mixtures of two-state Markov chain models, transition
probabilities incorporate smooth time trends and (joint)
spatial effects
Pine weevil studies; health status of individuals: describe
the transition process between states of health and
characterize the variation of this process in space and
time
Zero-heavy count data models with spatial effects
(Ainsworth); accommodating different types of zeros
Mixtures for isolating hotspots while incorporating smooth
spatial effects over the surface (Ainsworth)
Mixtures of intensity functions for the analysis of count
data, where subcomponent intensities are penalized
splines, with spline covariate effects
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The Modelling Framework
fire day:
a day during which
one or more fires are
reported in a region.
Z(t) = # fire days during time t.
Photo: Natural Resources Canada
Two possible mixtures with logistic GAM components:
1. Z(t) ~ q1
+ q2 Bin(7, p1(t))
+ (1 – q1 – q2) Bin(7, p2(t))
2. Z(t) ~ q1(t) + q2(t) Bin(7, p1(t)) + (1 – q1(t) – q2(t)) Bin(7, p2)
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Some Preliminary Results
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A Preliminary Model &
Some Goodness-of-Fit
Study Area:
- 9,884,983 hectare region of
boreal forest in northwestern
Ontario
0.25
- very little fire management
and human activity in this
region
0.20
0.15
0.10
0.05
2000
- a changing unorganized
detection system is a strong
confounding factor
1990
0.00
1980
10
20
30
wee
k
1970
40
50
Analysis:
- all detected lightning-ignitions
from 1963 through 2004
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60
40
20
0
number of fires
A Preliminary Model &
Some Goodness-of-Fit
0.25
0
5
10
15
20
25
fortnight
0.20
1990
0.00
1980
0
10
10
2000
5
0.05
number of fires
0.10
20
0.15
20
30
wee
k
1970
40
1970
50
1980
1990
2000
year
Observed (points) vs. expected (line)
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An Observation
6
0
2
4
observed
8
10
12
The smoothers are good at capturing overall mean trends.
But, they don’t adequately describe the extreme events.
1970
1980
1990
2000
year
Fortnight 12: observed (points) vs. expected (line)
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Handling the Extreme Events
extreme events act like low leverage outliers
identified as large standardized residuals (i.e.,
> 2)
heavy tailed ⇒ model with an extreme value distribution?
e.g., generalized Pareto:
ξˆ = −0.25
σˆ = 3.25
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Ongoing / Future Work
hypothesis test for change-point in Pr{extremes}
incorporating trend components into the residuals
extreme events more frequent?
intra-annual seasonality in extreme events?
accounting for strong confounding factor:
unorganized detection not constant
more smaller fires detected over time
sensitivity to scale of model (daily vs. weekly)
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Assessing and Communicating
Climate Change Effects
Aims:
Deciding on objectives: are they reasonable and objective
What are indices of change; of environmental health
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Assessing and Communicating
Climate Change Effects
Data:
Historical data
Perhaps from a widely dispersed collection with different
sources (temperature and weather data, forestry data);
Digitizing data from images, written records
Differences in collection schedule, format etc can also
occur within specific types of data (temperature) when
collected over long periods
In the forestry context detection changes over time
Data collected for different purposes than current
investigation
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Assessing and Communicating
Climate Change Effects
Data Considerations (continued):
Combining data with different precisions
Quality of data – assessment of precisions; few
opportunities for verification of historical records
Different study designs -- data collected over long time
periods
Incomplete data: missing responses, missing covariates;
little information on reasons for missingness
Different intervention strategies used over long series;
e.g. intervention strategies with regards fire management
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Assessing and Communicating
Climate Change Effects
Monitoring Systems:
Design
Long-term consistency and yet adaptive
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Assessing and Communicating
Climate Change Effects
Modeling and Analysis:
Standard analytical methods assumed may be improper
Typical assumptions in standard models don’t match
requirements for long-scale studies based on a variety of
data sources
Need for flexible modeling strategies; material in this area
needs to be amalgamated. Much of this research takes
place within specific environmental user communities
(coastal studies, forestry) and developments are not
usually shared across cultures; reinventions and parallel
developments
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Assessing and Communicating
Climate Change Effects
Modeling and Analysis (continued):
Requirements of regulatory bodies
Massive data
Skewed distributions; extremes; mixtures
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Assessing and Communicating
Climate Change Effects
Modeling and Analysis (continued):
Lack of inferential techniques and testing procedures;
diagnostics and goodness of fit procedures
Difficulties and questions surrounding simulation models
Evidence on emerging trends; inference on causal
relationships (attribution); forecasts of potential impacts
For climate change impacts analysis, incorporation of
outputs from weather “black-box” models
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Assessing and Communicating
Climate Change Effects
Communication:
Reliability of results
Validation of methods
Combining expert opinions: combining evidence in metaanalyses
Sometimes being overly critical of other research;
inability to see beyond one’s viewpoint
Creating meaningful summaries (data visualization) for
informing public discussion and policy making: methods
for conveying estimates of uncertainty, management
strategies under uncertainty
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Acknowledgements
Funding from the following sources is gratefully
acknowledged:
The National Institute
for Complex
Data Structures
GEOmatics for
Informed Decisions
The Natural Sciences and
Engineering Research
Council of Canada
CTEF
Thanks also to the Ontario Ministry of Natural Resources
for the use of their fire data, and to Vivien Wong for
related analyses.
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