Numerical Simulation of Crown Fire Hazard Immediately after Bark
Beetle-Caused Mortality in Lodgepole Pine Forests
Chad Hoffman, Penelope Morgan, William Mell, Russell Parsons, Eva K. Strand, and
Stephen Cook
Abstract: Quantifying the effects of mountain pine beetle (MPB)-caused tree mortality on potential crown fire
hazard has been challenging partly because of limitations in current operational fire behavior models. Such
models are not capable of accounting for fuel heterogeneity resulting from an outbreak. Further, the coupled
interactions between fuel, fire, and atmosphere are not modeled. To overcome these limitations, we used the
Wildland-Urban Interface Fire Dynamics Simulator (WFDS) to investigate the influences of tree spatial
arrangement and magnitude of MPB-caused tree mortality on simulated fire hazard. Field-collected, tree-level
data from 11 sites were used to populate WFDS simulation domains representing a range of lodgepole pine forest
structures for the postoutbreak period of time when dead needles are still present in the tree crowns. We found
increases in the amount of crown fuel consumption and the intensity of crown fires as the percentage of
MPB-caused tree mortality increased. In addition, we found complex interactions between the level of mortality,
stand structure, and spatial arrangement of trees. These results suggest that preoutbreak forest structure and
percent tree mortality influence crown fire behavior while dead needles are in the crown, and that the effect
varies with spatial heterogeneity among trees. FOR. SCI. 58(2):178 –188.
Keywords: crown fire behavior, fire modeling, mountain pine beetle, computational fluid dynamics, heterogeneous fuels
L
ODGEPOLE PINE (PINUS CONTORTA DOUGL. EX LOUD.)
FORESTS ranging from British Columbia to Colorado
are currently experiencing high levels of tree mortality
due to extensive outbreaks of mountain pine beetle (MPB)
(Dendroctonus ponderosae Hopkins) (Kaufmann et al. 2008).
Tree mortality associated with these extensive outbreaks potentially affects the condition and arrangement of fuels through
space and time, yet the implications for crown fire hazard and
fire severity are poorly understood.
The influence of MPB outbreaks on crown fire hazard is
thought to occur primarily through changes in fuel complexes and subsequent environmental conditions (i.e., wind
speeds and fuel moistures) caused by the mortality of overstory trees (Page and Jenkins 2007a). Jenkins et al. (2008)
suggested that, immediately after MPB-caused tree mortality, crown fire hazard is increased because of diminished
foliar moisture content of trees killed by MPB. Lower foliar
moisture is thought to increase the likelihood that a surface
fire will transition into a crown fire. It may also increase the
spread rate of crown fires by reducing the amount of heat
needed to initiate flaming combustion in unburned fuels
ahead of the fire front. Over time, as dead needles fall to the
forest floor, crown fire hazard is thought to fall below
preoutbreak levels because of a decrease in available canopy fuels (Jenkins et al. 2008). However, changes in wind
speeds, fuel moisture, and surface fuel loadings caused by
the loss of canopy fuels and their deposition onto the forest
floor may lead to no significant changes or increased potential fire hazard compared with the preoutbreak conditions. Over longer time scales, it is believed that crown fire
hazard increases. The deposition of large woody material
onto the forest floor may increase surface fire intensity;
additional tree regeneration may provide ladder fuels, allowing surface fires to burn into the forest canopy (Jenkins
et al. 2008). Although the influence of this sequence of
events on the fuel complex is logical, there is little quantitative information available about how these changes influence corresponding potential or observed crown fire behavior (Page and Jenkins 2007a).
The influence of MPB outbreaks on lodgepole pine fuel
complexes and subsequent fire behavior was investigated by
Page and Jenkins (2007a, 2007b) and Simard et al. (2011).
Both Page and Jenkins (2007a) and Simard et al. (2011)
used extensive fuel inventory data to develop custom fuel
models for use with the Rothermel (1972) surface fire
spread model to predict the surface fire behavior across a
Manuscript received December 1, 2010; accepted July 11, 2011; published online February 9, 2012; http://dx.doi.org/10.5849/forsci.10-137.
Chad Hoffman, Department of Forest and Rangeland Stewardship, Colorado State University, Fort Collins, CO 80523—Phone: (907) 491-1338; Fax:
(907) 491-6754; c.hoffman@colostate.edu. Penelope Morgan, Wildland Fire Program, College of Natural Resources, University of Idaho, Moscow,
ID—pmorgan@uidaho.edu. William Mell, Pacific Wildland Fire Sciences Lab, US Forest Service, Seattle, WA—wemell@fs.fed.us. Russell Parsons, US
Forest Service, Fire Sciences Laboratory, Missoula, MT—rparsons@fs.fed.us. Eva K. Strand, Wildland Fire Program, College of Natural Resources,
University of Idaho, Moscow, ID— evas@uidaho.edu. Stephen Cook, Department of Plant, Soils and Entomological Sciences, College of Agriculture and
Life Sciences, University of Idaho, Moscow, ID—stephenc@uidaho.edu.
Acknowledgments: This research was supported in part by funds provided by Forest Health Protection Special Technology Development, the US Forest
Service, and US Department of Agriculture STDP R6 –2008-04 under Research Joint Venture Agreement 08-JV011060123-103. We appreciate the assistance
of Erin Berryman and Harold Osborne in collecting all field data. We thank Helen Maffei, Eric Pfeiffer, and the rest of the staff on the Deschutes and
Salmon-Challis National Forests for help in identifying field locations.
Copyright © 2012 by the Society of American Foresters.
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Forest Science 58(2) 2012
temporal series after a MPB outbreak. Simard et al. (2011)
also used NEXUS (Scott and Reinhardt 2001) to estimate
crown fire potential across a range of times after severe
MPB-caused tree mortality. Page and Jenkins (2007a) found
increases in modeled surface fire rate of spread and surface
fire line intensities in epidemic and postepidemic sites compared with the control sites with an endemic level of bark
beetle-caused tree mortality. Contrary to their findings, Simard et al. (2011) found no significant differences across a
temporal series in either the surface fire rate of spread or the
fire intensity. Because of the limitations in operational fire
behavior models in accounting for dead aerial fuels, Page
and Jenkins (2007a) did not simulate crown fire hazard for
time periods immediately after bark beetle outbreaks, so
they only reported crown fire hazard data for their 20-year
postepidemic site. Postepidemic sites had an 81% decrease
in the fire line intensity needed for crown ignition and a
47% increase in the critical crown fire spread rate, probably
due to high levels of tree mortality and the consequential
increase in large-diameter fuel concentrations. Simard et al.
(2011) concluded that there is a decrease in active crown
fire hazard for up to 35 years after an outbreak and that the
passive crown fire hazard remains unchanged in the short
term but increases in the decades after the outbreak.
Page and Jenkins (2007a) and Simard et al. (2011) quantified fuel complexes and potential fire behavior, but these
studies are limited to nearly pure, even-aged lodgepole pine
forests. It is not known whether the relationships they identified apply to lodgepole pine forests that are not even-aged
or are composed of a mixture of species or how they vary
with degree of tree mortality. Although others have not used
fire behavior models to investigate the effect of MPB outbreaks on potential fire behavior in lodgepole pine forests,
several studies (e.g., Armour 1982, Gara et al. 1985,
Romme et al. 1986, Page and Jenkins 2007b, Klutsch et al.
2009) have investigated the effects on fuel loadings through
time (see Jenkins et al. 2008 for a review of past work).
The operational fire behavior models used by Page and
Jenkins (2007a) and Simard et al. (2011) rely on the same
theoretical background to make surface and crown fire
spread predictions (Rothermel 1972, 1991) and to estimate
crown fire initiation and crown fire spread (Van Wagner
1977). In these and other operational fire behavior models
based on the same fundamental mathematical equations,
fuels are represented as a single homogeneous layer. Sites
that have low to moderate levels of tree mortality are likely
to violate this assumption, because their overstory is influenced by variable spatial distributions in the size and number of trees with dead needles. In addition, the surface fuels
vary greatly in loading, bulk density, and continuity owing
to litter fall from trees killed by bark beetles. Stands that
have not had alterations due to recent disturbances, such as
bark beetle-caused tree mortality, may still be characterized
by discontinuous canopy fuels and should be considered as
aggregations of fuel particles separated by air spaces. Even
in forests without significant tree mortality, the lack of
continuous fuel in forest canopies results in minimum critical thresholds that must be met for crown fire to sustain
spread across the voids within the canopy fuels (Cohen et al.
2006). As a consequence, fire behavior in crown fires is a
nonlinear “feedback” process often resulting in marginally
sustainable spread and abrupt transitions and cessation in
crown fire (Cohen et al. 2006). Evidence for such minimum
thresholds has been shown in empirical studies (Van Wagner 1977, Cohen and Bradshaw 1986, Weise et al. 2005).
In addition to the assumptions of homogeneous fuel
properties, operational fire behavior models do not account
for the transient fire behavior created by fire-atmosphere
interactions (e.g., the influence of buoyant plumes on wind
speed and direction) or fuel-atmosphere interactions (e.g.,
the effect of vegetation on wind speed and direction). Sun et
al. (2009) suggested that changes in the flow environment
caused by fire-atmosphere and fuel-atmosphere interactions
can be major sources of uncertainty in fire behavior predictions. However, no one has studied how such within-site
variations in fuels or changes in fire-atmosphere and fuelatmosphere interactions created by bark beetle-caused tree
mortality affect fuel-atmosphere or fire-atmosphere interactions. The assumptions used in the development of operational fire behavior models have lead Cohen et al. (2006)
and Cruz and Alexander (2010) to suggest that operational
fire behavior models cannot accurately simulate crown fire
behavior. Cohen et al. (2006) suggested that models should
include radiative and convective heat transfer and account
for variable flame flow within the fuel bed.
Physics-based models that are capable of addressing
variability in fuels, as well as fire-atmosphere and fuel-atmosphere interactions, have been developed (Linn et al.
2002, Mell et al. 2006, 2007, 2009). Such models generate
two- or three-dimensional time-dependent predictions of
fire behavior based on physical mechanisms of heat and
mass transfer, fluid flow, and combustion chemistry. Physics-based simulations can be used to investigate the effects
of nonhomogeneous fuel arrangements and properties on
fire behavior and estimate the variability in fire behavior
over time. Because such models can incorporate nonhomogeneous fuel structures along with changes in fuel properties (e.g., moisture content), they are well suited to investigate questions that involve heterogeneous fuel complexes,
such as those likely to be found after bark beetle-caused tree
mortality. This is particularly true for the period of time
immediately after a bark beetle outbreak when dead needles
are in tree crowns.
Objective and Hypotheses
Our objective was to investigate how MPB-induced tree
mortality affects crown fire hazard across a range of site
conditions and spatial patterns during the period of time that
dead needles are retained in the canopy. We tested three null
hypotheses: first, that there are no significant differences in
either the percentage of canopy fuel consumption or the
crown fire intensity across eight levels of MPB-caused tree
mortality; second, that there are no significant differences in
predicted percent canopy fuel consumption and the crown
fire intensity between homogeneous, random, and clumpy
spatial point patterns of overstory trees; and third, that there
are no significant interactions between the nonhomogeneous fuels created by the combinations of different within-site tree populations, spatial point patterns, and MPBcaused tree mortality.
Forest Science 58(2) 2012
179
To test these hypotheses we used field-collected data
from 11 sites to create analogous, simulated forests in the
Wildland-Urban Interface Fire Dynamics Simulator (WFDS)
(Mell et al. 2006, 2009). The simulation experiments were
conducted as a randomized block design with the level of
MPB-caused mortality, site, and spatial arrangement serving as factorial treatments.
Methods
A total of 11 lodgepole pine sites were sampled on the
Deschutes National Forest in central Oregon and the
Salmon-Challis National Forest in central Idaho (Table 1).
Sampling locations were chosen in consultation with US
Forest Service personnel to represent a wide range of typical
site structures in terms of tree density, size and number of
canopy layers, and site compositions on each national forest. The 11 sites we sampled to populate our WFDS simulations were all experiencing recent active MPB mortality
and were considered by local forest service personnel to
have a high potential for MPB-caused mortality.
In each site, four fixed-radius 0.04-ha plots were sampled in a clustered design. The center plot of each cluster
was randomly placed within the site and the three additional
plots were located 76 m from the center point along three
azimuths (50, 180, and 290°). If any one of the cluster plots
was within 100 m of a road or fell in an area that had been
recently burned or logged, a new random distance and
azimuth for the center plot was chosen. Within each cluster,
all trees with a dbh (1.37 m from the ground) of at least 5 cm
had the following information recorded: dbh, total height,
height to lowest live branch, tree status (live or dead),
canopy position (dominant, codominant, intermediate, or
suppressed), and crown-base width. All tree data recorded
on each of the four subplots within a site were combined
into a single list for each of the 11 sites and were used to
build the simulated forests in our WFDS experiments.
WFDS Model Description
WFDS is a computational fluid dynamics model for
simulating fire spread through vegetative fuels or a mixture
of vegetative and structural fuels. WFDS is an extension of
the Fire Dynamics Simulator (FDS) developed by the National Institute of Standards and Technology in cooperation
Table 1.
with VTT Technical Research Center of Finland, industry,
and academic institutions. WFDS numerically solves the
Navier-Stokes equations in a form appropriate for lowspeed interactions, and it models subgrid turbulent dissipation using a large-eddy approach (McGrattan et al. 2010a).
The model approximates the conservation equations of
mass, momentum, and energy, as well as thermal radiation
and thermal degradation of fuels, on a three-dimensional
rectilinear grid giving temporally and spatially resolved
predictions of fire behavior. Forest fuels are represented as
thermally thin, optically black elements within the rectilinear grid. The thermal, radiative, and drag properties of
fuel are determined from the bulk density and surface
area/volume ratio of fuel in each cell. Representation of the
overstory trees within the rectilinear grid allows individual
trees within the simulation to be distinguished from each
other based on a number of parameters, including physical
dimensions, bulk density, fuel element density, surface
area/volume ratio, and moisture content. Verification and
validation studies for FDS, the parent model of WFDS, have
been described by McGrattan et al. (2010b) and McDermott
et al. (2010), whereas validation for WFDS has been conducted by Mell et al. (2007, 2009).
WFDS Setup
The simulated spatial domain was identical for all simulations, measuring 120 m ⫻ 48 m ⫻ 35 m along the x, y,
and z axes, respectively, and discretized as 0.5-m cubic
cells. An inflow “wind” condition was prescribed for the
boundary at x ⫽ 0 m (see below) and an “open” boundary
was prescribed at x ⫽ 120 m. The planes at y ⫽ 0 m and y ⫽
48 m were modeled as “mirrors” that act essentially as
free-slip, no-flux boundaries. All simulations were conducted on flat terrain and run for a total length of 1,250 s
(⬃20.4 min) of simulated time at a prescribed time step of
0.1 s. The domain consisted of five parts (Figure 1): a wind
entry field along the left boundary of the domain, an exiting
wind field along the right boundary of the domain, a zone
for the fire to develop (zone A), a zone representing the
experimental section (zone B), and the preboundary outflow
(zone C). Point ignition of a surface fire occurred along the
center of the left side domain boundary at x ⫽ 0 m, y⫽ 24 m
(Figure 1). In our simulations the point ignition resulted in
Mean stand-level characteristics of lodgepole pine sites used in WFDS simulations.
Site no.
Trees ha⫺1
BA
(m2 ha⫺1)
QMD
(cm)
HT
(m)
CBH
(m)
1
2
3
4
5
6
7
8
9
10
11
997
775
2,825
1,118
1,137
751
1,647
1,378
1,442
1,112
1,406
26.6
28.6
42.3
33.7
27.7
34.7
33.1
38.0
47.7
28.0
36.5
18.2
21.4
13.6
19.4
17.4
24.1
15.8
18.5
20.3
17.7
17.9
10.8
11.6
9.5
14.0
10.3
14.8
12.1
14.2
13.6
10.5
14.0
3.8
3.5
3.7
6.0
2.7
4.1
5.5
6.2
5.9
3.4
5.8
Species composition
LPP
LPP
LPP
LPP
LPP
LPP
LPP
LPP
LPP
LPP
LPP
100%
80%, GF 20%
100%
74%, MH 15%, SF 11%
100%
52%, SF 47%, ES 1%
91%, SF 9%
91%, SF 9%
93%, SF 4%, ES 3%
58%, WBP 28%, SF 14%
60%, DF 31%, ES 6%, SF 2%
BA, basal area; QMD, quadratic mean diameter; HT, mean tree height; CBH, mean canopy base height; LPP, lodgepole pine; GF, grand fir; MH, mountain
hemlock; SF, subalpine fir; ES, Engelmann spruce; WBP, whitebark pine; DF, Douglas-fir.
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Forest Science 58(2) 2012
Figure 1. WFDS simulation layout showing the overall spatial domain measuring 120 ⴛ 48 ⴛ 30 m, a predeveloped wind field
entering the domain along the left hand side, the ignition point, a fire development zone (zone A), the simulation experiments (zone
B), the preoutflow boundary zone (zone C), and the exiting wind field along the right hand side.
a line fire that spreads throughout the entire experimental
area (zone B). Thus, every tree within the MPB-affected
area was exposed to the surface fire.
For all simulations, wind entering the domain at x ⫽ 0 m
followed a power-law profile in the vertical direction, with
a constant speed of 2 m s⫺1 at 6.1 m above the ground. The
power law is of the form
U x ⫽ U r 共Z x /Z r 兲 ␣
(1)
where Ux is the wind speed at height Zx, Ur is a known wind
speed at height Zr, Zx is the height at which wind speed Ux
will be prescribed, and ␣ is a constant value of 1/7. A wind
profile following a power law has been used to describe the
inflow boundary conditions in several fire behavior-modeling studies (Morvan and Dupuy 2001, 2004; Mell et al.,
2007). The wind flow was allowed to run for the first 60 s
of each simulation so that a developed wind field was
present before the start of the surface fire.
Individual tree crown fuels were represented as cones
consisting of a homogeneous thermally thin fuel with a
surface area/volume ratio of 6,470 m⫺1 (Brown 1970) and
a bulk density of 0.7 kg m⫺3. The crown bulk density value
of 0.7 kg m⫺3 was estimated by using allometric equations
(Brown 1978) to estimate the total needle and half of the 1-h
woody fuel loading for each tree we sampled and dividing
the fine fuel biomass by the calculated volume of the tree.
We then averaged across all trees throughout each site to
develop an average crown bulk density of 0.7 kg m⫺3. In all
simulations, we arbitrarily assigned live trees with a foliar
moisture content of 100% and dead trees with 10%. To
create more realistic environmental conditions within the
simulation domain, a random set of trees was selected (from
all 11 sites) to populate zone A and C such that there were
800 trees ha⫺1. The inclusion of these trees ensured that
wind entering the domain, either as a result of the entering
windflow or from indrafts created by the fire itself, interacted with vegetation before influencing fire behavior
within the experimental area.
Simulation Experiment
The simulation experiment was set up as a randomized
block design with a factorial treatment structure, with eight
levels of bark beetle-caused tree mortality (0, 10, 25, 40, 55,
70, 85,and 100%), three spatial arrangements (clumpy, random, and homogeneous),and 11 sites. These levels of mortality correspond to reported MPB-caused mortality levels
of available host trees (Stone and Wolf 1996, Schmid and
Matta 2005). Our experimental design resulted in a total of
264 simulations.
To build the input files for the WFDS simulations, all
sampled trees from each site were first assigned x and y
locations for each spatial arrangement (Figure 2). Spatial
point pattern arrangements were generated using SpPack
(Perry 2004), where
1.
2.
3.
Random spatial arrangements were assigned using a
Poisson distribution.
Clumpy distributions were assigned using a three-part
process outlined by Diggle (2003).
Homogeneous distributions were assigned using a
simple “hard core” inhibition process (Diggle 2003).
Within each site, each spatial point pattern was built from
the same tree list; thus, all overstory properties including
total fine fuel load, canopy base height, and density were
constant within a site.
After spatial point patterns were assigned for each site,
they were randomly assigned one of the eight levels of tree
mortality. MPB-caused tree mortality was simulated by
identifying all trees within zone B (Figure 1) that were
susceptible to MPB-caused tree mortality. We considered
only lodgepole pine and whitebark pine (Pinus albicaulis
Engelm.) trees with a dbh of at least 10 cm to be susceptible
to MPB mortality (Furniss and Carolin 1977). The percent
mortality classes used in our simulations reflect the number
of susceptible tree species ⬎10 cm dbh that were killed relative
to the number of susceptible trees, not the total number of trees.
Forest Science 58(2) 2012
181
Figure 2. A1, B1, and C1 show differences in spatial arrangement between clumpy, random, and homogeneous point patterns for
site 1. A2–A8 show variation within the clumpy spatial arrangements for site 1 used in the WFDS simulations for the moderate
surface fire intensity simulations. In all cases total biomass was constant.
For instance, site 2 has 750 trees ha⫺1 of which 80% are
lodgepole pine and only 87% are larger than 10 cm dbh and
20% are subalpine fir. Therefore, at 100% mortality, only 69%
of the total stems per ha would be killed, and the remaining
31% of the trees would live because they were either too small
(dbh ⬍10 cm) or not a host species.
Once all susceptible trees within the domain were identified, one focal tree was randomly selected to initiate the
outbreak. After this, susceptible trees within 6 m of the focal
tree were selected as attacked, starting with the largest
diameter tree. After a tree was selected for attack, the
percentage of susceptible trees attacked was calculated and
compared against the assigned level of mortality. If the level
of mortality was not reached, then the next largest tree of
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Forest Science 58(2) 2012
susceptible species and size (⬎10 cm) within 6 m of the
focal tree was selected, and the mortality selection process
was repeated. This process continued until the assigned
level of mortality was met or until no additional trees were
within 6 m of the focal tree, in which case another focal tree
was randomly selected and the process began again.
The method used to simulate bark beetle-caused tree
mortality is a simplification of the spatial and temporal
biological and ecological mechanisms influencing bark beetle propagation. Our MPB mortality model resulted in the
selection of a group of trees for mortality similar to the
switching model proposed by Geiszler and Gara (1978) and
uses a successive selection process based on diameter to
determine which trees within the 6-m radius were killed
during the attack. This successive selection process resulted
in preferential selection of the largest trees within the 6-m
radius of the focal tree as suggested by Amman et al. (1977)
but also allows for smaller trees to be selected and killed
after the majority of larger-diameter lodgepole pines in a
stand have been infested and killed as suggested by Gibson
et al. (2009). In our simulations, patches of beetle-killed
trees coalesce within the stand as the level of mortality
increases as suggested by Mitchell and Preisler (1991). We
assumed that attack of a tree results in death, and selection
of focal trees is a random process, which is independent of
preexisting tree mortality. Although these assumptions do
not fully reflect the mechanisms driving MPB propagation
and mortality in real-world situations, they allowed us to
simplify this reality in a consistent and repeatable manner so
that we could populate WFDS.
In all of the simulations, a surface fire was modeled as a
steady-state fire with a rate of spread equal to 0.1 m s⫺1, a
residence time of 25 s, and a heat release per unit area of
250 kW m⫺2. This resulted in a fire line intensity of 625 kW
m⫺1 within zone B. The use of a steady-state surface fire
results in a one-way coupling of the interaction between
surface and crown fire behavior. In our simulations, the
surface fire propagation and heat release rate are independent of any interactions with the atmospheric flow and of
any effects of heat transfer from the crown fire to unburned
fuel ahead of the surface fire front. In other words, the
surface fire influences the crown fire, but the crown fire
does not influence the surface fire in our simulations. However, the use of a steady-state fire (which is not a limitation
of WFDS) allowed us to reduce the factors causing variation
in simulated fire behavior by simplifying the interactions
between the surface and crown fire.
We used two model outputs to describe crown fire hazard. First, we used the mass loss of crown fuels, which is a
global quantity tracked at each 0.1-s time step and describes
the consumption of total canopy fuel over time. We calculated the mean percent consumption for each simulation by
the following equation:
Percent consumption ⫽
冉
冊
Canopy biomasstend
⫻ 100
Canopy biomassto
(2)
where canopy biomasstend is the biomass (kg) remaining
at the end of the simulation and canopy biomasst0 is the
biomass at the start of the simulation. Both the start and end
canopy biomass are directly output from WFDS.
In addition to the percentage of canopy biomass consumed, we also calculated the mean crown fire intensity.
The crown fire intensity provides a measure of the energy
output per unit time per unit length of fire front regardless
of the depth and is commonly reported as kW m⫺1 (Byram
1959). We calculated the mean crown fire intensity as the
average crown fire intensity for the period of time in which
the fire was in zone B using the following equation:
n⫽850
冱n⫽400
共共Qn ⫺ Qfn 兲/FLn 兲
Mean crown fire intensity ⫽
450
(3)
where Qn is the total heat release rate per unit area at time
n (kW), Qfn is the heat release rate of the surface fire at time
n (kW), FLn is the length of fire line at time n (m), and 450
is the total time for which there was a fire within zone B (s).
The percentage of tree canopy fuel consumption and the
crown fire intensity provide insights into the amount of
crown fire hazard. The amount of canopy fuel consumption
provides an indication of the amount of crown fire activity,
whereas the crown fire intensity takes into account both the
amount of fuel consumed and the rate at which it is consumed (Byram 1959).
To test the effects of the level of MPB-caused tree
mortality, spatial point pattern, and site on crown fire hazard, we used a three-way mixed-effects analysis of variance
(ANOVA) with site as a random variable and Tukey’s
multiple comparison procedure to test whether there were
significant (␣ ⫽ 0.05) differences between the levels of
mortality and the spatial distributions for two dependent
variables: percentage of tree crown biomass consumed and
the average crown fire intensity. We used Bartlett’s test and
a Lillifors test to ensure that homogeneous variance and
normality assumptions, respectively, were met. To quantify
the relative importance of each factor in our explanatory
ANOVA, we calculated the factor effects using the ␻2
statistic (Hays 1994). All statistical tests met assumptions
required for ANOVA.
Results
Site Descriptions
The 11 sites used in this study varied greatly in tree
composition and forest structure. Mean tree densities ranged
from 751 to 2,825 trees ha⫺1, with mean basal area between
26.6 and 47.7 m2 ha⫺1 (Table 1). Mean canopy base height
in the sites ranged from ⬍3 to 6.2 m (Table 1). At least 50%
of all stems were lodgepole pine in each site (Table 1), with
three sites being entirely composed of lodgepole pine and
eight sites representing lodgepole pine mixed with other tree
species (Table 1). The mixed lodgepole pine sites included
grand fir (Abies grandis [Douglas ex D. Don] Lindl.),
mountain hemlock (Tsuga mertensiana [Bong.] Carrier),
subalpine fir (Abies lasiocarpa [Hook.] Nutt.), Engelmann
spruce (Picea engelmannii Parry ex Engelm.), whitebark
pine, and Douglas-fir (Pseudotsuga menziesii [Mirb.]
Franco). Four of the eight mixed-conifer sites were dominated by lodgepole pine and subalpine fir, and one site each
had lodgepole pine mixed with grand fir, mountain hemlock, whitebark pine, and Douglas-fir (Table 1).
Simulation Experiment Results
All three factors (level of MPB-caused tree mortality,
spatial point pattern, and site), significantly influenced the
amount of canopy fuels consumed, with the level of tree
mortality having the greatest effect (Table 2). The proportion of MPB-killed trees explained 67% of the total variation in canopy fuel consumption across all sites and spatial
arrangements (Table 2). Multiple comparison procedures
suggest that all eight levels of MPB-caused mortality differed significantly (P ⬍ 0.05) (Figure 3), with 70% or more
canopy fuels being consumed in sites with all susceptible
trees killed compared with those with no MPB-caused tree
Forest Science 58(2) 2012
183
Table 2. ANOVA results for fire hazard metrics for 11 sites under three different spatial point patterns and eight levels of bark
beetle-caused tree mortality.
% canopy biomass consumed
Crown fire intensity
Source of variation
df
SS
F
␻
SS
F
␻2
Spatial arrangement
Level of mortality
Site
Spatial arrangement ⫻ level of mortality
Spatial arrangement ⫻ site
Level of mortality ⫻ site
Error
Total
2
7
10
14
20
70
140
263
12,054.8
145,943.1
19,607.4
1,216.7
8,341.1
23,473.7
6,415.8
217,052.6
14.5*
62.2*
2.8*
1.9*
9.1*
7.32*
0.06
0.67
0.09
0.003
0.03
0.09
3,581,541.3
64,493,844.1
28,807,977.6
456,298.1
2,964,595.0
27,269,811.7
2,526,777.1
130,100,844.9
12.1*
23.6*
5.5*
1.8*
8.2*
21.5*
0.03
0.50
0.02
0.01
0.02
0.20
2
SS, sum of squares.
* Significance at P ⬍ 0.05.
mortality. A time series of images of the WFDS simulations
for 40 and 80% mortality for site 2 with a clumpy spatial
arrangement is provided in Figure 4.
The spatial point pattern of trees and differences in sites
also significantly (P ⬍ 0.05) influenced the percentage of
canopy fuels consumed (Table 2). However, these two vari-
ables only accounted for 6 and 9% of the total variability in the
percentage of canopy fuel consumption, respectively. Multiple
comparison procedures indicate that significant differences
(P ⬍ 0.05) among all spatial point patterns exist, with clumpy
spatial point patterns averaging 16 and 11% more consumption
than random or homogeneous point patterns, respectively
Figure 3. Box and whisker plots showing the predicted canopy fuel consumption and crown fire intensity by percent mortality and
spatial arrangement. A1 and B1 show the predicted percent canopy fuel consumption by percent mortality and spatial arrangement
respectively. A2 and B2 show the predicted crown fire intensity by percent mortality and spatial arrangement, respectively. Box and
whisker diagrams labeled with different letters are significantly different (␣ ⴝ 0.05).
184
Forest Science 58(2) 2012
Figure 4. Time series images of WFDS simulations for site 1 with 40% mortality (top) and 80% mortality (bottom). Time proceeds
from left to right in both cases.
(Figure 3). Of the 11 sites used in this study, site 8 had a
significantly lower percentage of canopy fuel consumption
compared with all others. Site 11 had a significantly higher
consumption than site 8 but lower than that of the remaining
9 sites. Sites 1 and 10, although not significantly different
from each other, had a significantly higher consumption
than all other sites tested.
In addition to the amount of tree canopy fuels consumed,
we also investigated the effects that differences in spatial
point pattern, site, and level of mortality have on predicted
crown fire intensity. The main effects of the level of MPBcaused tree mortality, the spatial point pattern, and site were
all found to be significant (P ⬍ 0.001) in terms of explaining the variability in the simulated crown fire intensity, with
the level of tree mortality explaining approximately 50% of
the variance (Table 2). Our results show that as the level of
MPB-caused tree mortality increases, there is an increase in
the intensity of the crown fire predicted. Simulations with no
MPB-caused tree mortality had an average crown fire intensity
of 171.6 kW m⫺1, whereas simulations with 100% MPBcaused mortality had an average crown fire intensity of 1,627
kW m⫺1 (approximately a 9.5-fold increase) (Figure 3).
There were also significant differences (P ⬍ 0.05)
among all levels of spatial point patterns (Figure 3) with
clumpy point patterns resulting in a crown fire intensity
282.6 kW m⫺1 higher than that of homogeneous point
patterns and 174.7 kW m⫺1 higher than that of random
spatial point patterns (Figure 3). Differences between sites
were more complicated because of the large number of
multiple comparisons performed. One noteworthy difference was for site 6, which had a significantly higher crown
fire intensity (P ⬍ 0.05) than that for all other sites.
The three interaction terms (spatial point pattern ⫻ percentage of MPB-caused tree mortality, spatial point pattern ⫻ site, and percentage of MPB-caused mortality ⫻ site)
were also found to be significant (P ⬍ 0.05) variables in
explanation of both the amount of canopy fuels consumed
and the crown fire intensity (Table 2). These results suggest
that the effect of MPB-caused mortality on canopy fuel
consumption and crown fire intensity is influenced by in-
teractions with both the site and spatial point pattern. In
addition, we found a significant interaction effect between
spatial point pattern and site on the percentage of canopy
fuel consumption and crown fire intensity. However, the
interaction terms in the ANOVA provided little explanation
of the variation in the percentage of canopy fuel consumption (Table 2), suggesting that the main effect of the level of
mortality was relatively more important than the interaction
terms. The level of mortality also explained the most variation in predicted crown fire intensity (50%). However, the
interaction of the level of mortality with site explained 20%
of the variation in crown fire intensity (Table 2). This
finding suggests that, although the fixed effects of MPBcaused tree mortality explain a large portion of the variation
in crown fire behavior, this effect depends on site variables.
Discussion
Crown Consumption and Crown Fire Intensity
Vary with Percent Tree Mortality
We found a strong linear relationship between the level
of MPB-caused tree mortality and both the predicted canopy
fuel consumption and the crown fire intensity for lodgepole
pine forests where the needles of dead trees are still retained
in the canopy. In terms of canopy fuel consumption, the
amount of MPB-caused tree mortality explained 67% of the
variation in our simulated canopy biomass consumption estimates and approximately 50% of the simulated crown fire
intensity. The strong linear relationship between tree mortality
for both crown consumption and crown fire intensity was
unexpected, given the large number of researchers who have
reported clear nonlinear relationships related to the fuel complex such as fuel moisture, fuel loading, and fuel arrangement
in determining fire behavior (Renkin and Despain 1992,
Turner and Romme 1994, Hargrove et al. 2000, Finney et al.
2010). There was a higher-order interaction between the level
of MPB-caused mortality and both site and spatial arrangement, although the explanatory power of these interactions was
relatively weak compared with the fixed effect for MPBcaused tree mortality. Further work is needed to improve our
Forest Science 58(2) 2012
185
understanding of how spatial heterogeneity influences fire
behavior at stand and landscape scales, particularly studies
that consider cross-scale interactions.
Because current operational fire behavior models were
developed using only live canopy fuels, there is debate
within the scientific literature as to the capability of these
models to describe the relationship between the amount of
dead canopy fuels in a site and the potential fire behavior.
Page and Jenkins (2007a) and Jenkins et al. (2008) both
suggested that the dead canopy fuels created by MPBcaused tree mortality will probably increase the ability of a
surface fire to transition into the forest canopy, thereby
increasing fire intensity and crown fire hazard. Experimental studies that have investigated fuel flammability have
shown that dry fuels are more likely to ignite (Xanthopoulos
and Wakimoto 1993, Dimitrakopoulos and Papaioannou
2001, Liodakis and Kakardakis 2008). Babrauskas (2008)
identified three tree moisture regimes that lead to different
burning characteristics: trees with ⬍30% foliar moisture
content ignite easily and have relatively quick fire spread
through the crown, leading to large amounts of consumption; trees with foliar moisture contents between 30 and
70% are considered in a transition region where crown
ignition results in partial consumption; and consumption in
trees with ⬎70% foliar moisture is largely dependent on the
heat flux exposure of the crown. In laboratory experiments
to validate WFDS, Mell et al. (2009) observed patterns in
moisture-dependent burning similar to those reported by
Babrauskas (2008). On the basis of simulations using an
operational fire behavior model, Simard et al. (2011) suggested that there was a decrease in crown fire spread and
no significant change in crown fire initiation based on
simulation results using operational fire behavior models.
Our results suggest that there is an overall increase in both
the amount of crown consumption and intensity of crown
fire as the level of MPB-caused tree mortality increases.
These findings contradict those reported by Simard et al.
(2011) but agree with the hypothesized fire behavior reported in both Page and Jenkins (2007a) and Jenkins et al.
(2008) as well as with experimental studies that have investigated the effect of moisture content on fuel ignition.
Therefore, our first hypothesis that increased levels of
MPB-caused tree mortality will result in a significant increase in the percentage of canopy fuel consumption and
intensity of crown fires is supported by our data.
Spatial Pattern of Trees Influence Crown Fire
Hazard
When fuels are represented as homogeneous layers, such
as in operational fire behavior models, the ignition and
propagation of crown fire depend on thresholds in bulk
density, surface fire intensity, and canopy base height. Pimont et al. (2006) suggested that canopy heterogeneity
significantly affects the thresholds of torching and crown
fire propagation. Our simulations suggest that the heterogeneity created by the variation in the level of MPB-caused
tree mortality within forested sites and the spatial pattern of
overstory trees had significant effects on the amount of
canopy fuel consumed and crown fire intensity. Our results
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Forest Science 58(2) 2012
are comparable to findings in other studies on the effects of
fuel heterogeneity on fire behavior in sites not affected by
MPB (Pimont et al. 2006, 2009). Pimont et al. (2006) found
decreases of 50 and 200% in canopy fuel consumption and
rate of spread in their simulations for a heterogeneous forest
compared with a forest in which fuels are represented as a
single homogeneous layer. These results suggest that modeling the fuels complex as a homogeneous layer probably
results in overestimates of both the amount of canopy fuel
consumed during a crown fire and the rate of crown fire
spread. Even when heterogeneous fuels are considered, the
nature of the arrangement has been shown to be significant.
Pimont et al. (2006) found an increase in canopy consumption of 18% between forests with 2-m versus 10-m patch
size, whereas our simulations show a 16% increase in crown
consumption from homogeneous to clumpy spatial patterns,
which corresponds to a reduction in the distance between
trees within clumps. Our second hypothesis that spatial
point patterns of overstory trees will affect the predicted
canopy fuel consumption and the crown fire intensity was
also supported by our results.
First-Order Interactions Influence Crown
Fire Behavior
We found that there are first-order interactions between
site-level properties (species compositions and individual
tree characteristics) and the spatial arrangement of those
trees (clumped, random, or regular) that determine not only
what is burned but also how it burns. Variations in crown
fuels between sites has typically been investigated using
site-level properties (i.e., canopy bulk density and canopy
base height) represented as some measure of the central
tendency of the site. However, when site-level properties are
used to represent fuels for fire behavior prediction, the heterogeneity in fuel distribution created by the spatial pattern of
overstory trees within a site is commonly ignored, yet our
results and those of Pimont et al. (2006) indicate that spatial
arrangement significantly affected crown fire behavior. In addition, we found that simulated fire behavior in sites that have
experienced MPB-caused tree mortality include additional
first-order interactions between the site-level properties and the
MPB-caused tree mortality. Thus, the effect of MPB-caused
tree mortality on crown fire intensity and crown fuel consumption is dependent on the site-level properties. Derose and Long
(2009) also found complex interactions between preoutbreak
fuels and level of spruce beetle (Dendroctonus rufipennis Kirby)-caused tree mortality after the deposition of dead crown
biomass on the forest floor. Our results support our third
hypothesis: there were significant interactions among site, tree
spatial point pattern, and MPB-caused tree mortality. Potential
fire behavior in sites with MPB-caused mortality depends on
the preoutbreak fuel complexes and the level of tree mortality caused by MPB.
Challenges in the Use of Physics-Based Fire
Behavior Models
WFDS was useful for investigating the effects of nonhomogeneous fuels on potential fire behavior, but there
were challenges with the use of WFDS. Because of the large
computing resources and issues with collecting the detailed
spatially explicit fuel data required, it is unlikely that such
physics-based models will soon replace operational models
such as BehavePlus (Andrews et al. 2003), which are used to
predict faster-than-real-time fire behavior (Linn et al. 2002).
Each simulation conducted in this study required 22 h of wall
clock time on eight (3.2 GHz) processors, so it took a total of
46,464 h of CPU time to complete the simulations in this study.
However, for numerical experiments, physics-based simulations have an advantage over operational models because they
can capture the complexities in fire behavior caused by nonhomogeneous fuel complexes, fire-atmosphere interactions,
and fuel-atmosphere interactions. Results of simulation studies
such as ours can provide information that may be useful to
forest and fire managers. For example, results from this study
and others may provide managers with further understanding
of the potential errors in predictions made by operational fire
behavior models.
Future Research Needs
Although our results build on the existing literature,
further experiments are needed. The lack of coupling between the flow-induced changes and heat transfer from
canopy fuel combustion on surface fire behavior that we
used in these simulations prevented us from including any
impact of crown fire on the behavior of the surface fire. This
assumption conveniently allowed us to focus on how tree
mortality and other factors affected crown fire behavior but
did not allow the fire to spread actively through the entire
fuel complex as a single unit fully coupled within the flame
zone. We expect that this decoupling resulted in a reduced
range of simulated fire behavior, but further exploratory
simulations are needed to better understand the effect of this
assumption. In addition, further testing of the interaction
between the level of mortality and crown consumption and
intensity for other forest type-beetle interactions and on
complex topography is also needed.
Time since outbreak was not investigated in this study.
The simulations we used in this study simplified the temporal dynamics of MPB outbreaks on subsequent fire behavior by assuming that mortality is synchronous within the
domain and that there is no movement of crown biomass
during the red phase. These simplifications result in discrepancies between our simulations and real-world fuel
complexes, which are likely to have a mixture of both
overstory trees with and without needles and variability in
needle fall with trees that have remaining red needles present. Further fieldwork and simulation studies that more
accurately capture a realistic temporal distribution of canopy and surface fuels when there are mixes of green, yellow, red, and gray trees after a MPB outbreak are needed to
better understand the effect of these simplifications.
In addition to further simulation studies, both laboratory
and field experiments are needed to further validate the
predictions from physics-based simulations such as those
performed in this study.
Conclusions
Our results suggest that both preoutbreak forest structure
and percent MPB-caused tree mortality influenced crown
fire behavior in the period of time immediately after mortality when dead needles remain in the tree canopy. Overall,
we found a strong positive linear relationship between the
level of MPB-caused mortality and both the amount of
canopy fuel consumption and crown fire intensity. These
results are contradictory to those reported by Simard et al.
(2011), who suggested that there is a reduction in crown fire
activity during the red stage. However, our results do agree
with the hypothesized fire behavior reported by Page and
Jenkins (2007a) and Jenkins et al. (2008) as well as with
laboratory-scale experiments that have investigated the effect of foliar moisture content on crown fire ignition. For
any given level of MPB-caused tree mortality, clumpy spatial arrangements of trees resulted in increased canopy fuel
consumption and crown fire intensity compared with random and homogeneous spatial patterns. Our results suggest
that there are interactions between the level of tree mortality, the spatial arrangement of trees, and the species composition of trees on a site, which influence the potential
crown fire hazard immediately after MPB-caused tree
mortality.
Literature Cited
AMMAN, G.G., M.D. MCGREGOR, D.B. CAHILL, AND W.H. KLEIN.
1977. Guidelines for reducing losses of lodgepole pine to the
mountain pine beetle in unmanaged stands in the Rocky Mountains. US For. Serv. Gen. Tech. Rep. INT-GTR-36. 19 p.
ANDREWS, P.L., C.D. BEVINS, AND R.C. SELI. 2003. BehavePlus
fire modeling system, version 2.0: User’s guide. US For. Serv.
Gen. Tech. Rep. RMRS-GTR-106. 132 p.
ARMOUR, C.D. 1982. Fuel and vegetation succession in response
to mountain pine beetle epidemics in northwestern Montana.
M.Sc. thesis, Univ. of Idaho, Moscow, ID. 47 p.
BABRAUSKAS, V. 2008. Heat release rates. P. 3-1–3-59. In The
SFPE handbook of fire protection engineering, 4th ed. National
Fire Protection Association, Quincy, MA.
BROWN, J.K. 1970. Ratios of surface area to volume for common
fine fuels. For. Sci. 16(1):101–105.
BROWN, J.K. 1978. Weight and density of crowns of Rocky Mountain
conifers. US For. Serv. Gen. Tech. Rep. INT-GTR-197. 56 p.
BYRAM, G.M. 1959. Combustion of forest fuels. P. 61– 89 in
Forest fires: Control and use, K.P. Davis (ed.). McGraw-Hill,
New York.
COHEN, J.D., AND B. BRADSHAW. 1986. Fire behavior modeling: A
decision tool. P. 1–5 in Proc. of Prescribed burning in the
Midwest: State-of-the-art symposium, Koonce, A.L. (ed.).
Univ. of Wisconsin, Stevens Point, WI.
COHEN, J.D., M.A. FINNEY, AND K.M. YEDINAK. 2006. Active
spreading crown fire characteristics: Implications for modeling.
In Proc. of 5th International conference on forest fire research
(CD-ROM), Viegas, D.X. (ed.). Figueira da Foz, Portugal.
CRUZ, M.G., AND M.E. ALEXANDER. 2010. Assessing crown fire
potential in coniferous forests of western North America: A
critique of current approaches and recent simulation studies.
Intl. J. Wildl. Fire 19(1):377–398.
DEROSE, R.J., AND J.N. LONG. 2009. Wildfire and spruce beetle
outbreak: Simulation of interacting disturbances in the central
Rocky Mountains. EcoScience 16(1):28 –38.
DIGGLE, P.J. 2003. Statistical analysis of spatial point patterns.
Arnold, London, UK. 159 p.
DIMITRAKOPOULOS, A.P., AND K.K. PAPAIOANNOU. 2001. Flammability assessment of Mediterranean forest fuels. Fire Technol. 37:143–152.
Forest Science 58(2) 2012
187
FINNEY, M.A., J.D. COHEN, I.C. GRENFELL, AND K.M. YEDINAK.
2010. An examination of fire spread thresholds in discontinuous fuel beds. Intl. J. Wildl. Fire 19(2):163–170.
FURNISS, R.L., AND V.M. CAROLIN. 1977. Western forest insects.
US For. Serv. Misc. Publ. No. 1339. 702 p.
GARA, R.I., W.R. LITTKE, J.K. AGEE, D.R. GEISZLER, J.D. STUART,
AND C.H. DRIVER. 1985. Influence of fires, fungi, and mountain
pine beetles on development of a lodgepole pine forest in
South-Central Oregon. P. 153–162 in Lodgepole pine: The
species and its management, Baumgartner, D., R. Krebill, J.
Arnott, and G. Weetman (eds.). Washington State Univ. Office
of Conf. and Inst., Pullman, WA.
GEISZLER, D.R., AND R.I. GARA. 1978. Mountain pine beetle attack
dynamics in lodgepole pine. P. 182–187 in Theory and practice
of mountain pine beetle management in lodgepole pine forests:
Symposium proceedings. Berryman, A.A., G.D. Amman, and
R.W. Stark (eds.). Washington State Univ., Pullman, WA
GIBSON, K., S. KEGLEY, AND B. BENTZ. 2009. Mountain pine
beetle. US For. Serv. FS-R6-RO-FIDL#2.
HAYS, W.L. 1994. Statistics, 5th ed. Harcourt Brace, Fort Worth,
TX. 1002 p.
HARGROVE, W.W., R.H. GARDNER., M.G. TURNER, W.H. ROMME,
AND D.G. DESPAIN. 2000. Simulating fire patterns in heterogeneous landscapes. Ecol. Model. 135(2):243–263.
JENKINS, M.J., E. HEBERTSON, W. PAGE, AND C.A. JORGENSEN. 2008.
Bark beetles, fuels, fires and implications for forest management
in the Intermountain West. For. Ecol. Manag. 254:16 –34.
KAUFMANN, M.R., G.H. APLET, M. BABLER, W.L. BAKER, B.
BENTZ, M. HARRINGTON, B.C. HAWKES, L.S. HUCKABY, M.J.
JENKINS, D.M. KASHIAN, R.E. KEANE, D. KULAKOWSKI, C.
MCHUGH, J. NEGORN, J. POPP, W.H. ROMME, T. SCHOENNAGEL, W. SHEPPERD, F.W. SMITH, E.K. SUTHERLAND, D. TINKER, AND T.T. VEBLEN. 2008. The status of our scientific
understanding of lodgepole pine and mountain pine beetles—A
focus on forest ecology and fire behavior. The Nature Conservancy GFI Tech. Rep. 2008-2. 22 p.
KLUTSCH, J.G., J.F. NEGRÓN, S.L. COSTELLO, C.C. RHOADES, D.R.
WEST, J. POPP, AND R. CAISSIE. 2009. Stand characteristics and
downed woody debris accumulations associated with a mountain pine beetle (Dendroctonus ponderosae Hopkins) outbreak
in Colorado. For. Ecol. Manage. 258:641– 649.
LIODAKIS, S., AND T. KAKARDAKIS. 2008. Measuring the relative
particle foliar combustibility of WUI forest species located near
Athens. J. Therm. Anal. Calorim. 93(2):627– 635.
LINN, R., J. RESNIER, J.J. COLMAN, AND J. WINTERKAMP. 2002.
Studying wildfire behavior using FIRETEC. Intl. J. Wildl. Fire.
11(1):193–203.
MCDERMOTT, R., K.B. MCGRATTAN, S. HOSTIKKA, AND J. FLOYD.
2010. Fire dynamics simulator (version 5) technical reference
guide: Verification, vol. 2. NIST Spec. Publ. 1018-5. 87 p.
MCGRATTAN, K.B., H. BAUM, R. REHM, W. MELL, R. MCDERMOTT, S. HOSTIKKA, AND J. FLOYD. 2010a. Fire dynamics
simulator (version 5) technical reference guide: Mathematical
model, vol. 1. NIST Spec. Publ. 1018-5. 124 p.
MCGRATTAN, K.B., S. HOSTIKKA, J. FLOYD, AND R. MCDERMOTT.
2010b. Fire dynamics simulator (version 5) technical reference
guide: Validation, vol. 3. NIST Spec. Publ. 1018-5. 316 p.
MELL, W., M.A. JENKINS, J. GOULD, AND P. CHENEY. 2007. A
physics-based approach to modeling grassland fires. Intl. J.
Wildl. Fire 16(1):1–22.
MELL, W.E., S.L. MANZELLO, AND A. MARANGHIDES. 2006. Numerical modeling of fire spread through trees and shrubs. In
Proc. of 5th International conference on forest fire research
(CD-ROM), Viegas, D.X. (ed.). Figueira da Foz, Portugal.
MELL, W., A. MARANGHIDES, R. MCDERMOTT, AND S.L. MAN-
188
Forest Science 58(2) 2012
ZELLO. 2009. Numerical simulation and experiments of burning
Douglas-fir trees. Combust. Flame 156(10):2023–2041.
MITCHELL, R.G., AND H.K. PREISLER. 1991. Analysis of spatial
patterns of lodgepole pine attacked by outbreak populations of
the mountain pine beetle. For. Sci. 37(5):1390 –1408.
MORVAN, D., AND J.L. DUPUY. 2001. Modeling fire spread through
a forest fuel bed using a multiphase formulation. Combust.
Flame 127:1981–1984.
MORVAN, D., AND J.L. DUPUY. 2004. Modeling the propagation of
a wildfire through a Mediterranean shrub using a multiphase
formulation. Combust. Flame 138:199 –210.
PAGE, W., AND M.J. JENKINS. 2007a. Predicted fire behavior in
selected mountain pine beetle-infested lodgepole pine. For. Sci.
53(6):662– 674.
PAGE, W.G., AND M.J. JENKINS. 2007b. Mountain pine beetle-induced changes to selected lodgepole pine fuel complexes
within the Intermountain region. For. Sci. 53(4):507–518.
PERRY, G.L.W. 2004. SpPack: Spatial point pattern analysis in
Excel using Visual Basic for Applications (VBA). Environ.
Model. Softw. 19:559 –569.
PIMONT, F., J. DUPUY, Y. CARAGLIO, AND D. MORVAN. 2009.
Effect of vegetation heterogeneity on radiative transfer in forest
fires. Intl. J. Wildl. Fire 18:536 –553.
PIMONT, F., R. LINN, J. DUPUY, AND D. MORVAN. 2006. Effects of
vegetation description parameters on forest fire behavior with
FIRETEC. For. Ecol. Manag. 234:120 –134.
RENKIN, R.A., AND D.G. DESPAIN. 1992. Fuel moisture, forest
type, and lightning-caused fires in Yellowstone National Park.
Can. J. For. Res. 22:37– 45.
ROMME, W.H., D.H. KNIGHT, AND J. FEDDERS. 1986. Mountain
pine beetle outbreaks in the Rocky Mountains: Effects on fuels
and fire in lodgepole pine forests (abstract). In Program of the
annual meeting of the Ecological Society of America. Syracuse
Univ., Syracuse, NY.
ROTHERMEL, R.C. 1972. A mathematical model for predicting fire spread
in wildland fuels. US For. Serv. Res. Paper INT-RP-115. 40 p.
ROTHERMEL, R.C. 1991. Predicting behavior and size of crown
fires in the northern Rocky Mountains. US For. Serv. Res.
Paper INT-RP-438. 46 p.
SCHMID, J.M. AND S.A. MATTA. 2005. Mountain pine beetlecaused tree mortality in partially cut plots surrounded by
unmanaged stands. US For. Serv. Res. Paper RMRS-RP-54. 11 p.
SCOTT, J.H., AND E.D. REINHARDT. 2001. Assessing crown fire
potential by linking models of surface and crown fire behavior.
US For. Serv. Res. Paper RMRS-RP-29. 59 p.
SIMARD, M., W.H. ROMME, J.M. GRIFFIN, AND M.G. TURNER. 2011.
Do mountain pine beetle outbreaks change the probability of
active crown fire in lodgepole pine forests? Ecol. Monog. 81:3–24.
STONE, W.E., AND M.L. WOLF. 1996. Response of understory
vegetation to variable tree mortality following a mountain pine
beetle epidemic in lodgepole pine stands in Northern Utah.
Vegetatio 122:1–12.
SUN, R., S.K. KRUEGER, M.A. JENKINS, M.A. ZULAUF, AND
J.J. CHARNEY. 2009. The importance of fire-atmosphere coupling and boundary-layer turbulence to wildfire spread. Intl. J.
Wildl. Fire 18(1):50 – 60.
TURNER, M.G., AND W.H. ROMME. 1994. Landscape dynamics in
crown fire ecosystems. Landsc. Ecol. 9(1):59 –77.
VAN WAGNER, C.E. 1977. Conditions for the start and spread of
crown fire. Can. J. For. Res. 7:23–34.
WEISE, D.R., X. ZHOU, L. SUN, AND S. MAHALINGAM. 2005. Fire
spread in chaparral—“go or no-go.” Intl. J. Wildl. Fire 14(1):99–106.
XANTHOPOULOS, G., AND R.H. WAKIMOTO. 1993. A time to ignition-temperature-moisture relationship for branches of three
Western conifers. Can. J. For. Res. 23:253–258.