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Fuel bulk density and fuel moisture content effects on fire rate of spread were assessed in shrub fuels, comparing experimental data observed in outdoor wind tunnel burns and predictions from the physically-based model FIRETEC. Statistical models for the combined effects of bulk density and fuel moisture content were fitted to both the experimental and the simulated rate of spread values using non-linear regression techniques. Results confirmed a significant decreasing effect of bulk density on rate of spread in a power law in both laboratory burns and simulations. However, experimental data showed a lesser effect than simulations, suggesting a difference in the effective drag. Fuel moisture content effect was highly consistent, showing a similar exponential relationship with rate of spread in laboratory and in simulations. FIRETEC simulations showed similar orders of magnitude with predictions of two field-based empirical models, finding a significant correlation between rate of spread values. The study confirms the efficacy of the combined approach through experimental data and simulations to study fire behaviour.
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Journal of Fire Sciences
http://jfs.sagepub.com/content/early/2012/02/06/0734904111434286
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DOI: 10.1177/0734904111434286
published online 6 February 2012Journal of Fire Sciences
Rodman Linn
Eva Marino, Jean-Luc Dupuy, François Pimont, Mercedes Guijarro, Carmen Hernando and
fuels
shrubcomparison between FIRETEC model predictions and experimental results in
Fuel bulk density and fuel moisture content effects on fire rate of spread: a
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DOI: 10.1177/0734904111434286
jfs.sagepub.com
Fuel bulk density and fuel
moisture content effects on
fire rate of spread: a
comparison between FIRETEC
model predictions and
experimental results in shrub
fuels
Eva Marino
1
, Jean-Luc Dupuy
2
, Francxois Pimont
2
,
Mercedes Guijarro
1
, Carmen Hernando
1
and
Rodman Linn
3
Date received: 29 September 2011; accepted: 7 December 2011
Abstract
Fuel bulk density and fuel moisture content effects on fire rate of spread were assessed in shrub
fuels, comparing experimental data observed in outdoor wind tunnel burns and predictions from
the physically-based model FIRETEC. Statistical models for the combined effects of bulk density
and fuel moisture content were fitted to both the experimental and the simulated rate of spread
values using non-linear regression techniques. Results confirmed a significant decreasing effect of
bulk density on rate of spread in a power law in both laboratory burns and simulations. However,
experimental data showed a lesser effect than simulations, suggesting a difference in the effective
drag. Fuel moisture content effect was highly consistent, showing a similar exponential relationship
with rate of spread in laboratory and in simulations. FIRETEC simulations showed similar orders
of magnitude with predictions of two field-based empirical models, finding a significant correlation
1
Laboratorio de Incendios Forestales, Centro de Investigacio
´
n Forestal (CIFOR), Instituto Nacional de Investigacio
´
ny
Tecnologı
´
a Agraria y Alimentaria (INIA), Madrid, Spain
2
Institut National pour la Recherche Agronomique (INRA), Unite
´
d’Ecologie des Fore
ˆ
ts Me
´
diterrane
´
ennes, Avignon,
France
3
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA
Corresponding author:
Jean-Luc Dupuy, Institut National pour la Recherche Agronomique (INRA), Unite
´
d’Ecologie des Fore
ˆ
ts Me
´
diterrane
´
ennes,
UR629, Site Agroparc, 84914 Avignon Cedex 9, France.
Email: dupuy@avignon.inra.fr
at Biblioteca Universitaria de Granada on February 13, 2012jfs.sagepub.comDownloaded from
between rate of spread values. The study confirms the efficacy of the combined approach through
experimental data and simulations to study fire behaviour.
Keywords
rate of spread, simulation, wind tunnel, shrubland, moisture content, bulk density
Introduction
The present study investigates fuel bulk density (BD) and fuel moisture content (FMC)
effects on fire rate of spread (ROS) in both outdoor wind tunnel experiments and landscape-
scale numerical simulations by the physically-based model, FIRETEC. There are many
benefits of combining the results of experiments and numerical simulations ranging from
validation of the simulation tool to dissection/interpretation of experimental results. The
potential benefits are most easily realized when numerical simulations are used to represent
experiments with the same configuration. This particular study is complicated by the fact
that the outdoor wind tunnel experiments capture fire behaviour at scales of several metres,
while FIRETEC is designed to simulate fire behaviour on landscape scale with resolutions
in the order of metres and domain fires in the order of 50 m to kilometres. However, valu-
able information can be obtained from a combination of experiments and numerical simula-
tions even when there are differences in configuration, providing that the implications of
these differences are considered and put in context.
Wildland fire behaviour is particularly difficult to study with field-scale experiments due
to its wide range of important length-scales and non-linear interactions between heteroge-
neous and transient environmental conditions. The difficulty in performing field-scale experi-
ments that can be reconstructed by numerical simulations stems from the fact that it is
currently very difficult to adequately measure fuels, winds and fire behaviour at adequate
detail to initialize, bind and validate simulation tools. Laboratory-scale experiments provide
the opportunity for better control and characterization of fuel properties and environmental
conditions than possible for field experiments. Unfortunately, the scale limitations and con-
straints on the experiments result in differences in the coupled wind/vegetation/fire beha-
viour, which must be considered in order to understand the implications of these experiments
for free burning fire behaviour. For some features of fire behaviour, the experimental con-
straints will likely make little difference, while other aspects will be significantly affected. In
order to compare landscape-scale FIRETEC simulation results to outdoor wind tunnel
experiments, these same issues are considered. The motivations for such comparison are
based on the fact that physically-based fire behaviour models are useful when they can be
run at forest-stand scale, which is the smallest spatial resolution suitable for both operational
purposes and investigation of complex phenomena like the interactions of fire, vegetation,
wind and topography. However, adequate data for studying BD and FMC are to date only
available from laboratory experiments. While the magnitudes of the ROS are expected to be
different in laboratory experiments versus landscape-scale model simulations, it is assumed
that comparing the simulated and experimentally observed trends in ROS is meaningful, and
as such, the present study is intended to investigate trends in fire behaviour and to under-
stand the possible implications of these outdoor wind tunnel experiments for landscape-scale
fires.
2 Journal of Fire Sciences 0(0)
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The vegetation constituting the fuel beds investigated in this study is typical of a wide-
spread shrubland fuel type of the northwest (NW) of Spain and Portugal. One advantage of
the laboratory-scale experiments over field studies is the ease with which a wide range of fuel
BD and FMC may be selected for sensitivity studies, while it is more difficult to specify these
same ranges of values in field experiments under similar fuel types and similar ambient con-
ditions. Unintended correlations between environmental variables affecting fire behaviour in
natural settings may also be a limitation to the analysis of experimental studies, whereas this
can be at least partially avoided in laboratory experiments. Indeed, previous work has shown
not only that ROS measured in the outdoor wind tunnel are consistently smaller than ROS
observed in field experiments conducted in similar fuel and wind conditions but also that a
good correlation exists between the ROS measured in the outdoor wind tunnel and in the
field.
1
A possible reason for these differences in laboratory versus field is probably the differ-
ent fire width that is known to significantly affect ROS.
2,3
Another very likely source of the
variance is the difference in wind penetration into the metre-scale-wide experimental fuel bed
and fire with open sides as opposed to the simulations where the fuel bed is much wider com-
pared to the fire processes and the height of the fuel bed.
Fuel BD effects on fire ROS have previously been studied in the laboratory in pine needle
fuel beds or artificial fuel beds (e.g. excelsior, sticks), but not in shrub fuel beds that are sig-
nificantly taller and usually less packed.
4,5
Crown fuel BD effects on the dynamics of crown
fire initiation have been investigated in shrub fuels, but the purpose was not to examine the
fuel BD effect on fire ROS.
6
These fire experiments were conducted in still air using a recon-
structed canopy shrub fuel above a surface fuel, which is a configuration different from the
present wind tunnel study.
Change in fuel BD also implies change in the fuel load available for combustion when the
height of the fuel layer is kept constant. In the present set of experiments, the fuel was col-
lected in the field and its BD was artificially adjusted for part of the tests to get a relatively
large range of values (2 to 7 kg/m
3
). However, despite this manipulation, the fuel character-
istics tested were within the range of values that can be found in the field in many shrubland
fuels.
Affects of dead FMC have previously been tested in the laboratory,
5,7,8
and this variable
is a significant parameter of most empirical models for fire spread based on field experi-
ments.
9
However, live FMC is often ignored. The present study deals with a shrub fuel made
of both live and dead parts in variable proportions, exhibiting a range of typical average
FMC of 10% to 80%. This range was achieved through the natural variation of this para-
meter and through differences in fuel conditioning prior to experimental burns.
Fires were conducted over 0.8 m 3 6 m fuel beds with two levels of wind speed.
FIRETEC was used to simulate fire spread in similar order of magnitude wind conditions
and similar fuels, but over a 40-m wide and 180-m long burn area. The size of these simula-
tion domains was adapted to model fire behaviour on plots with the same order of magni-
tude of size as field experiments conducted in similar fuels.
10,11
This allows more direct
comparison of ROS magnitude with prediction of empirical models for ROS already estab-
lished for such fuel types. It is worth noting that these empirical models do not account for
the effect of fuel BD; therefore, BD in the simulations is an unconstrained variable within a
range that is appropriate for these shrublands. Statistical models for the combined effects of
BD and FMC on ROS were fitted for both the experimental and the simulated ROS in order
to compare trends and sensitivities, even though the magnitudes of the ROS were not
expected to be the same.
Marino et al. 3
at Biblioteca Universitaria de Granada on February 13, 2012jfs.sagepub.comDownloaded from
Material and Method
Laboratory experiments
The experimental fires were conducted in an outdoor wind tunnel at Instituto Nacional de
Investigacio
´
n y Tecnologı
´
a Agraria y Alimentaria-Centro de Investigacio
´
n Forestal (INIA-
CIFOR) Forest Fires Laboratory in Madrid, Spain. The outdoor wind tunnel is composed
of a test section and a fan (Figure 1). The test section is 8-m long with a cross section of 2-m
wide by 3-m high. Between the fan and the test section, there is a stabilization chamber, and
the side walls of the test section are made of fibre cement plates 6-mm thick, with an area of
2-m high by 0.2-m wide each. The stabilization chamber involves a diffuser intended to break
down the fan-induced turbulence structure before it reaches the test section. These plates
can be shifted longitudinally along the side of the tunnel, allowing for open sections of up to
6-cm wide to have visual access inside the test section. A wire netting with 6 mm 3 6 mm
mesh covers the upper and lateral sides of the tunnel between the top end of the fibre cement
plates. Inside the central region of the test section, there are eight adjacent metal trays 1.0-m
long, 0.8-m wide and 0.25-m high. The trays are filled up with sand, thus forming a surface
of 8-m long by 0.8-m wide where fuel can be arranged. The fan is controlled by an electronic
system, which enables it to obtain flow speeds up to 7 m/s within the test section.
Shrub fuel samples were collected at several representative gorse and mixed-heathland
sites in Galicia (NW Spain). Fuel samples consisted of vegetation strips 6-m long by 0.8-m
wide. Shrubs were cut at the base of the stems in order to keep the field shrub structure as
much as possible. Litter present underneath shrub fuels was also collected. All samples
were transported in plastic bags to laboratory and stored in a cold chamber (at 4"C) to delay
water content losses. The samples were burned within 2 to 5 days after fuel collection in the
field. Fuel samples were arranged in the six central trays of the wind tunnel test section
(Figure 1).
Side view
1.50 m
1 m
Test section height = 3 m
Panels height in the test section = 2 m
Upper vie
w
1 m 0.8 m 2 m
m56.8m56.0
Test section
Fuel
8 m
6 m
0.33 m
Ignition
line
Fan
4.45 m
Diffuser
1.65 m
Figure 1. Schematic diagram of the wind tunnel and fuel arrangement used in the experimental tests.
4 Journal of Fire Sciences 0(0)
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Three series of tests were conducted. The first series of tests (Series A) corresponded to
mixed-heathland fuel samples, being dominated by Erica, Ulex and Pterospartum species.
Series B and C corresponded to fuel samples collected in gorse shrubland dominated by
Ulex europaeus. In Series A and B, fuel beds were reconstructed according to the original
fuel bed structure found in the field. In Series C, initial fuel loads were modified in several
experiments to obtain a wider range of BD in the shrub layer. Fuel bed characteristics and
environmental conditions for each series are summarized in Table 1. All fuel samples had
100% shrub cover, meaning that even though it might be possible to see through the fuels to
the ground, the shrubs overlapped and the canopy was continuous. Fuel heights reported
are mean values, obtained from six different measurement points in each tray and averaging
over all 36 measurements. FMC was calculated on an oven-dry basis (48 hours in oven at
100"C) from small samples collected throughout the fuel beds immediately before conduct-
ing each test. Additional destructive sampling was used to obtain dead fuel fraction from
total shrub biomass.
In this study, tests were carried out at two levels of wind speed: 2.3 m/s and 3.5 m/s,
measured 0.3 m above the tunnel bare ground, in the central part of the test section (four
central trays). A cotton strip impregnated with alcohol was used to ignite the fuels. For each
experimental test, ROS was calculated based on the time it took the fire front (base of the
flame) to burn over the four central trays of the test area. The first and the last burnt fuel
trays were omitted from the calculations due to the fact that they could easily be affected by
end effects. It is noted that depending on the distance it takes for the spread rate to equili-
brate, this amount of distance omitted at the leading edge of the experiment may affect the
spread rate calculations. Time delays were visually determined and registered with a
chronometer.
FIRETEC simulations
FIRETEC is a three-dimensional, two-phase transport model that solves the conservation
equations of mass, momentum, energy and chemical species. A detailed description of the
physical and chemical formulation of the model is available in Refs. 3, 12 and 13. In addi-
tion, FIRETEC equations are described in the Appendix attached to Ref. 14. FIRETEC is a
coupled fire-atmosphere model, thus it naturally includes both ambient winds and fire-
induced winds in addition to the feedback effects from the wind on the fire. FIRETEC
includes bulk volumetric representations of vegetation in order to simulate turbulent flows
and fire propagation at metre scales within and above heterogeneous vegetation canopies.
FIRETEC is based on a Large Eddy Simulation (LES) approach for turbulence, which
attempts to resolve large turbulent fluctuations while modelling smaller fluctuations (i.e.
below possible resolutions either because of mesh or unresolved turbulent generation fea-
tures) using a set of turbulent kinetic energy equations.
13
FIRETEC considers only fine fuel
elements, and in the version of the code used for this study, there is only one set of fuel prop-
erties per cell, representing the bulk-averaged properties of the various fuels present in any
given cell. A multiple fuel version of FIRETEC now exists but was still under testing at the
time of the experiments and simulations. For this study, we accounted for foliage and fine
twigs (diameter \6 mm). Larger twigs represent a small area exposed per unit volume, and
it is assumed that they play little role in fire propagation. Because only a single effective fuel
exists in each cell, fuel properties of the different fuel elements (e.g. different plant species or
Marino et al. 5
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Table 1. Fuel and environmental characteristics in the experimental burns and resulting fire rates of spread in the wind tunnel and FIRETEC simulations
U
(m/s)
T
("C)
RH
(%)
FMC
h
(%)
W
h
(kg/m
2
)
H
h
(cm)
FMC
live
(%)
FMC
dead
(%)
W
(kg/m
2
)
W
e
(kg/m
2
)
H
(m)
H
s
(m)
BD
(kg/m
3
)
BD
e
(kg/m
3
)
ROS
obs
(m/min)
ROS
firetec
(m/min)
Series A (n = 9)
Minimum 2.3 13.0 32 29 0.5 0.7 49 22 1.2 1.0 0.37 0.20 3.2 2.5 0.36 2.80
Maximum 2.3 26.0 82 76 2.9 3.4 84 36 3.6 3.2 0.61 0.47 8.1 7.0 0.76 10.09
Series B (n = 6)
Minimum 2.3 14.0 31 28 0.5 1.2 65 20 3.4 2.6 0.64 0.38 4.9 3.7 0.42 1.79
Maximum 2.3 28.8 52 42 0.8 2.9 105 34 4.7 3.6 0.77 0.59 7.3 5.6 1.50 3.58
Series C (n = 8)
Minimum 3.5 24.5 29 6 0.2 0.4 15
a
10 1.7 1.3 0.52 0.21 2.6 2.0 1.07 5.12
Maximum 3.5 32.0 60 152 0.3 1.1 113 20 4.5 3.4 0.65 0.33 6.9 5.3 4.19 24.29
Total (n = 23)
Minimum 2.3 13.0 29 6 0.2 0.4 15
a
10 1.2 1.0 0.37 0.20 2.6 2.0 0.36 1.79
Maximum 3.5 32.0 82 152 2.9 3.4 113 36 4.7 3.6 0.77 0.59 8.1 7.0 4.19 24.29
U: wind speed; T: air temperature; RH: relative humidity; FMC
h
: litter moisture content; W
h
: litter load; H
h
: litter depth; FMC
live
: live shrub moisture content; FMC
dead
: dead
shrub moisture content; W: total shrub load; W
e
: fine shrub load (diameter \ 6 mm); H: total shrub height; H
s
: dead shrub height; BD: shrub bulk density; BD
e
: fine shrub bulk
density (diameter \ 6 mm); ROS
obs
: observed rate of spread; ROS
firetec
: simulated rate of spread.
a
Minimum FMC
live
value in series C corresponds to initially live shrub fraction that dried up to low moisture content level before the experimental burn.
6 Journal of Fire Sciences 0(0)
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mixture of dead and live foliage in one cell) are combined through a mass weighted average.
The ramifications of this averaging will be investigated in future work.
Fuel BD impacts the wind profile near the ground through its effect on drag forces and
impacts the convective heat transfer between the fuel and the gaseous phase as well as the
absorption of thermal radiation.
In FIRETEC, fuel moisture affects the fire behaviour in several ways. First, water eva-
poration is an endothermic process that absorbs energy for every bit of moisture that is dri-
ven off of the fuel, and the temperature at which moisture evaporates is in the order of a
couple hundred degrees below the temperature at which pyrolysis becomes strong. This
means that if we consider any very small mass of fuel, the moisture of dead fuel is driven off
before the fuel can pyrolyze, thus presenting an additional hurdle to sustained burning of
moist fuels. Second, the fuel moisture increases the mass and effective specific heat of the fuel
particles, so as fuel moisture drops the fuel becomes increasingly easier to heat. Currently,
any mechanical resistance to moisture release is ignored in FIRETEC. Other researchers
have recently focused much attention on the fact that liberation of fuel moisture from live
fuels may have a variety of other complications that are not considered in the scope of this
work. FIRETEC does consider the fact that within a resolved volume with sides on the order
of metres, not all of the fuel will warm up or lose water at the same rate. In fact, depending
on the size of the fuel particle, there may be temperature or moisture gradients across a fuel
element itself. In order to allow the effects of such heterogeneous states, FIRETEC uses a
probability density function for the fraction of initial moisture that has been evaporated as a
function of solid fuel temperature. Moisture begins to evaporate from the solid fuel long
before the average fuel temperature reaches the boiling point of water, due to the fact that
the high temperature tail of the temperature distribution is higher than the boiling point.
With this notion in mind, half of the water is evaporated when the average temperature of
the fuel is 373 K, but a small fraction has evaporated by the time the temperature is 350 K,
and there is still moisture to evaporate at 400 K.
FIRETEC simulations were run at horizontal resolutions of 2 m and a vertical resolution
of 1.5 m near the ground. In the vertical direction, the height of the cells increased with alti-
tude (stretched grid). The physical domain was 320 m 3 200 m 3 615 m, respectively, in
x-, y- and z-directions (160 3 100 3 41 cells). The ambient wind blew in the longitudinal
x-direction. The fuel bed was uniformly distributed in a layer just above the ground, which
was completely within the first layer of cells (x, y plane at ground level). At the beginning of
the simulations, uniform fuel bed was only disturbed by two 6-m wide strips with no vegeta-
tion created in the x-direction and delimiting a burn area 40-m wide in the lateral y-direction
and situated in the central part of the domain. Fire was ignited simultaneously 80 m down-
wind of the inlet boundary along the full width (40 m) of the burn area. The position of the
fire front was defined by the fuel isotherm 600 K, and the fire ROS in the x-direction was
determined from time records of the most advanced point of the fire front in this direction.
ROS was computed as the slope of the linear regression of spread distance in time between
x = 160 m and x = 260 m.
Empirical laws were used to set initial vertical velocity profiles before fire ignition and to
set the ambient conditions that serve as the basis for the upwind, lateral and downwind
boundary conditions. These laws are based on wind profiles that depend on Leaf Area
Index (LAI) of the vegetation canopy.
15,16
These profiles are specified by a value of wind
speed at a height above ground where the flow is only minimally influenced by the presence
of the vegetation. In this study, the experimental reference wind speed was measured at a
Marino et al. 7
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reference height of 0.3 m in a section of the wind tunnel with no vegetation. The wind speed
for the simulation was specified at 10-m height, and its value was determined by extrapolat-
ing experimental reference wind using a power-law profile (exponent = 1/7) adapted to
open lands and neutral atmospheric conditions.
17
The two levels of experimental reference
wind speed, 2.3 m/s and 3.5 m/s, corresponded to wind speeds of 3.8 and 5.8 m/s at 10-m
height in the simulations.
Statistical analysis
Non-linear regression analyses were performed to summarize trends in fire ROS for both
experimental and simulation data. Least square fitting techniques were used in R statistical
software package to obtain coefficient estimates and corresponding significance level for each
parameter involved according to model formulations. Deviation measures, including root
mean square error (RMSE), mean absolute error (MAE), mean percentage error (MAPE)
and mean bias error (MBE), were used in addition to the coefficient of determination (R
2
) to
evaluate the models performances. Potential co-linearity among input variables included in
the models was checked by means of the variance inflation factor (VIF). Correlation analyses
were also used to assess the relationship between independent variables. In addition, linear
regressions were performed to analyse the existing correlations between observed and pre-
dicted values of ROS.
Results
Observed values of ROS are shown in Table 1. In spite of litter being present in fuel samples,
fire propagation was dominated by the shrub layer. Most empirical models include height
(H) or fuel load (W) as input variables accounting for fuel bed structure. In the present study,
we intentionally manipulated the fuel to avoid the negative correlation commonly found in
the field between H and BD, but W was significantly correlated with H and BD (Table 2). H
varied to a much lesser extent; therefore, initially BD was chosen as the variable representing
fuel bed structure. Because of the close relations between parameters, they were not
Table 2. Correlation matrix of fuel characteristics and actual wind speeds in FIRETEC simulations (n = 23)
Ucell1 Ucell2 FMC
med
HW
e
BD
e
MVR
Ucell2 0.527*
FMC
med
20.271 20.625*
H 20.588* 0.073 20.078
W
e
20.892* 20.151 0.099 0.669*
BD
e
20.808* 20.203 0.118 0.289 0.895*
MVR 0.557* 0.158 0.224 20.206 20.433* 20.514*
LAI 20.892* 20.118 20.004 0.655* 0.972* 0.889* 20.605*
Ucell1: wind speed at 0.75 m (first layer of cells); Ucell2: wind speed at 2.2 m (second layer of cells); FMC
med
: weighted
fuel moisture content according to the proportion of live and dead shrub load; H: shrub height; W
e
: effective fuel load
(shrub particles \ 6 mm); BD
e
: effective bulk density (shrub par ticles \ 6 mm); MVR: mass-to-volume ratio; LAI: leaf
area index.
*p \ 0.05.
8 Journal of Fire Sciences 0(0)
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combined in the same model in order to reduce the dimensionality of the model. Following
most empirical models in shrubland fuels, we also hypothesized an exponential relationship
between FMC and ROS. Therefore, a model, including fuel characteristics and wind effect,
was fitted to the experimental data from the wind tunnel according to the form:
ROS = a + bUðÞexp
c
FMC
med
BD
d
e
ð1Þ
where effective BD (BD
e
) corresponds to the BD of shrub fuels particles with diameter \6
mm. Fine fuels are predominantly responsible for fire propagation. With regards to wind
effects on ROS, we only had two different speeds in the wind tunnel, and it was expected
that the profile associated with a measured wind speed in the wind tunnel at some height
would not be the same as the wind velocity at the same height in a field experiment or even
a landscape-scale simulation. Therefore, the effect of U was included in the model as a linear
effect in order to account for the two levels of wind speed tested, but we emphasize that the
model has no predictive value for the wind effect. The model described in equation (1)
includes FMC as a weighted average (FMC
med
) between live shrub moisture content
(FMC
live
) and dead shrub moisture content (FMC
dead
) according to the proportion of live
and dead fuel load, thus reducing the number of parameters to estimate in the regression
analysis. As suggested in most empirical models, we tested FMC
dead
as input variable
accounting for FMC effect on ROS in model (1), but statistical results indicated that the sig-
nificance of parameter estimates decreased (p-values of 0.005 and 0.048 for c and d, respec-
tively, and not significant for a and b) and both R
2
(0.81) and absolute errors (0.366 for
MAE and 38% for MAPE) showed a worse fit compared to the model including FMC
med
(Table 3). This variable also allowed a better comparison with simulation results by testing
the predictive ability of an average moisture content of the whole fuel complex, as it is the
actual input of the FIRETEC model.
In order to compare with the effect of W, we used a similar model to equation (1), shown
in equation (2) with W
e
instead of BD
e
,
ROS = a + bUðÞexp
c
FMC
med
W
d
e
ð2Þ
Additionally, a third model (equation (3)) including shrub height (H), instead of BD
e
or
W
e
, was also fitted to test the effect of this variable to account for fuel bed structure:
ROS = a + b UðÞexp
c
FMC
med
H
d
ð3Þ
Empirical models (1) and (2) fit the observation data well, explaining more than 88% of
existing variation in ROS with a high significance for all parameters included, especially
wind and moisture content (Table 3). Nevertheless, model (1) showed higher R
2
, with BD
showing higher significance compared to W in model (2). In addition, deviation measures
indicated higher errors in model (2), namely RMSE and MBE were about 185% higher than
in model (1). Concerning parameter estimates, both models obtained a value of c = 20.017
for FMC
med
effect. The effect of wind was slightly higher in model (1), and BD
e
showed a
stronger negative effect on ROS (20.48) than W
e
(20.39). Co-linearity among independent
variables was dismissed as the highest VIF value was 1.67 in both models. In contrast, results
on model (3) confirmed that H was not a significant variable to explain ROS variation in the
current set of data. Our focus with this analysis of the experimental results was to look at
Marino et al. 9
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the relative impacts of fuel bed properties and not the specific values of ROS because they
are likely to be affected by the nature of experimental set up.
As expected, FIRETEC simulations resulted in higher values of ROS due to the different
size of the experimental burns and the simulations (Table 1). The mean proportionality fac-
tor (k = ROS
firetec
/ROS
obs
) was 6.9, ranging from 2.4 to 18.9. However, correlation between
both ROS values (ROS
obs
= 0.11 + 0.17ROS
firetec
) was highly significant (p \ 0.0001), with
a correlation coefficient of 0.817 thus accounting for 66% of ROS variation. Deviation mea-
sures indicated a good fit in terms of root mean square error (RMSE \ 0.001) and bias
(MBE \ 0.001), but a worse fit in terms of absolute error (MAE = 0.50, MAPE = 57.5%).
Figure 2a depicts wind tunnel observed ROS versus simulated ROS values and shows
their linear correlation. This figure shows a group of points where FIRETEC values are sig-
nificantly higher than values predicted by the linear correlation. In addition, there are points
where the experimental ROS is significantly greater than that predicted by the linear correla-
tion. These differences may be related to inherent variability of various conditions that exist
in the experiments, but which are not measured and included in the numerical calculations.
In order to focus on the trends in the relationships between BD and ROS, we compared
FIRETEC simulations with ROS prediction from model (1). Results indicated a significantly
better agreement (Figure 2b) than was observed when FIRETEC was compared to the raw
Table 3. Non-linear regression models fitted with the experimental data (n = 23) to predict fire ROS
Model (1) ROS = a + bUðÞexp
c
FMC
med
BD
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 25.335 1.978 22.697 0.0143 0.889 0.028 0.261 24.27 0.006
b 3.825 0.803 4.762 0.0001 (0.872)
c 20.017 0.004 24.690 0.0002
d 20.482 0.184 22.626 0.0166
Model (2) ROS = a + bUðÞexp
c
FMC
med
W
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 24.572 1.418 3.224 0.0045 0.882 0.080 0.286 27.17 0.017
b 3.045 0.487 6.256 \0.0001 (0.863)
c 20.017 0.004 24.713 0.0002
d 20.393 0.174 22.259 0.0358
Model (3) ROS = a + bUðÞexp
c
FMC
med
H
d
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 23.202 1.595 22.008 0.0591 0.846 0.043 0.307 27.72 0.009
b 2.398 0.843 2.845 0.0104 (0.822)
c 20.022 0.004 25.145 \0.0001
d 20.097 0.623 20.156 0.8781
ROS: rate of spread; U: wind speed (initial value at 0.3 m height); FMC
med
: weighted fuel moisture content according to
the proportion of live and dead shrub load; BD
e
: effective bulk density (shrub par ticles \ 6 mm); W
e
: effective fuel load
(shrub particles \ 6 mm); H: total shrub height; R
2
: coefficient of determination (and adjusted value to degrees of
freedom); RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; MBE:
mean bias error.
10 Journal of Fire Sciences 0(0)
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data, with a correlation coefficient (r) of 0.90 and R
2
= 80%. This suggests that there are
sources of variations in the experimental data that are likely not being measured or recorded
and are not being included in model (1) or the FIRETEC simulations. Nevertheless, even
when FIRETEC is compared to model (1), there is still a group of tests that exhibit
FIRETEC ROS values higher than values predicted by the linear correlation. Analyzing the
details of the fuel characteristics in these cases, we noticed that they corresponded to experi-
mental burns conducted in fuel beds from Series A. The fuel beds in Series A had lower
shrub height (<0.5 m) and load (<1.7 kg/m
2
) than the other experiments. Neither shrub
height nor load were included in model (1), leaving the possibility that this is a source of var-
iation in ROS that is being captured by FIRETEC but is not captured by model (1). Within
the subset of experimental burns conducted with the lower wind speed (Series A + B), these
tests also had lower BD than the rest of the experiments, ranging from 2.4 to 3.1 kg/m
3
. If
these tests are omitted from the analysis (n = 17), a better fit between observed and pre-
dicted values was obtained (ROS
obs
= 0.37 + 0.17ROS
firetec
,p\ 0.0001), explaining up to
85% of the variation (r = 0.92) and significantly reducing absolute errors (MAE = 0.34,
MAPE = 24.8%). Proportionality factor (k) was also reduced, with a mean value of 4.3
(range = 2.4–7.2). In addition, a significantly better fit was observed when comparing with
ROS values predicted by model (1) when these experiments with low BD were omitted from
the model (1) fit, with R
2
= 94% (Figure 3). These results highlighted the important role of
fuel structure on FIRETEC performance. These results might also suggest some limitations
reproducing experimental data that may be linked to the range of fuel characteristics tested.
Consequently, to better address the effect of the different fuel characteristics involved in
fire propagation in FIRETEC and compare it to experimental data, we fitted the same mod-
els (1) and (2) to simulated FIRETEC ROS values (n = 23). Similar to what is described for
the experimental data, U was not considered as a predictive variable but was included in the
model to account for the effect of wind speed (two reference values at 10-m height, 3.8 or
5.8 m/s, corresponding to wind tunnel tests conducted at 2.3 or 3.5 m/s, respectively). Results
confirmed that all variables included in resulting models (4) and (5) were highly significant to
explain FIRETEC simulations of ROS (Table 4). Remarkably, the negative correlation
R² = 0,6678
0
1
2
3
4
5
ROS
obs
ROS
firetec
a)
R² = 0,8049
0
1
2
3
4
5
ROSpred
ROS
firetec
b)
3020100
3020100
Figure 2. Correlation between FIRETEC predictions of ROS (m/min) and (a) observed values and
(b) predicted values from the empirical model obtained (model (1)), for the whole set of experimental
burns (n = 23). Experimental burns performed in shrub fuels with lower height (<0.5 m) and load (<1.7
kg/m
2
) are circled in (b). R
2
is the coefficient of determination.
ROS: rate of spread.
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between BD (or W) with ROS found in the wind tunnel is also captured by FIRETEC simu-
lations. However, d parameter estimates indicate a differing importance of fuel structure
effects, with both BD (d ’21.2) and W (d ’21.1) influences being higher in FIRETEC
than in experimental burns (where d ’20.5 for BD and d ’20.4 for W). The higher values
of a and b parameter estimates in models (4) and (5) were expected as they are only the con-
sequence of the changing scale between wind tunnel experiments (6 m 3 0.8 m) and simula-
tions (180 m 3 40 m). In contrast, FMC effect on ROS, which is more of a local fuel bed
impact on the heating and burning of the fuel, was very similar in experimental burns (c
20.017) and FIRETEC simulations (c ’20.015).
R² = 0,8485
0
1
2
3
4
5
0
ROS
obs
ROS
firetec
a)
R² = 0,9376
0
1
2
3
4
5
0
ROSpred
ROS
firetec
b)
30
20
10
302010
Figure 3. Correlation between FIRETEC predictions of ROS (m/min) and (a) observed values and
(b) predicted values from the empirical model obtained (model (1)), for a subset of experimental burns
excluding tests with shrub height \0.5 m (n = 17). R
2
is the coefficient of determination.
ROS: rate of spread.
Table 4. Non-linear regression models fitted to FIRETEC simulations of ROS for the whole data set (n = 23)
Model (4) ROS = a + bU
ðÞ
exp
c
FMC
med
BD
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 15.628 19.161 0.816 0.0248 0.936 0.359 1.141 23.04 20.075
b 10.157 2.973 3.416 0.0029 (0.926)
c 20.015 0.002 25.922 \0.0001
d 21.198 0.147 28.146 \0.0001
Model (5) ROS = a + bUðÞexp
c
FMC
med
W
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 210.542 3.431 23.072 0.0063 0.985 0.092 0.512 7.061 0.019
b 8.408 0.638 13.172 \0.0001 (0.982)
c 20.014 0.001 212.241 \0.0001
d 21.105 0.063 217.588 \0.0001
ROS: rate of spread; U: wind speed (initial value at 10 m height); FMC
med
: weighted fuel moisture content according to
the proportion of live and dead shrub load; BD
e
: effective bulk density (shrub par ticles \ 6 mm); W
e
: effective fuel load
(shrub particles \ 6 mm); R
2
: coefficient of determination (and adjusted value to degrees of freedom); RMSE: root mean
square error; MAE: mean absolute error; MAPE: mean absolute percentage error; MBE: mean bias error.
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To test the influence of particular fuel characteristics in FIRETEC simulations, the same
models were fitted for the subset of cases that excluded fuel beds with shrub height \0.5 m
(n = 17). As expected, resulting models (6) and (7) showed a better fit (Table 5).
Nevertheless, parameter estimates only showed slight differences, with a lower effect of BD
in model (6) than in model (4) and a higher effect of W in model (7) than in model (5).
To assess ambient wind effect contribution to variation in ROS, we excluded this variable
from model (4). Resulting model (equation (4)) explained 90% of ROS
firetec
.
ROS = a exp
c
FMC
med
BD
d
e
ð4Þ
We also explored individual models for FMC (equation (5)) and BD (equation (6)) finding
R
2
values of 61% and 58%, respectively, thus confirming that despite the expected strong
influence of wind, fuel moisture and fuel structure had significant contributions to the varia-
tion in ROS.
ROS = a exp
c
FMC
med
ð5Þ
ROS = a BD
d
e
ð6Þ
Models described used two levels of free wind speed tested in the experimental burns and
the simulations. In order to better assess the combined effect of wind and fuel structure on
simulated ROS, we considered models for the ROS with actual FIRETEC wind speeds act-
ing in the presence of the shrub layer. Averaged wind velocities in the first cell (Ucell1, at
0.75-m height) were extracted from the simulations prior to ignition. In the first cell, wind
speed was strongly affected by fuel bed structure, and there was much less vegetation influ-
ence above this first layer of cells (Table 2). Figure 4 shows the wind speed in the first cell
Table 5. Non-linear regression models fitted to FIRETEC simulations of ROS for a subset of experimental
burns excluding tests with shrub height < 0.5 m (n = 17)
Model (6) ROS = a + bUðÞexp
c
FMC
med
BD
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 230.759 13.351 22.304 0.0384 0.976 0.012 0.582 9.143 20.003
b 16.478 2.472 6.665 \0.0001 (0.970)
c 20.016 0.002 28.272 \0.0001
d 20.990 0.120 28.253 \0.0001
Model (7) ROS = a + bUðÞexp
c
FMC
med
W
d
e
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 29.844 4.864 22.024 0.0640 0.995 0.054 0.330 4.930 0.013
b 8.578 0.785 10.930 \0.0001 (0.994)
c 20.016 0.001 217.326 \0.0001
d 21.132 0.063 218.095 \0.0001
ROS: rate of spread; U: wind speed (initial value at 10 m height); FMC
med
: weighted fuel moisture content according to
the proportion of live and dead shrub load; BD
e
: effective bulk density (shrub par ticles \ 6 mm); W
e
: effective fuel load
(shrub particles \ 6 mm); R
2
: coefficient of determination (and adjusted value to degrees of freedom); RMSE: root mean
square error; MAE: mean absolute error; MAPE: mean absolute percentage error; MBE: mean bias error.
Marino et al. 13
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versus LAI of the fuel layer. LAI is commonly used in studies of wind flow over canopies
and is defined as surface area of foliage per unit area of the ground and was computed as
the product of fuel bed height, surface-to-volume ratio and BD, divided by 2 (one-sided area
of the vegetation per unit area of ground). A new model (8) was fitted with this wind effect
included as a power law but excluding fuel bed structure variables (Table 6). Results showed
a strong influence of Ucell1 on ROS (b 2) and confirmed the effect of fuel moisture with
the same parameter estimate as the one obtained in the experimental burns (c = 20.017).
Although no fuel structure variable was included in model (8), Ucell1 and FMC explained
97% of the ROS variability. This again suggests a strong influence of fuel structure variables
on the ROS through the wind speed in the first cell.
Discussion
Fuel bulk density effect
The relationship of increased BD resulting in decreased ROS observed in our study is consis-
tent with previous experimental works performed in other wind tunnels.
4,5,18,19
Anderson
20
y = 0,1714x
-0,442
R² = 0,9855
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0
U
norm1
LAI
252015105
Figure 4. Relationship between FIRETEC calculation of wind speed in the first cell with vegetation
presence (U
cell1
) and leaf area index (LAI). U
norm1
is the dimensionless wind speed U
cell1
/U
10
, with U
10
the
wind at 10-m height as the reference level. R
2
is the coefficient of determination.
Table 6. Non-linear regression model fitted to FIRETEC simulations of ROS for actual wind speed in the
presence of vegetation (n = 23)
Model (8) ROS = a Ucell1
b
exp
c
FMC
med
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 192.286 28.384 6.774 \0.0001 0.975 0.369 0.653 10.34 0.077
b 2.049 0.151 13.524 \0.0001 (0.973)
c 20.017 0.001 214.798 \0.0001
ROS: rate of spread; Ucell1: wind flow in the first layer of cells (m/s); FMC
med
: weighted fuel moisture content according
to the proportion of live and dead shrub load; R
2
: coefficient of determination (and adjusted value to degrees of
freedom); RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; MBE:
mean bias error.
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had already identified BD as an important variable to predict fire ROS, indicating that they
were inversely related. Carrier et al.
19
and Wolff et al.
4
reported that ROS } W
20.5
(here }
indicates ‘proportional to’). However, their wind tunnel experiments were performed with a
fixed fuel depth, hence ROS was proportional to BD
20.5
in their model. Catchpole et al.
5
used
packing ratio (b), which is proportional to BD, to account for fuel structure, finding a consis-
tent relationship with ROS in the form of a power law (ROS } b
20.49
). The results from our
experiments are consistent with a ROS } BD
20.48
. In the field, some authors also reported an
inverse relationship of fine fuel BD (i.e. effective BD) with fire ROS in shrubland fuels.
Thomas
21
observed a relation of the form ROS#BD } 1 + U, whereas Davies et al.
22
reported
BD effect through a Canopy Density Index (CDI) inversely related to BD (ln(ROS) } CDI).
FIRETEC simulations also predicted a decrease in ROS as BD was increased, following
the form of a power law (ROS } BD
d
). However, the higher coefficient obtained (d ’21)
indicated a stronger effect of BD compared to laboratory experiments. When the rest of the
variables were held constant in FIRETEC simulations, BD effect on ROS was slightly lower
(d = 20.95, Table 7, model (9)) but still far from the coefficient d = 20.5 found in the
experimental tests (Table 3).
Keeping in mind the high degree to which the variations in predicted ROS were explained
by variations in wind speed in the first cell (Table 6) and the fact that fuel BD impact is con-
nected closely to the wind speed in the first cell, it is reasonable to hypothesize that the source
of difference in BD power-law coefficients is due to differences in the way that the BD is
affecting the winds in the fuel bed. In the context of wildland fires and its coupled wind/fire
processes, there are a number of possible contributors to these differences. One likely source
of the difference in BD effects on wind speed comes from differences in the free wind penetra-
tion into the fuel bed in the experiments versus what occurs on a landscape scale. The experi-
mental fuel bed is only 0.8-m wide, and there is ventilating space on the sides of the fuel bed.
This arrangement provides ventilation into the fuel bed as well as directly into the base of the
fire. There would be continuous entrainment of faster-moving, free-stream winds into the fuel
Table 7. Individual effect of BD on fire ROS in FIRETEC
Model (9) ROS
40
=aBD
d
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 0.341 0.058 5.881 0.0277 0.959 0.001 0.009 10.13 20.001
d 20.958 0.165 25.800 0.0285 (0.938)
Model (10) ROS
8
=aBD
d
Estimate s.e. t p-value R
2
RMSE MAE MAPE MBE
a 0.278 0.018 15.18 0.004 0.994 5#10
24
0.003 3.90 22#10
24
d 20.992 0.065 215.33 0.004 (0.991)
ROS: rate of spread R
2
: coefficient of determination (and adjusted value to degrees of freedom); RMSE: root mean
square error; MAE: mean absolute error; MAPE: mean absolute percentage error; MBE: mean bias error.
Two different fire length widths were used in the simulations: 40 m (ROS
40
) and 8 m (ROS
8
).
Non-linear regressions were fitted to ROS values obtained in the simulations for four different levels of bulk density (BD) (2, 3,
5 and 7 kg/m
3
), with the rest of the variables held constant and close to average values used in the experimental tests: wind
speed (U = 4.5 m/s); shrub height (H = 0.6 cm); mass-to-volume ratio (MVR = 7000 m
-1
); fuel moisture content (FMC = 50%).
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bed over its entire length, resulting in a reduced influence of vegetation drag on fuel bed velo-
cities in the experiments compared to a homogeneous landscape-scale fuel beds. In addition,
the extra ventilation into the sides of the fire changes the interaction between the buoyant rise
and the upstream indraft, thus potentially changing the flame angle inside the fuel bed and
directly above it. It is also true that the wind tunnel forces air into the leading edge of the
experimental fuel bed. This is analogous to work done by previous authors reporting that at
the downwind side of a fuel break in a forest canopy, it takes on the order of 10 tree-heights
downwind of the fuel break for the winds to recover to a similar profile as they had upwind of
the fuel break.
23
It is not clear how significant this factor is once a fire is burning, since the air-
flow arriving at the fire front from upstream in both simulations and experiments is blowing
over fuel beds where the majority of the fuel bed has been consumed. A repeatable decrease in
ROS over the length of the fuel bed has never been observed in the wind tunnel, suggesting that
some equilibrium in wind speeds upstream of the fire and in the narrow fuel bed is reached.
This equilibrium could be influenced by the continual entrainment from the sides of the fuel
bed. The shear layer above the fuel is also different in the wind tunnel versus on landscape-scale
experiments and simulations. The wind vanishes a short height above the wind tunnel (a few
metres), while wind speed monotically increases up to some maximum value far above the vege-
tation in FIRETEC simulations as well as in field conditions. Wind profiles are thus necessarily
different, but the impact of this difference on spread rate is difficult to assess.
Another hypothesis is that the BD effect might be influenced by the fire width (here the
constant width of the vegetation strip), which was 0.8 m in the experiments and 40 m in the
simulations. Earlier simulations using FIRETEC have shown that the width of the fire influ-
ences the ROS: an increase of fire width may lead to an increase in fire ROS.
3
In the present
study, the isolated BD effect was also simulated with a fire width of 8 m (the strip of vegeta-
tion had four cells in y-direction). As expected from earlier simulations, the ROS decreased
when the width decreased from 40 to 8 m. The size parameter of the exponential function
fitted to the predicted ROS decreased from a = 0.34 to a = 0.28, but the shape parameter
changed only slightly from b = 20.96 to b = 20.99 (Table 7, models (9) and (10)).
Therefore, the influence of fire width is unlikely to explain the higher BD effect predicted by
FIRETEC (d ’21.0) as compared to the experimental BD effect (d ’20.5).
It is of course possible that the FIRETEC modelled effects of BD on wind penetration into
the fuel bed are too sensitive to BD variations, especially at very high surface-to-volume ratio
and BD values. This could be due to drag forces that increase linearly with BD in the FIRETEC
model (as well as in other physically-based models) even for high-density values, while one could
expect that such an increase is reduced by a shelter effect. Another source of modelling error
might be due to the relatively low spatial resolution in these FIRETEC simulations, in particular
in the vertical direction. In absence of trees, the fuel bed is most often entirely contained in the
first cell and this is the case in the present study. The prediction of wind profiles by FIRETEC
has been validated against wind measurements in tree canopies,
13
but the validity of the wind
predicted within shrub or grass canopies has not been explicitly validated. For the validation
studies of FIRETEC wind flows over tree canopies, the typical tree canopy BD (lower than 0.5
kg/m
3
) was considerably lower than the shrubland bulk densities of the present study.
Fuel moisture effect
A damping effect of FMC on ROS in the form ROS } exp
cFMC
(c \ 0) was confirmed by
our experiments. This exponential relationship with moisture content was often found by
16 Journal of Fire Sciences 0(0)
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previous authors for different kind of fuel beds, both in laboratory
5,7,8
and in field experi-
ments.
2,11,24–26
However, the coefficient estimates varied widely. Wilson
7
and Catchpole
et al.
5
found that moisture damping effect on ROS depended also on surface-to-volume ratio
of the fuel being lower for finer particles. Wilson
7
reported values of c as 20.02 for experi-
ments in wood sticks of 1.6 mm and about 20.04 for pine needles. Catchpole et al.
5
reported
similar values for excelsior (20.026 to 20.014) and pine needles (20.04). Much higher values
are reported by Burrows
8
for eucalypt litter, ranging from 20.14 to 20.08 depending on the
wind speed used in the burning tests. In field experiments, the range of values reported in
models by Fernandes et al.
11,24,25
was from 20.111 to 20.035. Cheney et al.
2
found a coeffi-
cient c = 20.097 for grasslands, whereas Marsden-Smedley and Catchpole
26
reported a sig-
nificantly lower value c = 20.024 in moorlands. In our experiments, coefficient estimate
resulted in c = 20.017, which is within the range of values reported. However, it is note-
worthy that our coefficient accounts for the effect of moisture of both live and dead shrub,
whereas previously mentioned studies only referred to dead FMC effect.
FIRETEC predictions also fit the exponential function well with a similar coefficient. The
weighted average FMC was found to be a good predictor for shrub fuels, while empirical
models use only the dead FMC. Field studies on fire propagation are often limited to a rela-
tively narrow range of live shrub moisture levels due to operational constraints, which may
explain the absence of this variable in most empirical models.
10,11,22,26
However, periods of
strong drought stress associated to future climate change scenarios could result in consider-
able lower values of average shrub moisture, which may lead to increased fire potential in
this type of community.
27
Despite recent works that have demonstrated the relevance of live
FMC when predicting ignition and fire sustainability in shrub fuels in laboratory,
28–30
and in
the field,
31
there are very few laboratory studies addressing combined live and dead shrub
moisture effect on fire ROS.
Catchpole and Catchpole
32
developed an extension of Wilson’s exponential damping
term for mixed live and dead fuels, proposing a theoretical approach that distinguished two
sources of damping: moisture released from unburnt fuel and from burning fuel. Thus, their
model needed to consider the moisture fraction given off before the fuel ignites (m
1
) and the
fraction given off within the combustion zone (m
2
) by a function of the form exp(c
1
m
1
+
c
2
m
2
). When applying their model to Van Wilgen et al.
33
data from the experimental fire in
South African shrubland (fynbos), these authors found coefficients of c
1
= 20.073 and
c
2
= 20.021. This approach to account for fuel moisture effect on ROS is clearly more
detailed than ours, but it is indeed more complex in terms of input variables than the sug-
gested weighted average FMC and also requires experimental determination of the coeffi-
cients involved.
When assessing the isolated effect of FMC on ROS, that is, with the rest of the variables
held constant, FIRETEC simulations confirmed the exponential function exp
cFMC
to have
the best fit. However, like observed for isolated BD effect, the coefficient found when moist-
ure effects were isolated was lower, c = 20.011, compared to model (4) or (5), thus showing
a less significant effect on ROS. Considering this effect in the context of the previously
described close agreement between influences on simulations and observations when all vari-
ables were considered, these results highlight the importance of the interaction between inde-
pendent variables. The non-linear interaction results in increased ROS when they are varied
together. Despite having checked the potential co-linearity between input variables in our
models through VIF values, there are in fact certain correlations that may not be important
Marino et al. 17
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in terms of modelling constraints but somehow could influence the results compared to a
model where only one variable is changing (Table 2).
Comparison with field empirical models
Two empirical models from Vega et al.
10
and Fernandes
11
were used for comparison with
observed and simulated ROS values in our study. These models were selected because they
were obtained from field experimental burns performed in similar shrubland vegetation.
The model by Vega et al.
10
was obtained from experimental data gathered in field burns
conducted in three types of shrubland (including mixed-heathland and gorse shrubland) in
Galicia, NW Spain. Live moisture content in the shrubs ranged from 69% to 183% and dead
moisture fraction varied from 3% to 26%. BD ranges were not reported by the authors, but
according to average height and fuel load from each shrubland community, mean BD for
these shrubland communities were approximately 2.1 to 3.3 kg/m
3
for total BD and 1.8 to
3.1 kg/m
3
for effective BD. The Vega et al.
10
model predicted ROS as a function of wind
speed (U), shrub height (H) and slope (S) according to the equation:
ROS = 0:249U
1:193
H
0:658
exp
1:088S
ð7Þ
The model by Fernandes
11
was obtained from field burns conducted in four kinds of
shrub communities of gorse and mixed-heathland in Portugal. Total and effective bulk den-
sities ranged from 3.4 kg/m
3
to 5.0 kg/m
3
and 1.6 kg/m
3
to 3.5 kg/m
3
, respectively, and fine
fuel moisture in the live shrubs was 72% to 113%, whereas the dead moisture fraction was
10% to 40%. This model also predicted ROS as a function of wind speed (U) and shrub
height (H), but included dead shrub moisture content (FMC
dead
) and did not account for
slope effect:
ROS = 1:764U
1:034
H
0:186
exp
$0:062FMC
dead
ð8Þ
The highly significant correlation (p \ 0.0001) previously observed between wind tunnel
experimental ROS and predictions from both empirical models is confirmed by this study.
1
The Fernandes
11
model showed better correlation (R
2
= 72%) than the Vega et al.’s
10
model
(R
2
= 53%), probably due to the dead shrub moisture content effect accounted in the for-
mer that is not included in the latter. As expected, the observed ROS values in the wind tun-
nel were over-predicted by the field models, with a proportionality factor (k) ranging from
5.2 to 41.4 for the Vega et al.
10
model and from 1.7 to 8.5 for the Fernandes
11
model; thus,
ROS predictions were in average about one order of magnitude higher than wind tunnel data
(Figure 5).
In a comparison of these two field experiment-based models with FIRETEC simulations,
a significant linear relationship was also found between ROS predictions. The Fernandes
11
model showed a better fit (p = 0.0007, R
2
= 43%) than the Vega et al.
10
model (p =
0.0271, R
2
= 21%). However, these correlations were lower compared to the correlations
obtained for observed values in the wind tunnel experiments. Despite the fact that simula-
tions were performed in a similar spatial scale as field experimental burns, FIRETEC ROS
values were lower than those predicted by the Vega et al.
10
model, with k factor between
0.1 and 1.1 (mean k = 0.5). In contrast, FIRETEC tended to simulate higher values than
the ones predicted by the Fernandes
11
model, with k factor ranging from 0.5 to 6.8 (mean
k = 2.1). These discrepancies between FIRETEC simulations and these two field
18 Journal of Fire Sciences 0(0)
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experiment-based models are not surprising as ROS predictions from both empirical models
were not consistent with each other. We argue two possible causes to these differences in
ROS. First, particular fuel structural characteristics associated to the shrub fuel beds tested
(e.g. BD) were accounted for in the simulations but were not included in the empirical mod-
els as they only considered shrub height. Second, fuel moisture effect was either not consid-
ered at all in the Vega et al.
10
model or only partially included in the Fernandes
11
model by
means of dead FMC, but never taking into account fuel moisture corresponding to the live
shrubs. Nevertheless, the general order of magnitude between ROS simulations and field
0
5
10
15
20
25
30
Predicted ROS
Observed ROS
Firetec Vega_1998 Fernandes_2001
543210
Figure 5. ROS values (m/min) observed in the wind tunnel experiments against predictions from FIRETEC
model and two field empirical models: Vega et al.
10
and Fernandes.
11
ROS: rate of spread.
0
5
10
15
20
25
30
0
ROS Firetec
ROS empirical model
Vega_1998 Fernandes_2001
30252015105
Figure 6. Comparison between ROS values (m/min) predicted by two field empirical models (Vega et al.
10
and Fernandes
11
) and FIRETEC simulations.
ROS: rate of spread.
Marino et al. 19
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empirical model predictions was similar, thus suggesting that FIRETEC predicts reasonable
ROS values in this kind of vegetation. However, further research would be needed to better
address fire behaviour correspondence between simulations and field experimental burns in
order to validate FIRETEC in shrubland fuels.
Conclusion
This study explored a comparison between wind tunnel-based fire experiments with
landscape-scale simulations in shrub fuels, which were briefly compared to field experiments.
The exploration suggests that some of the basic trends in fire behaviour exist in laboratory
and field experiments as well as numerical simulations. The difference in laboratory and
landscape-scale fuel bed configurations appears to contribute to difference in sensitivities
between fire ROS and some environmental conditions. The configuration differences seem
to be more significant in cases where fire behaviour is a response to both local and distant
fuel properties such as BD. In other cases, the configuration differences have minimal influ-
ence on the fire behaviour when fuel bed properties only have local influences, such as fuel
moisture. A better understanding of the configuration influences on ROS might make it pos-
sible to use laboratory experiments to study fire behaviour and extrapolate to field-scale
trends.
This study demonstrated the importance of fuel BD on fire propagation from data
obtained in both laboratory experimental burns and simulations performed in shrubland
fuels, thus suggesting also a significant effect in the field. Hence, future fire propagation
models may consider including fuel BD as an input variable in order to accurately account
for fuel structure effect in this type of vegetation. Despite the fact that the empirical models
tested were developed from field burns in the same kind of shrubland (i.e. same species col-
lected in the same geographical region), it has been shown that shrub height alone is not an
adequate characteristic to account for ROS variability due to changes in fuel bed structure.
Indeed, field-based empirical models are very useful for fire propagation prediction within
the range of specific fuel and environmental conditions for which they were built. But shrub-
land fuel complexes exhibit natural variations in structure (e.g. foliage BD) depending on
plant growth conditions and are also often submitted to important changes due to fuel treat-
ments, which may result in inaccurate predictions of fire ROS, hindering the generalized use
of these empirical models in apparently similar shrubland vegetation.
Our results illustrate the significant negative effect that fuel BD has on ROS, which can
be modelled through a power-law function, both in laboratory burns and in simulations.
However, a larger sensitivity of FIRETEC simulations to fuel BD than observed experimen-
tal data suggests that there could be significant influences of the wind tunnel fuel bed config-
urations on this sensitivity. Unfortunately, since field-scale experiments do not include this
parameter for this type of fuel, it is currently difficult to separate this laboratory-scale to
field-scale difference from possible model formulation problems. In future field-scale shrub
experiments, it would be helpful to include fuel BD (or another variable representing spatial
structure, like packing ratio) in the empirical models that are derived, and in future labora-
tory experiments, attention will be paid to understanding the wind penetration and entrain-
ment into the fuel bed in order to quantify the ramifications of these fuel configurations.
For instance, it would have been useful to have been able to quantify the winds at various
20 Journal of Fire Sciences 0(0)
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positions along the centreline of the fuel bed and used these in-stand winds as the basis for
the model formulation.
With regards to fuel moisture effects, laboratory and simulation results were highly con-
sistent. Statistical modelling confirmed the exponential function to be an adequate formula-
tion to account for fuel moisture effect on fire ROS. We also highlighted the importance of
including not only dead FMC effect but also live FMC to accurately predict ROS in shrub
fuel beds, suggesting the weighted average of both moisture content values as a good predic-
tor to be included in future fire propagation models.
Overall, this work showed the efficacy of multiple approach studies for wildland fire beha-
viour research. The combination of fire simulations with experimental data from laboratory
and field burns clearly benefits from the particular advantages of each individual approach
and is strongly recommended to further improve fire propagation models. At the same time,
it has been shown that it is important to carefully consider the influences of various aspects
of the experimental configuration compared to field-scale fires.
Acknowledgement
The authors are grateful to Javier Madrigal and Carmen
´
ez from INIA for their contribution to
laboratory experimentation and to Antonio Arellano from CIF-Louriza
´
n (Spain) for field assistance.
In addition, they appreciate the contributions of Los Alamos National Laboratory Institutional
Computing Program for the computational resources used for the simulations and the United States
Forest Service for their continued support of the development of FIRETEC.
Funding
Participation of Eva Marino in this research was possible through a PhD scholarship funded by
National Institute for Agricultural Research (INIA) from the Spanish Ministry of Science and
Innovation. The work carried out in this article was partially supported by the European Commission
(Integrated Project FIRE PARADOX FP6-018505).
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Author biographies
Eva Marino is a contracted researcher at Instituto Nacional de Investigacio
´
n y Tecnologı
´
a Agraria y
Alimentaria-Centro de Investigacio
´
n Forestal (INIA-CIFOR) Forest Fire Laboratory. She was super-
vised by Carmen Hernando, Mercedes Guijarro and Jean-Luc Dupuy, and received her PhD in forest
science in 2011 (Polytechnic University of Madrid, Spain). Since 2007, she has been working on fire
behaviour modelling in shrubland and the effectiveness of forest management for wildfire hazard
reduction.
Jean-luc Dupuy is a senior scientist at INRA Mediterranean Forest Ecology unit. He holds a PhD in
applied mathematics (1997, University of Lyon, France) and has 20 years of research experience in fire
behaviour modelling and experiments including his PhD thesis. He has been involved in several
European research projects and was the leader of the researches on physical mechanisms of forest fires
in the FIRE PARADOX project (2006–2010).
Francxois Pimont is a computer scientist at INRA Mediterranean Forest Ecology unit. He holds a PhD
in environmental sciences (2008, University of Marseille, France) and now has 6 years of experience in
the field of physically based modelling of fires.
Mercedes Guijarro is a senior scientist at INIA-CIFOR Forest Fire Laboratory. She holds a PhD in
forest science (2000, Polytechnic University of Madrid, Spain) and has more than 20 years of research
experience on forest fuel characteristics and forest fire behaviour modelling. She has been a team
22 Journal of Fire Sciences 0(0)
at Biblioteca Universitaria de Granada on February 13, 2012jfs.sagepub.comDownloaded from
leader in different national and international research projects on forest fuel characterisation, fire
behaviour and effects, including forest management for wildfire hazard reduction and prescribed burn-
ing use. She is an associate editor of the journal Forest Systems.
Carmen Hernando (PhD in Forest Science, 1990, Polytechnic University of Madrid, Spain) is a senior
scientist and head of INIA-CIFOR Forest Fire Laboratory. She has more than 20 years of research
experience and is a specialist in forest fuels flammability and forest fuel characteristics. She has been a
team leader in different national and international research projects on forest fuel characterisation, fire
behaviour and effects, including post-fire ecosystem recovery and mitigation, development of forest
danger rating systems and efficacy of fire retardants on forest fuels. She is an associate editor of the
journal Forest Systems.
Rodman Linn is a scientist in the Earth and Environmental Sciences Division at Los Alamos National
Laboratory. He holds a PhD in Mechanical Engineering (1997, New Mexico State University) and has
more than 16 years of experience modelling and studying coupled wildfire behaviour. He has been a
team leader for the atmospheric modelling team at Los Alamos for 11 years and leads the wildfire
behaviour modelling research at Los Alamos. He is an associate editor of the International Journal of
Wildland Fire.
Marino et al. 23
at Biblioteca Universitaria de Granada on February 13, 2012jfs.sagepub.comDownloaded from
... Fire behavior and effects depend on fuel type characteristics (moisture, chemistry, and particle size and shape) and fuel bed characteristics (continuity, compactness, composition, fuel load, and vertical orientation) (DeBano et al., 1998;Marino et al., 2012;Rossa and Fernandes, 2017;Weise et al., 2016;Whelan, 1995). Fuel characteristics influence all aspects of fire behavior (e.g., heating duration, maximum temperature, flame heights, and rates of spread), which can ultimately determine the structure of ecosystems by altering the abundance and distribution of plants, animals, and soil nutrients (Bowman et al., 2017;Keeley, 2009;Weise et al., 2016;Whelan, 1995). ...
... For example, bench top approaches are designed to measure plant flammability, ignitability, and combustibility, while manipulating fuel type characteristics of different species (e.g., Etlinger and Beall, 2004;Engstrom et al., 2004;Simpson et al., 2016). Larger scale laboratory methods have examined fire behavior responses to manipulated fuel beds and environmental conditions, including varying bulk density, fuel moisture, fuel type (species), proportion of live and dead fuels, and wind velocities (Marino et al., 2012;Rossa and Fernandes, 2017;Weise et al., 2016) (Fig. 1; Table 1). A particularly distinctive approach mimicked natural vertical fuel structure by placing cut shrubs in a clay aggregate substrate but the method was difficult to implement and has not been widely used (Rossa and Fernandes, 2017). ...
... Both approaches allow for fuel manipulations by adding or removing fuels to alter fuel type, fuel load, or both (e.g., Thaxton and Platt, 2006;Bowman et al., 2017). Fuel addition treatments utilizing a combustion table are predominantly piled for efficiency, similar to many lab-based experiments (Marino et al., 2012;Weise et al., 2016), but this approach disregards fuel bed characteristics, such as vertical structure, that can critically affect fire behavior (Ganteaume et al., 2014). Rossa and Fernandes (2017) mimicked natural vertical structure while using a combustion table approach by placing cut shrubs in a clay aggregate substrate, but acknowledged the difficulty of this process has discouraged researchers from doing so. ...
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... Marino et al. [12] conducted a combined experimental (laboratory-scale) and physics-based modelling (field-scale) study on the effect of moisture on the RoS of fire. The experiments were conducted in a wind tunnel and shrub fuel collected at several representative gorse and mixed-heathland sites in North-West Spain was used. ...
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... Other authors [154,237] have previously identified the need for improved representation of bulk density effects within detailed physics-based models. Marino et al. [237] previously observed an oversensitivity of the FIRETEC model to bulk density, during a numerical analysis of wind tunnel experiments involving shrub fuels. Similarly, while using a multi-phase model developed in OpenFOAM to simulate bench scale experiments (combustion of pine needles in the FPA), El Houssami et al. [154] observed weaker agreement with experimental observations at lower bulk densities. ...
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... On the one hand, forest activities are sometimes a source of wildfires (see Prométhée statistics, http://www.promethee.com/). On the other hand, higher wood use will lower biomass and fuel and decrease the risk of fire (Marino et al. 2012). ...
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... Live fuel moisture (LFM), the water content of live fuels expressed as a percentage of the oven-dry weight, is a key input variable in many models of fire behaviour, such as the dynamic fuel models of Scott and Burgan (2005) developed for use with Rothermel's fire spread model (Rothermel 1972). Fuel moisture is also a key variable in physics-based models such as the Wildland-Urban Interface Fire Dynamics Simulator (Mell et al. 2010;Overholt et al. 2014) and FIRETEC (Linn et al. 2002;Marino et al. 2012). However, direct measurement of LFM in grassland fuelbeds is laborious and time-consuming, requiring destructive biomass sampling, separation by hand of live and dead fuels, and oven-drying and weighing of samples. ...
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Soil moisture depletion during the growing season can induce plant water stress, thereby driving declines in grassland fuel moisture and accelerating curing. These drying and curing dynamics and their dependencies on soil moisture are inadequately represented in fire danger models. To elucidate these relationships, grassland fuelbed characteristics and soil moisture were monitored in nine patches of tallgrass prairie under patch-burn management in Oklahoma, USA, during two growing seasons. This study period included a severe drought (in 2012), which resulted in a large wildfire outbreak near the study site. Fuel moisture of the mixed live and dead herbaceous fuels (MFM) clearly tracked soil moisture, expressed as fraction of available water capacity (FAW). MFM decreased with decreasing soil moisture below an FAW threshold of 0.59 and fell below 30% only when FAW fell below 0.30. Likewise, the curing rate increased linearly as FAW declined below 0.30, while Normalized Difference Vegetation Index (NDVI) readings failed to adequately respond to rapid drying and curing of the fuelbed. Incorporating soil moisture observations into grassland fuelbed models could result in more accurate fuel moisture and curing estimates, contributing to improved wildfire danger assessments and reduced losses of life and property due to wildfire outbreaks.
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The fuel packing ratio (β) significantly influences the fire spread in discrete fuels; however, the underlying mechanism remains unclear. This study performed experiments using laser-cut cardboards with different packing ratios to explore the heat transfer in fire spread. We identify two distinct spread behaviors under varying packing ratios. Heat flux data indicate that radiation controls the surface heat transfer (denoting the heat transfer received by the fuel bed surface) far from the flame, while convective heating plays a considerable part surrounding the flame. The surface heat transfer is enhanced under lower packing ratios (Stage 1) and is responsible for the increase of the rate of spread (ROS) in this stage. Under higher packing ratios (Stage 2), the surface heat transfer does not vary significantly, and the surface radiation transfers more energy to fuels than surface convection. ROS reduction in Stage 2 is attributed mainly to the internal heat transfer (denoting the heat transfer received by the sides of the fuel particles) dominated by radiation. The dense fuel bed impedes the response of in-bed fuel to internal heat transfer, which, however, does not significantly influence the time integral of the internal total and radiant heat fluxes. Besides, the flame residence time almost linearly increases with the packing ratio when the flame can spread.
Conference Paper
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Fuel moisture plays a crucial role in determining fuel flammability and fire behaviour but most models of fire hazard only refer to dead fuel assuming that it is the most important component driving fire behaviour. In a number of fuel types, particularly shrublands such as Calluna-dominated heathlands, live fuels can form a significant or even dominant proportion of the total available fuel. Understanding variation in their moisture content is a crucial first step in developing a robust fire danger rating system. An existing system based on the CWFIS has been implemented for the UK but does not perform well for shrub fuels. Live Calluna does not always follow obvious patterns of variation in FMC with particularly low values encountered in spring in cold or freezing conditions. We review the need for and development of a fire danger rating system and the role of live fuel moisture. We describe the first stages in the development of a physiological model that accounts for seasonal variation in leaf conductance, water viscosity, freezing conditions and rates of water uptake. Keywords: Calluna vulgaris, heather, fire behaviour, Canadian Wildland Fire Information System, stomatal resistance, viscosity of water, Penman-Monteith equation, physiological model. 1 Introduction Wildfires are a significant problem in the United Kingdom despite our oceanic climate and the impact of climatic change is likely to make them not only more frequent, but also more intense and severe. Wildfires are most significant in upland regions where flammable fuels such as heather (Calluna vulgaris), gorse (Ulex europaeus) and purple moor grass (Molinia caerulea) dominate. Fires can