Aim of study
: To develop a fuel moisture content (FMC) attenuation factor for empirical forest fire spread rate (ROS) models in general fire propagation conditions.
Methods
: The development builds on the assumption that the main FMC-damping effect is a function of fuel ignition energy needs.
Main results
: The generic FMC attenuation factor was successfully used to derive ROS models from laboratory tests (
n
= 282) of fire spread in no-wind and no-slope, slope-, and wind-aided conditions. The ability to incorporate the FMC attenuation factor in existing field-based ROS models for shrubland fires and grassland wildfires (
n
= 123) was also positively assessed.
Research highlights
: Establishing
a priori
the FMC-effect in field fires benefits the proper assessment of the remaining variables influence, which is normally eluded by heterogeneity in fuel bed properties and correlated fuel descriptors.
Key words:fire behaviour;fire management;live and dead fuels;experimental fires;wildfires.Symbols used:a, b
(fitted coefficients);
c
(specific heat, kJ kg
-1
°C
-1
; subscripts: f, fuel; w, water);
fM
(fuel moisture content attenuation factor);
h
(fuel bed height, m);
M
(fine fuel moisture content, %; subscripts: d, dead fuels; l, live fuels);
Q
(heat per unit mass of fuel needs, kJ kg
-1
; subscripts: i, fuel ignition; w, water evaporation);
R
(fire spread rate, m min
-1
; subscripts: 0, no-wind and no-slope; S, slope-driven; U, wind-driven);
RH
(relative humidity, %);
S
(slope angle, °);
T
(temperature, °C; subscripts: a, air; f, fuel; i, ignition; v, vaporization);
U
(wind speed, km h
-1
; subscript indicates measurement height, m);
w
(oven-dry fuel load, kg m
-2
);
?b
(fuel bed density, kg m
-3
).
Authors´ contributions:
CGR conceived the theoretical approach, analysed the data, and wrote the paper.
Citation
Rossa, C. G. (2018). A generic fuel moisture content attenuation factor for fire spread rate empirical models. Forest Systems, Volume 27, Issue 2, e009.
https://doi.org/10.5424/fs/2018272-13175
Fundação para a Ciência e a Tecnologia (FCT) under post-doctoral grant SFRH/BPD/84770/2012 (financing programs POPH and FSE); FCT and Fundo Europeu de Desenvolvimento Regional (FEDER) (financing programs COMPETE 2020 and POCI), in the framework of projects BONFIRE (POCI-01-0145-FEDER-016727, PTDC/AAG¬MAA/2656/2014) and CITAB (UID/AGR/04033/2013, POCI-01-0145-FEDER-006958).
Competing interests:
The author has declared that no competing interests exist.
Introduction
Although many fire spread metrics can be analysed in the field of forest fire behaviour modelling, such as fuel time to ignition (
Madrigal
et al.
, 2011
), flame residence time (
Burrows, 2001
), and flame geometry (
Nelson & Adkins, 1988
), spread rate (
R
) prediction is the focus of most studies.
R
estimates can be useful to assist fire management activities, such as prescribed burning (
Fernandes
et al.
, 2009
) or wildfire suppression (
Finney, 1998
).
R
models can be obtained via two distinct methods (
Van Wagner, 1971
): a physical approach,
i.e.
, a mathematical description of the processes behind fire spread (
Linn
et al.
, 2002
), or an empirical approach,
i.e.
, the development of relationships between fuel and environmental parameters, derived from laboratory (
Rossa
et al.
, 2015a
) or field fires (
Fernandes
et al.
, 2000
). Nevertheless, because of key limitations associated with physical models (
Cruz
et al.
, 2017
), such as complexity and high computation time, support to fire management operations is and will continue to be based on empirically-based predictions for the foreseeable future (
Sullivan, 2009
).
Typical empirical
R
formulations (
Cruz
et al.
, 2015
) account for the fuel moisture content (
M
) effect through an
M
-damping function, hereafter called fuel content attenuation factor (
fM
). Most frequently,
fM
-functions are an exponential decay of the type exp(-
bM
) (
Cheney
et al.
, 1993
;
Fernandes, 2001
), but a power law of the type
aM-b
is sometimes used (
Cheney
et al.
, 2012
), where
a
and
b
are fitted coefficients. Both functional forms have advantages and shortcomings. Exponential decay
fM
vary between 0 (
M
= 8) and 1 (
M
= 0%) and allow obtaining a theoretical maximum
R
,
i.e.
, when fuel is moisture-free. However, because exponentials do not fit well to wide
M
-variations (
Rossa & Fernandes, 2017a
), extrapolations far outside the development
M
-range can be inaccurate. On the other hand, power law
fM
provide a good fit to large
M
-intervals (
Rossa, 2017
), but do not offer reliable estimates for very low
M
-values because
R
tends rapidly to infinity when
M
approaches zero (
Rossa & Fernandes, 2018a
).
Although
Rossa & Fernandes (2017a)
show a very similar
M
-effect on
R
in no-wind and no-slope (
R0
), slope- (
RS
), and wind-driven (
RU
) laboratory fires, currently, no
fM
-function has been confirmed for the suitability to a general fire spread situation. In the present work, the hypothesis that a generic
fM
can be used in empirical
R
models was tested.
fM
was developed from the heat per unit mass of fuel requirements to ignite the fuel (
Qi
) and does not have the above-mentioned constraints of exponential decay and power law functions.
fM
was used to build
R
models from laboratory data and the ability to incorporate
fM
in existing field-based models was also verified.
MethodsFuel moisture content attenuation factor
Several factors beyond the heat needed to dry-out and ignite the fuel ahead of a flaming front have been attributed to the
M
-damping effect on
R
(
Catchpole & Catchpole, 1991
), such as the entrainment of moisture into the combustion zone and the attenuation of infra-red radiation by water vapour released from unburnt fuel. Still, not discarding those effects, in the present work
Qi
will be assumed as the main responsible for slowing down fire spread.
Qi
is given by (
Rossa & Fernandes, 2018b
):
where
cf
,
cw
,
Ti
,
Tf
,
Tv
, and
Qw
, are, respectively, fuel specific heat, water specific heat, fuel igniting temperature, fuel initial temperature, water boiling temperature, and water latent heat of evaporation. In physically-based formulations (
Thomas, 1971
;
Rothermel, 1972
),
Qi
is commonly used to account for the
M
-damping, as opposed to field-derived models. The relative
M
-effect on
R
,
i.e.
,
fM
, results from dry-to-wet fuel ignition needs ratio:
Although exponential decay or power law
fM
-functions used in field-based
R
models are generally based solely on
M
, they implicitly account for the main variables determining the energy requirements to achieve ignition,
i.e.
,
Tf
and
M
(Eq. [1]). But because
Tf
and
M
are correlated for dead fuels, and dead fuels are present in most real-world fuel beds, specific
fM
-factors work fine without explicitly accounting for
Tf
. This does not apply if
fM
is based on
Qi
. As a result, defining the numerator of Eq. [2] requires establishing
Tf
for which
M
will become 0%. Otherwise, predicted
fM
will be systematically above real
fM
values, causing an over-prediction bias. I assumed that fuel will attain moisture-free conditions at
Tf
= 100 °C, which is water vaporization temperature and also roughly the temperature recommended to oven dry fuel samples (
Matthews, 2010
). If we consider the physical constants in Eq. [1] to be
cf
= 1.72 kJ kg
-1
°C
-1
(
Balbi
et al.
, 2014
),
cw
= 4.19 kJ kg
-1
°C
-1
,
Ti
= 320 °C,
Tv
= 100 °C, and
Qw
= 2260 kJ kg
-1
(
Catchpole & Catchpole, 1991
), we obtain:
Because it is not easy to measure or estimate
Tf
, air temperature (
Ta
) was used as a surrogate.
fM
can theoretically vary between 0 and 1, as in the case of an exponential decay. Throughout the remainder of the paper
fM
is Eq. [3], unless otherwise stated.
The
M
-effect on
R
will be restricted to fine fuels, which are responsible for 'carrying the fire' (
Catchpole
et al.
, 1993
).
M
represents fuel bed overall water content and, hence, is obtained by weighing dead (
Md
) and live (
Ml
) fuel moisture contents based on mass fractions in fuel beds composed of dead and live fuels (
Rossa & Fernandes, 2017b
). Usually, fuel bed
M
< 20% is achieved when vegetation is composed only of dead fuels, which respond to
Ta
variations. As
Md
gets closer to zero, lowering its value requires an exponential
Ta
increase. On the other hand, fuel bed
M
> 20-30% is typically attained when vegetation also contains live fuels, whose
Ml
is insensitive to
Ta
. To obtain a continuous plot of
fM
as a function of
M
, I considered an exponential
Tf
decrease between 100 °C for
M
= 0% and an arbitrary value of 15 °C for
M
= 20%, and constant
Tf
= 15 °C for
M
> 20%.
Laboratory data
A total of 282 laboratory fires were retrieved from several sources (Table 1).
R0
tests (
n
= 181) compiled in
Rossa & Fernandes (2018a)
include experiments from
Rossa (2009)
and
Oliveira (2010)
, and pertain to fire spread in litter, slash, and shrub-like fuel beds,
i.e.
, vertically placed tree branches with or without a surface litter layer. Fuel beds were built using quasi-live,
i.e.
, collected live with
M
decreasing as a function of storage time, and dead vegetation of several species (
Pinus pinaster
Ait.,
Eucalyptus globulus
Labill.,
Eucalyptus obliqua
L'Her.,
Acacia mangium
Willd.,
Quercus robur
L.,
Pinus resinosa
Sol. ex Ait.).
Data sources and summary of fuel bed, ambient, and fire spread metrics.
RS
burns (
n
= 50) with slope angle (
S
) set to 20° were retrieved from
Rossa
et al.
(2016)
. Fuel beds were made of vertically positioned quasi-live shrub and tree branches of four species:
Acacia dealbata
Link.,
Cytisus striatus
(Hill) Rothm.,
P. pinaster
, and
E. globulus
. In the
A. dealbata
tests, air-dried leaves had contracted folioles, because they fold inward when branches are cut from the plant and surface-to-volume ratio is greatly diminished, attaining a fire behaviour similar to the remaining fuel species.
The
RU
experiments (
n
= 51) from
Rossa & Fernandes (2017a)
were carried out under constant wind speed (
U
) of 8 km h
-1
wind in shrub-like fuel beds, composed of vertically placed quasi-live tree branches over a dead litter layer.
P. resinosa
and
P. pinaster
needles were over-layered by
P. pinaster
branches, and
E. globulus
leaves were over-layered by
E. globulus
branches. In all laboratory trials (
R0
,
RS
,
RU
), only the foliar fuel component was considered for computing oven-dry fuel bed load (
w
) and density (ρ
b
) in vegetation containing woody elements.
Experimental field fires and wildfires data
The applicability of
fM
to real-world fire spread was tested based on 123 outdoors fires (experimental and wildfires). A comprehensive data set (
n
= 100), representative of global shrubland fire behaviour, was retrieved from
Anderson
et al.
(2015)
, which compiled data from
Catchpole (1987)
,
Vega
et al.
(1998)
,
Fernandes (2001)
,
Vega
et al.
(2006)
,
(2009)
, and
Cruz
et al.
(2010)
.
Wildfires in fully cured grasslands (
n
= 23), compiled by
Cheney
et al.
(1998)
, were used to test
fM
for fire spread in very low
M
conditions, seldom attained in experimental fires. Data provenance was
Cheney
et al.
(1998)
own observations,
McArthur (1966)
,
Finocchiaro
et al.
(1970)
,
Douglas (1970)
,
McArthur
et al.
(1982)
,
Rawson
et al.
(1983)
,
Keeves & Douglas (1983)
,
Maynes & Garvey (1985)
, and
Noble (1991)
. Fuel beds were undisturbed, cut or grazed, and eaten-out pastures. Because
Cheney
et al.
(1998)
did not report
M
, the
Noble
et al.
(1980)
equation describing the
McArthur (1977)
model:
Md
= (97.7 + 4.06
RH
) / (
Ta
+ 6.0) - 0.00854
RH
, where
RH
is relative humidity, was used to obtain
M
estimates.
Data analysis and modelling
fM
was used to develop
R0
,
RS
, and
RU
models from the laboratory fire spread data. In the
Rossa & Fernandes (2018a)R0
formulation based on fuel bed height (
h
) and
M
, the
h
-exponent is close to unity. So, for the sake of simplicity, a linear
h
-effect was assumed. The present
R0
model was obtained by linear fitting
R0
to
h fM
. In the case of
RS
and
RU
data, structural fuel bed metrics of most trials were close to the experimental mean, despite some variation between observed minimum and maximum
h
and
w
values. Also, both
S
and
U
were kept constant. As a result,
M
was the parameter with most influence on
RS
and
RU
, and both models were obtained by establishing a linear relationship between
R
and
fM
.
Both studies where field fires were compiled (Cheney
et al.
, 1998;
Anderson
et al.
, 2015
) provide
R
models accounting for the
M
-effect through an exponential decay
fM
, which, like Eq. [3]fM
, varies in the 0-1 range. Thus, the concept of using a generic
fM
-function was tested by using the original
R
models, substituting their original (specific)
fM
by the proposed generic
fM
. In mixed live and dead fuel complexes, this exchange can only be done if the specific
fM
-function accounts for both
Md
and
Ml
, as in
Anderson
et al.
(2015)
. Specific
fM
were plotted against generic
fM
-values and predictions using both
fM
-functions were evaluated for comparison.
Goodness of fit of linear regressions was assessed based on the coefficient of determination (
R2
). All predictions (laboratory and field fires) were evaluated using deviation measures: root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and mean bias error (MBE) (
Willmott, 1982
).
Results
Both in the laboratory (6.0-179.3%) and outdoors (2.6-101.9%) fires the
M
-range was very wide (Table 1). Wildfires allowed testing
fM
for extreme fire spread conditions with
U10
(measured at a 10-m height) up to 55 km h
-1
and an impressive
R
of 383.4 m min
-1
(23 km h
-1
). As expected,
fM
evolution with
M
(Fig. 1) resembles the
M
-damping plots obtained using power law
fM
-functions (
Rossa, 2017
), which are able to describe the
M
-effect well over wide ranges.
Fuel moisture content attenuation factor (fM, Eq.
[3]) as a function of fuel bed moisture content (M). fM was
computed considering an exponential fuel temperature
(Tf) decrease between 100 °C for M = 0% and 15 °C for
M = 20%; Tf = 15 °C was assumed for M < 20%. See the
'Methods' section for details.
All laboratory
R
relationships yielded a good fit to the data (Fig. 2) with
R2
between 0.651 and 0.9. Model evaluation (Table 2) confirms these figures, with MAE and MAPE, respectively, in the range 0.06-0.19 m min
-1
and 16.2-28.9%.
fM
testing with field fires showed highly significant correlations (
p
<0.0001) between specific and generic
fM
-derived values (Fig. 3), respectively of 0.457 for shrubland and 0.995 for grassland fires. The lower correlation for shrubland suggests a diminished sensitivity of the generic
fM
to
M
. Nevertheless, generic
fM
produced accurate predictions of all field data (Fig. 4) and, in fact, allowed for an overall improvement in model performance, for example with a decrease in MAPE from 70.6 to 63.4% in shrubland fires and 26.7 to 24.8% in grassland wildfires. Of course, the quality of predictions is mostly dictated by the original
R
formulation and these results only demonstrate that the proposed generic
fM
is a reasonable surrogate for the specific
fM
.
Laboratory-derived fire spread rate (R) models
based on fuel moisture content attenuation factor (fM, Eq.
[3]) for: (a) no-wind and no-slope spread (R0) in litter,
slash, and shrub-like fuel beds, h is fuel bed height, linear
fit is model 1 in Table 2 (R2 = 0.900); (b) slope-driven
spread (RS) in shrub-like fuel beds, linear fit is model 2 in
Table 2 (R2 = 0.651); and (c) wind-driven spread (RU) in
shrub-like fuel beds, linear fit is model 3 in Table 2 (R2 =
0.795). All regressions were significant at p < 0.0001. See
Table 1 for data sources.
Model evaluation metrics (see Table 1 for details on fire spread data).
Specific vs. generic fuel moisture content
attenuation factor (fM) for shrubland fires and grassland
wildfires. Specific fM are given in Table 2; generic fM
is Eq. [3]. Solid line is perfect agreement; correlation
between variables is 0.457 for shrubland fires and 0.995
for grassland wildfires (p < 0.0001). See Table 1 for data
sources.
Observed vs. predicted wind-driven fire
spread rate (RU) using the specific fuel moisture content
attenuation factor (fM) (Table 2) and the generic fM (Eq.
[3]) for: (a) shrubland fires; and (b) grassland wildfires.
Solid lines are perfect agreement. See Table 1 for data
sources.
Discussion
f
M
performance and applicability
Laboratory-based
R
models built with the generic
fM
showed good agreement with data. They yielded
R2
slightly below those obtained using the original power law
fM
-based models (0.667-0.947), but significantly above the 0.566 and 0.665 values obtained for the
RS
and
RU
models using exponentials (
Rossa
et al.
, 2016
;
Rossa & Fernandes, 2017a
,
2018a
). Despite a small decrease in accuracy, when compared with the use of power laws, the generic
fM
provides important benefits, such as not becoming extremely sensible at very low
M
-values and allowing extrapolation to moisture-free conditions. The generic
fM
allowed improved prediction ability in relation to the specific
fM
-functions used in existing field-based models for shrubland experimental fires and grassland wildfires.
Laboratory data included a great number of tests in several fire spread conditions over a wide
M
-range, and fuel beds were very diverse in terms of species and structure.
R0
laboratory tests are representative of field
R0
and a reasonable surrogate for backing fires
R
(
Rossa, 2017
;
Rossa & Fernandes, 2018a
). That is not the case of slope and wind-driven laboratory trials, in which
R
is limited by the fire front width (
Fernandes
et al.
, 2009
). Shrubland and grassland outdoors fires enabled the positive testing of
fM
in
RU
conditions free of scaling issues. There is no apparent reason for
fM
not to hold for slope-driven field fires as well. Not excluding the need of further assessing
fM
with additional field data, its overall performance in all tested fire spread situations lends strong support to its ability of successfully incorporating empirically-based
R
models in generic fire spread conditions.
If Eq. [3] were developed without assuming that moisture-free conditions will be attained at
Tf
= 100 °C,
i.e.
, with the numerator becoming 1.72 (320 -
Tf
) instead of 378.4, using the generic
fM
in the field-derived
R
models would yield MBE of 3.92 and 41.7 m min
-1
, respectively for shrubland and grassland fires. The arising of this substantial over-prediction bias lends support to the supposition that
fM
-functions based only on
M
implicitly account for
Tf
. In other words, this means that in a hypothetical situation of fire spread through a dry fuel bed at, for example,
Tf
= 20 °C, predicted
R
using typical empirical field-based models would be higher than observed because the
M
-functions were fitted in conditions where the decrease in
M
is concurrent with increasing
Tf
. As a result, estimated
fM
attains its maximum,
i.e.
, fire spread attenuation is minimum, although fuel conditions will delay fuel ignition more than expected in an extrapolation to
M
= 0%, where
Tf
was supposed to grow concomitantly with diminishing
M
. It is important to notice that this rationale was derived from results using a limited field data set, hence further testing with additional data would benefit its confirmation.
Advantages and limitations
Md
of field fuels is easy to sample. Overall
M
determination requires measuring both
Md
and
Ml
(
Rossa
et al.
, 2015b
), as well as assessing dead and live fuel mass fractions, which may be problematic in very heterogeneous fuel complexes. This is a limitation of using the generic
fM
, when compared to
fM
-functions accounting for only the
Md
-effect. Most empirical fuel-dependent models rely on the sole use of
Md
(
Cruz
et al.
, 2015
) to provide a satisfactory
R
explanation, which restricted the data available to test the specific
fM
-function proposed in the present work. Field-based models based only on
Md
work well because, usually,
Ml
is either constant or correlated with
Md
for a given fuel complex (
Rossa & Fernandes, 2017b
).
Nevertheless, especially for experimental programs composed of a limited number of tests, possible difficulties in assessing overall
M
might pay-off in terms of the advantages of using a generic
fM
. The use of experimental outdoors fires as a source of development data is appealing because of the strong resemblance to real-world fire-spread. However, this option is often challenged by heterogeneity in fuel bed properties and correlated fuel descriptors, which elude the correct quantification of specific effects (
Rossa & Fernandes, 2017b
). Establishing
a priori
the
M
-effect through the use of
fM
significantly simplifies the proper assessment of the remaining influent variables.
Conclusions
A generic
fM
-function for empirical
R
models was developed based on the assumption that the main
M
-damping effect is a function of
Qi
.
fM
was successfully used to derive
R
models from laboratory fire spread in no-wind and no-slope, slope-, and wind-aided conditions. The ability to incorporate
fM
in existing field-based models was also positively assessed. Possible difficulties in assessing overall
M
due to fuel complex heterogeneities, might pay-off in terms of the advantages of using a tested generic
fM
. For example, establishing
a priori
the
M
-effect benefits the proper quantification of the remaining variables influence. Not excluding the need of further assessing
fM
with additional field data, its overall performance in all tested fire spread situations lends strong support to its ability of successfully incorporating empirically-based
R
models in generic fire spread conditions.
Acknowledgments
The author acknowledges the anonymous reviewers and the section editor for the thoughtful comments and suggestions that contributed to improve an early version of the manuscript.
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