Introduction
In order to better manage fire risk, several methods have been investigated.
Among the first are the fire risk indices, such as the Canadian Fire Weather
Index . This index relates to the expected
intensity of the fire line, expressed in energy output rate per unit length
of fire front. It is currently used as a fire risk indicator by the European
Forest Fire Information System (EFFIS) of the Joint Research Center (JRC) of
the European Commission. The Haines Index is another
indicator of dangerous fire development that focuses on atmospheric
stability. It can be used in conjunction with the Canadian Fire Weather Index
but is deemed less informative. These indices are empirically calibrated for
predicting whether the atmospheric and hydrological conditions are prone to
fire development. However, one of their main drawbacks is that they lack
temporal contrast: they identify correctly fire-prone seasons but fail to
provide short-term variability in fire risk e.g.,Figs. 7, 8, 12 and
15. Other approaches exist, based on different criteria of
fire risk. Using probabilistic cellular automata fire propagation models,
simulations of multiple starting points can lead to risk maps than can be
helpful for fire suppression forces deployment . The main
weak point of this method is the lack of strong validation for the
calibration of the propagation model. More in-depth simulations, using fully
physical models such as FIRETEC , can provide
accurate predictions of the propagation of a fire. This method can be very
demanding computation-wise and requires a precise knowledge of the initial
and boundary conditions. Using a probabilistic framework, a preliminary risk
assessment study was conducted . The aim of the study was
to reconstruct the probabilities of fire occurrence and large fire
propagation using meteorological and geographical covariates. The results,
although encouraging, gave only mitigated quality in the estimation of
monthly fire occurrence. Modelling accumulated seasonal burnt area time series
using meteorological predictors gave satisfying results, with adjusted R2
of 68 % for the July–August time period and northwestern region of Iberia
. Besides fire size or fire occurrence, another
important factor of risk regarding wildfires is the intensity of the fire
front. The propagation of particularly intense wildfires is indeed very hard
to control and can trigger very severe pollution episodes. However large data
sets do not exist for this quantity, so we focus instead on the fire
radiative power (FRP), a remotely-sensed variable strongly linked with the
fire intensity. The general framework of this study is the estimation of fire
size and intensity of individual fires in the Mediterranean Basin using
parametric statistical methods. Several studies focusing on the estimation of
fire size exist, proposing to derive this quantity based on meteorological
and geographical covariates. Their authors mainly use statistical learning
techniques in order to give a quantitative or qualitative insight on fire
size . In some cases this analysis is
extrapolated to future weather in the context of climate change
. However one can reproach to these studies their lack of
performance. An examination of lead to the observation
that the estimation of fire size done by the best tested method was only very
marginally better than the mean of the observations. For fire intensity no
studies of this kind were conducted. Our approach will be to provide
parametric estimations of both single-event fire size and intensity
distribution functions conditionally to weather covariates. We take a
multi-timescale approach for the choice of our weather covariates, with
seasonal and immediate weather information. Using these conditional
distribution estimations we can then compute probabilities that a given fire
grows particularly large or becomes very intense. Because of our methodology,
these probabilities would be both sensitive to seasonal trends and immediate
weather. These estimations would be much more informative than a conditional
mean of fire size of intensity with respect to weather. In Sect.
we describe the data we use. After presenting our fire variables, we show our
weather covariates and explain their relevance. In
Sect. we find an adequate parametric distribution
to model fire size and intensity of individual events. Using this result, we
develop in Sect. a methodology of fire risk
assessment that focuses on the use of probabilities of large and/or intense
wildfires.
Data
Fire variables
The detection of fires is performed using the fire products from MODIS (Moderate
Resolution Imaging Spectroradiometer), an instrument carried on
board of the Aqua and Terra polar heliosynchronous orbiting satellites. The
recorded fire variables are the burnt area (BA) and the fire radiative power (FRP)
which can be seen as a proxy of the fire intensity. We focus on the
Mediterranean Basin. We therefore select the fires occurring within the box
[35, 50∘ N] and [-10, 50∘ E]. We keep only individual wildfire events
occurring during the months of July and August in order to focus on the core
of the fire season in the study area . However
summer is not the only season when fires occur. For example in Northern
Iberia and Galicia the month of September also exhibits strong fire activity
e.g.Fig. 2. Winter and early spring fires can
also occur in Portugal and the Balkans
e.g.Table 1. However, we focus our analysis
on the summer period to avoid seasonal changes in the driving factors,
especially at the scale of the Mediterranean basin. Such a generalization of
our approach is left for future work. There are 5821 and 4840 wildfires in
our two BA data sets and 24 273 wildfires in our FRP data set. The FRP is
retrieved by using measured radiance of the 4 and 11 µm channels
at nadir. Other spectral bands are used for assessing cloud masking, glint,
bright surface and other sources of false alarms and disturbances. FRP is
provided at 1 km resolution by the MOD14 product. BA is retrieved from the
observed changes in land cover. Indeed, the albedo is modified by the
deposition of charcoal and ash, the loss of vegetation and the change in fuel
bed characteristics. Albedo alteration produces changes in surface
reflectance which are processed to produce daily burnt area at a 500 m
resolution in the MDC64A1 product . Only the
fraction of the detected burning pixel covered by vegetation is burned
following . The FRP and BA products are then
regridded at 10 km resolution which was chosen to be a good trade-off in
order to keep detailed enough information on the fire location and facilitate
the comparison with the ERA-Interim meteorological data. We use the first 10 years (2003–2012) of MODIS data. It should be noted that there are important
uncertainties on the date of beginning of wildfires taken individually. The
incertitude can be as large as 5 days and is caused by several factors such
as cloud cover impairment of remote sensing and lack of detection of
wildfires at the beginning of their development. As we deal with statistics
on a large number of such wildfires, the uncertainty is reduced. Additionally,
since the time period of study is mostly cloud-free, the uncertainty on the
day of detection should be low . This is confirmed
by the strong link between fire and synoptic weather dynamics observed using
the same methods in . In the following sections we will call
these BA and FRP data sets BAM and FRP respectively. We also use the EFFIS
Rapid Damage Assessment system, provided by the JRC of the European
Commission . This set is built using 250 m MODIS images. A
first step of automated classification is used to isolate fire events and a
post-processing using human visualization of the burnt scar is performed. A
cross-analysis using the active fire MODIS product, land-cover data sets as
well as fire event news collected in the EFFIS News module is finally done to
ensure a low number of misclassifications
(http://forest.jrc.ec.europa.eu/effis/). The system records burnt areas
of approximately 40 ha and larger . It also
contains smaller wildfires, but is less complete below this 40 ha
threshold. The JRC provided the data for the 2006–2012 time period. We call
this BA data set BAE in the following. A 3-D (latitude, longitude and
time) connected component algorithm is used to determine what are the
distinct fire events in the BAM data set. This algorithm aggregates the
adjacent fire spots into larger fire events. The main interest of this method
is that it allows for the detection of wildfires larger than 10 000 ha
which are those expected to be most influenced by weather conditions
e.g.. The main weakness is that it does not
take into account cloud cover impairment of remote sensing. Indeed an absence
of detection of 1 day between two detections could be caused by clouds.
Another problem is that two independent fire events taking place close to one
another (less than 20 km of distance and less than a day between the end of
the first event and the beginning of the second) are considered the same by
this method. “Megafire” events, such as those defined by ,
could also be grouped in clusters with this method of analysis. The
processing of the BAE data set is simpler. The data set provides the shape
and time of beginning of all detected wildfires. We take as location the
centroid of this shape. Detection of smaller wildfires being quite hard with
remote-sensing techniques, we choose to eliminate < 25 ha wildfires
from our burnt area data sets. They correspond to wildfires burning less than
one pixel in the BAM data set and the authors have doubts about the
completeness of the BA data sets below this value. In the following sections
it should therefore be stressed that the obtained results only hold for
such wildfires. Our fire data sources and preprocessing methods are identical
to that of . After
these preprocessing steps we retain 5821 observations for the BAM data
set, 4840 for the BAE data set and 24 273 wildfires for the FRP data set.
Meteorological covariates
Our weather database was built upon the ERA-Interim reanalysis of the
European Center for Medium-range Weather Forecast (ECMWF) .
The horizontal resolution of the reanalysis does not allow the derivation of
the small-scale weather conditions in the immediate vicinity of the fire. To
link the weather data to the fire data, we take the ERA-Interim grid point
nearest from the detected fire event. We then associate to this event the
weather recorded at 12:00 UTC the day of first detection. We extract the
following meteorological covariates:
ΔT2 (in K): the 2 m air temperature anomaly,
the difference between the 12:00 UTC 2 m air temperature and its
climatological daily mean;
WS10 (in m s-1): the 10 m wind speed;
ΔNprecip (in days): the anomaly with respect to the climatology
of the number of days when precipitations ≥0.5 mm occur during the
January–June time period preceding of the year of the fire.
ΔNprecip is mostly impacted by spring drought occurrence but
positive winter precipitation anomaly has also been linked to the 2003
Portugal megafire event . However, as shown in
and , anomalies of
precipitation during spring are favourable to summer heatwave conditions.
have also shown that deficit of precipitation during spring,
can trigger early vegetation growth, providing abundant fire fuels in summer.
Positive winter precipitation anomalies may amplify this mechanism. Our
choice of covariates was done to retain a broad range of timescales. We go
from the hourly to daily timescales (ΔT2, WS10) to seasonal
timescales (ΔNprecip). We also settled on covariates with proven
impact on wildfire activity. Wind speed accelerates the propagation of the
fire in the direction of the wind and
blocks back propagation. The temperature anomaly ΔT2 is an indicator
of heatwave occurrence. showed that in Portugal
wildfires often co-occurred with synoptic blockings and heatwaves. In
Sardinia, showed that large fire occurrence, daily
burnt area and daily number of fires were higher on high temperature days.
further this work
by showing that heatwaves and surface wind control wildfire size and duration
strongly. emphasized the link between
drought and wildfire activity (wildfire occurrence and area burnt) in Greece.
We chose ΔNprecip as an indicator of drought occurrence preceding the
wildfire. Low values of ΔNprecip indicate both low precipitation
amount and low overall cloudiness in the January–June time period.
Intuitively, we could say that more arid preceding seasons could lead to
lower values of soil and fuel moisture during summer.
showed that this quantity is linked to drought occurrence in summer.
Additionally and showed
that summer heatwave occurrences were also impacted by rainfall deficit in
previous months.
Evolution of 5th (blue), 25th (green), 50th (red),
75th (cyan) and 95th (purple) quantiles of BA (data set BAM
and BAE) and FRP (FRP data set) with ΔT2, WS10 and ΔNprecip. Top row corresponds to BAM, middle to BAE and bottom to
FRP. The red shaded area corresponds to 90 % confidence intervals for the
95th quantile.
![]()
Our first attempt at linking fire and weather data used regression techniques
to forecast the conditional mean. This approach failed, with maximum R2 of
0.10 and 0.05 for the FRP and BA data sets respectively using artificial
neural networks. We therefore chose to focus our analysis on the variability
of the distributions of BA and FRP with respect to weather, and at first
on the variations of the quantiles of these distributions. Figure
shows the variations of the 5th, 25th,
50th, 75th and 95th quantiles of BA and FRP for data sets
BAM, BAE and FRP with respect to the selected covariates. The
methodology consists in splitting the data sets into seven subsets containing an
equal number of points. This allows comparable uncertainties for each subset.
The number of bins was chosen as a trade-off between the smoothness of the
curve and the significance of the curve fluctuations. These statistics were
bootstrapped 1000 times, allowing an accurate estimation of each quantile and
of the associated confidence intervals. First, we can see that these
variations depend heavily on the selected quantile. In particular the
5th quantile seems roughly constant whereas the 95th is more
variable. BA and FRP show strong responses to ΔT2, with general
growth of fire size and radiative power. For the BAE and FRP data sets,
BA and FRP are growing functions of WS10. This is not seen for the
BAM data set. However show that by conditioning
on ΔT2 significant variations of BA and FRP can be observed at
the 70 and 90 % confidence levels respectively. We observe that BA and
FRP decrease with increasing ΔNprecip. In the following we use
ΔT2, WS10 and ΔNprecip to reconstruct the
conditional distribution functions of BA and FRP.
AD2R values for all different distributions and for all data sets. The AD2R values for the chosen distributions are in bold.
Criterion
Data set
Normal
Exponential
Cauchy
Gamma
Logistic
Log-Normal
GEV
AD2R
BAM
190
370
394
20.0
58.3
103
20.3
BAE
51.4
648
355
23.6
16.5
83.5
3.45
FRP
674
4951
1626
15.2
121
124
17.8
BA and FRP distributions
Figure shows that the variability of BA and FRP is
very high, and a proper way to build a risk metric would be to compute
probabilities of large fire size or large intensity using these variations. A
way of doing so would be to model the conditional distributions of BA and
FRP with respect to weather. To achieve this goal we want to find a
parametric distribution which fits these variables well. In this section we
proceed to this task independently of the weather covariates in order to
provide good models for the distributions of BA and FRP. The
meteorological covariates will be reintegrated at the beginning of Sect. .
As BA and FRP have very skewed distributions it becomes easier to study
their logarithm. We therefore from this point onward only discuss the
modelling of log10(BA) and log10(FRP). We also subtract a threshold
to each variable (log10(25) for the BA data sets and log10(4) for
the FRP data set), so as the data starts approximately at 0 and is always
non-negative.
The parametric forms that are tested for the distributions of the transformed fire variables are the following:
the Exponential distribution,
f(x;β)=βe-βx,x∈R+;
the Normal distribution,
f(x;μ,σ)=1σ2πe-(x-μ)22σ2,x∈R;
the Cauchy distribution,
f(x;x0,a)=1πa1+x-x0a2,x∈R;
the Gamma distribution,
f(x;α,β)=βαΓ(α)xα-1e-βx,x∈R+;
the Logistic distribution,
f(x;μ,s)=e-x-μss1+e-x-μs,x∈R;
the Log-Normal distribution,
f(x;μ,σ)=1xσ2πe-logx-μ22σ2,x∈R+;
the Generalized extreme value (GEV) distribution,
f(x;μ,σ,ξ)=1σ1+ξx-μσ-1/ξ-1e-1+ξx-μσ-1/ξ,x∈R,x≥μ-σ/ξ,ξ>0.
Here f denotes the corresponding probability density function.
If Y is a random variable, the truncated exponential distribution for
logY correspond to the truncated pareto distribution for Y. As the
Truncated Pareto distribution was shown alongside with the Tapered Pareto
distribution to be a good fit for the distribution of BA
, we included the exponential distribution
in our possible forms for log10(BA/25) and log10(FRP/4).
We fitted all these distributions for each data set (BAM, BAE and FRP)
using the minimization of the AD2R goodness-of-fit criterion
as fitting method. The AD2R criterion is defined as
follows:
AD2R(F)=∫F^n(x)-F(x)2Ψ(x)dx,with Ψ(x)=1-F(x)-2
with F^n being the empirical, step-wise cumulative density function of
the data to fit and F the cumulative density function for which the AD2R
criterion is calculated. The choice of the function Ψ gives more weight
to the quality of the fit for the right tail of the distribution. If F(x)
and F^n(x) were to have different asymptotic behaviours for large
values of x the AD2R criterion would be very large. The minimization of the
AD2R criterion then has the theoretical advantage of making a better fitting
of the distribution for larger values of the selected variable. All the AD2R
values found for each distribution and data set are available in Table .
Computations were done in R using the “fitdistrplus”
package . We see that for the BA data sets there are
two distributions selected, Gamma and GEV. We will continue using only the
GEV distribution since the difference seen for the BAM data set between
these two distribution is very small (AD2R values of 20.3 for the GEV
distribution and 20.0 for the Gamma distribution), whereas for the BAE
data set the difference is much larger (AD2R values of 3.45 for the GEV
distribution and 23.6 for the Gamma distribution). For FRP the Gamma
distribution is selected. Surprisingly the Exponential distribution fits the
BA data sets poorly. This could be due to the absence of the
< 25 ha wildfires in our BAM and BAE data sets, whereas they
are taken into account in .
Normalized histograms, modelled densities (a, c, e) and QQ-plots
(b, d, f) for the GEV and Gamma distributions for the BA and FRP data sets
respectively. The fitting method used is the AD2R criterion minimization. On
the densities panels the normalized histograms are in black and the modelled
distribution in red. The dashed green lines on the QQ-plots are the 95 % confidence envelopes.
![]()
Figure shows the normalized histograms and modelled densities of
BA and FRP with accompanying QQ-plots for all considered data sets. The
QQ-plots were computed using the car package . For values of BA
smaller than 40 ha, the QQ-plots depart from the 95 %-level confidence
intervals. Conversely, the QQ-plots are within the confidence intervals for
larger values. The distribution fits better the BAE data set than the
BAM. It may be due to the methodology of construction of this data set,
which considers burned only the fraction of the burning MCD64A1 pixels of
surface 25 ha covered by vegetation. A preference for multiples of 25 ha
arises and it is detrimental for the accuracy on the distribution tails of
BA, and especially the lower percentiles. However, the fit is still
accurate enough for our purpose. As only the largest wildfires are controlled
by the weather conditions , having an accurate
fit of the high values of BA and FRP is enough for our modelling
framework. Caution should therefore be taken when trying to interpret these
distributions for low values of BA. For FRP, the QQ-plot remains within
the 95 %-level confidence intervals for all values. Besides the AD2R
criterion, Fig. shows that the GEV and Gamma models fit the data
accurately and can be considered suited for our model. In the following, we
will take the strong hypothesis that the observations coming from the BA
and FRP data sets have respectively GEV and Gamma distributions
conditionally to the weather. This hypothesis was tested on large subsets of
the data sets corresponding to particularly favourable or unfavourable weather
conditions. We take as favourable conditions ΔT2≥5K and
WS10≥6 m s-1 and as unfavourable conditions ΔT2≤0
and WS10≤3 m s-1. We find that the hypothesis holds well for the
BAE and FRP data sets, but that there are more discrepancies with the
BAM data set, which is coherent with the deviations seen in
Fig. . This hypothesis is used to obtain the conditional
distribution of BA and FRP with respect to ΔT2, WS10 and
ΔNprecip.
Fire risk assessment using meteorological covariates
Methodology
The general framework of our methodology is the parametric estimation of the
conditional probability density function of BA or FRP with respect to
ΔT2, WS10 and ΔNprecip. In other words we seek
fY|X(y)=fY(y|X=x) with y the fire
variable, X the meteorological covariates and x a
specific value taken by the covariates. We made the hypothesis in the
previous section that flog10(BA/25)∼ GEV(μ, σ, ξ)
and flog10(FRP/4)∼ Gamma(α, β) for all subsets of
our data sets. Therefore to approximate the values of the parameters of these
distributions we need to compute the distribution of y near the point
X=x. To do so we choose to retain the 10 % of our data
sets nearest of the point X=x and to estimate the
parameters of the distribution by minimizing the AD2R criterion. The fraction
of nearest neighbours was chosen to be sufficient to estimate a distribution
function. The calculation of these nearest neighbours was done in R using the
FNN package . It must be noted that due to the curse of
dimensionality taking a larger number of covariates would lead to a very
large inaccuracy on x pp. 22–23. In order to tackle
this issue we select only three covariates for our density estimation. The choice
of these covariates was done using Fig. . We wish to retain
covariates that cover a broad range of temporal variability and for which
BA and FRP exhibit strong significant variability. We therefore choose to
take X=(ΔT2,WS10,ΔNprecip) for all data
sets. For computation purposes we choose not to estimate fY|X
at each possible value of x. Instead we take the values of
x corresponding to the 1st to 9th deciles of each of its
components. This makes 93=729 values of x for which each
conditional distribution parameters are estimated. In order to obtain
asymptotic confidence intervals for our estimates of the conditional
distribution parameters and of the probability of large or intense events we
perform 500 bootstrap estimations of these parameters using the determined
nearest neighbours. Bootstrap estimation was done using the bootstrap R
package .
Results
Estimated probabilities of fire size (BA) exceeding the 2000 ha threshold (BAM data set).
The x axis is the 2 m air temperature anomaly (ΔT2), the y axis the 10 m wind
speed (WS10) and each panel stands for values of January–June precipitation days
anomaly (ΔNprecip) centred on the given value on the panel titles.
![]()
Estimated probabilities of fire size (BA) exceeding the 2000 ha threshold
(BAE data set). The x axis is the 2 m air temperature anomaly (ΔT2),
the y axis the 10 m wind speed (WS10) and each panel stands for values of January–June
precipitation days anomaly (ΔNprecip) centred on the given value on the panel titles.
![]()
Estimated probabilities of fire intensity (FRP) exceeding the 200 ha threshold.
The x axis is the 2 m air temperature anomaly (ΔT2), the y axis the
10 m wind speed (WS10) and each panel stands for values of January–June
precipitation days anomaly (ΔNprecip) centred on the given value on the panel titles.
![]()
Mean values of the standard deviations calculated from the nearest neighbours search (ΔT2, WS10 and ΔNprecip).
Data set
ΔT2 (K)
WS10 (m s-1)
ΔNprecip (days)
BAM
1.41
0.74
4.4
BAE
1.22
0.83
3.9
FRP
1.17
0.74
4.4
Figures , and show the
estimated probability contours of particularly large or intense fire events
computed from our method. These events are defined by the wildfire exceeding
the 2000 ha or 200 MW thresholds in BA or FRP respectively. These
thresholds correspond approximately to the 95th quantiles of each
variable. The values of each class of ΔNprecip corresponds to the
mean of the ΔNprecip of each decile. Each panel displays the mean
distribution of the corresponding ΔNprecip class. The uncertainty
of the distribution can be inferred from Table which
displays the average standard deviation of each covariate. The probability of
large BA occurring is a growing function of ΔT2
(Figs. and ). The two modes of higher BA
commented and analysed in are visible in
Fig. . There is a clear significant increase in large BA
probabilities with increasing ΔT2 and WS10 for low values of
ΔNprecip. The role of WS10 is significantly damped when
ΔNprecip rises (wetter January–June time period) and ΔT2
becomes the main driving factor for the BAM data set
(Fig. ). Accounting for the confidence intervals of the
estimated probabilities (not shown) shows that WS10 has no explanatory
value in the pattern of the probability at the 90 % confidence level. The
variations between the minima and maxima of the estimated probabilities are
significant at the 90 % confidence level. However the two modes are hard to
distinguish statistically because of the low number of points in our BA
data sets (5821 for BAM and 4840 for BAE). The difference of results
between the BAM and BAE probabilities is due to the BAE data set
spanning over the 2006–2012 time period, therefore missing the 2003 and 2005
megafire events which are present in the BAM data set
. Regarding fire intensity, FRP is a growing
function of WS10, ΔT2 and a decreasing function of ΔNprecip, which is significant at the 90 % confidence level. The
variability linked to ΔT2 and WS10 is discussed in
and found back on this figure. Because we use a
meteorological covariate depending on past weather (ΔNprecip), a
seasonal preconditioning of high fire risk can be assessed. When a drought
occurs in the past months (ΔNprecip≤-7 days) the highest
probabilities of large BA can be found for high values of both ΔT2
and WS10 (Fig. ). For higher values of the past months
precipitation anomaly (ΔNprecip≥7 days), the highest risk
corresponds to heatwaves, with high ΔT2 and low WS10. This
difference could be exploited to adapt fire mitigation strategies and take
into account seasonal weather information. The absence of the 2003 and 2005
megafire events limits the number of observations
used to derive the parameters of the distributions, therefore explaining the
absence of significant discrimination between situations of spring drought
and the others in the BAE data (Fig. ).
Probabilities of observing a ≥2000 ha wildfire calculated from
the BAM (a) and BAE (b) data sets and probabilities of observing a ≥200 MW
wildfire calculated from the FRP data set (c) as a function of time for the 2003 July–August
period nearest the largest wildfire occurring in Portugal this season. Black dashed lines show
the beginning and the end of the wildfire event. In light shaded red are the 90 % confidence intervals.
![]()
Normalized histograms of the estimated probabilities (black), PDFs of
the mixture model (red) and normalized histograms of the 90 %-level confidence
intervals lengths (blue). (a, d) are for BAM, (b, e) for BAE and (c, f) for
FRP. The data set is made of each July–August time period everywhere a fire is detected.
The parameters of the gaussian mixture model (Eq. ) are displayed on each panel of the top row.
![]()
Let us illustrate the information provided by our method by focusing on the
2003 megafire event in Portugal. We take the largest wildfire event of the
BAM data set (262 520 ha BA, 731 MW FRP). It is recorded at
[-7.65∘ E, 40∘ N] and the considered weather is that of the
[-7.50∘ E, 39.75∘ N] ERA-Interim grid point. Figure
shows the time evolution of the probability of large BA and FRP with the
corresponding 90 % confidence intervals. Two black lines show the beginning
and the end of the fire event. During the wildfire the probability of large
BA peaks to 7 %, whereas it stays at about 3 % (BAM) or 2 % (BAE)
the rest of the time. The probability of large FRP behaves the same way,
going from 3 % to more than 6 %. The variations of these estimated
probabilities are significant at the 90 % confidence level. The
“background” probability refers to the background fire risk of large or intense fire
events during summer. We also see a secondary peak before the fire event,
even though no fire occurred. Our method can be used to identify time periods
when fire risk is especially high. When a fire occurs during one of these
“extreme” periods, the fire event has high odds of being catastrophic.
Regarding the uncertainties of the method the mean standard deviation of the
meteorological covariates have been calculated (Table ).
They stem from our nearest neighbours approach. The
uncertainties on the meteorological features are fairly small and, with the
exception of ΔNprecip, fall within measurement error.
Figure shows the normalized histograms of the
estimated probabilities and of the confidence intervals lengths for all
July–August time periods everywhere a fire is detected. We also quantify the
mean and standard deviation of the “background” and “extreme” fire
risk regimes. To do this, the densities of the estimated probabilities are
fitted with a mixture of two Gaussians, representing the “background” and
“extreme” fire risk regimes. The model can be written as follows:
PDF(x;μ1,σ1,μ2,σ2,α)=ασ12π×exp{-(x-μ1)22σ12}+1-ασ22π×exp{-(x-μ2)22σ22}.
For BAE data set, the distinction between “background” and
“extreme” is more difficult than for BAM due to the absence of major
megafires in the data set (2003 and 2005). Otherwise, the mean probability
that a fire exceeds 2000 ha is around 4 % for “background” summer fire
risk conditions with a standard deviation of 0.5 % and increases to 5 % in
extreme weather conditions favourable to larger fires. A similar behaviour is
found for fire intensity with an even more distinguishable two-mode
distribution. The mean probability that a fire exceeds 200 MW is around 2.4 % for “background” summer fire risk conditions with a standard deviation of
0.3 % and increases to 3.6 % in extreme weather conditions favourable to
intense fires. The 90 %-level confidence interval lengths remain large for
the BA data sets, with typical values of 2 and 1.8 % for the BAM and
BAE data sets respectively. For the FRP data set these lengths are smaller
because of the larger number of data points, with a mean value of
approximately 1 %.