e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Mapping lightning/human-caused wildfires occurrence
under ignition point location uncertainty
Giuseppe Amatulli a,b,c,∗ , Fernando Peréz-Cabello a , Juan de la Riva a
a
University of Zaragoza, Department of Geography and Spatial Management, Calle Pedro Cerbuna 12, 50009 Zaragoza, Spain
University of Basilicata, Department of Crop Systems, Forestry and Environmental Science,
Campus Macchia Romana, 85100 Potenza, Italy
c European Commission-DG Joint Research Centre, Institute for Environment and Sustainability,
Via E. Fermi, 21020 Ispra (VA), Italy
b
a r t i c l e
i n f o
a b s t r a c t
Article history:
Fire managers need to study fire history in terms of occurrence in order to understand and
Received 9 September 2005
model the spatial distribution of the causes of ignition. Fire atlases are useful open sources
Received in revised form
of information, recording each single fire event by means of its geographical position. In
18 July 2006
such cases the fire event is considered as point-based, rather than area-based data, com-
Accepted 9 August 2006
pletely losing its surface nature. Thus, an accurate method is needed to estimate continuous
Published on line 19 October 2006
density surfaces from ignition points where location is affected by a certain degree of uncertainty. Recently, the fire scientific community has focused its attention on the kernel density
Keywords:
interpolation technique in order to convert point-based data into continuous surface or
Fire occurrence
surface-data. The kernel density technique needs a priori setting of smoothing parameters,
Kernel density
such as the bandwidth size. Up to now, the bandwidth size was often based on subjective
Fire ignition points
choices still needing expert knowledge, eventually supported by empirical decisions, thus
Fire atlas
leading to serious uncertainties. Nonetheless, a geostatistical model able to describe the
Fire spatial patterns
point concentration and consequently the clustering degree is required. This paper tries
Location uncertainty
to solve such issues by implementing the kernel density adaptive mode. Lightning/humancaused fires occurrence was investigated in the region of Aragón’s autonomy over 19 years
(1983–2001) using 3428 and 4195 ignition points respectively for the two causes of fire origin.
An analytical calibration procedure was implemented to select the most reliable density surfaces to reduce under/over-density estimation, overcoming the current drawbacks to define
it by visual inspection or personal interpretation. Besides, ignition point location uncertainty
was investigated to check the sensitivity of the proposed model. The different concentration degree and the dissimilar spatial pattern of the two datasets, allow testing the proposed
calibration methodology under several conditions. After having discovered the slight sensitivity of the model to the exact point position, the obtained density surfaces for the two
causes were combined to discover hotspot areas and spatial patterns of the two causes.
Evident differences in spatial location of the origin causes were noted and described. The
general trend follows the geographical features and the human activity of the study areas.
The proposed technique should be promising to support decision-making in wildfire prevention actions, because of the occurrence map can be used as a response variable in fire
risk predicting models.
© 2006 Elsevier B.V. All rights reserved.
∗
Corresponding author.
E-mail address: [email protected] (G. Amatulli).
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2006.08.001
322
1.
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
Introduction
Wildland fire is considered one of the most important disturbance factors in natural ecosystems, and each year several biotypes are completely lost. In Europe an average of
48,600 ha are annually burnt and the wildfire phenomenon
was particularly dramatic in summer 2003 where 740,379 ha
were completely burnt, exceeding every estimation (European
Commission, 2004).
In order to assess fire risk and evaluate the ecological effect
of the wildfires, fire managers and scientists are trying to study
and predict the phenomena in terms of frequency, severity,
size, probability/density and spatial pattern distribution. The
world and/or national fire atlases are currently the most wideopen sources of fire database, where each fire event is recorded
by means of its geographical position and other attributes
(Morgan et al., 2001). Until now, fire data regarding perimeters
and size, severity and intensity, especially of small fires, are
often not included due to the not yet worldwide automation
and mapping of the burnt areas (Vázquez and Moreno, 2001).
Even countries significantly interested by wildfire phenomena
have not built up an appropriate fire database and a single fire
event is frequently recorded as a point-based concept, by its x
and y geographic position, rather than an area-based event,
thus losing its surface nature and its spreading behaviour
characteristic (Martı́n et al., 1994; Li, 2002). This concept is
nowadays real and evident in the Mediterranean countries
where the small size of the fire events and wide spatial resolution of the sensors (such as NOAA-AVHRR, MODIS), implemented for burnt area mapping, do not allow an area-data
recording but only an event point-data recognition (Amatulli
et al., 2005). Besides, in countries where no remote sensing
imageries are used for burnt area mapping, a fire event is
often recorded at administrative level (i.e. number of fires per
municipality) (de la Riva et al., 2004) by the operative suppression corps. In such cases, the fire events may suffer some
geographic position error due to: imprecise acquisition location; incorrect database compilation; recording of suppression
events rather than fire events; multiple recording of the same
fire event by two or more suppression teams; location acquisition by means of broad resolution topographic maps rather
than field data acquisition using GPS; acquisition location by
means of other nearby fire events; and often perimeters and
the areas are estimated approximately (Pew and Larsen, 2001;
Podur et al., 2003; Koutsias et al., 2004). These procedures may
lead to a certain amount of uncertainty in the actual fire location, producing unforeseen effects in fire risk modelling (de
la Riva et al., 2004). Consequently, fire managers are seeking an appropriate methodology able to minimise the effect
of fire location uncertainty, able to transform point-data into
continuous surface, or surface-data, and useful to map fire
occurrence and spatial pattern at national and local scales
(Davis et al., 2000).
Koutsias et al. (2004) and de la Riva et al. (2004) have
recently explored how kernel density technique (Rosenblatt,
1956; Parzen, 1962) can be used to map fire occurrence at
the local scale, converting point-data into surface-data. The
kernel density technique requires a priori setting of smoothing parameters, such as the bandwidth size, often based on
subjective choices, expert knowledge and/or eventually sup-
ported by empirical decisions, thus leading to ambiguous
results.
This paper goes one step further, achieving the earlier
statement by means of the kernel adaptive mode (Breiman et
al., 1977; Levine, 2002); a technique specially indicated for
zones with diverse degrees of fire concentration and clustering
patches as in the Mediterranean context. The kernel density
adaptive mode is able to yield a more reliable density surface
better following the variation of point concentrations. Moreover, a calibration procedure is performed, by means of the
goodness-of-fit criteria proposed by Breiman et al. (1977) in order
to analytically set up the kernel smoothing parameters, and
thus to select the more reliable density surface, overcoming
the current drawbacks in defining it. Besides, point location
uncertainty is explored to assess the sensitivity of the suggested ignition point density model to map fire occurrence at
regional scale.
The first section briefly outlines the current method of density estimation, describing the traditional technique present
in geostatistical literature and actually implemented in Geographic Information System (GIS) for ecology studies (Worton,
1989; Seaman and Powell, 1996), putting more emphasis in the
fire occurrence application. Next, the kernel density theory is
explained focusing more on the adaptive mode concepts and
usefulness. Finally, a study case is described pointing out the
spatial uncertainty of the points data used and the procedure
to calibrate and validate the model; lastly, the spatial uncertainty effects are illustrated.
2.
General concepts beyond density
estimation
Generally speaking, density estimation deals with modelling
a density surface f̂ (x) given a finite number of data points
recorded with x and y coordinates. When using a nonparametric density estimation method, no assumption of the
density shape has to be made. Therefore, the data distribution is directly modelled from the training dataset (Katkovnik
and Shmulevich, 2002). The problem of correctly estimating
the intensity of points (the density) is very similar to assessing the probability that one event occurred (Bailey and Gatrell,
1995). Therefore, probability and density surfaces can be estimated under the same equations obtaining the same spatial
pattern.
An obvious, and one of the most common ways, of estimating the density, consists of dividing the sample space into
a finite number of intervals, each with the same size, and
assigning the density value, counting the points that fall into
the corresponding interval. In geostatistical analysis literature
this technique is also known as a histogram and in the GIS
environment could be implemented by superimposing a grid
and counting the points that fall inside each cell (Gatrell et
al., 1996; Levine, 2002). The histogram requires two parameters to be defined in advance: the width of the intervals (or
cell grid size) and the starting position of the first interval (or
grid position). The histogram is a very simple form of density
estimation, but has various drawbacks. A first one is related
with the final shape of the density estimate, which depends on
the starting point of the intervals and, in a GIS environment,
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
is directly affected by the orientation of the superimposed
grid (Gutiérrez-Osuna, 2004). The other one is the size of the
intervals, which directly influences the roughness of the estimate density surface. In effect, a small cell size emphasises
the point presence in the cell, whereas a large cell grid size
induces a certain degree of generalisation in the spatial variability (Koutsias et al., 2004). The drawbacks of superimposing
a regular grid over a point distribution can be partially solved
by using a “moving window” of fixed dimension. In such a
case, the density at each grid cell is estimated by counting
the points falling within the moving window centred on each
grid cell (Bailey and Gatrell, 1995). However, only the points
within the window influence the density and also in this case,
the shape and the size of the window influence the roughness
and accuracy of the final density surface. Several approaches
have been proposed to define the size of the moving window
and the most common method is to use the mean distance
among the points (Koutsias et al., 2004; de la Riva et al., 2004).
2.1.
Kernel density method and smoothing parameters
Interpolation techniques allow the generalisation of point
position variable values to an entire area. There are several
interpolation methods, such as kriging-cokriging, trend surface
and local regression model, which are based on the analysis of
one variable as a function of the spatial point position. The
different techniques are used taking into account the variable
types (categorical and/or continuous) and their distribution
function (normal, uniform, exponential, etc.). In case of the
calculation of density of finite individual point location, such
as a point process variable, the kernel density estimate is
suitable (Bowman and Azzalini, 1997). The aim of the kernel
density estimate is to produce a smooth density surface.
The kernel density estimate method is a non-parametric
technique that takes into account the symmetric probability density function, for each point location, to produce a
smooth cumulative density function (Rosenblatt, 1956; Parzen,
1962; Levine, 2002). Mathematically the kernel density function could be defined for n samples with X1 , . . ., Xn coordinates
vector by Eq. (1)
1 K
nh2
n
f̂ (x) =
xj − Xi
(1)
h
i=1
where K is the kernel function, h the bandwidth, the smoothing parameter, and xj is the coordinates vector representing
the location of the function being estimated.
According to Levine (2002), the most commonly used kernel
function is the normal distribution (Kelsall and Diggle, 1995);
besides this other distributions can be implemented: the triangular function or the quartic function (Bailey and Gatrell, 1995;
Burt and Barber, 1996). The normal distribution function is
expressed by the Eq. (2) (Levine, 2002):
g(xj ) =
2
[Wi Ii ]
1
−[d2 /2h
e ij
h2 2
]
(2)
where dij is the distance between a point observation (i) and
any location in the region where the function is estimated (j),
h the bandwidth which is delineated by the standard devia-
323
tion of the normal distribution, Wi and Ii identified weight and
intensity factors at the point location, respectively. The kernel
function is usually symmetric to yield unbiased estimates by
using a symmetric distribution of the weights on both sides of
the point of estimate (South, 1998).
Usually, the bandwidth is the standard deviation of the normal distribution and is a parameter that directly influences the
smoothness of the density function (Levine, 2002). A narrower
bandwidth will produce a finer mesh density; on the contrary
a large bandwidth will create a smoother distribution density,
as a result of less variability between areas.
In the case of regular point spatial distribution, the
bandwidth can assume a constant value (fixed bandwidth),
whereas for irregular spatial distribution the bandwidth
should be modelled as a function of the point concentration
(adaptive bandwidth) (Katkovnik and Shmulevich, 2002). The
latter method gives more flexibility to density estimation since
the bandwidth is calculated as an inverse function of the point
concentrations (Van Kerm, 2003). Particularly, in areas with
high concentration of points the bandwidth is narrow; on the
contrary where there is low presence, the bandwidth will be
wide (Worton, 1989).
A potential problem that might arise in the use of the fixed
bandwidth is that for some points, where the data are quite
sparse, the cumulative density function is based on the density function of one or few points (Fotheringham et al., 2002).
Consequently, large standard errors and under-smoothing of
the final density surface are present at local areas. Therefore
the fixed bandwidth should be used in regions where the data
are dense and also homogenously distributed, without evident
clustering.
Several approaches have been proposed to define the optimal fixed and adaptive bandwidths. Due to the typical clustering distribution of fire phenomena (Telesca et al., 2005), also
evident in the study area hereinafter described, only the adaptive mode can be used; thus, the theory behind the fixed mode
will not be discussed.
Concerning the adaptive bandwidth determination, different methods have been tested. One of the first is the
well-known kth nearest neighbour estimate (Loftsgaarden and
Quesenberry, 1965), later on followed by the adaptive kernel estimate proposed by Breiman et al. (1977). In this method the
calculation of the adaptive bandwidth interval is based on
the distance from the point X1 and its kth nearest neighbour
point; therefore the final density is calculated as a function of
the points falling within the circle delineated by the chosen
bandwidth (Levine, 2002). This concept can be expressed by
Eq. (3):
1
Khi (x − Xi )
n
n
f̂ (x) =
(3)
i=1
where in this case hi is modelled as a function of x, h = h(x).
In other words, h is tuned to what is happening around Xi
(Devroye and Lugosi, 2000). Thus, each point has a different
bandwidth interval according to the distance of its kth nearest
neighbour point. The kth nearest neighbour order is chosen a
priori; therefore, several densities can be built up changing the
order of kth nearest neighbour point.
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e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
In case of a high order of the kth nearest neighbour point,
an over smoothed density surface will be produced with similar values across the study area, due to the large amount of
points considered to calculate the local density. On the contrary, choosing a small number of points an under smoothed
density surface will be created, with so much local variation
that it would be difficult to determine whether there are any
patterns at all (Fotheringham et al., 2002).
To our knowledge, in ecology modelling, and as well in fire
occurrence, the best kth nearest neighbour order was defined
looking at the variability of the estimate density in terms of
spatial pattern distribution and histogram analysis, avoiding
too much “spiky” or over-smooth surfaces (e.g. Koutsias et
al., 2004; Allgöwer et al., 2005). In other words the smoothing
parameter was the one that provides a “happy and acceptable” medium between these two extremes, and evidently not
supported by objective decisions (Devroye and Lugosi, 2000).
Consequently, an analytical calibration procedure is sought to
choose the surface that better shows the fire occurrence.
Theoretically, the kernel smoothing parameters and the
performance of the density estimator is measured by minimising the mean-square error between a true density and the
estimated densities (Katkovnik and Shmulevich, 2002; Albers
and Schaafsma, 2003) (see Eq (4)):
2
MSE{f̂ (x)} = {[f̂ (x) − f̂tr (x)] }
(4)
where f̂ (x) is the kernel density which has to be estimated,
whereas the f̂tr (x) is the true density. Obviously, in practice,
one does not have access to the true density f̂tr (x) which is proposed to be estimated. Thus, a number of heuristic approaches
can be taken to find the optimal smoothing parameters (Hall
et al., 1991; de Bruin et al., 1999; Katkovnik and Shmulevich,
2002; Albers and Schaafsma, 2003). In fact, Devroye and Lugosi
(2000) in “Variable kernel estimates: on the impossibility of
tuning the parameters” make a deep statistical analysis about
the impossibility of setting up the kernel parameter without
considering some statistical assumptions.
To overcome the previous statement Breiman et al. (1977)
proposed an adaptive bandwidth calibration procedure based
on the calculation and its minimisation of a goodness-of-fit criteria, indicated by Ŝ, and defined in Eq. (5):
Ŝ =
n 1
ŵ(i) −
kth
n
2
(5)
where ŵ(i) is defined by Eq. (6)
ŵ(i) = e−nf̂ (xi,k )A(r)i,k
(6)
with i denoting is each ith point, kth is the adaptive kernel
smoothing parameter, thus the kth nearest neighbour order
chosen, n is the total number of observations, f̂ (xi,k ) is the estimated kernel density, at each i sampled point, using the kth
nearest neighbour order chosen and lastly A(r)i,k is the area of a
circle of radius r, where r is equal to kth nearest neighbour distance at each i sampled point. This procedure emphasises the
under/overestimation in the neighbourhood of each ignition
point location, rather than considering the overall density sur-
face, and takes into account the clustering degree by means
of the A(r)i,k . Moreover, this calibration procedure can also be
considered as a validation procedure because it is based on the
minimisation of goodness-of-fit criteria Ŝ, which indirectly calculates the under/overestimation at each point location and
in its neighbourhood.
The adaptive kernel density method provides a geostatistical model able to convert point-data into continuous surfacedata. Nonetheless, it was deemed necessary to assess the
sensitivity of the proposed model in terms of bias of point
location uncertainty and variation in the smoothing parameters setting. A case study will be illustrated here to accomplish
and bear out the statistical statements previously described in
the framework of fire occurrence.
3.
Study area
The Aragón’s autonomy (47,500 km2 ) is mainly located in
the central part of the Ebro river basin (northeast Spain)
(Fig. 1). From a geomorpho-structural point of view, the
Pyrenees and the Iberian Ranges extend to the north and
south, respectively, surrounding a central topographic depression crossed by the Ebro river. The Iberian Ranges, trending northwest–southeast direction, are subdivided into three
units: the Paleozoic branches in the westernmost part, the
Turolenses Ranges and the Calatayud-Teruel Graben one of
the largest intramontane structural basin at about 1000 m in
altitude. In the Pyrenees we can distinguish four morphostructural dominions from north to south: the axial Pyrenees,
the Internal Ranges, the Intermediate Depression and the
External Ranges. The complex topography results in a wide
range of climatic conditions: semiarid Mediterranean conditions in the centre of the valley (with annual average precipitations below 400 mm and annual temperatures around
14 ◦ C); sub-Mediterranean types in the middle mountain environments (average annual precipitations below 900 mm and
annual temperatures around 11 ◦ C); and humid and subhumid continental climates in the high mountains. Both
topography and climate, combined with anthropic influence in
landuse change, cause a huge variety of vegetation types that
changes from woodlands and shrublands in the mountainous
to scarce shrubby vegetation in the central depression. The
human pressure has given to the territory a high level of landscape fragmentation leaving few wildland areas especially
in the poor and non-productive agricultural lands (Lasanta
et al., 2006). The result is a complex mixing of wildland
patches and agricultural land in the pre-mountain areas, more
homogenous areas covered by wildland in the mountains, and
almost pure agricultural lands in the valley (such as in the
Ebro Basin). Fig. 6 depicts the Aragón’s autonomy in terms
of wildland emphasising in the circles the different degree of
fragmentation.
Regarding wildfires, in the last decades an increased tendency in the number of events has been observed in Aragón
and the yearly trends change according to human activity
and climate variation. The origin and growth of wildfire in
Aragón’s autonomy is connected with the typical causes for
Mediterranean regions: (1) the decrease of population and the
abandonment of traditional forestry uses in the mountain-
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
325
Fig. 1 – Study area and geomorphic structures of the Aragón’s Autonomy.
ous areas, (2) the abundance of inflammable plant communities and overly-dense structure, and (3) the climatic conditions (prolonged drought and electrical storms). Indeed,
according to recent statistics (Gobierno de Aragón, 2000),
most fires are caused by lightning and agricultural-human
activities.
4.
Dataset and methods
The following sections describe the dataset and the methodology implemented. First, the ignition point location uncertainty
is described. Afterwards, the kernel density implementation is described emphasising the smoothing parameters
calibration and the sensitivity of the density surfaces to
the ignition point location. Lastly, it is illustrated how
to integrate the human-caused and lightning-caused fire
occurrence maps. The whole methodological approach is
depicted and summarised in Fig. 2. The flowchart shows
the main procedures involved, pointing out the main phases
concerning uncertainty, calibration and sensitivity of the
model. The series of numbers beside the boxes is intended
to help in following the explanations given in the next
paragraphs of this section, where the corresponding numbers are reported in superscript bold characters between
brackets.
4.1.
Dataset
The Aragón’s fire atlas is an archive of data providing information concerning fire location, final area burned, cover
type, weather, suppression information and the estimate
of causes (human-caused, lightning-caused and undefinedcaused fires). Analysing the Aragón’s database over 19 years
(1983–2001) 3131 events were assigned to human-caused, 2637
to lightning-caused and 1855 were noted as undefined-caused;
corresponding to 41.07%, 34.60% and 24.33% of the whole fire
events, respectively. The undefined-caused ones were randomly assigned to the known ones firstly keeping the same
proportion and successively giving more emphasis to the
human-caused events based on the expert knowledge of the
authors. As a result 4195 and 3428 ignition points were used
to build up respectively human-caused and lightning-caused
fire occurrence maps (indicated here after with “H” and “L”)(1) .
The idea behind the use of undefined-caused events was to
study the whole fire phenomenon without leaving out any
fire events, because excluding the undefined-caused events
would result in a limited dataset unable to represent the whole
fire occurrence in Aragón’s autonomy, consequently losing its
potential operative performances.
Concerning the geographic features, the Aragón atlas
records fire events at municipality level and by means of
a superimposed UTM 10 km × 10 km grid; consequently no
information concerning the exact geographic positions were
present. Thus, each single ignition point has no x and y coordinates, suffering a local-position uncertainty ranging in the
area delineated by the municipality boundary and by the UTM
10 km × 10 km net. Fig. 3 shows the potential point location
uncertainty suffered by each ignition point. In order to significantly reduce the local-position uncertainty of the recorded
points, a geographic information layer of the wildland types
(Mapa forestal de Aragón 1:50,000) was overlapped to the pre-
326
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
Fig. 2 – Overview of the methodological process. The dotted lines highlight the model procedure phases, and the numbers
between brackets are reported in text in order to easily follow the procedure implemented. Briefly, three main boxes can be
identified:
modelling point location uncertainty, by means of fire database and ancillary vector layers (see Section 4.1);
smoothing parameters calibration and internal validation procedure for each kernel densities surfaces;
sensitivity
analysis based on the influence of point location uncertainty (see Section 4.2).
vious ones highlighting the fire-prone wildland(2) . At this point
the ignition point position was enforced to be in a polygon
delimited by the UTM net, municipality boundary and wildland limits, thus substantial reducing the location uncertainty.
It was then necessary to check this degree of uncertainty in
order to explore the sensitivity of the proposed technique.
Concluding, the possibility to work on two distinct datasets
for the human-caused and lightning-caused fire events, each
with their different and own spatial distribution, frequency
and clustering degree, allows us to perform and test the proposed methodology under two scenarios. Moreover, it permits
the study of fire-caused patterns, analysing the potential reasons for the various anthropic and bio-physical factors. In
this study the density of ignition points for square kilometre,
referred to a period of 19 years, will be abbreviated as ip km−2 ,
and will not be expressed as a yearly occurrence to avoid long
decimal numbers.
4.2.
Methods—model calibration and sensitivity
In order to assess if point location uncertainty leads to bias
in the kernel surfaces, a model sensitivity analysis was performed generating random ignition points inside the potential
wildfire areas according to the Aragón’s fire atlas, using an
Arcview® extension(3) . The random operation was repeated
three times producing “RA”, “RB” and “RC” local point positions respectively for the human-caused and lightning-caused
fires. The random location series was useful to assess if point
location uncertainty bias the kernel smoothing parameter
and consequently the kernel density surfaces, since both are
directly modelled as a function of the point location. Using the
H RA, H RB, H RC and L RA, L RB, L RC ignition points dataset,
several adaptive kernels density surfaces at 250 m pixel resolution (hereafter indicated as DH RA, DH RB, . . ., DL RC) were
created, using the free software CrimeStat® (Levine, 2002). A
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
327
such a case, low correlation means divergence in the spatial
distribution of the two fire causes; on the contrary high correlation means equality and homogeneity in the cause locations.
To locate the cause’s patterns spatially, a normalised difference index (C) was computed using the Eq. (7).
C=
Fig. 3 – Spatial representation of the ignition point location
obtained by the Aragón’s fire atlas. Each ignition point
suffers uncertainty of position ranging in the wildland
areas and included in the municipality boundary and UTM
net.
priori setting of kernel smoothing parameter (bandwidth size)
using the distance of the 5th, 10th, 15th and 20th nearest
neighbour point (labelled kth) was applied(4) to get an overview
of the spatial pattern and to perform a first assessment of the
goodness-of-fit criteria (Ŝ)(5) . Successively, the calculation of
the Ŝ was repeated (second assessment)(6) in the interval of the
lowest Ŝ previously obtained allowing its minimisation(7) and
selection(8) of the three most reliable density surfaces respectively for the H and L datasets. As already mentioned in Section
2.1, the Ŝ calculation is also considered as an internal validation procedure because it calculates the under/overestimation
at each point location. Thus, the obtained density surfaces can
be considered reliable in the view of those ignition point distributions and for that specific fire period.
In order to assess if random point position could bias the
kernel densities, the correlation equation, Pearson’s correlation coefficient (r), and the root means square of the residual
errors (RMSE) were calculated among the kernel density surfaces with the lowest Ŝ respectively for the DH and DL kernel
density(9) . High values of r identify strong correlation and low
sensitivity of the kernel surface to the point positions; on the
contrary low r value implies influence in the points positions
to the kernel surface.
4.3.
Methods—density surfaces integration
Afterwards, having chosen the most reliable lightning/
human-caused density surfaces, based on the minimisation
of the Ŝ coefficient, and having analysed the sensitivity of the
model, a spatial comparison of the fire cause locations was
performed by means of a Pearson’s correlation coefficient. In
DH − DL
DH + DL
(7)
The C index ranges between +1 and −1 and it identifies areas
with more prevalence of human-caused (values close to +1)
and lightning-caused (values close to −1) fires. Besides, the
spatial representation of this index allows the identification of
the spatial pattern of the causes, being significant for further
explanation of the whole fire phenomena. Nonetheless, such
an index does not give information concerning the gravity or
the occurrence of the fire phenomena. Therefore, integration
with the total density (DH + DL) was necessary to combine the
two pieces of information: total occurrence and causes of origin. A graphical representation was done representing in a
third dimension (z) the total density and in graded colour the
C index.
Finally, in order to understand the spatial relation between
the fire causes and the landscape fragmentation level, an
analysis of the wildland/no-wildland areas was computed by
rasterising (250 m pixel resolution) the wildland map (Mapa
forestal de Aragón 1:50,000), and calculating the pixel variance
in a 3 × 3 moving window (hereafter indicated as W NW V). In
this case the variance is a measure of statistical spatial dispersion and gives high value to the pixels of the wildland/nowildland border and low value to the core areas. Successively,
the maximum and the average density values for the different
variance levels were calculated and analysed.
5.
Results and discussions
As stated above, a first assessment of the Ŝ coefficient was
performed using the 5th, 10th, 15th and 20th nearest neighbour distance to define the adaptive bandwidth size. In Fig. 4
a graphical representation of the goodness-of-fit criteria trend
is reported plotting the Ŝ values at logarithm scales versus the kth nearest neighbour orders. Two general trends
can be noted for the three DH and DL kernel density surfaces. Among the former ones the lowest Ŝ belong to k10
and three random positions have similar Ŝ values ranging
between 0.023837880 and 0.023837902. Instead, the Ŝ values
of the DL kernel density surfaces reach the minimum at k15
with values ranging from 0.070128919 to 0.128142936. The
results of this preliminary analysis emphasises the importance of fully investigating around the k10 for the DH surfaces and k15 for the DL surfaces in order to minimise the Ŝ
coefficient. Continuing with the analysis, the densities produced by H RA, H RB and H RC random dataset reach the
lowest Ŝ at k8 (0.015256009–0.015255865–0.015256172, respectively). On the other hand, for the L RA, L RB, L RC random
dataset, the lowest Ŝ values is obtained at k17 (0.091972699),
k14 (0.068114441) and k16 (0.074651968), respectively (Fig. 4).
Indeed, according to Breiman et al. (1977) the Ŝ values should
be near to 0. The different behaviour in the smoothing parameter sensitivity can be explained by two main reasons: firstly the
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e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
Fig. 4 – Assessment of the Ŝ values as a function of the kernel smoothing parameters, for the human-caused and
lightning-caused density surfaces. First the assessment was performed for the k5 , k10 , k15 and k20 density surfaces
(highlighted by the square boxes), and successively the Ŝ trend (indicated by the line-dots) was calculated on the
neighbourhood of the lowest Ŝ values (k10 for the DH surfaces–k15 for the DL surfaces). The minimum Ŝ are reached at k8 for
the human-caused fires. On the contrary for lighting-caused fires the minimum values Ŝ belongs to k17 , k14 and k16 .
human-caused fires are numerically more abundant than the
lightning-caused fires; secondly the human-caused events are
mainly concentrated in areas with high landscape fragmentation (Figs. 5b and 6), whereas the lightning-caused fires tended
to occur in large wildland patches (Figs. 5c and 6). These two
factors produce an evident difference in the random ignition
points position that directly affects the kernel density surfaces
and consequently the Ŝ values.
The most reliable density surfaces were compared by
means of the correlation equation and its r and by the RMSE
to explore the statistical similarity between them (Table 1).
The ˛ coefficient of the correlation equations range near to
1 ± 0.1 and the r values are >0.90. Moreover, the correlation
equations are in accordance with the minimum, maximum,
mean and standard deviation values reported in Table 2, where
slight variations are notable. The RMSE values are smaller
than 0.028, which implies little values in the residual error.
Thus, the most reliable density surfaces (with the lowest Ŝ)
do not have relevant differences among them and one can be
used to spatialise fire occurrence in the Aragón’s autonomy
without being strongly affected by the exact position of the
fire events. From here after, result analysis and observations
will be done considering a random selection of two densities
among six, having demonstrated the unbiased nature of the
points position. Therefore, to identify the spatial correlation
of the fire causes, the Pearson’s coefficient was calculated at
pixel level between DH RA k8 and DL RC k16 . The obtained r
was extremely low (0.348) implying spatial uncorrelation in
the patterns of fire causes. The C coefficient spatially represented in Figs. 5 and 6 show the trend of the spatial distribution
of the fire causes. It is clearly evident that the two causes have
diverse pattern and spatial distribution.
The spatial distribution pattern of lightning-ignited wildland fires cover mainly the mountain regions included
between 800 and 1600 m. The highest values, ranging from
0.30 to 1.83 ip km−2 , are concentrated in several hotspot areas
mainly located in the southeastern part of the Iberian Ranges.
On the other hand, the hotspot areas of the Pyrenees slightly
reach 0.25 ip km−2 and are mostly situated in the western and
in the centre-eastern areas, corresponding to the Intermediate
Depression and the External Ranges. This result suggests that
the lightning-caused fire patterns are clearly clustered in the
space (Fig. 5c). The clustered pattern can be easily explained by
two main reasons. Firstly, lightning storms are dynamic and
localised phenomena able to ignite multiple fires in a single
day (Podur et al., 2003). This characteristic is right for a daily
temporal scale, and it could decrease over a multi-temporal
scale. Since there is not an obvious relationship between lightning strike density and lightning-fire density (Podur et al.,
2003; Larjavaara et al., 2005; also confirmed for the Spanish territory by Vázquez and Moreno, 1993), the clustering
behaviour should be explained by the fuel characteristic (second reason) (Vázquez and Moreno, 2001). Indeed, vegetation,
climate and daily weather conditions (temperature, humidity
and wind) are localised and directly influence the fuel moisture content of the different vegetation types. Therefore, fuel
characteristics, in terms of moisture, bio/necro-mass quantity, horizontal/vertical structure, constitute the key element
explaining the spatial distribution of the lightning-caused fires
in Aragón (Fig. 5c). In fact, the most affected areas which suffer
from land abandonment in Aragón are mainly concentrated in
the inter-medium mountains where agriculture productivity
was extremely low. The abandonment of agricultural land has
caused an increase in brush and shrubs (such as Genista scorpius), inflammable plant communities, especially annual grass
ending their phenological life in summer, which are the bases
for the accumulation of fine fuel (Lasanta et al., 2005, 2006;
Valderrábano and Torrano, 2000). This homogenous landscape
combined with the presence of dry storms, typical of Aragón,
induce high susceptibility of the territory to the lightningcaused wildland fires (Moreno et al., 1998).
The spatial distribution pattern of wildland fires due to
human causes is more spatially distributed than lightning; in
fact, it is possible to observe many small hotspot areas (Fig. 5c).
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
329
Fig. 5 – Spatial patterns of fire events in the Aragón’s autonomy: (a) fire occurrence/cause maps in 3D view; the third
dimension indicates the total ignition point density (DH RA k8 + DL RC k16 ) (ip km−2 ), the colour shows the spatial
distribution of the fire causes by means of the C index (blue colour lightning-caused fires/red colour human-caused fires); (b)
human-caused fire occurrence map (DH RA k8 considering exclusively the wildland); (c) lightning-caused fire occurrence
map (DL RC k16 considering exclusively the wildland).
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e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
Fig. 6 – Aragón’s Autonomy and spatial pattern of the wildland areas. The more fragmented areas are mainly concentrated
in the pre-mountain zones. The colour variation shows the spatial distribution of the C index and gives information
concerning the relation between the fire causes and the wildland fragmentation. As can be noted the human-caused hot
spot areas are concentrated in the more fragmented areas and in the contact line between wildland/no-wildland areas; on
the contrary the lightning-caused hot spot areas are mainly concentrated in the large wildland patches.
Table 1 – Correlation equations, Pearson’s coefficients and root mean square errors (RMSE) among the most reliable
density surfaces
Kernel density surfaces
Correlation equations
y
x
8
DH RB k
DH RA k8
DH RB k8
DL RB k14
DL RA k17
DL RA k17
r
RMSE
0.9034
0.8932
0.9061
0.9671
0.9728
0.9646
0.026
0.028
0.026
0.012
0.011
0.013
y = ˛x + ε
8
DH RC k
DH RC k8
DH RA k8
DL RC k16
DL RC k16
DL RB k14
y = 0.9072x + 0.0068
y = 0.8994x + 0.0073
y = 0.9035x + 0.0073
y = 1.0145x − 0.0004
y = 0.9518x + 0.0030
y = 1.0342x ± 0.0014
The highest density values (>0.1 ip km−2 ) appear on the contact line between wild and agricultural lands, especially on the
northern edge of the Iberian Ranges and the southern edge of
the Pyrenees (on the contact line between the External Ranges
and the Ebro Basin). Besides, it is interesting to indicate the
existence of several areas of high density located in the Axial
Pyrenees and in the southern Turolense Ranges due to grazing
activity. In these areas, wildland fires due to human activity
show low values (<0.1 ip km−2 ) (Fig. 5c).
Visually, it is possible to observe a relationship between
human-caused hotspot areas and the level of landscape heterogeneity, considering wildland and no-wildland zones (Figs.
5b, c and 6). In fact, the mean and maximum values increase
in accordance with the variance (W NW V) for the DH RA k8 ;
Table 2 – Minimum, maximum, mean, standard deviation values for the most reliable density surfaces
Most reliable kernel densities (ip km−2 )
Minimum
Maximum
Mean
S.D.
DH RA k8
DH RB k8
DH RC k8
DL RA k17
DL RB k14
0.0095
1.5303
0.0759
0.0651
0.0108
1.6582
0.0760
0.0649
0.0102
1.6367
0.0762
0.0646
0.0107
1.8378
0.0692
0.0552
0.0093
1.7915
0.0701
0.0592
DL RC k16
0.0099
1.8380
0.0695
0.0565
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
331
Fig. 7 – Maximum and mean density values trend for the DH RA k8 and DL RC k16 in relation to the fragmentation variance
of wildland/no-wildland. The mean and maximum density values for human-caused fire increase in accordance to the
fragmentation of the landscape. On the contrary, maximum density values for lightning-caused fire keeps values almost
constant, showing no relation with the landscape fragmentation.
on the contrary, for the DL RC k16 the maximum values keep
a trend almost constant (Fig. 7), showing low correlation with
the landscape fragmentation. These results agree with several
works conducted in Mediterranean areas (Leone et al., 2003;
Maselli et al., 2003; de la Riva and Pérez-Cabello, 2005; de la
Riva et al., 2006) where the edges of agriculture-wildland are
considered one of the most susceptible areas to wildfire, as
also happens in tropical forests (Holdsworth and Uhl, 1997;
Cochrane and Schulze, 1999; Cochrane and Laureance, 2002).
In fact, the level of landscape fragmentation strongly increases
the fire susceptibility and the so-called edge effect (Leone et al.,
2003) is clearly evident in Fig. 5b and Fig. 6, where small wildland patches into the Ebro Basin are clearly evident as hotspot
areas.
Regarding the whole wildfire phenomena, in terms of
total density (DH RA k8 + DL RC k16 ), the maximum values are
mostly sited in the southeast and northwest Aragón (Turolenses Ranges and the Intermediate Depression–External
Ranges in the Pyrenees). Scattered hotspot areas in Ebro Basin,
in the Intermediate Depression–External Ranges and in the
north-facing slopes of the Paleozoic branches in the westernmost part of Aragón also contain high density values, while the
lowest densities are located in Ebro Basin, Calatayud-Teruel
Graben and the eastern of Axial Pyrennes (Fig. 5a). Concluding, in the Aragón’s autonomy, wildfire causes follow a specific
pattern distribution as a result of human-agricultural activity
and wildland fire susceptibility to lightning-ignition.
6.
Conclusions and recommendations
This article sought to provide a basic overview of kernel density techniques applied to ecology modelling, emphasising the
adaptive mode and its applicability in fire occurrence mapping
at regional level. Moreover, it has provided a methodology that
tends to minimise bias when transforming point-data into
surface-data for fire event locations, allowing possible integration with other data types. The ability of the adaptive mode to
model the density surface as a function of the point concentration grade was explored. Nonetheless, the selection of the
most reliable density surfaces were supported by analytically
setting the kernel smoothing parameters avoiding any kinds of
subjective decisions; since an imprecise selection of the kernel
smoothing parameters can serious mislead the overall density
surface and can become a cause of spatial inaccuracy when
using occurrence maps in fire modelling.
The fire occurrence maps that best represent a continuous density surface with a minimised effect of under/
overestimation, were DH RA k8 and DL RC k16 respectively for
the human-caused and lighting-caused fires. However, further
research, using a wider range of conditions covering more ignition point distributions and concentrations, and with different
pixel resolutions, are requested to additionally evaluate and
support the proposed methodology.
The sensitivity analysis points out that uncertainties in
ignition point position do not produce significant variation
among the kernel parameters and do not produce relevant
difference in the density estimation. This statement does not
mean that the kernel technique, and consequently the kernel
smoothing parameters, is insensitive to the spatial pattern or
to the clustering degree, but that an evident spatial change
is needed to note some variations in the kernel smoothing
parameters. Therefore, the spatial displacement of the points
should be related to the amount of points, because they are
responsible for the variation of Ŝi and thus only in part of Ŝ. On
the contrary, the kernel smoothing parameters are extremely
sensitive to the number of points (n) due to its presence in
the Ŝ value as an exponent, and also as a factor in each Ŝi .
Coming to some conclusion, the model seems more sensitive
to the number of ignition points (n) rather than their precise
332
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 321–333
position. Therefore, random location or identification of the
ignition point position through other data information, such
as municipality and locality, could be admitted and accepted
to build a fire occurrence map by means of the adaptive kernel
density technique.
Considering the general context of fire risk modelling, the
models developed up to now were based on several predictor
variables against a response variable. This response variable
expresses the fire susceptibility in terms of fire frequency, fire
occurrence and burnt area, only related to areas where fire
events have been recorded. Considering that the kernel density is able to estimate fire occurrence in terms of fire density
or fire probability and going towards a further implementation of complex and reliable fire models, the kernel density
surface can be used as response variable in several short/longterm fire risk models. In such cases, the resulting algorithms
would, in fact, be based on a continuous surface, covering the
whole considered area, and hence taking into account also
areas prone to fire but for which no event has been effectively recorded. In this context, an approach based on the
kernel density combined with new and powerful data mining techniques (Amatulli et al., 2006) can be useful to design
fire management zones according to their occurrence probabilities, in order to better support decision-making and prevention actions (Pew and Larsen, 2001; Amatulli et al., 2005).
Analogue to this and in our specific case, lightning/human
density surfaces can be useful to model different fire scenarios
and to derive separately lightning/human fire risk maps useful
for making decisions also based on the different nature of the
fire ignition. Moreover, the kernel density surface can play an
important role in the validation of fire danger models based on
meteo-data and/or spectral-data, with the advantage of having a continuous density surface instead of a delimited burnt
area. Therefore, national/regional and seasonal/monthly fire
occurrence maps are needed to train/calibrate/validate the
temporal-spatial fire risk model.
Acknowledgements
The authors wish to thank Prof. Vittorio Leone, Mr. Marco
Trombetti for their helpful advices in the early stages of this
research, Ms. T. Houston to review the final draft of this
manuscript and the anonymous peer reviewers for their precious comments. We also thank Mr. Andres Cabrerizo to process the Aragón’s fire atlas database. The work has been developed during the Ph.D. in Crop Systems, Forestry, and Environmental Science (Basilicata University—Italy) and was partially
financed by: “Ministerio de Asuntos Exteriores y de Cooperación—Agencia Española de Cooperación Internacional
(Beca 61241-Programa IIA)”; “Ministerio Español de Ciencia
y Tecnologı́a (EROFUEGO-Ren2002-00133; RS FIRE-CGL200504863/CLI)”; “Dirección General de Investigación, Innovación
y Desarrollo, Gobierno de Aragón (PIR FIRE-PIP098/2005)”.
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