de la riva 2004 remote sensing of environment
TRANSCRIPT
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 17
Mapping wildfire occurrence at regional scale
Juan de la Rivaa Fernando Perez-Cabelloa Noemı Lana-Renault a Nikos Koutsias b1
a Facultad de Filosofia y Letras Department of Geography University of Zaragoza Calle Pedro Cerbuna 12 Zaragoza E-50009 Spain b Department of Geography University of Zurich Winterthurerstrasse 190 Zurich CH-8057 Switzerland
Received 19 July 2003 received in revised form 31 May 2004 accepted 8 June 2004
Abstract
When assessing fire danger interpolation of the dependent variablemdashhistoric fire occurrencemdashis required in order to statistically compare
and analyze it with human factors environmental parameters and census statistics To confirm the compatibility between the distinct data
types occasionally for this kind of spatial analysis historical observations of the primary wildland fire (given as x and y coordinates) must be
transformed either to continuous surfaces or to area data The simple overlay approach converts single point observations to area data
However this procedure assumes lack of spatial uncertainties that would otherwise result in serious errors caused by the positional
inaccuracies of the original point observations
Here we used kernel density interpolation to convert the original data on wildland fire ignition into an expression of areal units defined
by a raster grid and subsequently by the administrative borders of the municipalities in two study areas in Spain By overlaying a normal
bivariate probability density function (kernel) over each point observation each ignition point was considered an uncertain point location
rather than an exact one
D 2004 Elsevier Inc All rights reserved
Keywords Wildfire Kernel density interpolation Ignition point
1 Introduction
Within the framework of the Firerisk project2 the
spatialisation of fire occurrence as a dependent variable
has been a necessary requirement in the fire risk modeling
Traditional methods based on occurrence indexes (eg
number of fires related to wildland area) have been shown
to be inadequate when exploring statistical relations with
causal factors Occurrence indexes are often calculated for vectorial units (eg municipalities) while casual factors can
have a continuous behaviour (eg climatic variables) high
spatial variability (eg land use) or punctual or lineal
representation (eg roads) Therefore new solutions of fire
pattern spatialisation must be investigated
Fire occurrence data in Spain were recorded before
1998 both on a UTM 10Acirc10-km grid (ie x and y
coordinates for each fire at 10-km resolution) and at
administrative level (ie number of fires per municipality)
Because of coarse grid resolution these records introduce
an enhanced degree of uncertainty in fire location which
may be further propagated during modeling The successto explain the spatial distribution of fire patterns and to
propose and test hypotheses about underlying causal
factors depends on the quality of fire ignition observations
Particularly the use of other geo-referenced data for
extracting complementary information (ie overlay point
observations on other spatial data proximity distances to
other features) may introduce significant errors into
analysis The lack of appropriate fire occurrence data in
terms of their content and accuracy has a significant
impact on the theoretical and applied research on wildland
0034-4257$ - see front matter D 2004 Elsevier Inc All rights reserved
doi101016jrse200406013
Corresponding author Tel +34 976 76 10 00 fax +34 976 76 15 06
E-mail addresses delarivapostaunizares (J de la Riva)8
lavasierpostaunizares (F Perez-Cabello)8 noemiipecsices
(N Lana-Renault)8 koutsiasgeounizhch (N Koutsias)1 Fax +41163568482 htt pwwwgeograuahesproyectosfirerisk
Remote Sensing of Environment 92 (2004) 288ndash294
wwwelseviercomlocaterse
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 27
fires and on their management Even countries heavily
affected by wildland fires often do not have proper data on
fire incidence (Martın et al 1994)
Multiple types of spatial data are available For instance
point data are used to represent wildland fire ignition
locations while area data are used to represent census
statistics that describe socio-economic and demographiccharacteristics Many complications may arise in relating
one type of data to the other when performing a statistical
comparison and analysis (Flowerdew amp Pearce 2001)
Moreover the location uncertainty of these data raises
further questions about the integrity of comparisons
The simple overlay approach converts single point
observations to area data (ie number of points falling
inside an areal unit) However this procedure can produce
serious artifacts caused by the positional inaccuracies of the
original point observations Koutsias et al (in press) found
that wildland fire occurrence patterns shown by the over-
laying approach (ie a regular grid of quadrats super-imposed over positional inaccurate ignition points) can be
highly inconsistent depending on the magnitude of the
positional errors and the resolution of the grid In the same
study it was proposed that an increment in cell size
eliminates these problems by simultaneously reducing the
level of detail which results in loss of spatial variability
Interpolation as a method to predict attribute values at
unsampled locations from observations sampled inside the
study area can be used to convert data from point
observations to continuous fields (Burrough amp McDonnel
1998) Several interpolation techniques are available for this
purpose However most require a variable to be estimated
as a function of location In contrast kernel density
estimation can be used as an interpolation technique for
individual point observations (Levine 2002) Originally
this approach was developed as an alternative method to
obtain a smooth probability density functionmdashunivariate or
multivariatemdashfrom a sample of observations ie histogram
(Bailey amp Gatrell 1995 Levine 2002) Since the estimation
of the intensity of point observations (given in x and y
coordinates) is very similar to the bivariate probability
density one the kernel approach can be adapted for this
purpose (Bailey amp Gatrell 1995)
Kernel density estimation a non-parametric statistical
method for estimating probability densities has beenextensively used for home range estimation in wildlife
ecology (Seaman amp Powell 1996 Tufto et al 1996
Worton 1989) By converting original wildland fire
ignition locations to continuous density surfaces and
simultaneously addressing some of their inherent posi-
tional inaccuracies this technique is also very useful in
defining spatial fire occurrence patterns at landscape level
(Koutsias et al in press) A kernel (ie normal bivariate
probability density) is placed over each point observation
and the intensity at each intersection of a superimposed
grid is estimated (Seaman amp Powell 1996) The method
is similar to the bmoving window Q concept where a
window of fixed-size is moved over the point observa-
tions exce pt in this case the window is replaced by a 3D
function (Gatrell et al 1996) Mathematically the kernel
density estimator is defined as (Seaman amp Powell 1996
Silverman 1986 Worton 1989)
ˆ f f xeth THORN frac14 1nh2
Xn
iAgrave1
K x Agrave X ih
where n is the number of point observations h is the
bandwidth K is the kernel x is a vector of coordinates
that represent the location where the function is being
estimated and X i are vectors of coordinates that represent
each point observation
The bandwidth expresses the size of the kernel and
controls the interpolation results Depending on whether a
fixed value or multiple adaptive values are used for the
bandwidth (smoothing parameter) the kernel is distin-
guished into the fixed and adaptive mode respectively
Regardless of the mode a kernel must be selected from avariety of functions for instance normal distribution
triangular function quartic function etc although the
normal distribution is the most commonly used (Levine
2002) Finally the smoothing parameter must be taken in
accordance with the rule that narrow kernels allow nearby
point observations to have a greater effect on the density
estimation than wide kernels (Seaman amp Powell 1996) In
this regard the size of the bandwidth controls the degree of
smoothing of density estimations
The goal of the present study is to spatialize fire
occurrence data as an input for fire risk modeling by using
a kernel approach to interpolate historic fire observationsThe analysis has been applied in two distinct mountain areas
in Spain to prove that such a technique can be applied in the
field of forest fires In fire risk modeling fire occurrence can
be considered a dependent variable this analysis implies
continuous data and a more accurate location of the ignition
points in order to obtain improved interpolation
When applying kernel interpolation each fire ignition
point was considered not as an exact point location but
rather an uncertain one that defines a broader surrounding
area within which the true point observation lies A bivariate
Fig 1 Density estimation is calculated by placing a kernel (ie bivariate
normal probability density) over each wildland fire ignition point and
estimating the intensity at each intersection of a superimposed grid The
mean density value was then obtained superimposing each administrative
areal unit to the resulting kernel density surfaces
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 289
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 37
probability density function was overlaid on each point observation (Fig 1) Since fire managers frequently work
with data that refers to administrative units (ie municipal-
ities) fire occurrence is also represented at municipality
level by superimposing these units to the resulting kernel
density surfaces and considering the mean density value
2 Materials and methods
21 Study area
Two study areas with similar physical characteristics but distinct administrative organizations and fire patterns were
selected the Central Spanish Pre-Pyrenees and the East-
central Iberian range (Fig 2) These two areas are located in
Mediterranean mountain environments and they can be
classified as high-risk areas for wildfires (Perez-Cabello amp
de la Riva 2001)The Central Spanish Pre-Pyrenees comprises an area of
4192 km2 with complex topography and altitudes that
range from 500 to 1700 m Vegetation is dominated by
Pinus sylvestris Pinus nigra (most afforested) Quercus
faginea Buxus sempervirens (indicative of some oceanic
influences) Aphyllantes monspeliensis etc The size of
the municipalities is highly heterogeneous since some
cover more than 600 km2 while others are smaller than
15 km2 Socio-economic changes in the mid-20th century
led to the abandonment of farming activities and intense
emigration Nowadays recreational activities have
increased in specific zones Most fires are caused byhumans between 1983 and 2001 there were 616 fires of
Fig 3 Spatial reference units polygons produced from overlaying the UTM grid (10Acirc10 km) and the municipality boundaries (a) Pre-Pyrenees and (b)
Iberian range
Table 1
Analysis of the parameters of bandwidths
Parameter Pre-Pyrenees Iberian range
Mean polygon size ( s)a 286 km2 1858 km2
Diagonal of a theoretical square ( D) 75628 m 60972 m
Length of the theoretical radius (r ) 37814 m 30486 m
Mean number of ignitions points per polygon ( N ) 38 23
Mean random distance (RDmean)Acirc2 27574 m 2842 m
Total acreage
(including surrounding area)
93012 km2 91117 km2
Number of ignition points
(including surrounding area)
1220 1134
Global mean random distanceAcirc2 27611 m 28346 m
a Polygons b5 km2 were not considered
Fig 2 Study areas
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294290
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 47
which 55 were caused by humans and 45 by
lightning
The East-central Iberian range area occupies 4060 km2
with elevations ranging from 400 to 1300 m The
vegetation consists predominantly of Pinus pinaster P
nigra Quercus ilex rotundifoliae Quercus coccifera and
Brachypodium ramosum The size of the municipalities isfairly homogeneous with a mean size of 398 km2
Similar to the Pre-Pyrenees the area has suffered a
drastic decline in population and agricultural activities
over the last century but no recreational activities have
been developed Between 1983 and 2001 there were 572
fires of which 56 were caused by humans and 44 by
lightning
22 The kernel approach in transforming point data to area
data
Because fire occurrence data obtained from the official
Spanish wildfire census were provided on a UTM 10Acirc10-
km grid and at municipality level there was no information
on the exact x y UTM position of the ignition points Toimprove the accuracy of fire location a new spatial
reference system was designed Data were referenced by
randomly sampling within each polygon created after
overlaying the UTM grid (10Acirc10 km) and the municipality
boundaries (Fig 3) Within each bnew polygon Q where the
number of fires is known points were randomly positioned
throughout the wildland area only (forest shrub and grass
Fig 4 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 291
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 57
areas) Using this random sampling we established fire
ignitions points at a finer spatial resolution Fire data from a
wider area were included to preserve the effect of the
external points and to minimize problems associated with
edge effect Including the surrounding area 1220 and 1134random points were introduced for the Pre-Pyrennes and
Iberian range areas respectively
Kernel density interpolation was then applied to these
fire ignition points using the fixed mode approach (ie
constant value for the smoothing parameter) and a bivariate
normal probability density function We did not use the
adaptive mode since the point observations were treated in a
distinct way according to their concentration in space
(Worton 1989) Fire densities were estimated at a grid
resolution of 100 by 100 m CrimeStat R3 a spatial statistics
program for the analysis of crime incident locations was
used to perform kernel density interpolation (Levine 2002)
The size of bandwidth (ie standard deviation of the normal
distribution) is critical because it determines the degree of
smoothing in the density output surfaces Bandwidth value
depends on the scale adopted and the specific characteristics
of the study case related to the spatial fire pattern This
implies knowledge of the mean polygon size and the mean
number of ignition points within each Several methods
were tested to define the appropriate size of the smoothing
parameter of the kernel
ndashThe first method was based solely on the mean polygon
size assuming the polygon as a theoretical square with the
same size In this case a theoretical distance was estimated
on the basis of the length of the theoretical radius (r )
r frac14 D=2
where D is the diagonal of a theoretical square
ndashThe second considered the mean random distance
calculations (RDmean) on the basis of a local approach
(ie mean polygon size and mean number of ignition points
per polygon) and on a global one (ie total size of the study
area and total number of ignition points) RDmean is
mathematically defined as
RDmean frac141
2
ffiffiffiffiffi A
N
r
where A is the mean size polygon and N is the mean number
of ignitions points falling inside the polygons
On the basis of previous experience the double of the
RDmean value was decided to be used for bandwidth
definition (Koutsias et al in press)
ndashIn the third method the effect of the randomly
distributed points on kernel density outputs at certain
bandwidths was evaluated Random sampling was per-
formed using a specific script of ArcView 32 each time the
script was applied a distinct sampling distribution was
obtained To test the sensitivity of the bandwidth to the
randomness of the ignition points distribution a correlation
Fig 5 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Iberian range
3 CrimeStat R V 20 is available on httpwwwicpsrumichedu
NACJDcrimestathtml
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294292
7312019 De La Riva 2004 Remote Sensing of Environment
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analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 27
fires and on their management Even countries heavily
affected by wildland fires often do not have proper data on
fire incidence (Martın et al 1994)
Multiple types of spatial data are available For instance
point data are used to represent wildland fire ignition
locations while area data are used to represent census
statistics that describe socio-economic and demographiccharacteristics Many complications may arise in relating
one type of data to the other when performing a statistical
comparison and analysis (Flowerdew amp Pearce 2001)
Moreover the location uncertainty of these data raises
further questions about the integrity of comparisons
The simple overlay approach converts single point
observations to area data (ie number of points falling
inside an areal unit) However this procedure can produce
serious artifacts caused by the positional inaccuracies of the
original point observations Koutsias et al (in press) found
that wildland fire occurrence patterns shown by the over-
laying approach (ie a regular grid of quadrats super-imposed over positional inaccurate ignition points) can be
highly inconsistent depending on the magnitude of the
positional errors and the resolution of the grid In the same
study it was proposed that an increment in cell size
eliminates these problems by simultaneously reducing the
level of detail which results in loss of spatial variability
Interpolation as a method to predict attribute values at
unsampled locations from observations sampled inside the
study area can be used to convert data from point
observations to continuous fields (Burrough amp McDonnel
1998) Several interpolation techniques are available for this
purpose However most require a variable to be estimated
as a function of location In contrast kernel density
estimation can be used as an interpolation technique for
individual point observations (Levine 2002) Originally
this approach was developed as an alternative method to
obtain a smooth probability density functionmdashunivariate or
multivariatemdashfrom a sample of observations ie histogram
(Bailey amp Gatrell 1995 Levine 2002) Since the estimation
of the intensity of point observations (given in x and y
coordinates) is very similar to the bivariate probability
density one the kernel approach can be adapted for this
purpose (Bailey amp Gatrell 1995)
Kernel density estimation a non-parametric statistical
method for estimating probability densities has beenextensively used for home range estimation in wildlife
ecology (Seaman amp Powell 1996 Tufto et al 1996
Worton 1989) By converting original wildland fire
ignition locations to continuous density surfaces and
simultaneously addressing some of their inherent posi-
tional inaccuracies this technique is also very useful in
defining spatial fire occurrence patterns at landscape level
(Koutsias et al in press) A kernel (ie normal bivariate
probability density) is placed over each point observation
and the intensity at each intersection of a superimposed
grid is estimated (Seaman amp Powell 1996) The method
is similar to the bmoving window Q concept where a
window of fixed-size is moved over the point observa-
tions exce pt in this case the window is replaced by a 3D
function (Gatrell et al 1996) Mathematically the kernel
density estimator is defined as (Seaman amp Powell 1996
Silverman 1986 Worton 1989)
ˆ f f xeth THORN frac14 1nh2
Xn
iAgrave1
K x Agrave X ih
where n is the number of point observations h is the
bandwidth K is the kernel x is a vector of coordinates
that represent the location where the function is being
estimated and X i are vectors of coordinates that represent
each point observation
The bandwidth expresses the size of the kernel and
controls the interpolation results Depending on whether a
fixed value or multiple adaptive values are used for the
bandwidth (smoothing parameter) the kernel is distin-
guished into the fixed and adaptive mode respectively
Regardless of the mode a kernel must be selected from avariety of functions for instance normal distribution
triangular function quartic function etc although the
normal distribution is the most commonly used (Levine
2002) Finally the smoothing parameter must be taken in
accordance with the rule that narrow kernels allow nearby
point observations to have a greater effect on the density
estimation than wide kernels (Seaman amp Powell 1996) In
this regard the size of the bandwidth controls the degree of
smoothing of density estimations
The goal of the present study is to spatialize fire
occurrence data as an input for fire risk modeling by using
a kernel approach to interpolate historic fire observationsThe analysis has been applied in two distinct mountain areas
in Spain to prove that such a technique can be applied in the
field of forest fires In fire risk modeling fire occurrence can
be considered a dependent variable this analysis implies
continuous data and a more accurate location of the ignition
points in order to obtain improved interpolation
When applying kernel interpolation each fire ignition
point was considered not as an exact point location but
rather an uncertain one that defines a broader surrounding
area within which the true point observation lies A bivariate
Fig 1 Density estimation is calculated by placing a kernel (ie bivariate
normal probability density) over each wildland fire ignition point and
estimating the intensity at each intersection of a superimposed grid The
mean density value was then obtained superimposing each administrative
areal unit to the resulting kernel density surfaces
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 289
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 37
probability density function was overlaid on each point observation (Fig 1) Since fire managers frequently work
with data that refers to administrative units (ie municipal-
ities) fire occurrence is also represented at municipality
level by superimposing these units to the resulting kernel
density surfaces and considering the mean density value
2 Materials and methods
21 Study area
Two study areas with similar physical characteristics but distinct administrative organizations and fire patterns were
selected the Central Spanish Pre-Pyrenees and the East-
central Iberian range (Fig 2) These two areas are located in
Mediterranean mountain environments and they can be
classified as high-risk areas for wildfires (Perez-Cabello amp
de la Riva 2001)The Central Spanish Pre-Pyrenees comprises an area of
4192 km2 with complex topography and altitudes that
range from 500 to 1700 m Vegetation is dominated by
Pinus sylvestris Pinus nigra (most afforested) Quercus
faginea Buxus sempervirens (indicative of some oceanic
influences) Aphyllantes monspeliensis etc The size of
the municipalities is highly heterogeneous since some
cover more than 600 km2 while others are smaller than
15 km2 Socio-economic changes in the mid-20th century
led to the abandonment of farming activities and intense
emigration Nowadays recreational activities have
increased in specific zones Most fires are caused byhumans between 1983 and 2001 there were 616 fires of
Fig 3 Spatial reference units polygons produced from overlaying the UTM grid (10Acirc10 km) and the municipality boundaries (a) Pre-Pyrenees and (b)
Iberian range
Table 1
Analysis of the parameters of bandwidths
Parameter Pre-Pyrenees Iberian range
Mean polygon size ( s)a 286 km2 1858 km2
Diagonal of a theoretical square ( D) 75628 m 60972 m
Length of the theoretical radius (r ) 37814 m 30486 m
Mean number of ignitions points per polygon ( N ) 38 23
Mean random distance (RDmean)Acirc2 27574 m 2842 m
Total acreage
(including surrounding area)
93012 km2 91117 km2
Number of ignition points
(including surrounding area)
1220 1134
Global mean random distanceAcirc2 27611 m 28346 m
a Polygons b5 km2 were not considered
Fig 2 Study areas
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294290
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 47
which 55 were caused by humans and 45 by
lightning
The East-central Iberian range area occupies 4060 km2
with elevations ranging from 400 to 1300 m The
vegetation consists predominantly of Pinus pinaster P
nigra Quercus ilex rotundifoliae Quercus coccifera and
Brachypodium ramosum The size of the municipalities isfairly homogeneous with a mean size of 398 km2
Similar to the Pre-Pyrenees the area has suffered a
drastic decline in population and agricultural activities
over the last century but no recreational activities have
been developed Between 1983 and 2001 there were 572
fires of which 56 were caused by humans and 44 by
lightning
22 The kernel approach in transforming point data to area
data
Because fire occurrence data obtained from the official
Spanish wildfire census were provided on a UTM 10Acirc10-
km grid and at municipality level there was no information
on the exact x y UTM position of the ignition points Toimprove the accuracy of fire location a new spatial
reference system was designed Data were referenced by
randomly sampling within each polygon created after
overlaying the UTM grid (10Acirc10 km) and the municipality
boundaries (Fig 3) Within each bnew polygon Q where the
number of fires is known points were randomly positioned
throughout the wildland area only (forest shrub and grass
Fig 4 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 291
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 57
areas) Using this random sampling we established fire
ignitions points at a finer spatial resolution Fire data from a
wider area were included to preserve the effect of the
external points and to minimize problems associated with
edge effect Including the surrounding area 1220 and 1134random points were introduced for the Pre-Pyrennes and
Iberian range areas respectively
Kernel density interpolation was then applied to these
fire ignition points using the fixed mode approach (ie
constant value for the smoothing parameter) and a bivariate
normal probability density function We did not use the
adaptive mode since the point observations were treated in a
distinct way according to their concentration in space
(Worton 1989) Fire densities were estimated at a grid
resolution of 100 by 100 m CrimeStat R3 a spatial statistics
program for the analysis of crime incident locations was
used to perform kernel density interpolation (Levine 2002)
The size of bandwidth (ie standard deviation of the normal
distribution) is critical because it determines the degree of
smoothing in the density output surfaces Bandwidth value
depends on the scale adopted and the specific characteristics
of the study case related to the spatial fire pattern This
implies knowledge of the mean polygon size and the mean
number of ignition points within each Several methods
were tested to define the appropriate size of the smoothing
parameter of the kernel
ndashThe first method was based solely on the mean polygon
size assuming the polygon as a theoretical square with the
same size In this case a theoretical distance was estimated
on the basis of the length of the theoretical radius (r )
r frac14 D=2
where D is the diagonal of a theoretical square
ndashThe second considered the mean random distance
calculations (RDmean) on the basis of a local approach
(ie mean polygon size and mean number of ignition points
per polygon) and on a global one (ie total size of the study
area and total number of ignition points) RDmean is
mathematically defined as
RDmean frac141
2
ffiffiffiffiffi A
N
r
where A is the mean size polygon and N is the mean number
of ignitions points falling inside the polygons
On the basis of previous experience the double of the
RDmean value was decided to be used for bandwidth
definition (Koutsias et al in press)
ndashIn the third method the effect of the randomly
distributed points on kernel density outputs at certain
bandwidths was evaluated Random sampling was per-
formed using a specific script of ArcView 32 each time the
script was applied a distinct sampling distribution was
obtained To test the sensitivity of the bandwidth to the
randomness of the ignition points distribution a correlation
Fig 5 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Iberian range
3 CrimeStat R V 20 is available on httpwwwicpsrumichedu
NACJDcrimestathtml
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294292
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 67
analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 37
probability density function was overlaid on each point observation (Fig 1) Since fire managers frequently work
with data that refers to administrative units (ie municipal-
ities) fire occurrence is also represented at municipality
level by superimposing these units to the resulting kernel
density surfaces and considering the mean density value
2 Materials and methods
21 Study area
Two study areas with similar physical characteristics but distinct administrative organizations and fire patterns were
selected the Central Spanish Pre-Pyrenees and the East-
central Iberian range (Fig 2) These two areas are located in
Mediterranean mountain environments and they can be
classified as high-risk areas for wildfires (Perez-Cabello amp
de la Riva 2001)The Central Spanish Pre-Pyrenees comprises an area of
4192 km2 with complex topography and altitudes that
range from 500 to 1700 m Vegetation is dominated by
Pinus sylvestris Pinus nigra (most afforested) Quercus
faginea Buxus sempervirens (indicative of some oceanic
influences) Aphyllantes monspeliensis etc The size of
the municipalities is highly heterogeneous since some
cover more than 600 km2 while others are smaller than
15 km2 Socio-economic changes in the mid-20th century
led to the abandonment of farming activities and intense
emigration Nowadays recreational activities have
increased in specific zones Most fires are caused byhumans between 1983 and 2001 there were 616 fires of
Fig 3 Spatial reference units polygons produced from overlaying the UTM grid (10Acirc10 km) and the municipality boundaries (a) Pre-Pyrenees and (b)
Iberian range
Table 1
Analysis of the parameters of bandwidths
Parameter Pre-Pyrenees Iberian range
Mean polygon size ( s)a 286 km2 1858 km2
Diagonal of a theoretical square ( D) 75628 m 60972 m
Length of the theoretical radius (r ) 37814 m 30486 m
Mean number of ignitions points per polygon ( N ) 38 23
Mean random distance (RDmean)Acirc2 27574 m 2842 m
Total acreage
(including surrounding area)
93012 km2 91117 km2
Number of ignition points
(including surrounding area)
1220 1134
Global mean random distanceAcirc2 27611 m 28346 m
a Polygons b5 km2 were not considered
Fig 2 Study areas
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294290
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 47
which 55 were caused by humans and 45 by
lightning
The East-central Iberian range area occupies 4060 km2
with elevations ranging from 400 to 1300 m The
vegetation consists predominantly of Pinus pinaster P
nigra Quercus ilex rotundifoliae Quercus coccifera and
Brachypodium ramosum The size of the municipalities isfairly homogeneous with a mean size of 398 km2
Similar to the Pre-Pyrenees the area has suffered a
drastic decline in population and agricultural activities
over the last century but no recreational activities have
been developed Between 1983 and 2001 there were 572
fires of which 56 were caused by humans and 44 by
lightning
22 The kernel approach in transforming point data to area
data
Because fire occurrence data obtained from the official
Spanish wildfire census were provided on a UTM 10Acirc10-
km grid and at municipality level there was no information
on the exact x y UTM position of the ignition points Toimprove the accuracy of fire location a new spatial
reference system was designed Data were referenced by
randomly sampling within each polygon created after
overlaying the UTM grid (10Acirc10 km) and the municipality
boundaries (Fig 3) Within each bnew polygon Q where the
number of fires is known points were randomly positioned
throughout the wildland area only (forest shrub and grass
Fig 4 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 291
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 57
areas) Using this random sampling we established fire
ignitions points at a finer spatial resolution Fire data from a
wider area were included to preserve the effect of the
external points and to minimize problems associated with
edge effect Including the surrounding area 1220 and 1134random points were introduced for the Pre-Pyrennes and
Iberian range areas respectively
Kernel density interpolation was then applied to these
fire ignition points using the fixed mode approach (ie
constant value for the smoothing parameter) and a bivariate
normal probability density function We did not use the
adaptive mode since the point observations were treated in a
distinct way according to their concentration in space
(Worton 1989) Fire densities were estimated at a grid
resolution of 100 by 100 m CrimeStat R3 a spatial statistics
program for the analysis of crime incident locations was
used to perform kernel density interpolation (Levine 2002)
The size of bandwidth (ie standard deviation of the normal
distribution) is critical because it determines the degree of
smoothing in the density output surfaces Bandwidth value
depends on the scale adopted and the specific characteristics
of the study case related to the spatial fire pattern This
implies knowledge of the mean polygon size and the mean
number of ignition points within each Several methods
were tested to define the appropriate size of the smoothing
parameter of the kernel
ndashThe first method was based solely on the mean polygon
size assuming the polygon as a theoretical square with the
same size In this case a theoretical distance was estimated
on the basis of the length of the theoretical radius (r )
r frac14 D=2
where D is the diagonal of a theoretical square
ndashThe second considered the mean random distance
calculations (RDmean) on the basis of a local approach
(ie mean polygon size and mean number of ignition points
per polygon) and on a global one (ie total size of the study
area and total number of ignition points) RDmean is
mathematically defined as
RDmean frac141
2
ffiffiffiffiffi A
N
r
where A is the mean size polygon and N is the mean number
of ignitions points falling inside the polygons
On the basis of previous experience the double of the
RDmean value was decided to be used for bandwidth
definition (Koutsias et al in press)
ndashIn the third method the effect of the randomly
distributed points on kernel density outputs at certain
bandwidths was evaluated Random sampling was per-
formed using a specific script of ArcView 32 each time the
script was applied a distinct sampling distribution was
obtained To test the sensitivity of the bandwidth to the
randomness of the ignition points distribution a correlation
Fig 5 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Iberian range
3 CrimeStat R V 20 is available on httpwwwicpsrumichedu
NACJDcrimestathtml
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294292
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 67
analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 47
which 55 were caused by humans and 45 by
lightning
The East-central Iberian range area occupies 4060 km2
with elevations ranging from 400 to 1300 m The
vegetation consists predominantly of Pinus pinaster P
nigra Quercus ilex rotundifoliae Quercus coccifera and
Brachypodium ramosum The size of the municipalities isfairly homogeneous with a mean size of 398 km2
Similar to the Pre-Pyrenees the area has suffered a
drastic decline in population and agricultural activities
over the last century but no recreational activities have
been developed Between 1983 and 2001 there were 572
fires of which 56 were caused by humans and 44 by
lightning
22 The kernel approach in transforming point data to area
data
Because fire occurrence data obtained from the official
Spanish wildfire census were provided on a UTM 10Acirc10-
km grid and at municipality level there was no information
on the exact x y UTM position of the ignition points Toimprove the accuracy of fire location a new spatial
reference system was designed Data were referenced by
randomly sampling within each polygon created after
overlaying the UTM grid (10Acirc10 km) and the municipality
boundaries (Fig 3) Within each bnew polygon Q where the
number of fires is known points were randomly positioned
throughout the wildland area only (forest shrub and grass
Fig 4 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 291
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 57
areas) Using this random sampling we established fire
ignitions points at a finer spatial resolution Fire data from a
wider area were included to preserve the effect of the
external points and to minimize problems associated with
edge effect Including the surrounding area 1220 and 1134random points were introduced for the Pre-Pyrennes and
Iberian range areas respectively
Kernel density interpolation was then applied to these
fire ignition points using the fixed mode approach (ie
constant value for the smoothing parameter) and a bivariate
normal probability density function We did not use the
adaptive mode since the point observations were treated in a
distinct way according to their concentration in space
(Worton 1989) Fire densities were estimated at a grid
resolution of 100 by 100 m CrimeStat R3 a spatial statistics
program for the analysis of crime incident locations was
used to perform kernel density interpolation (Levine 2002)
The size of bandwidth (ie standard deviation of the normal
distribution) is critical because it determines the degree of
smoothing in the density output surfaces Bandwidth value
depends on the scale adopted and the specific characteristics
of the study case related to the spatial fire pattern This
implies knowledge of the mean polygon size and the mean
number of ignition points within each Several methods
were tested to define the appropriate size of the smoothing
parameter of the kernel
ndashThe first method was based solely on the mean polygon
size assuming the polygon as a theoretical square with the
same size In this case a theoretical distance was estimated
on the basis of the length of the theoretical radius (r )
r frac14 D=2
where D is the diagonal of a theoretical square
ndashThe second considered the mean random distance
calculations (RDmean) on the basis of a local approach
(ie mean polygon size and mean number of ignition points
per polygon) and on a global one (ie total size of the study
area and total number of ignition points) RDmean is
mathematically defined as
RDmean frac141
2
ffiffiffiffiffi A
N
r
where A is the mean size polygon and N is the mean number
of ignitions points falling inside the polygons
On the basis of previous experience the double of the
RDmean value was decided to be used for bandwidth
definition (Koutsias et al in press)
ndashIn the third method the effect of the randomly
distributed points on kernel density outputs at certain
bandwidths was evaluated Random sampling was per-
formed using a specific script of ArcView 32 each time the
script was applied a distinct sampling distribution was
obtained To test the sensitivity of the bandwidth to the
randomness of the ignition points distribution a correlation
Fig 5 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Iberian range
3 CrimeStat R V 20 is available on httpwwwicpsrumichedu
NACJDcrimestathtml
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294292
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 67
analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 57
areas) Using this random sampling we established fire
ignitions points at a finer spatial resolution Fire data from a
wider area were included to preserve the effect of the
external points and to minimize problems associated with
edge effect Including the surrounding area 1220 and 1134random points were introduced for the Pre-Pyrennes and
Iberian range areas respectively
Kernel density interpolation was then applied to these
fire ignition points using the fixed mode approach (ie
constant value for the smoothing parameter) and a bivariate
normal probability density function We did not use the
adaptive mode since the point observations were treated in a
distinct way according to their concentration in space
(Worton 1989) Fire densities were estimated at a grid
resolution of 100 by 100 m CrimeStat R3 a spatial statistics
program for the analysis of crime incident locations was
used to perform kernel density interpolation (Levine 2002)
The size of bandwidth (ie standard deviation of the normal
distribution) is critical because it determines the degree of
smoothing in the density output surfaces Bandwidth value
depends on the scale adopted and the specific characteristics
of the study case related to the spatial fire pattern This
implies knowledge of the mean polygon size and the mean
number of ignition points within each Several methods
were tested to define the appropriate size of the smoothing
parameter of the kernel
ndashThe first method was based solely on the mean polygon
size assuming the polygon as a theoretical square with the
same size In this case a theoretical distance was estimated
on the basis of the length of the theoretical radius (r )
r frac14 D=2
where D is the diagonal of a theoretical square
ndashThe second considered the mean random distance
calculations (RDmean) on the basis of a local approach
(ie mean polygon size and mean number of ignition points
per polygon) and on a global one (ie total size of the study
area and total number of ignition points) RDmean is
mathematically defined as
RDmean frac141
2
ffiffiffiffiffi A
N
r
where A is the mean size polygon and N is the mean number
of ignitions points falling inside the polygons
On the basis of previous experience the double of the
RDmean value was decided to be used for bandwidth
definition (Koutsias et al in press)
ndashIn the third method the effect of the randomly
distributed points on kernel density outputs at certain
bandwidths was evaluated Random sampling was per-
formed using a specific script of ArcView 32 each time the
script was applied a distinct sampling distribution was
obtained To test the sensitivity of the bandwidth to the
randomness of the ignition points distribution a correlation
Fig 5 Fire densities using the kernel density approach at various bandwidths to randomly distributed points in Iberian range
3 CrimeStat R V 20 is available on httpwwwicpsrumichedu
NACJDcrimestathtml
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294292
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 67
analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 67
analysis between the results obtained in the three random
sampling for the each bandwidth was applied The Pearson
coefficient shows the bandwidth which is less affected by
the randomness of the ignition points distribution
ndashFinally a visual-subjective approach was used
These estimators define a range of values used as
indicators for selecting the bandwidth However only after the analysis of the results was the final bandwidth chosen
3 Results and discussion
31 Mapping fire densities
The bandwidth parameters estimated from the methods
described in the previous section are summarized in Table
1 Although the total area and the total number of ignition
points in the two study areas were almost the same the
mean polygon size differed considerably because of thegreater number of municipalities and therefore polygons in
the Iberian range This accounted for similar results in the
Pre-Pyrenees the theoretical radius was 3781 m the
RDmean 2757 m and the global mean random distance
2761 m while in the Iberian range these values were 3049
2842 and 2835 m respectively
To perform a visual-subjective evaluation distinct
bandwidths were tested
ndash 2500 3250 4000 5000 and 7500 m in the Pre-Pyrenees
(Fig 4)
ndash 2500 3000 and 5000 m in the Iberian range area (Fig 5)
and the best results were obtained with bandwidths of 3250
and 4000 m in the Pre-Pyrenees and 3000 m in the Iberian
range A narrower bandwidth allowed a high effect of the
localization of the established ignition points while a wider
one introduced excessive smoothing
The effect of the sampling method to establish the fire
ignition points was also considered The correlation
analyses applied between the three kernel density outputs
resulting from the three random samplings (Table 2) show
that the density results for the Pre-Pyrenees using a 2500-m
bandwidth are affected more by the method used to locate
the ignition points (mean Pearson correlation coeffi-
cient=089) than for a 3250-m bandwidth (mean Pearson
correlation coefficient=093) Differences between band-
widths of 4000 5000 or 7500 m were not as significant
(mean Pearson correlation coefficient is 095 to 099) For
the Iberian range the same analysis showed that r esults
were less affected using a 3000 m bandwidth (Table 3 mean
Pearson correlation coefficient=090)
According to the previous calculations the appropriate
bandwidth in the Pre-Pyrenees ranges between 2750 and
3800 m and we chose a width of 3250 m For the Iberianrange area the appropriate bandwidth ranges between 2800
and 3100 m and the bandwidth selected was 3000 m
32 Summarizing fire densities at administrative level
Application of the data on fire densities to administrative
units involves homogenizing fire occurrence to a single
value for each municipality and consequently the loss of
local spatial distribution However the use of these units at
regional scale is usually a requirement for fire management
The value densities obtained for each grid cell in the
interpolation applied maintains the sample size Thereforethese densities sum the total number of fires considered in
the random sampling process and express the probability of
fire occurrence for each cell in relation with the total number
of fires The final result for each administrative unit
Table 2
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Pre-Pyrenees area
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 090 088 090 089
3250 094 092 093 093
4000 096 095 095 095
5000 097 097 097 097
7500 099 099 099 099
Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Table 3
Correlation analysis to evaluate the effect of three random distribution
points (1 2 3) in the Iberian range
Bandwidth 1ndash2 1ndash3 2ndash3 Mean
2500 087 084 086 086
3000 091 090 090 090
5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern
and bandwidth mean value is also included
Fig 6 Fire density at municipality level using the mean kernel density
value (3250 m bandwidth) in Pre-Pyrenees
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294 293
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
References
Bailey T C amp Gatrell A C (1995) Interactive spatial data analysis (pp
84ndash88) England7 Longman
Burrough P A amp McDonnel R A (1998) Principles of geographical
information systems (pp 98ndash99) Oxford7 Oxford Univ Press
Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
mental Modelling 5 23ndash 41
Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294
7312019 De La Riva 2004 Remote Sensing of Environment
httpslidepdfcomreaderfullde-la-riva-2004-remote-sensing-of-environment 77
(municipality) is the mean of values inside the study area
Fig 6 (Pre-Pyrenees) and Fig 7 (Iberian range) show the
probability of occurrence in each municipality expressed in
five categories very high high medium low and very low
4 Concluding remarks
Data on the spatial distribution of fire occurrence is one
of the most common requirements for wildfire danger
assessment This data is essential in explaining wildfire
causal factors Although the current positioning system
allows accurate location of ignition points there is still a
substantial lack of information particularly for historic fire
data In Spain x y UTM coordinates to track fires have been
used only since 1998 before occurrence was recorded both
on a UTM 10Acirc10-km grid and at municipality level
Here we used kernel density interpolation to spatially
define historic fire occurrence In contrast to the overlay
approach where the locations of wildland fire ignition areconsidered as exact points in the kernel approach they are
taken as spatially uncertain points achieved by placing a
normal bivariate probability density over each event
Our results show that bandwidth is critical since it
determines the degree of smoothing in fire density results A
procedure including several methods to define the band-
width size was followed Bandwidth value depends on both
the scale adopted and the specific characteristics of the study
area especially those related to the spatial fire pattern
Therefore two distinct study areas were chosen to provide
rigorous results The analysis reveals that there is no single
method as the best results are obtained by combining
several methods The geometric estimator (RDmean) and
the analysis of the effect of the sampling method provide the
most appropriate bandwidth However these estimators
define a range of values rather than a single one
Data on the spatial distribution of fire occurrence in
administrative areas is useful for fire risk analysis and fire
management even if they homogenize the risk to a singlevalue However representation as a continuous surface
preserves a more realistic pattern of fire occurrence
according to the considered scale and thus allows the
spatial analysis of the causal factors
Acknowledgements
This research was supported by the Spanish Ministry of
Science and Technology (contract AGL2000-0842) FIRE-
RISK project (Remote Sensing and Geographic Information
Systems for forest fire risk estimation an integrated analysisof natural and human factors)
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Burrough P A amp McDonnel R A (1998) Principles of geographical
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Flowerdew R amp Pearce J (2001) Linking point and area data to model
primary school performance indicators Geographical and Environ-
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Gatrell A C Bailey T C Diggle P J amp Rowlingsont B S (1996)
Spatial point pattern analysis and its application in geographicalepidemiology Transactions of the Institute of British Geographers
21 256ndash 274
Koutsias N Kalabokidis K D amp Allgfwer B (in press) Fire occurrence
patterns at landscape level beyond positional accuracy of ignition
points with kernel density estimation methods Natural Resource
Modeling (in press)
Levine N 2002 CrimeStat II A Spatial Statistics Program for the
Analysis of Crime Incident Locations (version 20) Ned Levine and
Associates Annandale VA and The National Institute of Justice
Washington DC
Martın M P Viedma D amp Chuvieco E (1994) High versus low
resolution satellite images to estimate burned areas in large forest fires
In D X Viegas (Ed) 2nd International Conference of Forest Fire
Research (pp 653ndash663) University of Coimbra Coimbra Portugal7
ADAI
Perez-Cabello F amp de la Riva J 2001 Forest fires and land degradation
in Spain The Huesca Western Pre-Pyrenees case study Keynote in the
workshop bLandnutzungswandel und Landdegradation in Spanien Q
Frankfurt am Main Germany
Seaman D E amp Powell R A (1996) An evaluation of the accuracy of
kernel density estimators for home range analysis Ecology 77
2075ndash2085
Silverman B W (1986) Density estimation for statistics and data analysis
(pp 7 ndash 94) London England7 Chapman amp Hall
Tufto J Andersen R amp Linnell J (1996) Habitat use and ecological
correlates of home range size in a small cervid the roe deer Journal of
Animal Ecology 65 715ndash 724
Worton B J (1989) Kernel methods for estimating the utilization
distribution in home-range studies Ecology 70 164ndash168
Fig 7 Fire density at municipality level using the mean kernel density
value (3000 m bandwidth) in Iberian range
J de la Riva et al Remote Sensing of Environment 92 (2004) 288ndash294294