De La Riva 2004 Remote Sensing of Environment

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



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



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


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



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




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




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


points (1 2 3) in the Iberian range


2500 087 084 086 086

3000 091 090 090 090

5000 097 096 097 097Table shows the Pearson correlation coefficients for each random pattern


Fig 6 Fire density at municipality level using the mean kernel density

value (3250 m bandwidth) in Pre-Pyrenees




(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


value (3000 m bandwidth) in Iberian range




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










21 Study area



















Iberian range

Table 1








Total acreage


93012 km2 91117 km2



1220 1134



Fig 2 Study areas





lightning











lightning


data












































r frac14 D=2








RDmean frac141

2

ffiffiffiffiffi A

N

r















NACJDcrimestathtml


























(Fig 4)




































Table 2




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 3




2500 087 084 086 086

3000 091 090 090 090














































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085



















21 Study area



















Iberian range

Table 1








Total acreage


93012 km2 91117 km2



1220 1134



Fig 2 Study areas





lightning











lightning


data












































r frac14 D=2








RDmean frac141

2

ffiffiffiffiffi A

N

r















NACJDcrimestathtml


























(Fig 4)




































Table 2




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 3




2500 087 084 086 086

3000 091 090 090 090














































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085














lightning











lightning


data












































r frac14 D=2








RDmean frac141

2

ffiffiffiffiffi A

N

r















NACJDcrimestathtml


























(Fig 4)




































Table 2




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 3




2500 087 084 086 086

3000 091 090 090 090














































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085










































r frac14 D=2








RDmean frac141

2

ffiffiffiffiffi A

N

r















NACJDcrimestathtml


























(Fig 4)




































Table 2




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 3




2500 087 084 086 086

3000 091 090 090 090














































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085



































(Fig 4)




































Table 2




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 3




2500 087 084 086 086

3000 091 090 090 090














































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085



















































Acknowledgements





References










21 256ndash 274




Modeling (in press)




Washington DC





ADAI







2075ndash2085











Documents

De La Riva 2004 Remote Sensing of Environment