The identification and assessment of areas at risk of forest fire using fuzzy methodology Miguel E. Castillo Soto * Forest Fire Laboratory, University of Chile, Faculty of Forestry and Nature Conservation, Avenida Santa Rosa 11.315, La Pintana, Box: 9206, Santiago, Chile Keywords: Forest fire Fire risk Urbanewildland interface Buffer Fuzzy set abstract A new method is proposed and applied to determine areas at risk of forest fires produced by the combination of three territorial variables: the spatial localization of the fires, the road network, and areas with an urbanewildland interface. An area in central Chile, at latitude 33 S, was used as a case study in which variables were analyzed using fuzzy logic. As a result, irregular areas were identified that rep- resented the combined effects of these criteria. In practice, the spatial effects of the model used reflected the size and shape of areas with greater forest fire incidence and loss. This combination of variables produced increases in critical area intersections of between þ66.02% and þ252.09%, associated with areas of greater fire severity. The combined effects of these criteria allowed layers of geographical information to be obtained, which can be weighted with other territorial variables to create an integrated model of fire protection. Ó 2012 Elsevier Ltd. All rights reserved. Introduction Forest fires constitute an ongoing threat in areas with an urbanewildland interface. The risk of the spread of fire and high material losses can be observed and quantified after measuring the size, shape and location of fires in burned areas. Fires associated with road networks can be studied and evaluated by desegregation or through the classification of infrastructure type and quality differentiated or classified with a geographic information system (GIS) database (Burrough, 1989). In all previous studies, areas of influence have been defined based on expert experience or using vicinity and distance tools (Bonham-Carter, 1994, 398 pp.) to obtain a homogeneous numerical value of the phenomenon within the analyzed area and to represent spatial differences in the study subject in relation to areas not considered in the analysis (Chen & Hwang, 1992). However, in practice, it has not always been possible to represent the spatial distribution of fires in proximity to roads with GIS based on a homogeneous (buffer) definition of distance. The same difficulty exists with regard to the border effect in areas with an urbanewildland interface, where there are no enclosed areas to indicate the exact boundaries of wildfire occur- rence. Therefore, there are no adequate references defining the distances surrounding interface areas, which limits analyses to the definition of regular distances only (Burrough, 1989; Kumar & Goel, 1994; Robinson, 2003; Sasikala & Petrou, 2001), which have, in some cases, been determined for fire evacuation strategies (Larsen, Dennison, Cova, & Jones, 2011). The aim of the present research is to establish the combined effect of the influence of three factors involved in the spatial distribution of and risk levels for forest fires. The most common factor is the influence of roads in the spatial distribution of fires found in areas with an urbanewildland interface. The area of research was the region of Valparaiso, central Chile (see Fig. 1), which has a considerable history of fires resulting from human activity that have caused substantial material and envi- ronmental losses (Rodriguez y Silva et al., 2010, 52 pp.). These fires have increased despite efforts to reduce the risk for and incidence of fires. The present analysis was undertaken in two stages. In the first stage, thresholds or average distances at which the effect of fire density (the number of events per unit area) is significant were established. In the second stage, areas of influence were deter- mined around the occurrence gradient, depending on cumulative distance. The fuzzy logic method was applied for this purpose and consisted of constructing a spatial model of the effect of one or more variables on the territory with which they were associated. This is a new method of studying forest fire risk that has not been discussed in other publications. The results represent a first approximation adequate for the vicinity-analysis processes avail- able in geographical information systems (GIS) software and serve as a complement to classic buffer analysis. * Tel.: þ562 9785901; fax: þ562 9785744. E-mail addresses: [email protected], [email protected]. Contents lists available at SciVerse ScienceDirect Applied Geography journal homepage: www.elsevier.com/locate/apgeog 0143-6228/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apgeog.2012.07.001 Applied Geography 35 (2012) 199e207
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Applied Geography 35 (2012) 199e207
Contents lists available
Applied Geography
journal homepage: www.elsevier .com/locate/apgeog
The identification and assessment of areas at risk of forest fire using fuzzymethodology
Miguel E. Castillo Soto*
Forest Fire Laboratory, University of Chile, Faculty of Forestry and Nature Conservation, Avenida Santa Rosa 11.315, La Pintana, Box: 9206, Santiago, Chile
Keywords:Forest fireFire riskUrbanewildland interfaceBufferFuzzy set
0143-6228/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.apgeog.2012.07.001
a b s t r a c t
A new method is proposed and applied to determine areas at risk of forest fires produced by thecombination of three territorial variables: the spatial localization of the fires, the road network, and areaswith an urbanewildland interface. An area in central Chile, at latitude 33�S, was used as a case study inwhich variables were analyzed using fuzzy logic. As a result, irregular areas were identified that rep-resented the combined effects of these criteria. In practice, the spatial effects of the model used reflectedthe size and shape of areas with greater forest fire incidence and loss. This combination of variablesproduced increases in critical area intersections of between þ66.02% and þ252.09%, associated withareas of greater fire severity. The combined effects of these criteria allowed layers of geographicalinformation to be obtained, which can be weighted with other territorial variables to create an integratedmodel of fire protection.
� 2012 Elsevier Ltd. All rights reserved.
Introduction
Forest fires constitute an ongoing threat in areas with anurbanewildland interface. The risk of the spread of fire and highmaterial losses can be observed and quantified after measuring thesize, shape and location of fires in burned areas. Fires associatedwith road networks can be studied and evaluated by desegregationor through the classification of infrastructure type and qualitydifferentiated or classified with a geographic information system(GIS) database (Burrough, 1989). In all previous studies, areas ofinfluence have been defined based on expert experience or usingvicinity and distance tools (Bonham-Carter, 1994, 398 pp.) to obtaina homogeneous numerical value of the phenomenon within theanalyzed area and to represent spatial differences in the studysubject in relation to areas not considered in the analysis (Chen &Hwang, 1992). However, in practice, it has not always beenpossible to represent the spatial distribution of fires in proximity toroads with GIS based on a homogeneous (buffer) definition ofdistance. The same difficulty exists with regard to the border effectin areas with an urbanewildland interface, where there are noenclosed areas to indicate the exact boundaries of wildfire occur-rence. Therefore, there are no adequate references defining thedistances surrounding interface areas, which limits analyses to thedefinition of regular distances only (Burrough, 1989; Kumar & Goel,
1994; Robinson, 2003; Sasikala & Petrou, 2001), which have, insome cases, been determined for fire evacuation strategies (Larsen,Dennison, Cova, & Jones, 2011). The aim of the present research is toestablish the combined effect of the influence of three factorsinvolved in the spatial distribution of and risk levels for forest fires.The most common factor is the influence of roads in the spatialdistribution of fires found in areas with an urbanewildlandinterface.
The area of research was the region of Valparaiso, central Chile(see Fig. 1), which has a considerable history of fires resulting fromhuman activity that have caused substantial material and envi-ronmental losses (Rodriguez y Silva et al., 2010, 52 pp.). These fireshave increased despite efforts to reduce the risk for and incidenceof fires.
The present analysis was undertaken in two stages. In the firststage, thresholds or average distances at which the effect of firedensity (the number of events per unit area) is significant wereestablished. In the second stage, areas of influence were deter-mined around the occurrence gradient, depending on cumulativedistance. The fuzzy logic method was applied for this purpose andconsisted of constructing a spatial model of the effect of one ormore variables on the territory with which they were associated.This is a new method of studying forest fire risk that has not beendiscussed in other publications. The results represent a firstapproximation adequate for the vicinity-analysis processes avail-able in geographical information systems (GIS) software and serveas a complement to classic buffer analysis.
An area of approximately 176,000 ha was considered, whichincludes much of the municipalities of Viña del Mar in the Provinceof Valparaiso in Region V of Chile. For validation purposes, a quad-rant of 29,378 ha was defined, corresponding to the city of Quilpueand the surrounding area (Fig. 1), for which data related to forestfires were examined. The conditions in this quadrant are perfectlycomparable with those present in the wider area. The climate ischaracterized by the presence of mist moving inland to the hills,forming a temperate zone with temperatures ranging between 17and 25 �C and annual rainfall of approximately 370 mm. Accordingto the description in Chile’s Land Registry and Native PlantResource Assessment (CONAF-CONAMA-BIRF, 1999, 102 pp.),native forests in the communes of Valparaiso and Vina del Mar aresimilar to Mediterranean forest and scrubland, with speciesadapted to repeated cycles of forest fires associated with hightemperatures.
Information
A database of forest fires for the period 1986e2010 from theNational Forestry Corporation (CONAF) and processed by the ForestFire Laboratory at the University of Chile was analyzed. A total of13,977 fires were included and analyzed in relation to road prox-imity as a risk factor against forest fires. Of this total, 25% (3499fires) was reserved for validation analysis within the quadrantdescribed in Fig. 1. Roads considered were classified into threecategories: main paved roads with two or more carriageways andtwo-way traffic; urban paved roads with two-way traffic; and rural,unpaved one-way roads.
Process phases
Phase I. The determination of homogeneous distances by roadtype (buffer)
All records of fires were entered into a geographic informationsystem (GIS) to analyze their spatial relationships to roads. Subse-quently, areas of influence around each type of road were estab-lished using references to studies that propose buffers withdifferent distance values (Rodríguez y Silva. et al., 2010, 52 pp.). Thisprocess included all fires within each buffer distance (from 25 to2000mwith an interval of 25m, as recommended by Bosque (1992,323 pp.) for raster analysis) and determining the change infrequency as distance increases toward the periphery of each typeof road (Fig. 2) by constructing histograms to locate the criticalpoints in relation to road axes. As a result of this analysis, recom-mended distances for the study of the spatial variation of fires weredetermined in order to establish a buffer value appropriate for thiszoning criterion.
Phase II. The determination of fuzzy areasMembership function uA(x) is proposed, which defines the
extent to which a variable is associated with the phenomenonmodeled (Yen, 1999; Zadeh, 1965; Zhang & Wang, 1992;Zimmerman, 1996, p. 435). In this case, the fuzzy gradient is thechange in fire density occurring in areas close to roads, mainlyassociated with areas with an urbanewildland interface (Burrough,1989; Guan, 2004; Iliadis, 2005). In practice, according to fieldobservations, the highest concentration of fires is not always foundat roadsides but some distance away, usually varying according toroad type and occurrence density. Therefore, the first requirementwas to undertake a frequency analysis (described in phase I) toassign thresholds or tipping points (Jenks, 1963) to establish anappropriate statistical distribution of factors associated with fire
Fig. 2. The quantification of forest fires at different distances from roads. Distances from three types of roads were analyzed: urban, secondary urban and rural. The diagram showsa small section of the total area of research as an example.
occurrence. Burrough (1989) suggested applying a sigmoid func-tion in the case of distance gradients, whereas Schmucker (1982)proposed the establishment of decreasing J-shape functions,especially for risk assessment. With regard to the former andconsidering the findings of Rodríguez y Silva et al., 2010, 52 pp.,Iliadis (2005), and Iliadis, Spartalis, and Tachos (2008), concerningfire risk assessment, a sigmoid function (Thole, Zimmerman, &Zysno, 1979) was defined with parameters determined for thedistance of each fire from various road types. This function is rep-resented by (Zadeh, 1965; Zimmerman, 1996, p. 435):
f fx; a; cg ¼ fð1=ð1þ exp f�aðx� cÞgÞÞg: (1)
A diagram of the methodology applied is illustrated in Fig. 3. In f{x; a,c}, xmatches the degree of association of the sigmoid functionwith fire density and the distance of fires from roads. Parameter a isthe lower threshold at which f{x; a,c}acquires increasing associa-tion; c is the lower threshold at which fire density begins todiminish gradually up to a distance (x � c). A flow chart summa-rizing the process is illustrated in Fig. 3.
Idrisi Andes� raster functions were used to elaborate layers offuzzy data and their parameters, particularly for distance calcula-tion, and ArcGIS 9.1� was used for analysis of the vicinity andintersection of the fire area together with the creation of a Python�
application, the purpose of whichwas to count intersections of firesfound along the function pathway uA(x). A monotonicallydecreasing sigmoid functionwas used, as described in Equation (1).
The specialized literature tends to prefer this type of functionover others, such as J-shaped or Gaussian curves (Bellman & Zadeh,1970; Dubois & Prade, 1979; Guan, 2004; Iliadis, 2005; Iliadis et al.,2008). Tsataltzinos, Iliadis, and Spartalis (2009) applied thismethod specifically to study fire risk, mainly because the sigmoidfunction is better able to represent the gradual change around
vector layers (Gill & Bector, 1997; Yanar & Akyurek, 2006), in thiscase the road network, the interpretation of which depends onother explanatory variables, such as fires occurring in surroundingareas.
The information layers described in Fig. 3 were created usinga cell size of 25 � 25 m (Bosque, 1992, 323 pp.), as recommendedfor this scale of information analysis, to permit further analysis ofthe membership function value, as described in Equation (1). Thepermissible range for uA(x) considered the interval [0 / 1](Ahmed, Rao, & Murthy, 2000; Duprey & Taheri, 2010; Schmucker,1982), and the vicinity or distance (pixels) permitted were deter-mined over the range of value variation. The raster generated fromthis analysis was combined with that of road proximity tocombine both layers of information with map algebra by diffuseoverlay:
mAðxÞ ¼ Pi¼1/nmi; (2)
where m represents the standard raster layer i in the vicinity ofuA(x).
The criteria intersection of distance and road type was obtainedby calculating the sigmoid function complement presented inEquation (1):
Cðf fx; a; cgÞ ¼ mAðxÞ ¼ 1�Yn
i¼1
ð1� miÞ (3)
Fuzzy overlay was applied in the GIS using the Fuzzy GammaOperator (Cox, 2005; Schmucker, 1982; Wang, Elhag, & Hau, 2006),expressed as follows:
Cðf fx; a; cgÞ ¼ mAðxÞ ¼n1�
Yn
i¼1
ð1� miÞod
*n Yn
i¼1
mi
o1�d; (4)
Fig. 3. A diagram of the process and a schematic summary of the proposed methodology.
where n corresponds to raster data layers and the coefficient dwithvalues of between 0 and 1. Normally, this number falls betweenvalues of 0.5e0.8 to achieve the combined effect between the totaland gamma product, expressed as
mðxÞ ¼ cos2$a; (5)
where m(x) is a monotonically decreasing function and a is thefunction path. Thus, values around the function path correspond to
a ¼ x� cd� c
*p
2; when x < c;m ¼ 1: (6)
In the above expression, x is the membership function path,which represents the fire density variation as the distance fromroads increases. Value c represents the maximum density value,which begins to decrease from threshold d, monotonicallydecreasing as it moves farther from areas with an urbanewildlandinterface. The variable p�2 represents the period a, which attainsa value of 1 when maximum membership is reached.
Results
Distance analysis
Similar values for fire frequencies at different distances fromroads were obtained for different types of roads, extending the
effect on highways with two or more roads, particularly in interfaceareas. This first analysis confirmed values reported by Rodríguez ySilva. et al. (2010, 52 pp.), who recommended different bufferdefinitions, or areas of influence, depending on the road type. Therecommended buffers associated with paved roads range from 250to 750 m. For rural unpaved roads, the authors defined a buffer of250 m, with decreasing values of between 100 and 500 m. Thesevalues were determined in terms of distance analysis and thecalculation of fire frequency in each buffer area. Finally, for pavedroads located in towns and urban interface areas, recommendedbuffer values were at 150 m, with 100 and 300 m considered asvicinity values. The stabilization of fire frequency above a limiteddistance should be noted, which, in the case of rural roads, wasachieved at approximately 1 km.
Fuzzy application
The sigmoid function values noted above were extracted froma raster layer to determine the association between fire frequencyand distance in relation to each type of road (see Graphs 1e3).
The m(x) function pathway in each case depended greatly on theconcentration of fires, which varied in terms of distance from roadsand, therefore, from the location of the main interface areas, whichwas previously reported as a fundamental explanatory variable forfire occurrence (Julio, 2007; Keramitsoglou, Kiranoudis, Sarimveis,& Sifakis, 2004; Marzano, Camia, & Bovio, 1998; Rodríguez y Silva.
Fig. 4. The fuzzy sigmoid function effect around roads. Areas of interface and greater concentration of fires are highlighted. The difference with a normal buffer is that the areasdepend on fire density. The fuzzy gradient can be seen more clearly in the enlarged inset. The area corresponds to Quilpue, an area severely affected by fire.
Fig. 5. The fuzzy map for the results-validation area with impact values classified into three categories according to background information available on the number of fires andtheir location and severity levels. Buffer values do not assume the classic homogeneous figure obtained from a distance analysis with fixed values, and higher impact levels surroundothers of less severity in interface areas. The area classification can be seen more clearly in the enlarged inset.
et al., 2010, 52 pp.; Vakalis, Sarimveis, Kiranoudis, Alexandridis, &Bafas, 2004). However, m(x) did not follow a uniform spatialpattern in the trajectory for each type of road network. This findingis logical because previous results were attributed to the concen-tration of fire, which is typical of spatial fire risk assessment (Julio,2007) that must account for additional factors, such as the locationsof population centers and agricultural and forestry activities in thearea of direct influence. In all reported cases, there is spatialagreement for the areas classified as high fire risk (Bonazountas,Kallidromitou, & Kassomenos, 2005; Chuvieco, Allgower, & Salas,2003; Rodríguez y Silva et al., 2010, 52 pp.), based on multi-criteria methods (Burrough, 1989) that consider the criteriadefined here by the sigmoid function as main variables.
Taking these values into account parameters a, b and c ofmembership function a ¼ {(x � c}/{d � c}*{p/2} were obtained,setting the values of 250 and 750 at threshold c as monotonicallydecreasing from m ¼ 1. The result is a raster map with values[0 / 1], in which the highest fuzzy values are not necessarilyconcentrated at the road axes themselves, but rather in interfaceareas with high fire density (Fig. 4). This result contrasts with thetraditional linear buffer criterion for a given distance value that canonly model an average effect on road-associated interface, preciselywhere levels of forest fire risk and danger are highest.
Fuzzy gamma adjustment
Fuzzy gamma was applied to these results to consider roadlayers (roads, urban roads and unpaved roads) as a raster alongside
Graph 2. The fuzzy membership values for urban roads in interface areas.
the sigmoid function gradient linked to distance analysis from axesin interface areas with a high fire concentration. The result corre-sponds to a layer integrating these criteria and allows the fuzzy-values histogram (Graph 4) to be established, giving a value rangebetween 0 and 1. Jenks’ pixel reclassification (16 categories) wasapplied (Jenks, 1963; Tahsin & Zuhal, 2006) with the objective ofidentifying and separating those values corresponding to the fuzzyinfluence area described in Fig. 5. Because the areas are irregular,the maximum histogram breaks were analyzed, resulting in threecategories of vulnerability: low, medium, and high, with fuzzythresholds of 0.69, 0.76 and 0.89, respectively (Fig. 5).
The concentration of values described in Graph 4 correspondmainly to areas in which forest fire occurrence is associated withurbanewildland interface areas, as shown in studies by Rodríguez ySilva et al. (2010, 52 pp.). Areas determined by fuzzy gamma reflectthe combined effects of the above factors, allowing for the identi-fication of areas with different geometries based on the allocationof homogeneous distances via a GIS buffer.
Reclassified irregular areas were associated with levels ofimpact, according to those previously recorded in Rodríguez y Silvaet al. (2010, 52 pp.), for areas at risk of forest fire. As a result of thisvalue grouping, a map was produced showing those areas whererecurrence and fire impact are considerably greater than in moredistant areas.
Validation and discussion
The validation area and result comparison indicated in Fig. 1featured 3499 fires, representing 25% of the total territory. Theresults obtained from this number of fires using traditional bufferapplication were compared with the values reported by Rodríguezy Silva et al. (2010, 52 pp.) for this type of study, and the resultsobtained by fuzzy gamma for the assessed areas were compared atdifferent levels of impact on the risk of fire occurrence and damagecaused by fire (Figs. 4 and 5). The number of fires per area ofinfluence and fire density (number of fires in an area of 1 km2) andissues related to levels of risk were used as validation indicators ina comparison between the two methods. Tables 1 and 2 show thecomparative results obtained using fuzzy analysis (showing impactlevels) and buffer application (showing road types).
The table above shows the basic background to be consideredwhen comparing results based on the application of fuzzy logicwith results obtained by the application of buffer areas with fixedvalues (rings of constant width). The impact levels presented inTable 1 display a high proportion of fires classified as medium(yellow) to high risk (red or maximum level of severity) for the
Graph 4. The fuzzy histogram values, demonstrating the cut-off values for the reclassification process.
quadrant used for validation of the model. Table 2 providesa comparison with the results obtained by applying traditionalbuffer areas.
A comparative analysis between the data in Tables 1 and 2shows that there are differences between fire density values forlevels of low impact or severity. The application of homogeneousbuffer values results in a greater intersection of fires (useful data forgeographic analysis of potential risk) associated with roads withtwo or more carriageways (17.54 density) than when density isobtained using fuzzy gamma (11.83).
However, with regard to the more relevant fire density valuesassociatedwith areas of high priority and impact, gamma values arehigher, at 28.99 for impact level two (17.44 in traditional buffer) and48.73 for level three (13.84 in traditional buffer), which indicatesimprovements in the results of þ66.02% and þ252.09%, respec-tively. Considering that these are the areas with the greatest historyof problems caused by forest fires and that their values areconcentrated in much smaller areas, this finding suggests that it ispossible to improve economic efficiency in terms of the allocationof protection measures.
Furthermore, this comparative analysis has the advantage that itconsiders all types of roads and does not limit its analysis results toroad type, a common error that results in the overestimation of thebuffer effect in areas in which the buffer effects of multiple roadsoverlap.
Another difference between the methods that supports the useof fuzzy methodology is the total number of red alert (extremelyserious) fires included in these areas. Fuzzy gamma obtains betterresults than the traditional buffer method because the former
Table 1Characteristics of fires within the area of validation using fuzzy-gamma.
a Severity and priority levels defined by the National Forestry Corporation(CONAF) of Chile, to assess and plan the allocation of resources for prevention andcoordination with other agencies for protection against forest fires.
b Number of fires present in an area of 11 km2.
provides more data for a smaller surface area (a difference of14,058 ha), resulting in more precise calculations. The same applieswhen counting the number of fires in an area greater than 10 ha.Thus, calculations of areas of influence using fuzzy gamma includea greater number of fires over a smaller surface area. Table 3 showsa comparison of the results with regard to the intersection betweenroad type and alert level.
With regard to road classification, the differences between thetraditional and fuzzy gamma buffer estimations are even greater.With fuzzy gamma, it is possible to include a greater proportion ofsmaller surface area fires, especially the most severe, and the totalamount of data for all high-impact categories for severe fires is alsogreater (50 fires in fuzzy gamma and 40 in the homogeneousbuffer).
The method described here for calculating areas of influencealso provides background information regarding the locations ofcritical areas, especially in urbanewildland areas (Radeloff et al.,2001) or in other cases similar to that reported by Iliadis,Vangeloudha, and Spartalis (2010), to study the cluster effectusing fuzzy cluster algorithms, and Pieczynski and Obuchowicz(2004), who used a general Gaussian membership function.Nadeau and Englefield (2006) studied effects similar to thisresearch but in the field of vegetation through the application offuzzy-sets to generate forest fuel maps for Canada. Kahraman,Ruan, and Dogan (2003) applied multi-criteria fuzzy analysis tothe calculation of areas suitable for certain purposes for whichvicinity analysis is considered, in the same manner as Sadiq and
Table 2Fire rating and density within buffer areas (homogeneous values).
a 1: Main asphalted roads, two or more carriageways. 2: Urban asphalted roads,one or two carriageways. 3: Rural non-asphalted roads, one or two carriageways.
b Values assigned according to the results obtained in the initial distance analysis.c Values calculated considering the subtraction of smaller buffers (cumulative
sum of areas).d Values calculated minus the accumulated value from the smaller buffers.
Table 3Number of fires by number of alerts in each impact zone, and type of roads.
Id Fires Fire densitya Number of alerts in the impact zone (fuzzy gamma)
High Medium Low
Normal Yellow Red Normal Yellow Red Normal Yellow Red
Hussain (2005), Tangestani (2004), Tsataltzinos (2007), Tsataltzinoset al. (2009), and Vadrevu and Eaturu (2010), by applying fuzzygamma to estimate forest fire risk.
We recommend further research on this type of study, with anemphasis on interface areas. For new calculations based on fuzzylogic, it is desirable to include other parameters, such as charac-teristics of forest fuels that directly influence the risk of fire spreadand intensity levels. According to previous research in the area offire risk, fire risk areas with irregular boundaries reflect areas ofurban growth in interface areas and, to a large extent, the combinedeffects of roads and vegetation fuel.
Finally, the method developed here can support and comple-ment results based on the development of other models of risk andvulnerability that have already been tested in areas with similarcharacteristics. A quality vicinity analysis could further improve theresults obtained.
Conclusions
The results of this study indicate that this method providesmore background data for a more detailed definition of areas ofinfluence, typically created by GIS software. Because inalso considering road type this method also takes intoaccount the number, density and location of fires as inputparameters.
For this reason, it is useful to consider a greater number ofexplanatory variables for the calculation of areas of influence,enabling amore accurate estimation of fire risk in interface areas. Inpractice, using regular geometry to delineate protection buffers,such as rings, does not always represent the best areas in which toconcentrate monitoring resources.
The methodology described here can provide better estimatesfor the construction of fuzzy-based, multi-criteria models throughGIS, in which it is possible to assign relative weights to variablesthat provide information for the calculation of these areas.
This modification to the traditional scheme of the calculation ofareas of influence has the potential to generate cost savings in areaswith excess protection monitoring as well as minimizing the severedamage and effects usually caused by fire, especially in areas ofinterface.
In future research, these results may also contribute to thespatial effects of the causes of fires, especially in areas wherehumans suffer the greatest damage as a result of the spread of fire.
This method is completely applicable to other areas and ondifferent geographical scales. All that is required for input data isa complete and up-to-date fire record database, with additionalinformation such as road types and interface areas.
Finally, one of the most important areas where the fuzzy gammamethod can be of use is in the identification of areas where it iscritical to effect fire prevention and vegetation fuel management,given that in practice, these activities require a great deal ofeconomic resources within an integrated forest fire protectionprogram.
Acknowledgments
The author wishes to thank the Fondecyt Project 1095048 forproviding useful cartographic information for this study; theNational Forestry Corporation (CONAF) Valparaíso Region forproviding data on forest fires; and, finally, Roberto Chavez of theLaboratory of Geo-Information Science and Remote Sensing,Wageningen University, for his valuable contributions and exten-sive review of this manuscript.
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