Modeling Wildland Fire Susceptibility Using Fuzzy Systems

Murat Ercanoglu Hacettepe University, Geological Engineering Department, 06532 Ankara, Turkey

Keith T. Weber1, Jackie Langille, and Richard Neves Idaho State University, GIS Training and Research Center,Campus Box 8130, Pocatello Idaho, 83209-8130

Abstract: Due to fire suppression efforts, many areas have developed conditionswhereby fire susceptibility is high. To help identify those areas and improve firemanagement, two fire susceptibility models were developed for a study area insoutheastern Idaho. Both models used the same intrinsic parameters (topography,fuel characteristics, etc). The difference between the models is the first used expertknowledge to weight input parameters, whereas the second relied upon fuzzysystems to derive the weighting. Comparing the resulting output models indicatesthat the first more accurately capture fire susceptibility. This lends credibility to theuse of expert knowledge in geo-spatial modeling.

INTRODUCTION

Wildland fires are part of natural systems. As such, people need to live compati-bly with wildland fire and be prepared for the eventuality of fire (Owens and Durland2002). As people move into the wildland-urban interface (WUI), planners and agen-cies responsible for fire management and protection require tools to help them: (1)assess fire susceptibility; and (2) make decisions regarding funding, development,and deployment of fire suppression resources. Susceptibility models involve onlyintrinsic parameters (e.g., topography and vegetation) known, or believed to play arole in the feature or phenomena being modeled. In our case, this was wildfire. Awildfire susceptibility models does not, by definition then, involve ignition source oremergency response time, although these factors are important to fully characterizethe fire ecology of a region (Weber and Russell, 2003; Loboda and Csiszar, 2006).One valuable tool used by fire managers is Geographic Information Systems (GIS)(Gouma and Chronopoulou-Sereli, 1998). GIS allows fire managers to conduct spa-tial analysis of large geographic areas and easily incorporate satellite remote sensingdata. Using both GIS and remote sensing, researchers at Idaho State University have

1Corresponding author; email: webekeit@isu.edu

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GIScience & Remote Sensing, 2006, 43, No. 3, p. 268–282.Copyright © 2006 by V. H. Winston & Son, Inc. All rights reserved.

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created WUI fire susceptibility models. These models utilize digital terrain modelingtechniques along with satellite remote sensing–derived biophysical informationwithin a multi-criteria evaluation to assess fire susceptibility over large areas ofsoutheastern Idaho. Using bootstrap techniques, we validated input parameters devel-oped using remote sensing classification (i.e., fuel load predictive models). Resultingoverall accuracy ranged from 60 to 75%, depending upon the individual model (n =143). While these accuracies were acceptable, we also initiated a study to use fuzzysystems to improve the accuracy and reliability of these models and the final WUI firesusceptibility model (cf. Bone et al., 2005).

In most natural systems, change is gradual, and crisp or sharp distinctions arerare. This applies to evolution, the succession of vegetation, and other processes suchas biomass production and fuel loading. When ecologists and wildlife researchersmeasure natural communities, we find that these graduations are prevalent in the datasets. Hence, non-normal distributions are often encountered, necessitating the use oftransformations and non-parametric statistical techniques to deal with these problems.Ecological models are usually fraught with assumptions and caveats, and only rarelyprovide high reliability or predictability coefficients. As a result, many efforts haveyielded unsatisfactory or inaccurate and unreliable conclusions. The primary cause ofthis dilemma is the application of crisp logic to studies of the natural world. Distinc-tions are often forced where no real distinctions exist. Fuzzy logic assumes no abruptdistinctions but rather allows overlap among groups and deals with such graduationswith fuzzy set membership proportions (McNeill and Freiberger, 1993). For example,a point on the landscape can belong to a high fuel-load class (0.6) and to a moderatefuel-load class (0.4). Systems that can incorporate fuzzy information should be capa-ble of more accurately describing the natural world and have the potential to vastlyimprove modeling efforts.

Conventional mathematical models generally use the principles of physics and/ormechanics, which are predominantly based on linear behavior. These methods aresuitable when the behavior of the studied system is known. However, nature exhibitscomplex non-linear behavior in general. When natural engineering problems areconsidered, therefore, exact solutions to these problems rarely exist. One of the mostimportant reasons for this situation is that the relationship between the input and out-put data describing the natural processes is not known exactly, and is not easy todefine due to the uncertainty. Fortunately, in the last two decades, new computingtechniques have been evolving. Soft computing techniques such as fuzzy logic, artifi-cial neural networks, and genetic algorithms are potential solutions to these problems.Fuzzy logic, one of the most widely used soft computing techniques, was used in thisstudy to model fire susceptibility at Bear Lake County, Idaho, USA.

Fuzzy logic is based on fuzzy set theory, introduced by Zadeh (1965). A fuzzy setis defined as a collection of paired numbers that consists of members and degrees ofsupport or confidence for those numbers (Juang et al., 1992). The membership offuzzy sets is defined in [0, 1]. This means that fuzzy sets also include crisp (classical)sets. One of the most important aspects regarding the use of fuzzy sets in engineeringapplications is that the user can apply both numeric and linguistic information tosolve engineering problems. When compared to other mathematical models, fuzzy settheory can be considered one of the most easily adaptable methodologies to practicalapplications because of its relativity, variability, and flexibility features. In addition,

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its ability to solve problems similar to the human brain using expert-based or data-driven linguistic data, when insufficient statistical data exists, makes fuzzy logic avery effective tool. Expert opinion can be considered a very important tool, as itprovides flexibility without requiring detailed information or data for the problemunder consideration. This process is performed by using experience and theoreticalknowledge of the expert.

This paper describes an approach using fuzzy systems to modeling WUI fire sus-ceptibility in Bear Lake County, Idaho. Bear Lake County, located in the southeasterncorner of Idaho (Fig. 1) is well known for recreation and tourism. The county is 374km2 in size and has a population of 6,409 residents. The human population increasesdramatically in the summer due to the large number of seasonal residents. The topog-raphy of the county is diverse. Bear Lake (elevation 1799 m) is surrounded by a val-ley that grades into more mountainous terrain with elevations ranging to 3035 m.Much of the county is mountainous and a large part is forested (primarily Douglas fir[Pseudotsuga menzesii]). Vegetation in the valley consists of grasses, shrubs, andcultivated agriculture. Modeling WUI fire susceptibility for this county is describedalong with validation results and a comparison with an alternative WUI fire suscepti-bility model developed using multi-criteria evaluation and crisp-logic systems.

METHODOLOGY

In this study, we used seven different input parameters (Fig. 2) to model firesusceptibility in Bear Lake County. These parameters and their parametric effects onfire susceptibility were selected and rated (Fig. 2) according to regional fire experts(Mr. Fred Judd and Mr. Ben Estes, pers. comm., 2002).

Three general types of data were used. The first represented topographic effects(Barnwell et al., 2005), the second land cover effects (Gustafson et al., 2004), and thethird structural elements at risk to fire (Cohen, 1991; Barnwell et al., 2005). The topo-graphic parameters were extracted from Shuttle Radar Topography Mission (SRTM)–derived digital elevation data provided at a spatial resolution of 30 × 30 m. TheSRTM-derived digital elevation model (DEM) was used to generate slope and aspectdata that were then reclassified to represent slope-based suppression difficulty, rate ofspread, and aspect-based sun position models using the fire susceptibility ratingcurves developed by regional fire experts. The land cover parameters described fuelload and were derived from current (August 2004) Landsat Thematic Mapper (TM) 5data. The resulting fuel-load model (developed using maximum likelihood classifica-tion with 231 field training sites) (Langille et al., 2005) was then reclassified to repre-sent the rate of spread and fire intensity components. The rate-of-spread model wassensitive to fine fuels that can accelerate fire spread rate, whereas the fire intensitymodel is more sensitive to the total fuel load present within each pixel. In addition, anormalized difference vegetation index (NDVI) was developed from the same Land-sat imagery and used, along with field observations, to determine locations of moistvegetation that may have high fuel loads but a low probability of burning due to thenature of the vegetation/fuel. Pixels with high vegetation-moisture values negativelyinfluence the overall fire susceptibility model. Structural-elements parameters wereobtained by heads-up digitizing of each home and structure visible in a natural colordigital orthophotograph (1 × 1 m pixels) obtained in September 2004 (the same year

MODELING WILDLAND FIRE SUSEPTIBILITY 271

as the study). The accuracy of the digitized structural elements was verified by BearLake County personnel (Mr. Don Burdick, Mr. Steve Higgins, and Mr. Mitch Poulsen,pers. comm., 2004).

A final WUI fire susceptibility model was produced using a fuzzy logic approachand two different input parameter weighting methodologies. Parameter weightings for

Fig. 1. Fire suspectibility model developed for Bear Lake County, Idaho. Note the difference inrelief and the prominence of Bear Lake itself.

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the first method (FS1) were based entirely upon expert knowledge (i.e., the impor-tance of each parameter was based upon how much each parameter was perceivedto influence fire susceptibility based upon numerous years of experience). For thesecond version of the model (FS2), component weightings were calculated basedupon parametric fuzzy relations and only partially upon expert knowledge.

Method 1

Analysis began by defining membership functions (Fig. 3) of each input parame-ter and normalizing each parameter within the interval of [0, 1]. Next, the normalizedmembership degrees (estimating fire susceptibility) were assigned to each pixel ofeach parameter using IDRISI Kilimanjaro software (Eastman, 2003). Finally, calcula-tions were performed using fuzzy “max” and “min” operators. These operators aredefined as:

µ∪(x) = µ1(x) V (x) V......... V µj(x) x € X, (1)

µ∩(x) = µ1(x) Λ µ2(x) Λ ......... Λ µj(x) x € X, (2)

where Equation 1 presents the max operator and Equation 2 presents the min operator,µ is the membership function on X, the universe of discourse. The max operator orthe union of fuzzy sets (j of them) defined over the same universe of discourse is anew fuzzy set with a membership function that represents the maximum degree ofrelevance between each element and the new fuzzy set. In contrast, the min operatoror the intersection of fuzzy sets (j of them) defined over the same universe of dis-course is a new fuzzy set with a membership function that represents the minimumdegree of relevance between each element and the new fuzzy set (Berkan andTrubatch, 1997). We considered each input parameter as µj in Equations 1 and 2, andwe performed calculations for each pixel similar to the max-min composition opera-tion in fuzzy mathematics. To do this, we took the minimum(s) of the each inputparameter pair (P) (i.e., P1 and P2, P1 and P3, and … P6 and P7) at each pixel, anddetermined the maximum(s) value within these pairs. Final values were stored in anew image predicting fire susceptibility (Fig. 4) using parameter weights summarizedin Table 1.

Method 2

For the second methodology, parametric weights were obtained using IDRISI’s“Decision Support Module.” This module uses the normalized parameter files to pro-duce a decision support file based on the relationship between the parameters. Inaddition, this module allowed users to define parametric importance by selecting oneof three options (equal weight, user-defined weight, or Analytical Hierarchy Process[AHP]). Instead of equal weight or user-defined options (i.e. expert opinion), AHPwas selected which utilized a pair-wise comparison approach to derive parameterweights empirically. This option allowed the user to define parametric importance ona nine-point continuous scale ranging from less important (1) to more important (9).To evaluate the relationship among the input parameters (with respect to fire suscepti-bility) the cosine amplitude method (a widely used similarity method [Zadeh, 1971;

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Fig. 3. Membership functions of each parameter used to determine wildfire susceptibility forBear Lake County, Idaho.

MODELING WILDLAND FIRE SUSEPTIBILITY 275

Dubois and Prade, 1980]), was used. The cosine amplitude method calculates rij(range of rij values varies from 0 to 1 (0 ≤ rij ≤ 1)) using the following equation:

(3)rij

xik xjk×k 1=

m

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xik2

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m

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where xik and xjk are the elements of the pairwise parameters. Close inspection ofEquation 3 reveals that this method is related to the dot product for the cosine func-tion. When two vectors are colinear (most similar), their dot product is unity; whentwo vectors are at right angles to one another (most dissimilar), their dot product iszero. To evaluate the relation strength of each input parameter, normalized data files

Fig. 4. Fire susceptibility model (FS1) calculated using fuzzy systems with parameter weightsdetermined by expert knowledge.

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(with values ranging between 0 to 1) were calculated in the FULLSA (Ercanoglu andGokceoglu, 2004) computer software based on Equation 3. Results of this calculationare summarized in Table 2.

Using data from Table 2, eigenvectors for the parameter weights were obtained(Table 3) using the Calculate Weights tool in IDRISI. These results were used asparameter weights. The results of this calculation also report a Consistency Ratio

Table 1. Parameter Weights Assigned Using Expert Knowledge for Fire Susceptibility Model (FS1)

Parameter Weighting (proportion of total model)

Aspect 0.05Slope (rate of spread) 0.17Slope (suppression difficulty) 0.11Fuel load (vegetation moisture) 0.11Fuel load (rate of spread) 0.17Fuel load (fire intensity) 0.17Structure density 0.22

Table 2. Pairwise Relation Strength (rij) Values of Input Parameters (P)

P1 P2 P3 P4 P5 P6 P7

P1 1P2 0.949 1P3 0.597 0.621 1P4 0.637 0.668 0.789 1P5 0.589 0.625 0.562 0.666 1P6 0.567 0.606 0.693 0.853 0.754 1P7 0.068 0.063 0.190 0.213 0.126 0.197 1

Table 3. The Eigenvector of Parameter Weights Calculated Using Data from Table 2

Parameter Weight

P1 0.2306P2 0.2243P3 0.1530P4 0.1355P5 0.1243P6 0.1118P7 0.0204

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(CR) for the matrix indicating the uncertainty of the ratings. Values ≤0.10 indicategood consistency, whereas values >0.10 indicate that the matrix of weightings shouldbe re-evaluated, and a consistency ratio re-calculated (Eastman, 2003). The CR forthe matrix given in Table 1 was 0.02, representing very good consistency.

Fig. 5. Fire susceptibility model (FS2) calculated using fuzzy systems with parameter weightsderived using fuzzy logic.

MODELING WILDLAND FIRE SUSEPTIBILITY 279

Finally, the calculated weightings were assigned to the parameters and the secondfire susceptibility model (Fig. 5) was derived based upon equation 4:

FS2 = (P1*0.2306) + (P2*0.2243) + (P3*0.1530) + (P4*0.1355) + (P5*0.1243) + (P6*0.1118) + (P7*0.0204), (4)

Fig. 6. Difference between fire susceptibility models (FS1 and FS2) for Bear Lake County,Idaho.

280 ERCANOGLU ET AL.

where FS2 is fire susceptibility and P1, P2, …P7 are the parameter files.Both final models (FS1 and FS2) were then evaluated to determine which best

captured fire susceptibility information. To do this, we examined those areas whereeach model predicted high susceptibility (>0.8). These areas were compared to theresults from an independent assessment of fire regime condition performed by theU.S. Department of the Interior Bureau of Land Management. Fire regime condition(FRC) indicated what condition the area was in relative to its historic fire regime/firereturn interval (Mr. Kevin Conran, pers. comm., 2004). Five fire regimes conditionswere used based on the vegetation community’s historic fire return interval andhistoric fire severity (i.e., stand-replacing or not). Typically, higher FRC values indi-cated higher wildfire susceptibility due to a lack of recent fires and essentially, fuel-load stockpiling. However, a high FRC can also indicated a system where too manyfires have occurred recently due to a change in the vegetation community towarda more fire-induced system typified by non-native annual grasses like cheatgrass(Bromus tectorum). The sagebrush steppe found within the Snake River Plain ofIdaho is a good example of a vegetation community in which a dramatically increasedfire return interval exists compared with historic fire return intervals due to a continu-ous bed of cheatgrass (Ms. Sara Heide, pers. comm., 2004). It should be noted thatfire-induced systems with high FRC values are also considered high-susceptibilityareas, even though a fire may have occurred recently.

RESULTS AND DISCUSSION

Maps of the final models, FS1 and FS2, are presented in Figures 4 and 5, respec-tively. Upon close inspection, one may notice a contrast between the models whereFS1 predicted high fire susceptibility in the valley and where FS2 predicted high firesusceptibility in the mountains. To illustrate this graphically, a map showing thedifference between FS1 and FS2 is provided in Figure 6. The results of comparativevalidation indicate that FS1 more closely captured wildfire susceptibility in BearLake County, Idaho (Table 4). This is interesting because it lends merit to the use ofexpert knowledge in geo-spatial processing and modeling. In addition, this resultplaces increased significance upon rangeland fires where lower total biomass/fuelload exist compared with forested ecosystems. However, fires in rangeland ecosys-tems are typically larger in area and exhibit a longer fire season (approximately 90

Table 4. Comparison of FS1 and FS2 Fire Susceptibility Models and Independent Fire Regime Condition Assessments in Areas Predicted to Have High Fire Susceptibility (> 0.80)

Fire regime condition class FS1 (pixels) FS2 (pixels)

0 2769 32311 356 492 168 303 17 0Total 3310 3310

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days compared with approximately 9 days in forested ecosystems; Fred Judd, pers.comm., 2002). For example, between 1980 and 2005 there were 1,995 fires in range-land areas in southeastern Idaho totaling 479,363 ha ( = 240.3 ha). During the sametime period, there were 1,552 fires in forested areas within southeastern Idaho totaling211,488 ha ( = 136 ha).

ACKNOWLEDGMENTS

This research was supported by the USDI, Bureau of Land Management. Theauthors would like to acknowledge the support and information provided by Mr. FredJudd, Mr. Kevin Conran, and Ms. Sara Heide of the BLM.

REFERENCES

Barnwell, C., Rodman, S., and J. Koltun, 2005, Urban Wildfire Exposure Modeling inthe Municipality of Anchorage, Alaska. ESRI Users’ Conference, 2005. 38 p.

Berkan, R. C. and S. L. Trubatch, 1997, Fuzzy Systems Design Principles, New York,NY: IEEE Neural Networks Council, 496 p.

Bone, C., Dragicevic, S., and A. Roberts, 2005, Integrating High Resolution RemoteSensing, GIS, and Fuzzy Set Theory for Identifying Susceptibility Areas ofForest Insect Infestations,” International Journal of Remote Sensing,26(21):4809–4828.

Cohen, J., 1991, A Site-Specific Approach For Assessing The Fire Risk To StructuresAt The Wildland/Urban Interface. Proceedings of the Fire and the Environment,Symposium, Ogden, UT: U.S. Department of Agriculture, Forest Service, RockyMountain Research Station.

Dubois, D. and H. Prade, 1980, Fuzzy Sets and Systems: Theory and Applications,New York, NY: Academic Press.

Eastman, J. R., 2003, IDRISI Kilimanjaro, Guide to GIS and Image Processing.User’s Guide (Ver. 14), Worcester, MA: Clark University Press.

Ercanoglu, M. and C. Gökçeoglu, 2004, “Use of Fuzzy Relations to Produce Land-slide Susceptibility Map of a Landslide Prone Area (West Black Sea Region,Turkey),” Engineering Geology, 75:229–250.

Gouma, V. and A.Chronopoulous-Sereli, 1998, “Wildland Fire Danger Zoning,”International Journal of Wildland Fire, 8(1):37–43.

Gustafson, E. J., Zollner, P. A., Sturtevant, B. R., He, H. S., and D. J. Mladenoff,2004, “Influence of Forest Management Alternatives and Land Type on Suscepti-bility to Fire in Northern Wisconsin, USA,” Landscape Ecology, 19(3):327–341.

Juang, C. H., Lee, D. H., and C. Sheu, 1992, “Mapping Slope Failure Potential UsingFuzzy Sets,” Journal of the Geotechnical Engineering Division, ASCE, 118:475–493.

McNeill, D. and P. Freiberger, 1993, Fuzzy Logic, New York, NY: Simon andSchuster, 319 p.

Langille, J. M., Neves, R., Weber, K. T., and M. Ercanoglu, 2005, “Joint Fire Model-ing Project for Bear Lake County Idaho,” 34 p. [http://giscenter.isu.edu/Research/techpg/blm_fire/bearlake/bearlake_wui_report.pdf], accessed June 1,2006.

x

x

282 ERCANOGLU ET AL.

Loboda, T. V. and I. A. Csiszar, 2006, “Assessing the Risk of Ignition in a DynamicModeling Framework of Fire Threat: An Example from the Russian Far East,”Ecological Applications (forthcoming).

Owens J. and P. Durland, 2002, Wildfire Primer: A Guide for Educators, Washington,DC: United States Government Printing Office.

Weber, K. T. and G. Russell, 2003, “Modeling Lightning as an Ignition Source ofRangeland Wildfire in Southeastern Idaho,” African Journal of Range and For-age Science, 20(2):127.

Zadeh, L. A., 1965, “Fuzzy Sets,” Information and Control, 8:338–353.Zadeh, L. A.. 1971, “Outline of a New Approach to the Analysis of Complex Systems

and Decision Processes,” IEEE Transactions on Systems, Man and Cybernetics,SMC-3:28–44.