Modeling Wildland Fire Susceptibility Using Fuzzy Systems

Transcription

1 Modeling Wildland Fire Susceptibility Using Fuzzy Systems Murat Ercanoglu Hacettepe University, Geological Engineering Department, Ankara, Turkey Keith T. Weber 1, Jackie Langille, and Richard Neves Idaho State University, GIS Training and Research Center, Campus Box 8130, Pocatello Idaho, Abstract: Due to fire suppression efforts, many areas have developed conditions whereby fire susceptibility is high. To help identify those areas and improve fire management, two fire susceptibility models were developed for a study area in southeastern Idaho. Both models used the same intrinsic parameters (topography, fuel characteristics, etc). The difference between the models is the first used expert knowledge to weight input parameters, whereas the second relied upon fuzzy systems to derive the weighting. Comparing the resulting output models indicates that the first more accurately capture fire susceptibility. This lends credibility to the use of expert knowledge in geo-spatial modeling. INTRODUCTION Wildland fires are part of natural systems. As such, people need to live compatibly with wildland fire and be prepared for the eventuality of fire (Owens and Durland 2002). As people move into the wildland-urban interface (WUI), planners and agencies 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 only intrinsic parameters (e.g., topography and vegetation) known, or believed to play a role in the feature or phenomena being modeled. In our case, this was wildfire. A wildfire susceptibility models does not, by definition then, involve ignition source or emergency response time, although these factors are important to fully characterize the 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 spatial analysis of large geographic areas and easily incorporate satellite remote sensing data. Using both GIS and remote sensing, researchers at Idaho State University have 1 Corresponding author; webekeit@isu.edu 268 GIScience & Remote Sensing, 2006, 43, No. 3, p Copyright 2006 by V. H. Winston & Son, Inc. All rights reserved.

2 MODELING WILDLAND FIRE SUSEPTIBILITY 269 created WUI fire susceptibility models. These models utilize digital terrain modeling techniques along with satellite remote sensing derived biophysical information within a multi-criteria evaluation to assess fire susceptibility over large areas of southeastern Idaho. Using bootstrap techniques, we validated input parameters developed using remote sensing classification (i.e., fuel load predictive models). Resulting overall 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 fuzzy systems to improve the accuracy and reliability of these models and the final WUI fire susceptibility model (cf. Bone et al., 2005). In most natural systems, change is gradual, and crisp or sharp distinctions are rare. This applies to evolution, the succession of vegetation, and other processes such as biomass production and fuel loading. When ecologists and wildlife researchers measure natural communities, we find that these graduations are prevalent in the data sets. Hence, non-normal distributions are often encountered, necessitating the use of transformations and non-parametric statistical techniques to deal with these problems. Ecological models are usually fraught with assumptions and caveats, and only rarely provide high reliability or predictability coefficients. As a result, many efforts have yielded unsatisfactory or inaccurate and unreliable conclusions. The primary cause of this dilemma is the application of crisp logic to studies of the natural world. Distinctions are often forced where no real distinctions exist. Fuzzy logic assumes no abrupt distinctions but rather allows overlap among groups and deals with such graduations with 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 moderate fuel-load class (0.4). Systems that can incorporate fuzzy information should be capable of more accurately describing the natural world and have the potential to vastly improve modeling efforts. Conventional mathematical models generally use the principles of physics and/or mechanics, which are predominantly based on linear behavior. These methods are suitable when the behavior of the studied system is known. However, nature exhibits complex non-linear behavior in general. When natural engineering problems are considered, therefore, exact solutions to these problems rarely exist. One of the most important reasons for this situation is that the relationship between the input and output data describing the natural processes is not known exactly, and is not easy to define due to the uncertainty. Fortunately, in the last two decades, new computing techniques have been evolving. Soft computing techniques such as fuzzy logic, artificial 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 this study to model fire susceptibility at Bear Lake County, Idaho, USA. Fuzzy logic is based on fuzzy set theory, introduced by Zadeh (1965). A fuzzy set is defined as a collection of paired numbers that consists of members and degrees of support or confidence for those numbers (Juang et al., 1992). The membership of fuzzy 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 engineering applications is that the user can apply both numeric and linguistic information to solve engineering problems. When compared to other mathematical models, fuzzy set theory can be considered one of the most easily adaptable methodologies to practical applications because of its relativity, variability, and flexibility features. In addition,

3 270 ERCANOGLU ET AL. its ability to solve problems similar to the human brain using expert-based or datadriven linguistic data, when insufficient statistical data exists, makes fuzzy logic a very effective tool. Expert opinion can be considered a very important tool, as it provides flexibility without requiring detailed information or data for the problem under consideration. This process is performed by using experience and theoretical knowledge of the expert. This paper describes an approach using fuzzy systems to modeling WUI fire susceptibility in Bear Lake County, Idaho. Bear Lake County, located in the southeastern corner of Idaho (Fig. 1) is well known for recreation and tourism. The county is 374 km 2 in size and has a population of 6,409 residents. The human population increases dramatically in the summer due to the large number of seasonal residents. The topography of the county is diverse. Bear Lake (elevation 1799 m) is surrounded by a valley 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, and cultivated agriculture. Modeling WUI fire susceptibility for this county is described along with validation results and a comparison with an alternative WUI fire susceptibility model developed using multi-criteria evaluation and crisp-logic systems. METHODOLOGY In this study, we used seven different input parameters (Fig. 2) to model fire susceptibility in Bear Lake County. These parameters and their parametric effects on fire 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 the third structural elements at risk to fire (Cohen, 1991; Barnwell et al., 2005). The topographic parameters were extracted from Shuttle Radar Topography Mission (SRTM) derived digital elevation data provided at a spatial resolution of m. The SRTM-derived digital elevation model (DEM) was used to generate slope and aspect data that were then reclassified to represent slope-based suppression difficulty, rate of spread, and aspect-based sun position models using the fire susceptibility rating curves developed by regional fire experts. The land cover parameters described fuel load and were derived from current (August 2004) Landsat Thematic Mapper (TM) 5 data. The resulting fuel-load model (developed using maximum likelihood classification with 231 field training sites) (Langille et al., 2005) was then reclassified to represent the rate of spread and fire intensity components. The rate-of-spread model was sensitive to fine fuels that can accelerate fire spread rate, whereas the fire intensity model is more sensitive to the total fuel load present within each pixel. In addition, a normalized difference vegetation index (NDVI) was developed from the same Landsat imagery and used, along with field observations, to determine locations of moist vegetation that may have high fuel loads but a low probability of burning due to the nature of the vegetation/fuel. Pixels with high vegetation-moisture values negatively influence the overall fire susceptibility model. Structural-elements parameters were obtained by heads-up digitizing of each home and structure visible in a natural color digital orthophotograph (1 1 m pixels) obtained in September 2004 (the same year

4 MODELING WILDLAND FIRE SUSEPTIBILITY 271 Fig. 1. Fire suspectibility model developed for Bear Lake County, Idaho. Note the difference in relief and the prominence of Bear Lake itself. as the study). The accuracy of the digitized structural elements was verified by Bear Lake 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 approach and two different input parameter weighting methodologies. Parameter weightings for

5 272 ERCANOGLU ET AL. Fig. 2. Input parameters used to determine wildfire susceptibility in Bear Lake County.

6 MODELING WILDLAND FIRE SUSEPTIBILITY 273 the first method (FS1) were based entirely upon expert knowledge (i.e., the importance of each parameter was based upon how much each parameter was perceived to influence fire susceptibility based upon numerous years of experience). For the second version of the model (FS2), component weightings were calculated based upon parametric fuzzy relations and only partially upon expert knowledge. Method 1 Analysis began by defining membership functions (Fig. 3) of each input parameter and normalizing each parameter within the interval of [0, 1]. Next, the normalized membership degrees (estimating fire susceptibility) were assigned to each pixel of each parameter using IDRISI Kilimanjaro software (Eastman, 2003). Finally, calculations were performed using fuzzy max and min operators. These operators are defined as: µ (x) = µ 1 (x) V (x) V... V µ j (x) x X, (1) µ (x) = µ 1 (x) Λ µ 2 (x) Λ... Λ µ j (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 or the union of fuzzy sets (j of them) defined over the same universe of discourse is a new fuzzy set with a membership function that represents the maximum degree of relevance between each element and the new fuzzy set. In contrast, the min operator or the intersection of fuzzy sets (j of them) defined over the same universe of discourse is a new fuzzy set with a membership function that represents the minimum degree of relevance between each element and the new fuzzy set (Berkan and Trubatch, 1997). We considered each input parameter as µ j in Equations 1 and 2, and we performed calculations for each pixel similar to the max-min composition operation in fuzzy mathematics. To do this, we took the minimum(s) of the each input parameter pair (P) (i.e., P1 and P2, P1 and P3, and P6 and P7) at each pixel, and determined the maximum(s) value within these pairs. Final values were stored in a new image predicting fire susceptibility (Fig. 4) using parameter weights summarized in 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 produce a decision support file based on the relationship between the parameters. In addition, this module allowed users to define parametric importance by selecting one of three options (equal weight, user-defined weight, or Analytical Hierarchy Process [AHP]). Instead of equal weight or user-defined options (i.e. expert opinion), AHP was selected which utilized a pair-wise comparison approach to derive parameter weights empirically. This option allowed the user to define parametric importance on a 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 susceptibility) the cosine amplitude method (a widely used similarity method [Zadeh, 1971;

7 274 ERCANOGLU ET AL. Fig. 3. Membership functions of each parameter used to determine wildfire susceptibility for Bear Lake County, Idaho.

8 MODELING WILDLAND FIRE SUSEPTIBILITY 275 Fig. 3. Continued Dubois and Prade, 1980]), was used. The cosine amplitude method calculates r ij (range of r ij values varies from 0 to 1 (0 r ij 1)) using the following equation: r ij = m x ik x jk k = (3) m m 2 x 2 ik x jk k = 1 k = 1

9 276 ERCANOGLU ET AL. Fig. 4. Fire susceptibility model (FS1) calculated using fuzzy systems with parameter weights determined by expert knowledge. where x ik and x jk are the elements of the pairwise parameters. Close inspection of Equation 3 reveals that this method is related to the dot product for the cosine function. When two vectors are colinear (most similar), their dot product is unity; when two vectors are at right angles to one another (most dissimilar), their dot product is zero. To evaluate the relation strength of each input parameter, normalized data files

10 MODELING WILDLAND FIRE SUSEPTIBILITY 277 Table 1. Parameter Weights Assigned Using Expert Knowledge for Fire Susceptibility Model (FS1) Parameter Weighting (proportion of total model) Aspect 0.05 Slope (rate of spread) 0.17 Slope (suppression difficulty) 0.11 Fuel load (vegetation moisture) 0.11 Fuel load (rate of spread) 0.17 Fuel load (fire intensity) 0.17 Structure density 0.22 Table 2. Pairwise Relation Strength (r ij ) Values of Input Parameters (P) P1 P2 P3 P4 P5 P6 P7 P1 1 P P P P P P Table 3. The Eigenvector of Parameter Weights Calculated Using Data from Table 2 Parameter Weight P P P P P P P (with values ranging between 0 to 1) were calculated in the FULLSA (Ercanoglu and Gokceoglu, 2004) computer software based on Equation 3. Results of this calculation are 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 as parameter weights. The results of this calculation also report a Consistency Ratio

11 278 ERCANOGLU ET AL. Fig. 5. Fire susceptibility model (FS2) calculated using fuzzy systems with parameter weights derived using fuzzy logic. (CR) for the matrix indicating the uncertainty of the ratings. Values 0.10 indicate good consistency, whereas values >0.10 indicate that the matrix of weightings should be re-evaluated, and a consistency ratio re-calculated (Eastman, 2003). The CR for the matrix given in Table 1 was 0.02, representing very good consistency.

12 MODELING WILDLAND FIRE SUSEPTIBILITY 279 Fig. 6. Difference between fire susceptibility models (FS1 and FS2) for Bear Lake County, Idaho. Finally, the calculated weightings were assigned to the parameters and the second fire 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)

13 280 ERCANOGLU ET AL. 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) Total 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 where each model predicted high susceptibility (>0.8). These areas were compared to the results from an independent assessment of fire regime condition performed by the U.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/fire return interval (Mr. Kevin Conran, pers. comm., 2004). Five fire regimes conditions were used based on the vegetation community s historic fire return interval and historic fire severity (i.e., stand-replacing or not). Typically, higher FRC values indicated higher wildfire susceptibility due to a lack of recent fires and essentially, fuelload stockpiling. However, a high FRC can also indicated a system where too many fires have occurred recently due to a change in the vegetation community toward a more fire-induced system typified by non-native annual grasses like cheatgrass (Bromus tectorum). The sagebrush steppe found within the Snake River Plain of Idaho is a good example of a vegetation community in which a dramatically increased fire return interval exists compared with historic fire return intervals due to a continuous bed of cheatgrass (Ms. Sara Heide, pers. comm., 2004). It should be noted that fire-induced systems with high FRC values are also considered high-susceptibility areas, 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, respectively. Upon close inspection, one may notice a contrast between the models where FS1 predicted high fire susceptibility in the valley and where FS2 predicted high fire susceptibility in the mountains. To illustrate this graphically, a map showing the difference between FS1 and FS2 is provided in Figure 6. The results of comparative validation indicate that FS1 more closely captured wildfire susceptibility in Bear Lake County, Idaho (Table 4). This is interesting because it lends merit to the use of expert knowledge in geo-spatial processing and modeling. In addition, this result places increased significance upon rangeland fires where lower total biomass/fuel load exist compared with forested ecosystems. However, fires in rangeland ecosystems are typically larger in area and exhibit a longer fire season (approximately 90

14 MODELING WILDLAND FIRE SUSEPTIBILITY 281 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 rangeland areas in southeastern Idaho totaling 479,363 ha ( x = ha). During the same time period, there were 1,552 fires in forested areas within southeastern Idaho totaling 211,488 ha ( x = 136 ha). ACKNOWLEDGMENTS This research was supported by the USDI, Bureau of Land Management. The authors would like to acknowledge the support and information provided by Mr. Fred Judd, Mr. Kevin Conran, and Ms. Sara Heide of the BLM. REFERENCES Barnwell, C., Rodman, S., and J. Koltun, 2005, Urban Wildfire Exposure Modeling in the Municipality of Anchorage, Alaska. ESRI Users Conference, 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 Remote Sensing, GIS, and Fuzzy Set Theory for Identifying Susceptibility Areas of Forest Insect Infestations, International Journal of Remote Sensing, 26(21): Cohen, J., 1991, A Site-Specific Approach For Assessing The Fire Risk To Structures At The Wildland/Urban Interface. Proceedings of the Fire and the Environment, Symposium, Ogden, UT: U.S. Department of Agriculture, Forest Service, Rocky Mountain 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 Landslide Susceptibility Map of a Landslide Prone Area (West Black Sea Region, Turkey), Engineering Geology, 75: Gouma, V. and A.Chronopoulous-Sereli, 1998, Wildland Fire Danger Zoning, International Journal of Wildland Fire, 8(1): 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 Susceptibility to Fire in Northern Wisconsin, USA, Landscape Ecology, 19(3): Juang, C. H., Lee, D. H., and C. Sheu, 1992, Mapping Slope Failure Potential Using Fuzzy Sets, Journal of the Geotechnical Engineering Division, ASCE, 118: McNeill, D. and P. Freiberger, 1993, Fuzzy Logic, New York, NY: Simon and Schuster, 319 p. Langille, J. M., Neves, R., Weber, K. T., and M. Ercanoglu, 2005, Joint Fire Modeling Project for Bear Lake County Idaho, 34 p. [ Research/techpg/blm_fire/bearlake/bearlake_wui_report.pdf], accessed June 1, 2006.

15 282 ERCANOGLU ET AL. Loboda, T. V. and I. A. Csiszar, 2006, Assessing the Risk of Ignition in a Dynamic Modeling 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 of Rangeland Wildfire in Southeastern Idaho, African Journal of Range and Forage Science, 20(2):127. Zadeh, L. A., 1965, Fuzzy Sets, Information and Control, 8: Zadeh, L. A , 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.