Potential hazard analysis and risk assessment of debris flow by fuzzy modeling

Transcription

1 Nat Hazards (2012) 64: DOI /s z ORIGINAL PAPER Potential hazard analysis and risk assessment of debris flow by fuzzy modeling Jeng-Wen Lin Cheng-Wu Chen Cheng-Yi Peng Received: 7 January 2012 / Accepted: 24 May 2012 / Published online: 17 June 2012 Ó Springer Science+Business Media B.V Abstract Taiwan is a mountainous country, so there is an ever present danger of landslide disasters during the rainy seasons or typhoons. This study aims to develop a fuzzyrule-based risk assessment model for debris flows and to verify the accuracy of risk assessment so as to help related organizations reduce losses caused by debris flows. The database is comprised of information from actual cases of debris flows that occurred in the Hualien area of Taiwan from 2007 to The established models can assess the likelihood of the occurrence of debris flows using computed indicators, verify modeling errors, and make comparisons between the existing models for practical applications. In the establishment of a fuzzy-based debris flow risk assessment model, possible for accounting it on the basis of far less information regarding a real system and the information can be of an uncertain, fuzzy or inexact character, the influential factors affecting debris flows include the average terrain slope, catchment area, effective catchment area, accumulated rainfall, rainfall intensity, and geological conditions. The results prove that the risk assessment model systems are quite suitable for debris flow risk assessment, with a resultant ratio of success 96 % and a normalized relative error 4.63 %. Keywords Uncertainty Debris flow Fuzzy rule Influential factors Risk assessment model J.-W. Lin C.-Y. Peng Department of Civil Engineering, Feng Chia University, Taichung 407, Taiwan, ROC C.-W. Chen (&) Institute of Maritime Information and Technology, National Kaohsiung Marine University, Kaohsiung, Taiwan, ROC chengwu@mail.nkmu.edu.tw C.-W. Chen Global Earth Observation and Data Analysis Center (GEODAC), National Cheng Kung University, No 1, Ta-Hsueh Road, Tainan 701, Taiwan, ROC

2 274 Nat Hazards (2012) 64: Introduction In recent years, various fuzzy-rule-based models have been proposed to solve many kinds of practical problems in civil engineering. Some researchers have applied the fuzzy theory and adapted it for the development of risk assessment models for natural hazard prevention. Haque and Etkin (2007) addressed that nature-triggered hazards and disasters had traditionally been treated only from geophysical and biophysical processes in the natural domain rather than in a coupled human environment system. They intended to further the idea that the aspects of community and peoples power to mitigate, to improve coping mechanisms, to respond effectively, and recover with vigor against the environmental extremes were of paramount conceptual and policy importance. Lin et al. (2007) examined several factors related to hazard mitigation behavior including: social economic status (education, income), psychological vulnerability (sense of powerlessness and helplessness), risk perception (perceived impact and control), and social trust. Risk perceptions were also addressed in the work of Raaijmakers et al. (2008), who introduced a methodology combining the virtues of three different methods: the quantifiable conventional approach to risk, the taxonomic analysis of perceived risk, and the analytical framework of a spatial multi-criteria analysis. Their risk perception information was collected with the aid of an on-site survey, and the risk perception entered the multi-criteria analysis as complementary weights for the criteria risk and benefit. The geographic information systems (GIS) have also aided the mitigation of natural hazards. Pandey et al. (2010) presented a spatial, GIS-based assessment of flood and waterlogging vulnerability and risk for the northern Bihar plains in India. They derived flood waterlogging risk maps based on the satellite data, flood proneness, and census data. In addition, Yi et al. (2010) provided a GIS-based technique for distributed flood damage assessment from both an engineering and economic perspective, i.e. flood inundation analysis and multi-dimensional flood damage analysis. To perform this assessment, they used a GIS-based framework and data processing method to assess damages. However, sudden debris flows often occur in mountainous areas with steep slopes. Their characteristics include high particle concentration, high flow speed, coming in full fury, strong erosive force, and high destructive power. Earth loosened by recent earthquakes, a problem in Taiwan, becomes the source of debris. Once there is a heavy rain, a debris flow may very likely occur (Lee 2006), causing serious damage to farms, orchards, houses, roads, bridges, and other structures and threatening human lives (Jan 1994). The debris flow is a very common type of natural disasters and since Typhoon Herb struck Taiwan, more attention has been paid to this issue. There are many conditions affecting the occurrence of debris flows, but some are very difficult to investigate. Therefore, many experts and scholars have carried out many research studies related to debris flows. Fuzzy theory might be the most commonly used tool to predict the probability of debris flows. Lu et al. (2007) proposed a GIS-based decision support system, which incorporated local topographic and rainfall effects on debris flow vulnerability. Multiple remotely sensed, fuzzy-based debris flow susceptibility parameters were used to describe the characteristics of the watersheds. Lin et al. (2009) argued that the proposed SVM-based (support vector machines) models offered better performance and were more robust and efficient than the existing BPN-based models. To further improve the long lead-time forecasting, typhoon characteristics were added as key input to the proposed models. Fleissner et al. (2009) also presented a new approach that could aid the design of protective barriers, in which an uncertainty analysis of the flow around a debris barrier was carried out

3 Nat Hazards (2012) 64: using a chute flow laboratory model of the actual debris flow, and the transformation method of fuzzy mathematics was used to investigate the influence of epistemically uncertain models. Liu et al. (2010) selected the upper Min River from Yinxiu to Wenchuan as the study area, who interpreted the unconsolidated deposits and discussed their relationship to distance from the fault. Then, applying that information and the values of other factors relating to debris flow occurrence, the locations of potential debris flows were analyzed by multi-factor comprehensive identification and rapid identification, whose multi-factor identification method employed fuzzy matter-element extension theory. Although there have been many successful designs developed for the forecasting of debris flows, simple, straightforward, and easy to use approaches have seldom proposed. In other words, the topic of model construction of debris flows is still an open-ended area and further studies are needed. For example, Chang et al. (2010) proposed using a genetic algorithm to weigh seven important variables based on principles similar to natural selection, whose work simultaneously input these variables into a neural network model to predict debris flow occurrence based on relevant factors, and information from 154 potential cases of debris flow collected from eastern Taiwan was fed into the model for testing. Information about numerous debris flows triggered by typhoons was used as the control data. Shieh (1993) used the slope of the riverbed and catchment area in their set-up criteria, in order to survey and identify the streams and rivers in Hualien and Taitung where there was a risk of debris flow. The thresholds of debris flow risk were defined by the amount of rainfall as an early warning criterion, so that threshold rainfall lines differentiating two levels were determined as indication of the warning criterion and the evacuation criterion. Lin and Jan (1995) utilized the catchment area, average riverbed slope, slope of the valley side, shape coefficient of the catchment area, direction of slope, and geology as factors to determine the debris flow risk. All the factors were input in a GIS framework and analyzed. The concept of risk factors was adopted so that factors of different units and measurements could be calculated together to assess the risk. The results showed that there was a significant relationship between the characteristics of the regions around the streams and rivers and the debris flow risk. Other studies regarding the model construction of debris flows can be found in the work of Jan and Chen (1999), who discussed the relationships between hydrological and physiographic features and occurrence of debris flows. The hydrological feature was represented by the high water mark of past flow deposits on the mountainside, while the physiographical features included the thickness of the soil layer, slope of the soil layer, specific gravity of the soil layer, volume concentration of soil in the soil layer, soil cohesion, and soil friction angle. Sheu (2003) utilized the spatial analysis ability provided by the GIS applied to neural network training simulation analysis. The research area was Nantou County, Taiwan. Data related to the catchment area, effective catchment area, average slope inside the catchment area, shape coefficient, average slope of the riverbed, and collapse area inside catchment area were obtained from the physiographical factor database of the GIS. Fuh et al. (2005) adopted the multi-stage fuzzy synthetic decision method with 12 factors and used an earthquake weighting coefficient to measure the effect of earthquakes to the estimation of the risk grade in Taiwan. The debris flow information was applied to Toun-Me village and the Chen-Yeou-Lan watershed prior to the earthquake and to the Jun-Keng ravine and Fongshan after the earthquake as examples for the purpose of comparison. Based on the arguments above, this study extends the fuzzy theory and adapts it for the development of a debris flow hazard assessment model. First, the hazard of debris flows in

4 276 Nat Hazards (2012) 64: the Hualien County of Taiwan and the influential factors of debris flows in this area are introduced (Lin 2011; Lin et al. 2012). Second, the fuzzy-rule-based risk assessment model is developed to account for the possibility of far less information concerning a real system, and in addition, the information can be of an uncertain, fuzzy or inexact character, as well as to verify the accuracy of the debris flow risk assessment. Finally, the efficiency of the developed fuzzy model is analyzed and discussed on the output values of the 25 sites studied, where the ratio of success and normalized relative error are calculated to verify the model. 2 Influential factors of debris flows in Hualien County The types of terrain in Hualien County include mountains, rivers, and plains. However, plains and rivers cover only 13 % of the total area while the remaining 87 % is covered by mountains. The mountains include the Central Mountains on the west side and the Coastal Mountains on the east. This study is based on data provided from 25 observation stations. Other geological conditions are combined with these data as influential factors for analyses. The data from real cases provided by the Soil and Water Conservation Bureau, Council of Agriculture, Executive Yuan are used for validation (Lin 2011; Lin et al. 2012). On the basis of related studies (Yu and Chen 1991; Shieh et al. 1992; Lin and Jan 1995; Chang 1995), the major influential factors for debris flows include: 1. Slope of the riverbed: Debris flows mostly occur when the slope of the riverbed is between 15 and 30 degrees. The slope of the riverbed can be calculated as follows: S ¼ sin 1 ½ðupstream elevation downstream elevationþ= length of river valleyš ð1þ 2. Rainfall: Analysis of the relationship between debris flow occurrences in the Hualien area and rainfall shows that debris flows often occur when the amount of rainfall exceeds 27 mm/h and accumulated rainfall exceeds 360 mm. 3. Catchment area: Shieh et al. (1992) proposed that, in Hualien County, debris flows often occur in areas with slopes over 10 degrees and catchment areas over 5 ha. Therefore, the minimum effective catchment area for debris flow occurrence is set to 5 ha. The influential factors above are used in this study to build a fuzzy-rule-based model. 3 Fuzzy-rule-based decision systems With the advancement of fuzzy logic, some mathematical models have been developed based on fuzzy theories and addressed to achieve greater accuracy, dimensionality and also to simplify the structure of the model. Compared to conventional mathematical models, the main advantage of the fuzzy models is the possibility of elaborating them on the basis of far less information concerning real systems, and in addition, the information can be of uncertain, fuzzy or inexact characters. These fuzzy models include Mamdani (1977), relational, T-S types etc. This study aims to build a fuzzy inference system based on real case data, where each case is deconstructed into fuzzy rules, and all the rules are collected to create a knowledge base for the system (Chen 2006). The tasks required to be completed include choosing parameters, fuzzification of parameters, and building a decision system (Fig. 1). Six

5 Nat Hazards (2012) 64: Defining the ranges of parameters Defining the membership functions corresponding to the variables Constructing the fuzzy rule base Defuzzification to obtain values for evaluation Fig. 1 The process of constructing a fuzzy-rule-based decision system variables including the average terrain slope, catchment area, effective catchment area, accumulated rainfall, rainfall intensity, and geological conditions are used as system inputs. Membership functions of these parameters are defined first. Then, these membership functions are used to fuzzify the input values. Output values are obtained after defuzzification is performed by applying Mamdani s fuzzy inference method (1977). The output values are used to determine the result of categorization. By referencing the work of Chang (1995) and Chen (2006), this study adopts the 6 variables according to the parameter information in Table 1. Debris flows often occur in terrains with slopes of degrees. Terrains with slopes of over 22 degrees often directly collapse due to unstable earth. Therefore, before the occurrence of debris flows, they often collapse to form gentler slopes (Jan 2000). Thus, the gradient criterion for a middle risk of debris flows is set to 22 degrees, meaning that larger values of parameters (e.g. average gradient) do not necessarily indicate higher risk. A value of w i is given to each of the other factors in ascending order. All the values of w i are then added up to determine the resultant output by the system. This study selects the 6 influential factors, and, because there are interactions between them, the fuzzy system rules are built using and. Considering the completeness of the system rules, we assign degrees of belonging to the categories (w) for each parameter. The values of w for the variables are listed in Table 1. There are 3 w values for each parameter, and there are 6 parameters. Hence, there are a total of 729 (3 6 ) rules with all the combinations. The rules are constructed using the Matlab Fuzzy Toolbox as shown in Fig. 2, where the rules include low-risk, middle-risk, and high-risk rules. The fuzzy rules constructed for this study are shown in Table 2. The w values of each input variables are added up to obtain the output w value. By referencing Table 2, the risk category of debris flows can be inferred. 4 Analysis and discussion The factor values of the 25 sites are input into the fuzzy-rule-based decision system above to obtain the output values listed in Table 3. The output values close to 1 (or30.5) mean a higher chance of the occurrence of debris flows, while values close to 0 mean the opposite. In addition, related documentation is collected to obtain the number of actual occurrences

6 278 Nat Hazards (2012) 64: Table 1 Parameter settings for fuzzy variables (Chen 2006) Variable w i w = 0 w = 1 w = 2 Average gradient () w Catchment area (ha) w Effective catchment area (ha) w Accumulated rainfall (mm) w Rainfall intensity (mm/h) w Geological conditions w Fig. 2 User interface of the fuzzy rule editor Table 2 Fuzzy system rules Sum of w i Low risk Middle risk High risk P 6 i¼1 w i (including warnings) of debris flows at these 25 sites for the purpose of error evaluation (Table 4). Considering that there have never been any debris flows in some places over the years, the normalized relative errors are used to measure the differences between the output values and actual values.

7 Nat Hazards (2012) 64: Table 3 Output values of the fuzzy-rule-based decision system for debris flow assessment for the Hualien area Spot Output values Assessment result Bazi stream No occurrence (success) Chongde village Occurrence (success) Chutian No occurrence (success) Dafong village Occurrence (success) Dafu village Occurrence (success) Daquan village Occurrence (success) Dashing village Occurrence (success) Fahua mountains No occurrence (success) Fonglin stream Occurrence (success) Fushi village Occurrence (success) Fuxing stream No occurrence (success) Hepin village Occurrence (success) Hongye stream No occurrence (success) Jiamin villiage Occurrence (success) Jingmei village Occurrence (success) Qingshui stream No occurrence (success) Rongshu tribe No occurrence (success) Shapodang stream Occurrence (success) Shofeng stream No occurrence (success) Shuiyuan village Occurrence (success) Tongmen Occurrence (success) Tongshing tribe No occurrence (success) Wanrong village Occurrence (success) Xiulin village Occurrence (success) Xumeiji stream No occurrence (failure) Ratio of success 96 % The fuzzy system output values (Table 3) and the number of actual occurrences (including warnings) of debris flows for the Hualien area (Table 4) are taken into account so as to calculate theoretical output value ratios and actual value ratios by dividing an output/actual value by the value from the nearby site. If the numerators of the output value ratios are close to the ones of the actual value ratios and the same is true for the denominators, the adaptation of the normalized relative error (Lin 2011; Lin et al. 2012) becomes meaningful, and the required relative errors can be further obtained. The formulas used to calculate these values are listed below: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n E ¼ ½ða 1 b 1 Þ 2 þða 2 b 2 Þ 2 þþða n b n Þ 2 Š qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2þ 1 n ða2 1 þ a2 2 þþa2 n Þ where n is the number of terms; a denotes the actual value ratio while b denotes the output value ratio. Both ratios are dimensionless, satisfying the unit consistency. Equation (2) can be used to obtain the relative error of 4.63 %. This means that when the numerators and denominators of the fuzzy system output values and actual values are very close, the relative error of the ratio is 4.63 %.

8 280 Nat Hazards (2012) 64: Table 4 Statistics showing the number of actual occurrences (including warnings) of debris flows for the Hualien area (Lin et al. 2012) Site Bazi stream 0 Chongde village 3 Chutian 0 Dafong village 1 Dafu village 1 Daquan village 1 Dashing village 5 Fahua mountains 0 Fonglin stream 4 Fushi village 3 Fuxing stream 0 Hepin village 3 Hongye stream 0 Jiamin villiage 2 Jingmei village 2 Qingshui stream 0 Rongshu tribe 0 Shapodang stream 2 Shofeng stream 0 Shuiyuan village 2 Tongmen 2 Tongshing tribe 0 Wanrong village 4 Xiulin village 2 Xumeiji stream 2 Number of actual occurrences (including warnings) 5 Results and conclusions Taiwan is located on the west side of the Pacific Rim. This precipitous, long narrow shape of the island has been created due to plate movement. The large 921 Chi Chi Earthquake shattered stones in the mountains into smaller pieces and loosened and softened the earth. Since then, debris flows have often occurred after heavy rains, leading to serious damage. In recent years, several typhoons have struck Taiwan bringing high rainfall accumulations. These are all key factors affecting the occurrence of debris flows. Currently, there are over 1,500 rivers and streams in Taiwan considered having the potential for debris flows. It is obvious that the risk of debris flows in Taiwan has become more and more significant. This study has developed a fuzzy-rule-based risk assessment model of debris flows to verify the accuracy of the risk assessment in order to help related organizations reduce losses caused by debris flows. Actual cases of debris flows that occurred in the Hualien area of Taiwan from 2007 to 2008 were utilized as the database, and the 6 influential factors, including the average gradient, catchment area, effective catchment area, accumulated rainfall, rainfall intensity, and geologic condition, were selected as variables. A fuzzy-rule-based decision system was adopted to determine the risk of debris flows and to verify the real case

9 Nat Hazards (2012) 64: estimations made by the Soil and Water Conservation Bureau, Council of Agriculture, Executive Yuan, and by the debris flow disaster prevention information website for the Hualien area. The efficiency of the developed fuzzy model for debris flow assessment was verified for the 25 sites studied, showing a resultant ratio of success 96 % and a normalized relative error 4.63 %. Acknowledgments The authors would like to thank the National Science Council of the Republic of China, Taiwan, for their financial support of this research under Contract Nos. NSC E , E MY2 and E MY2. References Chang CP (1995) The study of debris hazard rivers using the GIS approach. Master thesis, National Cheng Kung University, Taiwan (in Chinese) Chang TC, Wang ZY, Chien YH (2010) Hazard assessment model for debris flow prediction. Environ Earth Sci 60(8): Chen KH (2006) The study of using fuzzy theory to the prediction system of debris flow. Master thesis, Feng Chia University, Taiwan (in Chinese) Fleissner F, Haag T, Hanss M, Eberhard P (2009) Uncertainty analysis for a particle model of granular chute flow. Comput Model Eng Sci 52(2): Fuh YS, Chao C, Shyu YJ (2005) Application of fuzzy theory to the analysis of the risky grade of debris flow. J Chin Soil Water Conserv 36(2): Haque CE, Etkin D (2007) People and community as constituent parts of hazards: the significance of societal dimensions in hazards analysis. Nat Hazards 41(2): Jan CD (1994) Assessment and prediction of debris flow hazards. J Chin Soil Water Conserv 25(2): Jan CD (2000) Introduction to Debris Flow. Techbook Co. Ltd Jan CD, Chen JC (1999) Probabilistic analysis of debris-flow occurrence application to Tounmen and Tungshing villages. J Chin Soil Water Conserv 30(1):65 75 Lee CH (2006) Household debris-flow disaster damage assessment in Taiwan. Master thesis, National Taipei University, Taiwan (in Chinese) Lin JW (2011) Neural network model and geographic grouping for risk assessment of debris flow. Int J Phys Sci 6(6): Lin ML, Jan SS (1995) A preliminary research of application of geographic information system in determining risk of debris flow. J Chin Inst Civil Hydraul Eng 7(4): Lin SY, Shaw DG, Ho MC (2007) Why are flood and landslide victims less willing to take mitigation measures than the public? Nat Hazards 44(2): Lin GF, Chen GR, Wu MC, Chou YC (2009) Effective forecasting of hourly typhoon rainfall using support vector machines. Water Resour Res 45:W08440 Lin JW, Chen CW, Peng CY (2012) Kalman filter decision systems for debris flow hazard assessment. Nat Hazards 60(3): Liu JF, You Y, Chen XC, Fan JR (2010) Identification of potential sites of debris flows in the upper Min river drainage, following environmental changes caused by the Wenchuan earthquake. J Mt Sci 7(3): Lu GY, Chiu LS, Wong DW (2007) Vulnerability assessment of rainfall-induced debris flows in Taiwan. Nat Hazards 43(2): Mamdani EH (1977) Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Trans Comput C-26(12): Pandey AC, Singh SK, Nathawat MS (2010) Waterlogging and flood hazards vulnerability and risk assessment in Indo Gangetic plain. Nat Hazards 55(2): Raaijmakers R, Krywkow J, van der Veen A (2008) Flood risk perceptions and spatial multi-criteria analysis: an exploratory research for hazard mitigation. Nat Hazards 46(3): Sheu RW (2003) Assessment of debris-flow potential using geographical information system and artificial neural network. Master thesis, National Chiao Tung University (in Chinese) Shieh CL (1993) A study of the debris flow warning system (2). Hydraulic Laboratory of National Cheng Kung University, Research report 139:1 183 Shieh CL, Jiang JH, Chen LJ (1992) Field investigation of debris flow in Hualien and Taitung counties. J Chin Soil Water Conserv 23(2):

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