GIS-models with fuzzy logic for Susceptibility Maps of debris flow using multiple types of parameters: A Case Study 1 in

19 Debris flow is one of the main causes of life loss and infrastructure damage in mountainous areas. This hazard 20 should be recognized in the early stage of land development planning. According to field investigation and expert 21 experience, a scientific and effective quantitative susceptibility assessment model was established in Pinggu District 22 of Beijing. This model is based on Geographic Information System (GIS), combining with grey relational, data-23 driven and fuzzy logic methods. The influence factors, which are divided into two categories and consistent with the 24 system characteristics of debris flow gully, are selected, also a new important factor is proposed. The results of the 25 17 models are verified using data published by the authority, and validated by two other indexes as well as Area 26 Under Curve (AUC). Through the comparison and analysis of the results, we believe that the streamlining of factors 27 and scientific classification should attract attention from other researchers to optimize a model. We also propose a 28 good perspective to make better use of the watershed feature parameters. These parameters fit well


Introduction 36
Debris flows are processes of rapid transport of water and soil materials in mountain watersheds, with sudden 37 and destructive outbreaks (Di et al., 2019). Some debris flows can often cause devastating disasters and huge 38 losses (Zhang et al., 2021) and seriously threaten the lives and properties of people in the mountains, the safety of 39 major projects, and restrict social and economic development (Iverson, 1997 to catastrophic rock avalanches frequently mobilize to form debris flows, threatening the ecological environment of 42 the mountainous area (Zhong et al., 2004). Especially, in recent years, due to the superposition of extreme rainstorm 43 weather and human engineering activities, debris flow events have increased gradually (Li et al., 2021b). As the capital 44 of China, Beijing also has strong influence and radiation at home and abroad, where geological disasters are widely 45 concerned (Xie et al., 2004;Li et al., 2020b). With the deepening understanding of debris flow disaster and the 46 updating of database, a new and more accurate evaluation is also very necessary. Therefore, it is of great significance 47 to establish accurate and scientific debris flow susceptibility map. 48 Through previous studies, it can be summarized that the current research on debris flow mainly focuses on the 49 following aspects: study on mechanism of debris flow, study on early warning and prediction of debris flow, study 50 on numerical simulation of debris flow and study on debris flow hazard analysis. Especially, studies on debris flow 51 hazard analysis have raised the attention of the researchers as soon as it appears (Dong et al., 2009). Communicating 52 information about debris flow hazard analysis is a crucial component of preparedness and hazard mitigation (Chiou 53 et al., 2015). Susceptibility assessment, an important part of a hazard assessment of geological processes, is more 54 flexible (Li et al., 2021a). In the early days, the susceptibility assessment of debris flows was mainly qualitative 55 research using geomorphological information (Guzzetti et al., 1999). In 1976, the United Nations commissioned the 56 International Union of Engineering Geology to conduct a risk assessment of debris flows, which marked the 57 beginning of research on the susceptibility assessment of debris flows as an important research direction for disaster 58 prevention and prediction (Li et al., 2020b). Many methods and techniques have been proposed to evaluate debris 59 Fig. 4 Debris flow basin division and inventory. 137 Note: The data of debris flow points comes from Beijing Municipal Commission of Planning and Natural Resources 138 websites (http://ghzrzyw.beijing.gov.cn/zhengwuxinxi/zxzt/dzzhfzzt/zzzhdcpg/202008/t20200807_1976436.html) 139

Debris flow controlling and triggering factors 140
The basic requirement for the assessment of debris flows is that some factors included are easily obtainable, 141 meaningful for susceptibility assessment, and can be used for evaluating the need for passive or active debris flow 142 mitigation. According to previous studies, 19 factors are selected in this study. the factors are divided into two types 143 (Table 1) because of their different characteristics. Watershed characteristic factors (Type A) can be directly 144 quantified, once the basin is determined (Fig. 5). The influence of these parameters is bounded by the watershed; 145 Geology and geomorphology factors (Type B) need to be further processed, even if the watershed is determined. The 146 scope of these parameters is independent of the watershed boundary. 147

Fuzzy logic in susceptibility modelling 157
Fuzzy set theory is proposed by Zadeh (1965). It is an efficient way of expressing the concept of partial set 158 membership degree. This concept differs from classical binary (0-1 value) logic. More words with a transitional fuzzy 159 descriptions (such as low, medium, and high) are used (Kritikos and Davies, 2015). This fuzzy expression is 160 particularly applicable to geological hazard classification. In the theory of fuzzy sets, elements have different degrees 161 of membership in the interval [0,1]. 1 represents complete membership, and 0 represents non membership. Ross 162 (1995) showed that fuzzy systems are useful in two general situations (Kritikos and Davies, 2015). The method is 163 very consistent with the characteristics of debris flow system, whose predisposing factors are fuzzy in nature and 164 mechanism is complex and not fully understood. Application of fuzzy logic method, the critical step is to find the 165 suitable fuzzy membership of factors. And fuzzy membership degree is equivalent to the weight in expert scoring 166 method, which is calculated by objective method rather than given subjectively. 167

3.4.1Grey Relational Analysis (GRA) in susceptibility modeling 169
GRA is proposed by Deng (1982) and it is an important part of grey system theory (Wang et al., 2014). 170 Comparing with mathematical statistics methods which need lots of sample data, typical probability distribution and 171 large calculation, GRA is applicable to small sample size with the data whether regular or not. There will be no 172 inconsistency between qualitative analysis and quantitative analysis (Deng, 1988). Besides it is to excogitate the 173 leading and potential factors that affect the development of the system, and quantitatively describe the development 174 and change trend of the system by studying whether the relative change trend of the grey factor variables with 175 complex relationship is consistent in the process of system development and evolution (Liu et al., 2004). Thus, grey 176 correlation analysis is introduced to quantify the correlation between each factor and the evaluation results according 177 to field investigation expert experience. First, the procedure of GRA is to translate the performance of every susceptibility are obtained, which are used as the reference sequence of grey relation method (Table 2). Second, the 182 grey correlation coefficient of all A factors is calculated by Eq. (1). Finally, the average grey relational coefficient 183 (the correlation degree) is calculated by Eq. (2) as the fuzzy memberships (Table 3). 184 Where ξi(k) is the grey relational coefficient, i=1, 2, …, n are the number i type A factors, k=1, 2, …, n are the 186 number of basins, x0(k) is the reference sequence (ideal target sequence), xi(k) is the number i type A factor sequence 187 (2) 188 Where ri is the correlation degree in the range (0,1). N is the total number of basins in Table 2 189

DFSI map 232
To derive the debris flow susceptibility index (DFSI) map by overlaying the factor thematic layers using fuzzy 233 logic method, the "fuzzified" factors represented by information layers in raster format with values ranging from 0 234 to 1 need to be combined. Compared with other four fuzzy operators, Fuzzy Gamma (Eq.5) is more suitable for the 235 research (Kritikos and Davies, 2015). To determine the appropriate γ value, the results of different gamma values 236 were compared by the greatest distance (Kritikos and Davies, 2015) between the average DFSI curves of the debris 237 flows locations and non-debris flows locations (For example, flat pixels) (Fig. 6). Finally, 0.9 is determined for the γ 238 value, because there is the greatest difference between debris flow and non-debris flows locations areas. In order to 239 illustrate the superiority of our model through comparison, 17 results are calculated in ArcGIS. 240 where μ(x) is the combined membership value, μi is the fuzzy membership function for the ith map, i=1,2, …, n 242 are the numbers of thematic layers to be combined, and γ is a parameter in the range (0,1). 243 244 Fig. 6 Effect of γ value on Debris flow susceptibility index (DFSI). Curves d, e and f correspond to debris flow pixels, 245 and curves a, b and c correspond to non-debris flow area where a Debris flow is unlikely. According to curve i, the 246 maximum difference between the average DFSI values is observed for γ≈0.9 247 248 To find the optimal model, 17 results were compared (Table 5)  Through the modelling process, relatively satisfactory results are obtained in this paper. The predictive 289 performance of the output debris flow susceptibility maps, obtained from 17 different models, is verified by 290 comparing with maps published by authority. By comparing the results, the following results are discussed: 291 Firstly, comparing R1, R2, R3, R4 and R5, it can be concluded that the model based on field investigation and 292 expert experience is more effective than data-driven directly, when the information is insufficient. This is mainly 293 because when the basin area reaches a certain size, it is no longer controlled by one or several factors, but becomes 294 a complex system. It is not only the factors that affect the system, but also the system will react on each factor. 295 Geomorphic evolution is basically the result of interaction of the endogenic and exogenic geological processes. A 296 geological period can be regarded as the beginning of an endogenic geological processes to the next one. In the early 297 stage of geological period, endogenic geological processes play a major role, and in the later relatively stable period, 298 exogenic geological processes will take on more important parts. In this large cycle, the basin continuously occurs a 299 small cycle of energy accumulating and releasing, which leads to extremely complex system changes. In addition, 300 there is a contradiction between the scale of geological evolution and the scale of engineering activities. So limited 301 information can be obtained under these conditions that leads to the unreliability of data-driven evaluation. Therefore, 302 in the current period, field investigation and expert experience are fundamental. 303 Secondly, by comparing R4 and R5, R6 and R9, R7 and R10, R8 and R11, R12 and R15, R13 and R16, R14 and R17, it 304 can be concluded that the accuracy and resolution of the model can be improved by simplifying the factors, which 305 will eliminate the ones with weak correlation and independence. In practical application, even if the susceptibility 306 map is obtained, the classification of the susceptibility degree is still a very difficult problem. Because everyone's 307 subjective definition of "susceptibility degree" is different. By simplifying the factors, the main ones can be selected, 308 which magnifies the differences between basins, so the boundaries between different susceptibility degrees are more 309 obvious. 310 Thirdly, by comparing R6 and R12, R7 and R13, R8 and R14, R9 and R15, R10 and R16, R11 and R17, it can be 311 concluded that the model in which factors are classified into two types is better than the one in which all factors as a 312 single thematic layer without classification. Because the factors categorized separately are more closely linked and 313 has consistent influence on the system in mechanism. We can also infer that the non-linear combination characteristics 314 between different types are stronger and scientific classification can improve the performance of the model. 315 Fourthly, comparing R12 and R13, R15 and R16, it can be concluded that the frequency ratio method is better than 316 the cosine amplitude method in the study. Different from the study of (Kritikos and Davies, 2015), the watershed unit 317 rather than the grid unit is used, which indicates that the former has a wide range of application, while the latter has 318 a disadvantage of strict conditions. 319 Based on the results of the above four analyses, the most optimal model should have the features of being based 320 on expert experience, using selected factors, classifying factors before using them, and using frequency ratio method. 321 Then the model R16 is selected according to the features, which is well in accordance with theoretical method 322 performance score, and gets fine mutual verification. 323 There is also much to discuss, the selection of factors is still a very complex dilemma. Although 19 factors 324 selected cannot fully evaluate the character of a basin, it is necessary to consider that they are easily and relatively 325 accurately obtainable for each basin. This will facilitate a wide range of applications. Besides, rainfall and total 326 amount of loose material source are also very important influencing factors. But according to the Beijing hydrological 327 manual, the rainfall change in the study area is not obvious, so it is excluded in model. And the total amount of loose 328 material source cannot be obtained for the watershed without on-site investigation, so calculations are impossible. In 329 fact, we indirectly consider the influence of natural loose material source by evaluating geological conditions, but 330 cannot consider the impact of human activities. As for the factors describing debris flow magnitude, usually, several 331 channels have the recorded data. 332 The scientific and systematic principle of model building is another challenge. To correctly classify the factors, 333 it is necessary to grasp the characteristics of the formation, movement and accumulation of debris flow. Therefore, 334 the classification should comprehensively consider the development background (geology, geomorphology, climate, 335 hydrology, soil, vegetation, human activities and other factors). The practical principle refers to that the study should 336 not only fully obtain scientific and accurate results, but also make the professional results understood by decision 337 makers. Although the susceptibility grade and susceptibility value of each watershed is obtained, the results are 338 relatively effective in this study area. In addition, with the development of technology and theory, we should replace 339 some traditional factors which are not easy to quantify with more precise quantitative factors to improve the efficiency 340 and accuracy of evaluation, such as surface roughness instead of drainage density. 341 For the results derived from Table 3, we would like to further discuss. It can be seen from the results that the 342 occurrence of debris flow is highly correlated with basin volume, basin area and main gully bending coefficient with 343 fuzzy membership above 0.7 in Beijing area. Rainfall in the study area is abundant to induce the debris flow. Loose 344 source and sinks the total volume of catchment become more important. The watershed area determines the total 345 volume of catchment. For the same rainfall, generally, the larger the area, the larger the catchment. The bending 346 coefficient reflects the replenishment sources along the channel. The greater the coefficient, the slower the flow. Then 347 loose source along the channel has more time to replenish. Basin volume characterizes the maximum amount of loose 348 material that can be supplied. These three features reflect the development characteristics of debris flow in the study 349 area. It also provides ideas for disaster prevention and mitigation. 350 Finally, we should consider decision making under uncertainty, because the debris flow phenomenon is 351 extremely complex. The classification of geologists (high, moderate and low) is ambiguous for decision makers. It is 352 more beneficial for them to use mathematically rigorous definitions. Considering that geological conditions tend to 353 vary greatly from region to region, it is not appropriate to define a fixed limit. the Jenks method (chosen in this paper) 354 can be used to classify sensitivity maps according to the characteristics of the data itself. We can also further process 355 the data according to the needs of decision makers, such as identifying 10% of the watersheds in the entire region as 356 high risk. However, the applicability of the model to extreme rainfall and seismic conditions is not considered. 357

Conclusion 358
In this study, a new combination model for debris-flow susceptibility based on GIS was developed in Pinggu. 359 The objective and motivation of this study is to demonstrate a simple, extensible, and convenient analytical model 360 for the debris flow prediction. Three methods are selected in the model with their own advantages. GRA has great 361 advantages in the case of less samples, data-driven method is mainly used to reduce subjectivity and fuzzy logic is 362 fitted to solve nonlinear problems with fuzzy classification. The output optimal debris flow susceptibility maps 363 demonstrated satisfactory performance with the relative higher susceptibility values corresponding to AUC=0.768. 364 The predictive performance of the susceptibility maps and the spatial correlation of debris flow gully with H and 365 VH susceptibility with recorded debris flows illustrate that the assessment at regional scale using the proposed 366 method is feasible. Compared with the previous results(Li et al., 2020b) based on grid units, the evaluation results 367 are basically the same, but the model are more targeted for debris flow disasters for decision makers. Besides, 368 considering that the meaning of the used factors is clear and the data is easy to obtain, these conditions mentioned 369 enable the model to be widely applied. In addition, a new factor (Basin) is proposed in our study, which contributes 370 higher weight up to 0.79. From our 17 results by comparing the control variables, we suggest that other scholars 371 should pay more attention to the classification and streamlining of factors, which has indicated the potential value 372 to improve model accuracy. It was also found that the watershed characteristic parameters can better reflect the 373 advantages of watershed unit, but further development is needed. 374 In short, an effort has been made to develop a cost-and time-efficient debris flow susceptibility assessment 375 model. The model has an acceptable degree of accuracy for regional-scale planning and contributes to make 376 susceptibility and risk maps more accessible to individuals and local authorities. The GIS-based methods and modern 377 data availability especially through online databases are significantly beneficial to this aim. However, a challenge 378 remains in producing results with practical accuracy for the scale of planning, using available resources. Previous 379 studies highlight that the effectiveness of the final map depends on the quality of input data. Updating and improving 380 existing debris flow catalogues and inventories are crucial for the development of reliable susceptibility and risk 381 assessment methods. 382