Exploring the impact of introducing a physical model into statistical methods on the evaluation of regional scale debris flow susceptibility

Abstract

Regional scale debris flow susceptibility is widely evaluated by statistical methods. However, the initiation mechanism of debris flow is not considered, which leads to the neglect of the microtopographic characteristics. To address this problem, we established three novel combined models by introducing the physical model into statistical methods. The integrating models consists of two parts, the statistical models and the TRIGRS model. The eventual results obtained with the integrating model consider both the prediction result of the statistical method for debris flow susceptibility and the mechanism of debris flow initiation. To test the feasibility of the integrating model, three representative statistical models, the analytic hierarchy process (AHP), Shannon entropy (Entropy) and support vector machine (SVM) were selected to evaluate debris flow susceptibility in Yongji County of Jilin Province, China. The results demonstrate that the performance of the integrated models is significantly better than that of the single statistical model, especially in the local areas. The integrating models (AHP-TR, Entropy-TR, SVM-TR) can generate higher quality debris flow susceptibility maps (DFSMs) than the single model, which clearly reflect the scope and boundaries of the areas which are most prone to debris flow and identify the flat land and valleys between adjacent high-prone areas. It also reduces the overprediction generated by the physical model. In general, combining the statistical methods with the TRIGRS model can maximize the strengths of these models and avoid their weaknesses and obtain the effect of 1 + 1 > 2.

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References

  1. Ahmed B (2015) Landslide susceptibility mapping using multi-criteria evaluation techniques in Chittagong Metropolitan Area. Bangladesh Landslides 12:1077–1095. https://doi.org/10.1007/s10346-014-0521-x

    Article  Google Scholar 

  2. Alvioli MBR (2016) Serial and parallel versions of the transient rainfall infiltration and grid-based regional slope-stability model (TRIGRS): US geological survey software release. https://doi.org/10.5066/F73J3B27

  3. Ayalew L, Yamagishi H (2005) The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains. Central Japan Geomorphol 65:15–31. https://doi.org/10.1016/j.geomorph.2004.06.010

    Article  Google Scholar 

  4. Ayalew L, Yamagishi H, Marui H, Kanno T (2005) Landslides in Sado Island of Japan: Part II GIS-based susceptibility mapping with comparisons of results from two methods and verifications. Eng Geol 81:432–445. https://doi.org/10.1016/j.enggeo.2005.08.004

    Article  Google Scholar 

  5. Ayalew L, Yamagishi H, Ugawa N (2004) Landslide susceptibility mapping using GIS-based weighted linear combination, the case in Tsugawa area of Agano River. Niigata Prefect Japan Landslides 1:73–81. https://doi.org/10.1007/s10346-003-0006-9

    Article  Google Scholar 

  6. Baum RL, Savage WZ (2010) Estimating the timing and location of shallow rainfall induced landslides using a model for transient, unsaturated infiltration. J Geophys Res Earth Surf. https://doi.org/10.1029/2009JF001321

    Article  Google Scholar 

  7. Baum RL, Savage WZ, Godt JW (2002) Trigr-a fortran program for transient rainfall infiltration and grid-based regional slope-stability analysis. Open-File Report

  8. Baum RL, Savage WZ, Godt JW (2008) TRIGRS—a fortran program for transient rainfall infiltration and grid-based regional slope-stability analysis, version 2.0 Open-File Report

  9. Beven K, Kirkby M (1979) A physically based variable contributing area model of basin hydrology. Hydrol Sci Bull 24(1):43–69. https://doi.org/10.1080/02626667909491834

    Article  Google Scholar 

  10. Blahut J, van Westen CJ, Sterlacchini S (2010) Analysis of landslide inventories for accurate prediction of debris-flow source areas. Geomorphol 119:36–51. https://doi.org/10.1016/j.geomorph.2010.02.017

    Article  Google Scholar 

  11. Brenning A (2005) Spatial prediction models for landslide hazards: review, comparison and evaluation. Nat Hazard Earth Sys Sci 5(6):853–862

    Article  Google Scholar 

  12. Cao J, Zhang Z, Du J, Zhang LL, Song Y, Sun G (2020) Multi-geohazards susceptibility mapping based on machine learning-a case study in Jiuzhaigou. China Nat Hazard 102:851–871. https://doi.org/10.1007/s11069-020-03927-8

    Article  Google Scholar 

  13. Chang KT, Merghadi A, Yunus AP, Pham BT, Dou J (2019) Evaluating scale effects of topographic variables in landslide susceptibility models using GIS-based machine learning techniques. Sci Rep 9:12296. https://doi.org/10.1038/s41598-019-48773-2

    Article  Google Scholar 

  14. Chang Z, Du Z, Zhang F, Huang F, Chen J, Li W, Guo Z (2020) Landslide susceptibility prediction based on remote sensing images and GIS: comparisons of supervised and unsupervised machine learning models. Remote Sens 12(3):502

    Article  Google Scholar 

  15. Chen HX, Zhang LM (2015) EDDA 1.0: integrated simulation of debris flow erosion, deposition and property changes. Geosci Model Develop 8(3):829–844

    Article  Google Scholar 

  16. Chen W, Li W, Chai H, Hou E, Li X, Ding X (2016) GIS-based landslide susceptibility mapping using analytical hierarchy process (AHP) and certainty factor (CF) models for the Baozhong region of Baoji City. China Environ Earth Sci. https://doi.org/10.1007/s12665-015-4795-7

    Article  Google Scholar 

  17. Chen W et al (2015) Application of frequency ratio, statistical index, and index of entropy models and their comparison in landslide susceptibility mapping for the Baozhong Region of Baoji. China Arabian J Geosci 8:1829–1841. https://doi.org/10.1007/s12517-014-1554-0

    Article  Google Scholar 

  18. Chen Y et al (2020a) Spatial predictions of debris flow susceptibility mapping using convolutional neural networks in Jilin Province. China Water 12:2079. https://doi.org/10.3390/w12082079

    Article  Google Scholar 

  19. Chen YP et al (2020b) Relationships of ozone formation sensitivity with precursors emissions, meteorology and land use types, in Guangdong-Hong Kong-Macao Greater Bay Area. China J Environ Sci 94:1–13. https://doi.org/10.1016/j.jes.2020.04.005

    Article  Google Scholar 

  20. Ciurleo M, Mandaglio MC, Moraci N (2018) Landslide susceptibility assessment by TRIGRS in a frequently affected shallow instability area. Landslides 16:175–188. https://doi.org/10.1007/s10346-018-1072-3

    Article  Google Scholar 

  21. Cortes C, Vapnik V (1995) Support vector network. Mach Learn 20:273–297. https://doi.org/10.1007/BF00994018

    Article  Google Scholar 

  22. Dietrich WE, Wilson CJ, Montgomery DR, McKean J (1993) Analysis of erosion thresholds, channel networks, and landscape morphology using a digital terrain model. J Geol 101:259–278. https://doi.org/10.1086/648220

    Article  Google Scholar 

  23. Dormann CF et al (2013) Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecogr 36(1):27–46

    Article  Google Scholar 

  24. Dou J, Chang K-T, Chen S, Yunus A, Liu J-K, Xia H, Zhu Z (2015a) Automatic Case-Based Reasoning Approach for Landslide Detection: Integration of Object-Oriented Image Analysis and a Genetic Algorithm. Remote Sens 7:4318–4342. https://doi.org/10.3390/rs70404318

    Article  Google Scholar 

  25. Dou J et al (2015b) Optimization of causative factors for landslide susceptibility evaluation using remote sensing and GIS data in parts of Niigata Japan. PLoS One 10:e0133262. https://doi.org/10.1371/journal.pone.0133262

    Article  Google Scholar 

  26. Dou J, Yamagishi H, Pourghasemi HR, Yunus AP, Song X, Xu Y, Zhu Z (2015c) An integrated artificial neural network model for the landslide susceptibility assessment of Osado Island Japan. Nat Hazard 78:1749–1776. https://doi.org/10.1007/s11069-015-1799-2

    Article  Google Scholar 

  27. Dou J et al (2019a) Improved landslide assessment using support vector machine with bagging, boosting, and stacking ensemble machine learning framework in a mountainous watershed Japan. Landslides 17:641–658. https://doi.org/10.1007/s10346-019-01286-5

    Article  Google Scholar 

  28. Dou J et al (2020) Different sampling strategies for predicting landslide susceptibilities are deemed less consequential with deep learning. Sci Total Environ 720:137320. https://doi.org/10.1016/j.scitotenv.2020.137320

    Article  Google Scholar 

  29. Dou J et al (2019b) Assessment of advanced random forest and decision tree algorithms for modeling rainfall-induced landslide susceptibility in the Izu-Oshima Volcanic Island Japan. Sci Total Environ 662:332–346. https://doi.org/10.1016/j.scitotenv.2019.01.221

    Article  Google Scholar 

  30. Dou Q et al (2019c) A Method for improving controlling factors based on information fusion for debris flow susceptibility mapping: a case study in Jilin Province. China Entropy. https://doi.org/10.3390/e21070695

    Article  Google Scholar 

  31. Esper Angillieri MY (2020) Debris flow susceptibility mapping using frequency ratio and seed cells, in a portion of a mountain international route. Dry Central Andes of Argent Catena. https://doi.org/10.1016/j.catena.2020.104504

    Article  Google Scholar 

  32. Ewen J, Parkin G, O’Connell PE (2000) SHETRAN: distributed river basin flow and transport Modeling system. J Hydrol Eng 5(3):250–258

    Article  Google Scholar 

  33. Gan L, Wang Y, Lin Z, Lev B (2019) A loss-recovery evaluation tool for debris flow. Int J Disaster Risk Reduct. https://doi.org/10.1016/j.ijdrr.2019.101165

    Article  Google Scholar 

  34. Gomes R, Guimarães R, de Carvalho JO, Fernandes N, doAmaralJúnior E (2013) Combining Spatial Models for Shallow Landslides and Debris-Flows Prediction. Remote Sens 5:2219–2237. https://doi.org/10.3390/rs5052219

    Article  Google Scholar 

  35. Guzzetti F, Carrara A, Cardinali M, Reichenbach P (1999) Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study. Central Italy Geomorphol 31:181–216. https://doi.org/10.1016/s0169-555x(99)00078-1

    Article  Google Scholar 

  36. Hammond CJ, Prellwitz RW, Miller SM, Bell D (1992) Landslide hazard assessment using monte carlo simulation christchurch. New Zealand, Rotterdam, Netherlands AA 10:959–964

    Google Scholar 

  37. He S, Pan P, Dai L, Wang H, Liu J (2012) Application of kernel-based fisher discriminant analysis to map landslide susceptibility in the qinggan River delta. Three Gorges, China Geomorphol 171–172:30–41. https://doi.org/10.1016/j.geomorph.2012.04.024

    Article  Google Scholar 

  38. Hong H, Pourghasemi HR, Pourtaghi ZS (2016) Landslide susceptibility assessment in Lianhua County (China): a comparison between a random forest data mining technique and bivariate and multivariate statistical models. Geomorphol 259:105–118

    Article  Google Scholar 

  39. Hong HY, Pradhan B, Xu C, Tien Bui D (2015) Spatial prediction of landslide hazard at the Yihuang area (China) using two-class kernel logistic regression, alternating decision tree and support vector machines. Catena 133:266–281

    Article  Google Scholar 

  40. Horton P, Jaboyedoff M, Rudaz B, Zimmermann M (2013) Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale. Nat Hazard Earth Sys Sci 13:869–885

    Article  Google Scholar 

  41. Huang F, Cao Z, Guo J, Jiang S-H, Li S, Guo Z (2020) Comparisons of heuristic, general statistical and machine learning models for landslide susceptibility prediction and mapping. Catena. https://doi.org/10.1016/j.catena.2020.104580

    Article  Google Scholar 

  42. Huang F, Yin K, Huang J, Gui L, Wang P (2017) Landslide susceptibility mapping based on self-organizing-map network and extreme learning machine. Eng Geol 223:11–22. https://doi.org/10.1016/j.enggeo.2017.04.013

    Article  Google Scholar 

  43. Iverson R, Iverson RM (2000) Landslide triggering by rain infiltration. Water Resour Res 36:1897–1910

    Article  Google Scholar 

  44. Jacoby BS, Peterson EW, Dogwiler T (2011) Identifying the stream erosion potential of cave levels in carter cave state resort park Kentucky, USA. J Geographic Inform Sys 03:323–333. https://doi.org/10.4236/jgis.2011.34030

    Article  Google Scholar 

  45. Kang S, Lee S-R, Vasu NN, Park J-Y, Lee D-H (2017) Development of an initiation criterion for debris flows based on local topographic properties and applicability assessment at a regional scale. Eng Geol 230:64–76. https://doi.org/10.1016/j.enggeo.2017.09.017

    Article  Google Scholar 

  46. Kannan SS, Ramaraj N (2010) A novel hybrid feature selection via symmetrical uncertainty ranking based local memetic search algorithm. Knowl-Based Syst 23:580–585. https://doi.org/10.1016/j.knosys.2010.03.016

    Article  Google Scholar 

  47. Kappes MS, Malet JP, Remaître A, Horton P, Jaboyedoff M, Bell R (2011) Assessment of debris-flow susceptibility at medium-scale in the Barcelonnette Basin France. Nat Haz Earth Sys Sci 11:627–641. https://doi.org/10.5194/nhess-11-627-2011

    Article  Google Scholar 

  48. Li D, Huang F, Yan L, Cao Z, Chen J, Ye Z (2019) Landslide susceptibility prediction using particle-swarm-optimized multilayer perceptron: comparisons with multilayer-perceptron-only BP Neural Network, and Information Value Models. Appl Sci. https://doi.org/10.3390/app9183664

    Article  Google Scholar 

  49. Liang Z, Wang C-M, Zhang Z-M, Khan K-U-J (2020) A comparison of statistical and machine learning methods for debris flow susceptibility mapping. Stoch Environ Res Risk Assessment. https://doi.org/10.1007/s00477-020-01851-8

    Article  Google Scholar 

  50. Luo W, Liu C-C (2017) Innovative landslide susceptibility mapping supported by geomorphon and geographical detector methods. Landslides 15:465–474. https://doi.org/10.1007/s10346-017-0893-9

    Article  Google Scholar 

  51. Ma Z, Qin S, Cao C, Lv J, Li G, Qiao S, Hu X (2019) The influence of different knowledge-driven methods on landslide susceptibility mapping: a case study in the Changbai Mountain Area. North China Entropy. https://doi.org/10.3390/e21040372

    Article  Google Scholar 

  52. Merghadi A, Abderrahmane B, Tien Bui D (2018) Landslide susceptibility assessment at mila basin (algeria): a comparative assessment of prediction capability of advanced machine learning methods. ISPRS Int J Geo-Inform. https://doi.org/10.3390/ijgi7070268

    Article  Google Scholar 

  53. Merghadi A et al (2020) Machine learning methods for landslide susceptibility studies: a comparative overview of algorithm performance. Earth-Sci Rev. https://doi.org/10.1016/j.earscirev.2020.103225

    Article  Google Scholar 

  54. Moore ID, Grayson RB (1991) Terrain-based catchment partitioning and runoff prediction using vector elevation data. Water Resour Res 27:1177–1191

    Article  Google Scholar 

  55. Moore ID, Wilson JP (1992) Length-slope factors for the Revised Universal Soil Loss Equation: Simplified method of estimation. J Soil Water Conserv 47:423–428

    Google Scholar 

  56. O’brien RM, (2007) A caution regarding rules of thumb for variance inflation factorsm. Quality Quantity 41:673–690

    Article  Google Scholar 

  57. Pack RT, Tarboton DG, Goodwin CN (2001) Assessing terrain stability in a GIS using SINMAP

  58. Park DW, Lee SR, Vasu NN, Kang SH, Park JY (2016) Coupled model for simulation of landslides and debris flows at local scale. Nat Hazards 81:1653–1682. https://doi.org/10.1007/s11069-016-2150-2

    Article  Google Scholar 

  59. Park DW, Nikhil NV, Lee SR (2013) Landslide and debris flow susceptibility zonation using TRIGRS for the Seoul landslide event. Nat Hazards Earth Sys Sci 13:2833–2849. https://doi.org/10.5194/nhess-13-2833-2013

    Article  Google Scholar 

  60. Pham BT, Pradhan B, Tien Bui D, Prakash I, Dholakia MB (2016) A comparative study of different machine learning methods for landslide susceptibility assessment: a case study of Uttarakhand area (India). Environ Model Software 84:240–250

    Article  Google Scholar 

  61. Pham BT, Prakash I, Singh SK, Shirzadi A, Shahabi H, Tran T-T-T, Bui DT (2019) Landslide susceptibility modeling using reduced error pruning trees and different ensemble techniques: hybrid machine learning approaches. Catena 175:203–218. https://doi.org/10.1016/j.catena.2018.12.018

    Article  Google Scholar 

  62. Pham BT, Tien Bui D, Dholakia MB, Prakash I, Pham HV (2016) A comparative study of least square support vector machines and multiclass alternating decision trees for spatial prediction of rainfall-induced landslides in a tropical cyclones area. Geotech Geol Eng 34:1807–1824. https://doi.org/10.1007/s10706-016-9990-0

    Article  Google Scholar 

  63. Pham BT, Tien Bui D, Pourghasemi HR, Indra P, Dholakia MB (2015) Landslide susceptibility assesssment in the Uttarakhand area (India) using GIS: a comparison study of prediction capability of naïve bayes, multilayer perceptron neural networks, and functional trees methods. Theor Appl Climatol 128:255–273

    Article  Google Scholar 

  64. Poiraud A (2014) Landslide susceptibility–certainty mapping by a multi-method approach: a case study in the tertiary basin of Puy-en-Velay (Massif central, France). Geomorphol 216:208–224

    Article  Google Scholar 

  65. Prenner D, Kaitna R, Mostbauer K, Hrachowitz M (2018) The value of using multiple hydrometeorological variables to predict temporal debris flow susceptibility in an alpine environment. Water Resour Res 54:6822–6843. https://doi.org/10.1029/2018wr022985

    Article  Google Scholar 

  66. Qiao S, Qin S, Chen J, Hu X, Ma Z (2019) The application of a three-dimensional deterministic model in the study of debris flow prediction based on the rainfall-unstable soil coupling mechanism. Process 7(2):99

    Article  Google Scholar 

  67. Qin S et al (2019) Mapping debris flow susceptibility based on watershed unit and grid cell unit: a comparison study geomatics. Nat Hazard Risk 10:1648–1666. https://doi.org/10.1080/19475705.2019.1604572

    Article  Google Scholar 

  68. Regmi NR, Giardino JR, Vitek JD (2010) Modeling susceptibility to landslides using the weight of evidence approach: Western Colorado. USA Geomorphol 115:172–187. https://doi.org/10.1016/j.geomorph.2009.10.002

    Article  Google Scholar 

  69. Saaty T (1980) The analytic hierarchy process: planning. Priority Setting, Resource Allocation

    Google Scholar 

  70. Saaty T, Vargas L (2001) Models, methods, Concepts & Applications of the Analytic Hierarchy Process

  71. Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281

    Article  Google Scholar 

  72. Salciarini D, Godt JW, Savage WZ, Conversini P, Baum RL, Michael JA (2006) Modeling regional initiation of rainfall-induced shallow landslides in the eastern Umbria Region of central Italy. Landslides 3:181–194. https://doi.org/10.1007/s10346-006-0037-0

    Article  Google Scholar 

  73. Shahabi H, Khezri S, Ahmad BB, Hashim M (2014) Landslide susceptibility mapping at central zab basin, Iran: a comparison between analytical hierarchy process, frequency ratio and logistic regression models. Catena 115:55–70

    Article  Google Scholar 

  74. Shannon CE (1948) A mathematical theory of communication. Bell System Tech J 27(4):623–656

    Article  Google Scholar 

  75. Shaw S, Johnson D (1995) Slope morphology model derived from digital elevation data Northwest Arc/Info Users Conference

  76. Shen P, Zhang L, Chen H, Fan R (2018) EDDA 2.0: integrated simulation of debris flow initiation and dynamics considering two initiation mechanisms. Geosci Model Develop 11:2841–2856

    Article  Google Scholar 

  77. Sidle R, Ochiai H (2013) Landslides: Processes Prediction. Land Use. https://doi.org/10.1029/WM018

    Article  Google Scholar 

  78. Süzen ML, Doyuran V (2004) A comparison of the GIS based landslide susceptibility assessment methods: multivariate versus bivariate. Environ Geol 45:665–679. https://doi.org/10.1007/s00254-003-0917-8

    Article  Google Scholar 

  79. Süzen ML, Doyuran V (2004) Data driven bivariate landslide susceptibility assessment using geographical information systems: a method and application to Asarsuyu catchment. Turkey Eng Geol 71:303–321. https://doi.org/10.1016/s0013-7952(03)00143-1

    Article  Google Scholar 

  80. Taylor DW (1948) Fundamentals of Soil Mechanics. Soil Sci 66(2):161

    Article  Google Scholar 

  81. Tien Bui D, Ho T-C, Pradhan B, Pham B-T, Nhu V-H, Revhaug I (2016) GIS-based modeling of rainfall-induced landslides using data mining-based functional trees classifier with AdaBoost Bagging, and MultiBoost ensemble frameworks. Environ Earth Sci. https://doi.org/10.1007/s12665-016-5919-4

    Article  Google Scholar 

  82. Tran TV, Alvioli M, Lee G, An HU (2017) Three-dimensional, time-dependent modeling of rainfall-induced landslides over a digital landscape: a case study. Landslides 15:1071–1084

    Article  Google Scholar 

  83. Viet TT, Lee G, Thu TM, An HU (2016) Effect of digital elevation model resolution on shallow landslide modeling using TRIGRS. Nat Hazard Rev 18(2):04016011

    Article  Google Scholar 

  84. Wang Y, Feng L, Li S, Ren F, Du Q (2020) A hybrid model considering spatial heterogeneity for landslide susceptibility mapping in Zhejiang Province China. Catena. https://doi.org/10.1016/j.catena.2019.104425

    Article  Google Scholar 

  85. Weimin Wu, Sidle RC (1996) A distributed slope stability model for steep forested basins: water resources research. Int J Rock Mech Mining Sci Geomech Abstr 33:178–170

    Google Scholar 

  86. Xiong K, Adhikari BR, Stamatopoulos CA, Zhan Y, Wu S, Dong Z, Di B (2020) Comparison of different machine learning methods for debris flow susceptibility mapping: a case study in the Sichuan Province China. Remote Sens. https://doi.org/10.3390/rs12020295

    Article  Google Scholar 

  87. Yang Y, Yang J, Xu C, Xu C, Song C (2019) Local-scale landslide susceptibility mapping using the B-GeoSVC model. Landslides 16:1301–1312. https://doi.org/10.1007/s10346-019-01174-y

    Article  Google Scholar 

  88. Yao J, Qin S, Qiao S, Che W, Chen Y, Su G, Miao Q (2020) Assessment of landslide susceptibility combining deep learning with semi-supervised learning in Jiaohe County, Jilin Province China. Appl Sci 10:5640. https://doi.org/10.3390/app10165640

    Article  Google Scholar 

  89. Zhang G, Cai Y, Zheng Z, Zhen J, Liu Y, Huang K (2016) Integration of the statistical index method and the analytic hierarchy process technique for the assessment of landslide susceptibility in Huizhou China. Catena 142:233–244. https://doi.org/10.1016/j.catena.2016.03.028

    Article  Google Scholar 

  90. Zhang S, Yang H, Wei F, Jiang Y, Liu D (2014) A model of debris flow forecast based on the water-soil coupling mechanism. J Earth Sci 25:757–763. https://doi.org/10.1007/s12583-014-0463-1

    Article  Google Scholar 

  91. Zhu AX et al (2018) A comparative study of an expert knowledge-based model and two data-driven models for landslide susceptibility mapping. Catena 166:317–327. https://doi.org/10.1016/j.catena.2018.04.003

    Article  Google Scholar 

  92. Zhu AX et al (2014) An expert knowledge-based approach to landslide susceptibility mapping using GIS and fuzzy logic. Geomorphol 214:128–138. https://doi.org/10.1016/j.geomorph.2014.02.003

    Article  Google Scholar 

  93. Zhu Z, Wang H, Peng D, Dou J (2019) Modelling the hindered settling velocity of a falling particle in a particle-fluid mixture by the tsallis entropy theory. Entropy 21(1):55

    Article  Google Scholar 

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Acknowledgements

This research was funded by the National Natural Science Foundation of China (Grant Nos. 41977221 and 41202197) and the Jilin Provincial Science and Technology Department (Grant Nos. 20190303103SF and 20170101001JC).

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Sun, J., Qin, S., Qiao, S. et al. Exploring the impact of introducing a physical model into statistical methods on the evaluation of regional scale debris flow susceptibility. Nat Hazards 106, 881–912 (2021). https://doi.org/10.1007/s11069-020-04498-4

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Keywords

  • Integrating model
  • Statistical model
  • Physical model
  • Debris flow susceptibility mapping
  • Yongji County