, Volume 8, Issue 1, pp 67–79 | Cite as

FLaIR and SUSHI: two mathematical models for early warning of landslides induced by rainfall

Original Paper


The development of Early Warning Systems in recent years has assumed an increasingly important role in landslide risk mitigation. In this context, the main topic is the relationship between rainfall and the incidence of landslides. In this paper, we focus our attention on the analysis of mathematical models capable of simulating triggering conditions. These fall into two broad categories: hydrological models and complete models. Generally, hydrological models comprise simple empirical relationships linking antecedent precipitation to the time that the landslide occurs; the latter consist of more complex expressions that take several components into account, including specific site conditions, mechanical, hydraulic and physical soil properties, local seepage conditions, and the contribution of these to soil strength. In a review of the most important models proposed in the technical and international literature, we have outlined their most meaningful and salient aspects. In particular, the Forecasting of Landslides Induced by Rainfall (FLaIR) and the Saturated Unsaturated Simulation for Hillslope Instability (SUSHI) models, developed by the authors, are discussed. FLaIR is a hydrological model based on the identification of a mobility function dependent on landslide characteristics and antecedent rainfall, correlated to the probability of a slide occurring. SUSHI is a complete model for describing hydraulic phenomena at slope scale, incorporating Darcian saturated flow, with particular emphasis on spatial–temporal changes in subsoil pore pressure. It comprises a hydraulic module for analysing the circulation of water from rainfall infiltration in saturated and nonsaturated layers in non-stationary conditions and a geotechnical slope stability module based on Limit Equilibrium Methods. The paper also includes some examples of these models’ applications in the framework of early warning systems in Italy.


Landslide Mathematical models Rainfall 


  1. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration—guidelines for computing crop water requirements: FAO Irrigation and Drainage Paper 56. FAO, RomeGoogle Scholar
  2. Basha HA (1999) One-dimensional nonlinear steady infiltration. Water Resour Res 35(6):1697–1704CrossRefGoogle Scholar
  3. Baum RL, Godt JW, Harp EL, McKenna JP, McMullen SR (2005) Early warning of landslides for rail traffic between Seattle and Everett, Washington, U.S.A. In: Proceedings International of Conference on Landslide Risk Management, Vancouver, pp 731–740.Google Scholar
  4. Caine N (1980) The rainfall intensity-duration control of shallow landslides and debris flows. Geogr Ann 62A(1–2):23–27CrossRefGoogle Scholar
  5. Campbell RH (1975) Soil slips, debris flows and rainstorms in the Santa Monica mountains and vicinity, Southern California. U.S. Geological Survey Professional Paper 851.Google Scholar
  6. Cannon SH, Ellen SD (1985) Rainfall conditions for abundant debris avalanches, San Francisco Bay region, California. Cal Geol 38(12):267–272Google Scholar
  7. Capparelli G (2006) Il ruolo della circolazione idrica sotterranea nei pendii soggetti a fenomeni di in stabilizzazione. Dissertation, University of Calabria.Google Scholar
  8. Capparelli G, Tiranti D (2010) Application of the MoniFLaIR as an early warning system for rainfall-induced landslides in Piedmont region (Italy). Landslides. Springer Berlin/Heidelberg doi: 10.1007/s10346-009-0189-9
  9. Capparelli G, Biondi D, De Luca DL, Versace P (2009) Hydrological and complete models for forecasting landslides triggered by rainfalls. In: Proceedings of the First Italian Workshop on Landslides, 8-10 June 2009, Napoli (Italy), pp 162–173.Google Scholar
  10. Capparelli G, Giorgio M, Greco R, Versace P (2009) Rainfall height stochastic modeling as a support tool for floods and flowslides early warning. In: Proceedings of 33rd International Association of Hydraulic Engineering & Research (IAHR), Vancouver- British Columbia, 9-14 August 2009, pp. 6812–6819.Google Scholar
  11. Cascini L, Versace P (1988) Relationship between rainfall and landslide in a gneissic cover. In: Proceedings of the fifth International Symposium on Landslides, Lausanne, pp 565–570.Google Scholar
  12. Chen JM, Tan YC, Chen CH (2003) Analytical solutions of one-dimensional infiltration before and after ponding. Hydrol Process 17:815–822CrossRefGoogle Scholar
  13. Cole K, Davis GM (2002) Landslide warning and emergency planning systems in West Dorset, England. In: McInnes RG, Jakeways J (eds) Instability, Planning and Management. Thomas Telford, London, pp 463–470Google Scholar
  14. Corominas J, Moya J (1999) Reconstructing recent landslide activity in relation to rainfall in the Llobregat River Basin, Eastern Pyrenees, Spain. Geomorphol 30:79–93CrossRefGoogle Scholar
  15. D’Orsi RN, D’Avila C, Ortigao JAR, Moraes L, Santos MD (1997) Rio-The Rio de Janeiro landslide watch. In: Proceedings of 2nd PSL Pan-Am Symposium on Landslides, Rio de Janeiro, Vol 1:21–30.Google Scholar
  16. Droogers P (2000) Estimating actual evapotranspiration using a detailed agro-hydrological model. J Hydrol 229:50–58CrossRefGoogle Scholar
  17. Fathani TF, Karnawati D, Sassa K, Fukuoka H, Honda K (2009) Development of landslide monitoring and early warning system in Indonesia. In: Proceedings of The First World Landslide Forum, 18-21 November 2008, Tokyo, pp 195–198.Google Scholar
  18. Feddes RA, Kowalik PJ, Zaradny H (1978) Simulation of field water use and crop yield simulation monograph series. Wageningen, PUDOCGoogle Scholar
  19. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. John Wiley and Sons, INC, New YorkGoogle Scholar
  20. Fredlund DG, Xing A (1994) Equations for the soil-water characteristic curve. Can Geotech J 31:521–532CrossRefGoogle Scholar
  21. Gabet EJ, Burbank DW, Putkonen JK, Pratt-Sitaula BA, Ojha T (2004) Rainfall thresholds for landsliding in the Hymalayas of Nepal. Geomorphol 63:131–143CrossRefGoogle Scholar
  22. Giorgio M, Greco R, Capparelli G, Versace P (2009) A new empirical predictor of rainfall-induced landslides mobility function. In: Proceedings of The First Italian Workshop on Landslides, 8-10 June 2009, Napoli (Italy), pp 181–185.Google Scholar
  23. Glade T, Crozier M, Smith P (2000) Applying probability determination to refine landslide-triggering rainfall thresholds using an empirical “Antecedent Daily Rainfall Model”. Pure Appl Geophys 157(6–8):1059–1079CrossRefGoogle Scholar
  24. Graziani A, Rotonda T, Tommasi P (2009) Stability and deformation mode of rock slide along interbeds reactivated by rainfall. In: Proceedings of The First Italian Workshop on Landslides, 8-10 June 2009, Napoli (Italy), pp 62–71.Google Scholar
  25. Guzzetti F, Peruccacci S, Rossi M, Stark CP (2007) Rainfall thresholds for the initiation of landslides in central and southern Europe. Meteorol and Atmos Phys 98:239–267CrossRefGoogle Scholar
  26. Heneker TM, Lambert MF, Kuczera G (2001) A point rainfall model for risk-based design. J Hydrol 247(1–2):54–71CrossRefGoogle Scholar
  27. Hogart WL, Parlange JY (2000) Application and improvement of a recent approximate analytical solution of Richards’ equation. Water Resour Res 36:1965–1968CrossRefGoogle Scholar
  28. Huygen J, Van Dam JC, Kroess JG, Wesseling JG (1997) SWAP 2.0: input and output manual. Wageningen Agricultural University, Wageningen, The NetherlandsGoogle Scholar
  29. IFLDM (2007) Proceedings of the international forum on landslide disaster management, 10-14 December, Hong Kong (eds) Ken Ho and Victor Li.Google Scholar
  30. Iiritano G, Versace P, Sirangelo B (1998) Real-time estimation of hazard for landslides triggered by rainfall. Environ Geol 35(2–3):175–183CrossRefGoogle Scholar
  31. ILF (2008) Proceedings of the first world landslide forum, 18-21 November 2008, Tokyo. pp 726Google Scholar
  32. Iverson RM (2000) Landslide triggering by rain infiltration. Water Resour Res 36:1897–1910CrossRefGoogle Scholar
  33. IWL (2009) Proceedings of the first Italian workshop on landslides, 8-10 June 2009, Napoli (Italy) pp 250Google Scholar
  34. Kalsnes B, Nadim F, Glade T (2009) Study effects of global change on landslide risk. In: Proceedings of The First World Landslide Forum, 18-21 November 2008, Tokyo, pp 19–33.Google Scholar
  35. Keefer DK, Wilson RC, Mark RK, Brabb EE, Brown WM III, Ellen SD, Harp EL, Wieczoreck GF, Alger CS, Zatkin RS (1987) Real-time landslide warning during heavy rainfall. Science 238:921–926CrossRefGoogle Scholar
  36. Lhomme J-P (1996) A theoretical basis for the Priestley-Taylor coefficient. Bound-Layer Meteorol 82:179–191CrossRefGoogle Scholar
  37. Menziani M, Pugnaghi S, Vincenzi S (2007) Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions. J Hydrol 332:214–225CrossRefGoogle Scholar
  38. Montgomery DR, Dietrich WE (1994) A physically based model topographic control on shallow landsliding. Water Resour Res 30:1153–1171CrossRefGoogle Scholar
  39. Paniconi C, Putti M (1994) A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems. Water Resour Res 30(12):3357–3374CrossRefGoogle Scholar
  40. Paniconi C, Alvaro AA, Wood EF (1991) Numerical evaluation of iterative and noniterative methods for the solution of the nonlinear Richards equation. Water Resour Res 27(6):1147–1163CrossRefGoogle Scholar
  41. Priestley CHB, Taylor RG (1972) On the assessment of surface heat flux and evaporation using large scale parameters. Mon Weather Rev 100:81–92CrossRefGoogle Scholar
  42. Pun WK, Wong ACW, Pang PLR (2003) A review of the relationship between rainfall and landslides in Hong Kong. In: Proceedings of the 14th Southeast Asian Geotechnical Conference. Vol 3:211–216Google Scholar
  43. Rigon R, Bertoldi G, Over TM (2006) Geotop: a distributed hydrological model with coupled water and energy budgets. J hydrometeorol 7(3):371–388CrossRefGoogle Scholar
  44. Shuttleworth WJ (1993) Evaporation. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, Inc, p 1424Google Scholar
  45. Sirangelo B, Versace P (1992) Modelli stocastici di precipitazione e soglie pluviometriche di innesco dei movimenti franosi. In: Proceedings of XXIII Convegno Nazionale di Idraulica e Costruzioni Idrauliche, Florence (Italy), Vol D: 361–373.Google Scholar
  46. Sirangelo B, Versace P (1996) A real time forecasting for landslides triggered by rainfall. MECC 31:1–13Google Scholar
  47. Sirangelo B, Versace P, Iiritano G (1998) The performances of the FLaiR model in the analysis of different landslides". Atti del convegno "XXIII EGS General Assembly", Nice (FRA), 1998.Google Scholar
  48. Sirangelo B, Versace P, Capparelli G (2003) Forwarning model for landslides triggered by rainfall based on the analysis of historical data file. In: Servat E, Najem W, Leduc C, Shakeel A (eds), Hydrology of the Mediterranean and Semi-Arid Regions, IAHS Publ. 278 (Red Book), pp. 298–304Google Scholar
  49. Sirangelo B, Versace P, De Luca DL (2007) Rainfall nowcasting by at site stochastic model P.R.A.I.S.E. Hydrol Earth Syst Sci 11:1341–1351CrossRefGoogle Scholar
  50. Takara K, Apip Bagiawan A (2009) Study on early warning system for debris flow and landslide in the Citarum River Basin, Indonesia. In: Proceedings of The First World Landslide Forum, 18-21 November 2008, Tokyo, pp 573-576.Google Scholar
  51. Tsai TL, Yang JC (2006) Modelling of rainfall triggered shallow landslide. Environ Geol 50:525–534CrossRefGoogle Scholar
  52. UNDRO (1991) Mitigation natural disaster. In: Phenomena, Effects and Options. United Nations, New York, p 164Google Scholar
  53. van Asch WJ, van Beek LPH, Bogaard TA (2009) The diversity in hydrological triggering systems of landslides. In: Proceedings of The First Italian Workshop on Landslides, 8-10 June 2009, Napoli (Italy), pp 151–156.Google Scholar
  54. van Dam JC, Feddes RA (2000) Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. J Hydrol 233:72–85CrossRefGoogle Scholar
  55. van Genuchten M-T, Nielsen DR (1985) On describing and predicting the hydraulic properties of unsaturated soils. Ann Geophys 3(5):615–628Google Scholar
  56. Vanapalli SK, Fredlund DG, Pufahl DE, Clifton AW (1996) Model for the prediction of shear strength with respect to soil suction. Can Geotech J 33:379–392CrossRefGoogle Scholar
  57. Vauclin M, Khanji D, Vachaud G (1979) Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem. Water Resour Res 15(5):1089–1101CrossRefGoogle Scholar
  58. Versace P, Capparelli G (2008) Empirical hydrological models for early warning of landslides induced by rainfall. In: Proceedings of The First World Landslide Forum, 18-21 November 2008, Tokyo, pp 627–630.Google Scholar
  59. Versace P, Capparelli G, Picarelli L (2007) Landslide investigations and risk mitigation. The Sarno case. In: Ho K, Li V (ed), Proceedings of 2007 International Forum on Landslide Disaster Management, Vol 1, Hong Kong, pp. 509–533Google Scholar
  60. Wang HF, Anderson MP (1995) Introduction to groundwater modelling- finite difference and finite element methods. Academic Press, Elsevier ScienceGoogle Scholar
  61. Weeks SW, Sander GC, Braddock RD, Matthews CJ (2004) Saturated and unsaturated water flow in inclined porous media. Environ Model and Assess 9:91–102CrossRefGoogle Scholar
  62. Wieczorek GF (1987) Effect of rainfall intensity and duration on debris flows in central Santa Cruz Mountains, California. Geol Soc of Am, Rev in Eng Geol 7:93–104Google Scholar
  63. Wilson RC, Wieczorek GF (1995) Rainfall thresholds for the initiation of debris flow at La Honda, California. Environ and Eng Geosci 1(1):11–27Google Scholar
  64. Yano K, Senoo K (1985) How to set standard rainfalls or debris flow warning and evacuation. Sabo Symposium, SEDD Japan, pp 451–455Google Scholar
  65. Yu YF, Lam JS, Siu CK, Pun WK (2004) Recent advance in landslip warning system. In: Proceedings of the 1 day Seminar on Recent Advances in Geotechnical Engineering, organized by the Hong Kong Institution of Engineers Geotechnical Division, pp 139–147.Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Dipartimento di Difesa del SuoloUniversità della CalabriaRendeItaly

Personalised recommendations