Skip to main content
SpringerLink
Log in

Tsunami Inundation, Modeling of

  • Reference work entry
Encyclopedia of Complexity and Systems Science

Definition of the Subject

Tsunami inundation is the one of the final stages of tsunami evolution, when the wave encroaches upon and floods dry land. It is during this stagethat a tsunami takes the vast majority of its victims. Depending on the properties of the tsunami (e. g. wave height and period) and the beachprofile (e. g. beach slope, roughness), the tsunami may approach as a relatively calm, gradual rise of the ocean surface or as an extremelyturbulent and powerful bore – a wall of white water. The characteristics of this approach determine the magnitude and type of damage tocoastal infrastructure and, more importantly, the actions required of coastal residents to find a safe retreat or shelter.

To gage the nearshore impact of tsunami inundation, engineers and scientists rely primarily on three different methods: 1) Field survey of pastevents, 2) Physical experimentation in a laboratory, and 3) Numerical modeling. It is the last of these methods – numerical simulation oftsunami...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Abbreviations

Beach profile:

A cross-shore, or normal to the beach, survey of the seafloor and dry ground elevation (bathymetry and topography); a series of spatial location and bottom elevation data pairs.

Bore:

A steep hydraulic front which transitions between areas of different water level. Tsunamis can approach land as a turbulent, breaking bore if the incident tsunami is of sufficiently large height.

Boussinesq equations:

An approximate equation model, used for waves with wave length of at least two times the local water depth; a long-wave-based model, but includes some frequency dispersion

Dispersion, amplitude:

The separation of wave components due to a wave‐height related difference in wave speed; all else being equal, a wave with a large height will travel faster than one with a small height.

Dispersion, frequency:

The separation of wave components due to a frequency related difference in wave speed; all else being equal, a wave with a longer period will travel faster than one with a short period.

Navier–Stokes equations:

The full equations of fluid motion, including dissipation through the fluid molecular viscosity only. Other models discussed here, namely the Shallow Water Wave and Boussinesq equations, are approximations to these equations.

Runup, or runup height:

The ground elevation (a vertical measure) at the furthest point of landward inundation.

Shallow water wave equations:

An approximate equation model, used for waves with wave length many times larger than the water depth; a non‐dispersive, long-wave model; there is no frequency dispersion in this model.

Tsunami inundation:

The spatial area flooded as a tsunami rushes inland.

Bibliography

  1. Arakawa A, Lamb VR (1977) Computational design of the basic dynamical processesof the UCLA general circulation model. In: Chang J (ed) Methodsin computational physics. Academic Press, New York, pp 174–267

    Google Scholar 

  2. Birknes J, Pedersen G (2006) A particle finite element method applied tolong wave run-up. Int J Numer Methods Fluids 52(3):237–261

    MathSciNet  MATH  Google Scholar 

  3. Borrero JC, Bourgeois J, Harkins G, Synolakis CE (1997) How small-scalebathymetry affected coastal inundation in the 1992 Nicaraguan tsunami. Fall AGU Meeting, San Francisco

    Google Scholar 

  4. Briggs MJ, Synolakis CE, Harkins GS, Green D (1994) Laboratory experiments oftsunami runup on a circular island. PAGEOPH 144(3/4):569–593

    Google Scholar 

  5. Carrier GF (1966) Gravity waves on water of variable depth. Fluid J Mech24:641–659

    MathSciNet  ADS  MATH  Google Scholar 

  6. Chang K-A, Hsu T-J, Liu PL-F (2001) Vortex generation and evolution in waterwaves propagating over a submerged rectangular obstacle. Part I solitary waves. Coast Eng 44:13–36

    Google Scholar 

  7. Chen Q, Kirby JT, Dalrymple RA, Kennedy AB, Chawla A (2000) Boussinesq modelingof wave transformation, breaking, and runup: Part I 2D. J Waterw Port Coast Ocean Eng 126(1):57–62

    Google Scholar 

  8. Cheung K, Phadke A, Wei Y, Rojas R, Douyere Y, Martino C, Houston S, Liu PL-F,Lynett P, Dodd N, Liao S, Nakazaki E (2003) Modeling of storm‐induced coastal flooding for emergency management. Ocean Eng30:1353–1386

    Google Scholar 

  9. Cienfuegos R, Barthelemy E, Bonneton P (2007) A fourth‐order compactfinite volume scheme for fully nonlinear and weakly dispersive Boussinesq‐type equations. Part II: Boundary conditions and model validation. IntJ Numer Meth Fluids 53(9):1423–1455

    MathSciNet  MATH  Google Scholar 

  10. Cross RH (1967) Tsunami surge forces, ASCE Jl Waterways & Harbors DivisionWW4:201–231

    Google Scholar 

  11. Danielsen F, Sørensen MK, Olwig MF, Selvam V et al (2005) The Asian tsunami:A protective role for coastal vegetation. Science 310:643

    Google Scholar 

  12. Fernando HJS, McCulley JL, Mendis SG, Perera K (2005) Coral poaching worsenstsunami destruction in Sri Lanka. Eos Trans AGU 86(33):301

    ADS  Google Scholar 

  13. Fujima K, Masamura K, Goto C (2002) Development of the 2d/3d hybrid model fortsunami numerical simulation. Coastal Eng J 44(4):373–397

    Google Scholar 

  14. Geist E, Lynett P, Chaytor J (2008) Hydrodynamic modeling of tsunamis from thecurrituck landslide, Marine Geology (in press)

    Google Scholar 

  15. Gopalakrishnan TC, Tung CC (1983) Numerical analysis of a moving boundaryproblem in coastal hydrodynamics. Intl J Numer Meth Fluids 3:179–200

    MATH  Google Scholar 

  16. González FI, Satake K, Boss EF,Mofjeld HO (1995) Edge wave and non‐trapped modes of the 25 April 1992 Cape Mendocino tsunami. Pure ApplGeophys PAGEOPH 144(3–4):409–426

    Google Scholar 

  17. Goring DG, Raichlen F (1992) Propagation of long waves ontoshelf. J Waterw Port Coast Ocean Eng 118(1):43–61

    Google Scholar 

  18. Guignard S, Grilli ST, Marcer R, Rey V (1999) Computation of shoaling andbreaking waves in nearshore areas by the coupling of BEM and VOF methods. Proc. 9th Offshore and Polar Engng. Conf., vol III, ISOPE99, Brest, France,pp 304–309

    Google Scholar 

  19. Hammack J, Segur H (1978) Modelling criteria for long water waves. J FluidMech 84(2):359–373

    MathSciNet  ADS  MATH  Google Scholar 

  20. Hibberd S, Peregrine DH (1979) Surf and run-up on a beach. J FluidMech 95:323–345

    MathSciNet  ADS  MATH  Google Scholar 

  21. Horrillo, Juan, Kowalik, Zygmunt, Shigihara, Yoshinori (2006) Wave dispersionstudy in the Indian Ocean–Tsunami of December 26, 2004. Marine Geodesy 29(3):149–166(18)

    Google Scholar 

  22. Hsu T-J, Sakakiyama T, Liu PL-F (2002) A numerical model for waves andturbulence flow in front of a composite breakwater. Coast Eng 46:25–50

    Google Scholar 

  23. Johnson DB, Raad PE, Chen S (1994) Simulation of impacts of fluid freesurfaces with solid boundaries. Int J Num Methods Fluids 19:153–176

    MathSciNet  MATH  Google Scholar 

  24. Johson RS (1972) Some numerical solutions of a variable‐coefficientKorteweg–de Vries equation (with application to solitary wave development on a shelf). J Fluid Mech 54:81

    ADS  Google Scholar 

  25. Kennedy AB, Chen Q, Kirby JT, Dalrymple RA (2000) Boussinesq modeling of wavetransformation, breaking, and runup. 1: 1D. J Waterway Port Coastal Ocean Eng ASCE 126:39–47

    Google Scholar 

  26. Korycansky DG, Lynett P (2007) Runup from impact tsunami. Geophys J Int 170:1076–1088

    ADS  Google Scholar 

  27. Kowalik Z, Murty TS (1993) Numerical simulation of two‐dimensionaltsunami runup. Marine Geodesy 16:87–100

    Google Scholar 

  28. Kulikov E (2005) Dispersion of the Sumatra tsunami waves in the Indian Oceandetected by satellite altimetry. Report from P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow

    Google Scholar 

  29. Imamura F (1995) Review of tsunami simulation with a finite differencemethod, long-wave runup models. World Scientific, Singapore, pp 25–42,http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake

  30. Ioualalen M, Asavanant JA, Kaewbanjak N, Grilli ST, Kirby JT, Watts P (2007)Modeling of the 26th December 2004 Indian Ocean tsunami: Casestudy of impact in Thailand. J Geophys Res 112:C07024, doi:10.1029/2006JC003850

    ADS  Google Scholar 

  31. Lay T, Kanamori H, Ammon C, Nettles M, Ward S, Aster R, Beck S, Bilek S,Brudzinski M, Butler R, DeShon H, Ekström G, Satake K, Sipkin S (2005) The great Sumatra–Andaman earthquake of December 26, 2004. Science308:1127–1133, doi:10.1126/science.1112250

  32. LeVeque RJ, George DL (2004) High‐resolution finite volume methods forthe shallow water equations with bathymetry and dry states. In: Liu PL, Yeh H, Synolakis C (eds) Advanced numerical models for simulating tsunami wavesand runup. vol 10 of Advances in Coastal and Ocean Engineering.World Scientific, Singapore

    Google Scholar 

  33. Losada MA, Vidal V, Medina R (1989) Experimental study of the evolution ofa solitary wave at an abrupt junction. J Geophys Res 94:14557

    ADS  Google Scholar 

  34. Liu PL-F, Synolakis CE, Yeh H (1991) Report on the international workshop onlong-wave run-up. J Fluid Mech 229:675–688

    ADS  MATH  Google Scholar 

  35. Liu PL-F, Cho Y-S, Yoon SB, Seo SN (1994) Numerical simulations of the 1960Chilean tsunami propagation and inundation at Hilo, Hawaii. in: El-Sabh MI (ed) Recent development in tsunami research. Kluwer, Dordrecht, pp 99–115

    Google Scholar 

  36. Liu PL-F, Cho Y-S, Briggs MJ, Kanoglu U, Synolakis CE (1995) Runup of solitarywaves on a circular island. J Fluid Mech 320:259–285

    MathSciNet  ADS  Google Scholar 

  37. Liu PL-F, Cheng Y (2001) A numerical study of the evolution ofa solitary wave over a shelf. Phys Fluids 13(6):1660–166

    ADS  Google Scholar 

  38. Liu PL-F, Lynett P, Fernando H, Jaffe BE, Fritz H, Higman B, Morton R, Goff J,Synolakis C (2005) Observations by the International Tsunami Survey Team in Sri Lanka. Science 308:1595

    Google Scholar 

  39. Liu PL-F, Wu T-R, Raichlen F, Synolakis CE, Borrero JC (2005) Runup andrundown generated by three‐dimensional sliding masses. J Fluid Mech 536:107–144

    ADS  MATH  Google Scholar 

  40. Lynett P (2006) Nearshore modeling using high-order Boussinesq equations. J Waterway Port Coastal Ocean Eng (ASCE) 132(5):348–357

    Google Scholar 

  41. Lynett P (2007) The effect of a shallow water obstruction on long wave runupand overland flow velocity. J Waterway Port Coastal Ocean Eng (ASCE) 133(6):455–462

    Google Scholar 

  42. Lynett P, Liu PL-F (2002) A numerical study of submarine landslide generatedwaves and runup. Proc R Soc London A 458:2885–2910

    MathSciNet  ADS  MATH  Google Scholar 

  43. Lynett P, Wu T-R, Liu PL-F (2002) Modeling wave runup withdepth‐integrated equations. Coast Eng 46(2):89–107

    Google Scholar 

  44. Lynett P, Borrero J, Liu PL-F, Synolakis CE (2003) Field survey and numericalsimulations: A review of the 1998 Papua New Guinea tsunami. Pure Appl Geophys 160:2119–2146

    ADS  Google Scholar 

  45. Madsen OS, Mei CC (1969) The transformation of a solitary wave over anuneven bottom. J Fluid Mech 39:781

    ADS  Google Scholar 

  46. Madsen PA, Sorensen OR, Schaffer HA (1997) Surf zone dynamics simulated by a Boussinesq‐type model: Part I. Model description and cross-shore motion of regular waves. Coast Eng 32:255–287

    Google Scholar 

  47. Matsuyama M, Ikeno M, Sakakiyama T, Takeda T (2007) A study on tsunamiwave fission in an undistorted experiment. Pure Appl Geophys 164:617–631

    ADS  Google Scholar 

  48. Özkan‐Haller HT, Kirby JTA (1997) Fourier‐Chebyshevcollocation method for the shallow water equations including shoreline run-up. Appl Ocean Res 19:21–34

    Google Scholar 

  49. Pedersen G (2006) On long wave runup models. In: Proceedings of the 3rdInternational Workshop on Long-Wave Runup Models, in Catalina Island, California

    Google Scholar 

  50. Pedersen G, Gjevik B (1983) Runup of solitary waves. J Fluid Mech142:283–299

    ADS  Google Scholar 

  51. Pedrozo‐Acuna A, Simmonds DJ, Otta AK, Chadwick AJ (2006) On thecross-shore profile change of gravel beaches. Coast Eng 53(4):335–347

    Google Scholar 

  52. Petera J, Nassehi V (1996) A new two‐dimensional finite elementmodel for the shallow water equations using a Lagrangian framework constructed along fluid particle trajectories. Int J Num Methods Eng39:4159–4182

    MathSciNet  MATH  Google Scholar 

  53. Priest GR et al (1997) Cascadiasubduction zone tsunamis: Hazard mapping at Yaquina Bay, Oregon. Final Technical Report to the National EarthquakeHazard Reduction Program DOGAMI Open File Report 0-97-34, p 143

    Google Scholar 

  54. Ramsden JD (1996) Forces on a vertical wall dueto long waves, bores, and dry-bed surges. J Waterway Port Coast Ocean Eng 122(3):134–141

    Google Scholar 

  55. Seabra‐Santos FJ, Renouard DP, Temperville AM (1987) Numerical andexperimental study of the transformation of a solitary wave over a shelf or isolated obstacles. J Fluid Mech176:117

    Google Scholar 

  56. Shen M, Meyer R (1963) Climb of a bore on a beach Part 3. Run-up. J Fluid Mech 16(1):113–125

    MathSciNet  ADS  Google Scholar 

  57. Sielecki A, Wurtele MG (1970) The numerical integration of the nonlinearshallow‐water equations with sloping boundaries. J Comput Phys 6:219–236

    ADS  MATH  Google Scholar 

  58. Sittanggang K, Lynett P, Liu P (2006) Development of a Boussinesq‐RANSVOF Hybrid Wave Model. in Proceedings of 30th ICCE, San Diego, pp 24–25

    Google Scholar 

  59. Synolakis CE (1987) The runup of solitary waves. J Fluid Mech185:523–545

    ADS  MATH  Google Scholar 

  60. Synolakis CE, Imamura F, Tsuji Y, Matsutomi S, Tinti B, Cook B, Ushman M(1995) Damage, Conditions of East Java tsunami of 1994 analyzed. EOS, Transactions, American Geophysical Union 76(26):257 and261–262

    Google Scholar 

  61. Tadepalli S, Synolakis CE(1994) The runup of N-Waves on sloping beaches, Proc R Soc London A 445:99–112

    ADS  MATH  Google Scholar 

  62. Tadepalli S, Synolakis CE (1996) Model for the leading waves of tsunamis. PhysRev Lett 77:2141–2144

    ADS  Google Scholar 

  63. Tao J (1983) Computation of wave runup and wave breaking. InternalReport. Danish Hydraulics Institute, Denmark

    Google Scholar 

  64. Tao J (1984) Numerical modeling of wave runup and breaking on the beach. ActaOceanol Sin 6(5):692–700 (in chinese)

    Google Scholar 

  65. Titov VV, Synolakis CE (1995) Modeling of breaking and nonbreaking long waveevolution and runup using VTCS-2. J Harbors Waterways Port Coast Ocean Eng 121(6):308–316

    Google Scholar 

  66. Titov VV, Synolakis CE (1998) Numerical modeling of tidal wave runup. J Waterway Port Coast Ocean Eng ASCE 124(4):157–171

    Google Scholar 

  67. Tomita T, Honda K (2007) Tsunami estimation including effect of coastalstructures and buildings by 3D model. Coastal Structures '07, Venice

    Google Scholar 

  68. Yeh H (2006) Maximum fluid forces in the tsunami runup zone. J Waterway PortCoast Ocean Eng 132(6):496–500

    Google Scholar 

  69. Yeh H, Ghazali A, Marton I (1989) Experimental study of bore runup. J FluidMech 206:563–578

    ADS  Google Scholar 

  70. Yeh H, Liu P, Briggs M, Synolakis C (1994) Propagation and amplification oftsunamis at coastal boundaries. Nature 372:353–355

    ADS  Google Scholar 

  71. Ward SN, Day S (2001) Cumbre Vieja Volcano – Potential collapse andtsunami at La Palma, Canary Islands. Geophys Res Lett 28(17):3397–3400

    ADS  Google Scholar 

  72. Weiss R, Wunnemann K, Bahlburg H (2006) Numerical modelling of generation,propagation, and run-up of tsunamis caused by ocean impacts: model strategy and technical solutions. Geophys J Int67:77–88

    ADS  Google Scholar 

  73. Woo S-B, Liu PL-F (2004) A finite element model for modified Boussinesqequations. Part I: Model development. J Waterway Port Coast Ocean Eng 130(1):1–16

    Google Scholar 

  74. Zelt JA (1991) The run-up of nonbreaking and breaking solitary waves. CoastEng 15(3):205–246

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Texas A&M University, College Station, USA

    Patrick J. Lynett

Authors
  1. Patrick J. Lynett
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Lynett, P.J. (2009). Tsunami Inundation, Modeling of. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_569

Download citation

Publish with us

Policies and ethics

Search

Navigation