Mathematical Geosciences

, Volume 40, Issue 2, pp 147–157 | Cite as

Tephra Fallout Models: The Effect of Different Source Shapes on Isomass Maps

  • Leng L. Lim
  • Winston L. Sweatman
  • Robert McKibbin
  • Charles B. Connor


Numerous tephra dispersion and sedimentation models rely on some abstraction of the volcanic plume to simplify forecasts of tephra accumulation as a function of the distance from the volcano. Here we present solutions to the commonly used advection–dispersion equation using a variety of source shapes: a point, horizontal and vertical lines, and a circular disk. These may be related to some volcanic plume structure, such as a strong plume (vertical line), umbrella cloud (circular disk), or co-ignimbrite plume (horizontal line), or can be used to build a more complex plume structure such as a series of circular disks to represent a buoyant weak plume. Basing parameters upon eruption data, we find that depositions for the horizontal source shapes are very similar but differ from the vertical line source deposition. We also compare the deposition from a series of stacked circular disk sources of increasing radius above the volcanic vent with that from a vertical line source.


Volcanic plume Eruption column Tephra Volcanic hazard Advection–dispersion 


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  1. Armienti P, Macedonio G, Pareschi MT (1988) A numerical-model for simulation of tephra transport and deposition: applications to May 18, 1980, Mount St Helens eruption. J Geophys Res 93(B6):6463–6476 Google Scholar
  2. Bonadonna C (2006) Probabilistic modeling of tephra dispersion. In: Mader HM, Coles S, Connor C, Connor L (eds) Statistics in Volcanology. IAVCEI series 1. Geol Soc Lond, pp 243–259 Google Scholar
  3. Bonadonna C, Phillips JC (2003) Sedimentation from strong volcanic plumes. J Geophys Res 108(B7):2340 CrossRefGoogle Scholar
  4. Bonadonna C, Ernst GGJ, Sparks RSJ (1998) Thickness variations and volume estimates of tephra fall deposits: the importance of particle Reynolds number. J Volcanol Geotherm Res 81(3/4):173–187 CrossRefGoogle Scholar
  5. Bonadonna C, Macedonio G, Sparks RSJ (2002) Numerical modeling of tephra fallout associated with dome collapses and vulcanian explosions: application to hazard assessment on Montserrat. In: Druitt TH, Kokelaar BK (eds) The eruption of Soufrière hills volcano, Montserrat, from 1995 to 1999. Memoir. Geological Society, London, pp 517–537 Google Scholar
  6. Bonadonna C, Connor CB, Houghton BF, Connor L, Byrne M, Laing A, Hincks TK (2005) Probabilistic modeling of tephra dispersal: hazard assessment of a multiphase rhyolitic eruption at Tarawera, New Zealand. J Geophys Res 110(B3):2340 CrossRefGoogle Scholar
  7. Bursik MI, Carey SN, Sparks RSJ (1992) A gravity current model for the May 18, 1980 Mount St. Helens plume. Geophys Res Lett 19(16):1663–1666 Google Scholar
  8. Connor LJ, Connor CB (2006) Inversion is the key to dispersion: understanding eruption dynamics by inverting tephra fallout. In: Mader HM, Coles S, Connor C, Connor L (eds) Statistics in volcanology. IAVCEI series 1. Geol Soc Lond, pp 231–242 Google Scholar
  9. Connor CB, Hill BE, Winfrey B, Franklin NM, La Femina PC (2001) Estimation of volcanic hazards from tephra fallout. Nat Hazards Rev 1 33–42 CrossRefGoogle Scholar
  10. Hill BE, Connor CB, Jarzemba MS, La Femina PC, Navarro M, Strauch W (1998) 1995 eruptions of Cerro Negro volcano, Nicaragua, and risk assessment for future eruptions. Geol Soc Am Bull 110(10):1231–1241 CrossRefGoogle Scholar
  11. Hurst AW (1994) ASHFALL—a computer program for estimating volcanic ash fallout. Report and user guide, Institute of Geological and Nuclear Sciences Science Report 94/23 Google Scholar
  12. Pyle DM (1989) The thickness, volume, and grainsize of tephra fall deposits. Bull Volcanol 51:1–15 CrossRefGoogle Scholar
  13. Sparks RSJ, Wilson L, Sigurdsson H (1981) The pyroclastic deposits of the 1875 eruption of Askja, Iceland. Philos Trans Roy Soc Lond Ser A 229(1447):241–273 CrossRefGoogle Scholar
  14. Sparks RSJ, Bursik MI, Carey SN, Gilbert JS, Glaze LS, Sigurdsson H, Woods AW (1997) Volcanic Plumes. Wiley, New York, 574 p Google Scholar
  15. Suzuki T (1983) A theoretical model for the dispersion of tephra. In: Shimozuru D, Yokoyama I (eds) Arc volcanism, physics and tectonics. Terra Scientific Publishing, Tokyo, pp 95–113 Google Scholar
  16. Sweatman WL, Chatwin PC (1996) Dosages from instantaneous releases of dense gases in wind tunnels and into a neutrally stable atmosphere. Bound Layer Meteorol 77(3/4):211–231 CrossRefGoogle Scholar
  17. Woods AW (1988) The fluid dynamics and thermodynamics of eruption columns. Bull Volcanol 50(3):169–193 CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geology 2008

Authors and Affiliations

  • Leng L. Lim
    • 1
  • Winston L. Sweatman
    • 1
  • Robert McKibbin
    • 1
  • Charles B. Connor
    • 2
  1. 1.Institute of Information and Mathematical SciencesMassey UniversityNorth ShoreNew Zealand
  2. 2.Department of GeologyUniversity of South FloridaTampaUSA

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