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Bulletin of Volcanology

, 75:738 | Cite as

Modeling thickness variability in tephra deposition

  • Emily Kawabata
  • Mark S. Bebbington
  • Shane J. Cronin
  • Ting Wang
Collection: Monogenetic Volcanism
Part of the following topical collections:
  1. Topical Collection on Monogenetic Volcanism

Abstract

The attenuation of tephra fall thickness is most commonly estimated after contouring isolated and often irregular field measurements into smooth isopachs, with varying degrees of subjectivity introduced in the process. Here, we present an explicit description of the variability introduced into a semiempirical tephra attenuation relation. This opens the way to fitting models to actual tephra observations through maximum likelihood estimation, rather than using weighted least-squares estimation on the isopachs. The method is illustrated for small-scale basaltic explosive eruptions using a simple, but typical, data set of the actual tephra thickness data published from the 1973 Heimaey eruption. Of the distributions considered to describe variability in these measurements, the lognormal performed poorly, due to its tendency to predict a small number of greatly over-thickened deposits. The Weibull and gamma distributions fitted the data to a very similar degree and produced very similar estimates for the “effective volume,” mean wind direction, and mass/thickness attenuation rate. The latter can be inverted to obtain an estimate of the mean column height. The estimated wind direction, and the column height derived from the estimated thickness attenuation parameter, agreed very well with the direct observations made during the eruption. Augmented by a mixture framework allowing for the incorporation of multiple lobes and/or vents, the model was able to identify the source and direction of tephra deposition for the 1977 Ukinrek Maars eruptions from only the tephra thickness data.

Keywords

Tephra Ukinrek Maars Aleatory uncertainty Statistical method 

Notes

Acknowledgments

The first author (E.K.) is supported by the New Zealand Earthquake Commission and GNS Science. M.B. and S.C. are supported by the New Zealand Natural Hazards Research Platform, project “Living with Volcanic Risk.” We thank Christina Magill and an anonymous reviewer for improvements suggested to the original manuscript.

References

  1. Akaike H (1977) On entropy maximization principle. In: Krishnaiah PR (ed) Applications of statistics. North-Holland, Amsterdam, pp 27–41Google Scholar
  2. Barberi F, Macedonio G, Pareschi MT, Santacroce R (1990) Mapping the tephra fallout risk: an example from Vesuvius, Italy. Nature 344:142–144CrossRefGoogle Scholar
  3. Baxter PJ, Ing R, Falk H, French J, Stein GF, Bernstein RS, Merchant JA, Allard J (1981) Mount St. Helens eruptions, May 18 to June 12, 1980: an overview of the acute health impact. J Am Med Assoc 246:2585–2589CrossRefGoogle Scholar
  4. Bebbington M, Cronin SJ (2011) Spatio-temporal hazard estimation in the Auckland Volcanic field, New Zealand, with a new event-order model. Bull Volcanol 73:55–72CrossRefGoogle Scholar
  5. Bebbington M, Cronin S, Chapman I, Turner M (2008) Quantifying volcanic ash fall hazard to electricity infrastructure. J Volcanol Geotherm Res 177:1055–1062CrossRefGoogle Scholar
  6. Bonadonna C, Houghton BF (2005) Total grain-size and volume of tephra-fall deposits. Bull Volcanol 67:441–456CrossRefGoogle Scholar
  7. Bonadonna C, Costa A (2012) Estimating the volume of tephra deposits: a new simple strategy. Geology 40:415–418CrossRefGoogle Scholar
  8. 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 81:173–187CrossRefGoogle Scholar
  9. Bonadonna C, Connor CB, Houghton BF, Connor L, Byrne M, Laing A, Hincks T (2005) Probabilistic modeling of tephra dispersion: hazard assessment of a multi-phase eruption at Tarawera, New Zealand. J Geophys Res 110:B03203CrossRefGoogle Scholar
  10. Bonasia R, Macedonio G, Costa A, Mele D, Sulpizio R (2010) Numerical inversion and analysis of tephra fallout deposits from the 472 AD sub-Plinian eruption at Vesuvius (Italy) through a new best-fit procedure. J Volcanol Geotherm Res 189:238–246CrossRefGoogle Scholar
  11. Carey S, Sparks RSJ (1986) Quantitative models of the fall and dispersal of tephra from volcanic eruption columns. Bull Volcanol 48:109–125CrossRefGoogle Scholar
  12. Connor CB, Hill BE, Winfrey B, Franklin NM, LaFemina PC (2001) Estimation of volcanic hazards from tephra fallout. Nat Haz Rev 2:33–42CrossRefGoogle Scholar
  13. Connor LJ, Connor CB (2006) Inversion is the key to dispersion: understanding eruption dynamics buy inverting tephra fallout. In: Mader H et al. (ed) Statistics in volcanology, vol 1: special publications of IAVCEI. Geological Society, London, pp 231–242Google Scholar
  14. Costa A, Macedonio G, Folch A (2006) A three-dimensional Eulerian model for transport and deposition of volcanic ashes. Earth Planet Sci Lett 241:634–647CrossRefGoogle Scholar
  15. Costa A, Dell’Erba F, Di Vito MA, Isaia R, Macedonio G, Orsi G, Pfeiffer T (2009) Tephra fallout hazard assessment at the Campi Flegrei caldera (Italy). Bull Volcanol 71:259–273CrossRefGoogle Scholar
  16. Cronin SJ, Hedley MJ, Neall VE, Smith G (1998) Agronomic impact of tephra fallout from 1995 and 1996 Ruapehu volcano eruptions, New Zealand. Environ Geol 34:21–30CrossRefGoogle Scholar
  17. Fierstein J, Nathenson M (1992) Another look at the calculation of fallout tephra volumes. Bull Volcanol 54:156–167CrossRefGoogle Scholar
  18. Gonzalez-Mellado AO, De la Cruz-Reyna S (2010) A simple semi-empirical approach to model thickness of ash-deposits for different eruption scenarios. Nat Haz Earth Syst Sci 10:2241–2257CrossRefGoogle Scholar
  19. Heiken G, Murphy M, Hackett W, Scott W (1995) Volcanic hazards on energy infrastructure of the United States. United States Department of Energy, Washington DC, LA-UR 95-1087Google Scholar
  20. Hurst AW, Turner R (1999) Performance of the program ASHFALL for forecasting ashfall during the 1995 and 1996 eruptions of Ruapehu volcano. NZ J Geol Geophys 42:615–622CrossRefGoogle Scholar
  21. Hurst T, Smith W (2004) A Monte Carlo methodology for modelling ashfall hazards. J Volcanol Geotherm Res 138:393–403CrossRefGoogle Scholar
  22. Johnston EN, Phillips JC, Bonadonna C, Watson IM (2012) Reconstructing the tephra dispersal pattern from the bronze age eruption of Santorini using an advection-diffusion model. Bull Volcanol 74:1485–1507CrossRefGoogle Scholar
  23. Kienle J, Kyle PR, Self S, Motyka RJ, Lorenz V (1980) Ukinrek Maars, Alaska, I. April 1977 eruption sequence, petrology and tectonic setting. J Volcanol Geotherm Res 7:11–37CrossRefGoogle Scholar
  24. Kratzmann DJ, Carey SN, Fero J, Scasso RA, Naranjo J-A (2010) Simulations of tephra dispersal from the 1991 explosive eruptions of Hudson volcano, Chile. J Volcanol Geotherm Res 190:337–353CrossRefGoogle Scholar
  25. Macedonio G, Pareschi MT, Santacroce R (1988) A numerical simulation of the Plinian fall phase of 79 AD eruption of Vesuvius. J Geophys Res 93:14817–14827CrossRefGoogle Scholar
  26. Miller TP, Casadevall TJ (2000) Volcanic ash hazards to aviation. In: Sigurdsson H (ed) Encyclopedia of volcanoes. Academic, San Diego, pp 915–930Google Scholar
  27. Pfeiffer T, Costa A, Macedonio G (2005) A model for the numerical simulation of tephra fall deposits. J Volcanol Geotherm Res 140:273–294CrossRefGoogle Scholar
  28. Pyle DM (1989) The thickness, volume and grain size of tephra fall deposits. Bull Volcanol 51:1–15CrossRefGoogle Scholar
  29. Pyle DM (2000) Sizes of volcanic eruptions. In: Sigurdsson H et al. (eds) Encyclopedia of volcanoes. Academic, San Diego, pp 263–269Google Scholar
  30. Rhoades DA, Dowrick DJ, Wilson CJN (2002) Volcanic hazard in New Zealand: scaling and attenuation relations for tephra fall deposits from Taupo volcano. Nat Hazards 26:147–174CrossRefGoogle Scholar
  31. Rose WI (1993) Comment on ‘another look at the calculation of fallout tephra volumes’ by Judy Fierstein and Manuel Nathenson. Bull Volcanol 55:372–374CrossRefGoogle Scholar
  32. Scollo S, Del Carlo P, Coltelli M (2007) Tephra fallout of 2001 Etna flank eruption: analysis of the deposit and plume dispersion. J Volcanol Geotherm Res 160:147–164CrossRefGoogle Scholar
  33. Scollo S, Tarantola S, Bonadonna C, Coltelli M, Saltelli A (2008) Sensitivity analysis and uncertainty estimation for tephra dispersal models. J Geophys Res 113:B06202CrossRefGoogle Scholar
  34. Self S, Sparks RSJ, Booth B, Walker GPL (1974) The 1973 Heimaey Strombolian scoria deposit, Iceland. Geol Mag 111:539–548CrossRefGoogle Scholar
  35. Self S, Kienle J, Huot J-P (1980) Ukinrek Maars, Alaska, II. Deposits and formation of the 1977 craters. J Volcanol Geotherm Res 7:39–65CrossRefGoogle Scholar
  36. Sparks RSJ (1986) The dimension and dynamics of volcanic eruption columns. J Volcanol Geotherm Res 48:13–15Google Scholar
  37. Sparks RSJ, Bursik MI, Ablay GJ, Thomas RME, Carey SN (1992) Sedimentation of tephra by volcanic plumes. 2: controls on thickness and grain-size variations of tephra fall deposits. Bull Volcanol 54:685–695CrossRefGoogle Scholar
  38. Sparks RSJ, Bursik M, Carey SN, Gilbert JS, Glaze LS, Sigurdsson H, Woods AW (1997) Volcanic plumes. Wiley, Chichester, pp 574Google Scholar
  39. Stewart C, Johnston DM, Leonard G, Horwell C, Thordarsson T, Cronin SJ (2006) Contamination of water supplies by volcanic ashfall: a literature review and simple impact modelling. J Volcanol Geotherm Res 158:296–306CrossRefGoogle Scholar
  40. Sulpizio R (2005) Three empirical methods for the calculation of distal volume of tephra-fall deposits. J Volcanol Geotherm Res 145(3–4):315–33CrossRefGoogle Scholar
  41. Thorarinsson S, Steinthorsson S, Einarsson Th, Kristmannsdottir H, Oskarsson N (1973) The eruption on Heimaey, Iceland. Nature 241:372–375CrossRefGoogle Scholar
  42. Volentik ACM, Bonadonna C, Connor CB, Connor LJ, Rosi M (2010) Modeling tephra dispersal in absence of wind: insights from the climatic phase of the 2450 BP Plinian eruption of Pululagua volcano (Ecuador). J Volcanol Geotherm Res 193:117–136CrossRefGoogle Scholar
  43. Wilson L, Sparks RSJ, Huang TC, Watkins ND (1978) The control of volcanic column heights by eruption energetics and dynamics. J Geophys Res 83:1829–1836CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Emily Kawabata
    • 1
  • Mark S. Bebbington
    • 2
  • Shane J. Cronin
    • 2
  • Ting Wang
    • 3
  1. 1.Institute of Fundamental Sciences–StatisticsMassey UniversityPalmerston NorthNew Zealand
  2. 2.Volcanic Risk SolutionsMassey UniversityPalmerston NorthNew Zealand
  3. 3.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand

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