Tephra Fallout Models: The Effect of Different Source Shapes on Isomass Maps
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Tephra Fallout Models: The Effect of Different Source Shapes on Isomass Maps Leng L. Lim · Winston L. Sweatman · Robert McKibbin · Charles B. Connor
Received: 8 November 2006 / Accepted: 14 December 2007 / Published online: 11 January 2008 © International Association for Mathematical Geology 2008
Abstract 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. Keywords Volcanic plume · Eruption column · Tephra · Volcanic hazard · Advection–dispersion
1 Introduction Tephra fallout is one of the main hazards to communities located in volcanic regions. During eruptions, tephra is carried upwards in plumes from heights of a few kilometers to heights of tens of kilometers above the volcano vent, and this material settles L.L. Lim · W.L. Sweatman () · R. McKibbin Institute of Information and Mathematical Sciences, Massey University, Albany Campus, Private Bag 102 904, North Shore 0745, Auckland, New Zealand e-mail: [email protected] C.B. Connor Department of Geology, University of South Florida, Fowler Ave., SCA 528, Tampa, FL 33620, USA
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Math Geosci (2008) 40: 147–157
through and is dispersed by the atmosphere. Within tens of kilometers of volcanic vents, tephra accumulation can be sufficient to completely devastate property. Beyond this immediate region, tephra accumulation over areas of tens of thousands of square kilometers may still result in significant social disruption and economic loss (Bonadonna 2006). Tephra sedimentation was first modeled by applying the advection–dispersion equation to model accumulation, relying on a simplified, probabilistic treatment of the volcanic plume ‘source term’ (Suzuki 1983). Subsequent authors have utilized similar approaches (Hill et al. 1998; Connor et al. 2001; Bonadonna et al. 2005) and have approximated the advection–dispersion equation using finite difference methods (Armienti et al. 1988). All of these models rely on assumptions about the geometry of the volcanic plume which lofts tephra into the atmosphere. Although a great range of plume geometries are found in nature (Sparks et al. 1997), tephra sedimentation models tend to rely on highly simp
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