Volcan Cotopaxi, 1862, Painting by F. Church 
Tephra Fallout Models must be physically realistic:
 capture major elements of the eruption process
(eg. plume diffusion)
 account for major features of atmospheric transport
(eg. wind advection, atmospheric diffusion)
 consider particle size variation and settling velocity
Tephra Fallout Models must be tested (validated and verified):
 given model assumptions, is the result correctly calculated?
 does the model explain observed variation in tephra deposition?
TEPHRA2 forecasts tephra dispersion by:
 relying on an analytical solution to tephra transport and sedimentation
 making the code specific to a region by using:
 archived meteorological data sets (REANALYSIS data, see http://www.cdc.noaa.gov/cdc/reanalysis ) or locally collected wind data,
 high resolution DEMs of specific active volcanoes in the region.
 Note: TEPHRA2 is an improved and optimized version of TEPHRA. Further details.

Steps and Assumptions in Our Implementation 
1 A vertical eruption column is assumed to extend above the vent. This column is discretized. Particles fall from each of these heights.
2 The total grainsize distribution is estimated for the eruption, assuming a normal distribution in phi units.


3 The total tephra mass is distributed vertically in the eruption column based on a probability density function for mass as a function of height. For example, for an umbrella cloud, mass might be equally distributed in the upper 20% of the total column height. Further details. 

4 Calculate the total fall time of a particle from the point of release in the eruption column to the ground surface (accounting for the topography). The particle fall time depends on particle properties (density, diameter) and atmospheric density. Settling velocity is determined assuming spherical particles and accounting for the variation in particle Reynolds Number and atmospheric density. 

5 Eruption column radius increases with height and this affects deposition. Particles are more spread out than they would be if they were released from a vertical line source. This effect is accounted for by increasing the diffusion time as a function of height in the column (see step 6). Further details. 

6 Diffusion of particles in the atmosphere is estimated using a bivariate Gaussian probability density function to approximate turbulence. The scale of diffusion (described by the diffusion law) depends on total particle fall time, which depends on particle size, release height, and elevation of the terrain the particle impacts. Further details. 

7 Particles fall through a stratified atmosphere. Wind speed and direction change between layers, based on REANALYSIS or locally collected wind data. 

8 Total tephra accumulation is estimated as mass per unit area; most hazard results from excessive mass loading. The isomass is contoured over a region about the volcano. Mass per unit area can be easily converted into thickness knowing the deposit bulk density (i.e. thickness (m) = kgm2/density). 



Volcan Reventador, 2002, Photo by G. Eguiguren. 
HAZARD MODELS
Numerical models used for tephra hazard assessment (Hazard Models) typically result from the combination and integration of different theories and modeling approaches depending on the specific eruptive scenario and mitigation program required. They can be grouped within two main categories: particletracking models and advectiondiffusion models. Particletracking models are Eulerian or Lagrangian models that can forecast volcaniccloud position at specific times and space. They are mainly used for aviationsafety purposes. Advectiondiffusion models are Eulerian models that describe the solution of the equations of particle diffusion, transport, and sedimentation and can forecast tephra accumulation on ground relative to a particlerelease source. These models are mainly used for civil protection purposes, such as giving public warnings and planning mitigation measures. See the website of the IAVCEI Tephra Group for a detailed review of these models.
Examples of particletracking models:
 CANERM (CANadian Emergency Response Model used by the Canadian Meteorological Centre; D'Amours 1998)
 MEDIA (Model for DIspersion in the Atmosphere used by the Toulouse VAAC)
 PUFF (particle tracking model used by the U.S. National Weather Service, Anchorage, Alaska; Searcy 1998)
 VAFTAD (Volcanic Ash Forecast Transport And Dispersion model developed by the NOAA Air Resources Laboratory; Heffter and Stunder 1993)
Examples of advectiondiffusion models based on the analytical solution by Suzuki et al. 1983:
 ASHFALL (Hurst and Turner 1999)
 FALL3D (Costa et al. 2006)
 HAZMAP (Macedonio et al. 1988; Barberi et al. 1990)
 TEPHRA and TEPHRA2 (Connor et al. 2001; Bonadonna et al. 2005)

