Ash3d:A new USGS tephra fall model
Hans SchwaigerLarry Mastin
Roger Denlinger
Why do we need a tephra fall model?
Forecasting ash distribution during unrest Constraining eruption parameters through
observation & modeling Research into the physics & hazards of ash
eruptions
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What we were using
Ashfall: A 2-D model Developed by Tony Hurst
For Redoubt, Evan Thoms & Rob Wardwell wrote a Python script to automatically run Ashfall & plot these maps.
Main disadvantages:•We don’t have the source code•It’s limited to 2-D runs in a 1-D wind field.
What the model does
Calculated advection-diffusion of multiple grain sizes for 4-D wind field
Calculates deposit thickness and its variation with time.
Calculates time of arrival of ash at airports.
Writes out 3-D ash-cloud migration at time steps, for animation.
Model overview
The equation for advection of ash by wind and diffusion of ash by turbulent eddies is solved by method of fractional steps, treating advection and diffusion independently.
Advection step: Solve advection equation to get concentration at intermediate time step (q*):
Diffusion step: Solve diffusion equation, integrating the remaining fractional step:
Where q is ash concentration in kg/km3, u is velocity in km/hr, and K is an eddy diffusivity in units of km2/hr
( ) 0q
u qt x
* 2 *
20
q qK
t x
Methods of Solution
A domain of cells is constructed either in a spherical (lat./lon.) or Cartesian coordinates
Wind fields must be provided and are used to passively transport ash as it settles.
The numerical schemes used are: Finite volume methods with Riemann solvers, in which
ash flux occurs at cell boundaries. Semi-Lagrangian methods that backtrack ash transport
along wind streamlines in a fixed Eulerian framework. Turbulent diffusion is treated either explicitly (Forward
Euler) or implicitly (Crank-Nicolson)
Illustration of advection schemes
Donor CellUpwind withDimensionSplitting
CornerTransportUpwind
Semi-Lagrangian
t t+t
Illustration of advection schemesDonor CellUpwind withDimensionSplitting
CornerTransportUpwind
Semi-Lagrangian
•Conserves mass•Moderately fast•t = x/v•Increased numerical diffusion
•Conserves mass•Slow•t = x/v•Low numerical diffusion
•Conserves mass only approximately•Fast•t = c x/v•Low numerical diffusion•Accuracy depends on order of interpolation
Illustration of diffusion schemesExplicit Forward Euler
•Easily implemented•First-order accurate •t = (x)2/K
tt+t
Implicit Crank-Nicolson
•Assumes linearity•Requires solving Ax=b•Second-order accurate •t limited only by accuracyt
t+t
Why so many options?
Fast, but non-conservative, calculations can be automated for ensemble forecast runs
Fully conservative calculations (slower) might be necessary for greater confidence in particular results
Full mass conservation might also be required when including additional physics (aggregation)
Verification and Validation
• Verification – Is your code solving the equations correctly?•Construct suite of test cases to check behavior in idealized conditions
o Linear advection in x,yo Linear advection in zo Diffusion in x,y,zo Circular advection
• Method of manufacturedsolutions
• Validation – Are you even solving the right equations?• Comparison with experimental data• Comparison with field data
Convergence for different schemes
Circular advection test case
• Smooth boundaries are modeled well
•Sharp boundaries are smoothed by numerical diffusion
Types of calculation thatAsh3d can do
Calculation on a sphere Calculation on a plane•Uses lower-resolution Global Forecast System winds
•Doesn’t conserve mass as well
•But, it can model an eruption from any volcano on Earth.
•Uses high-resolution winds from projected models (e.g. NAM, WRF)
•Conserves mass very well
•But, it can only model eruptions in certain geographic locations.
<12-50 km
0.5-2.5 deg.(50-250 km)
Projected Meteorological models used
NAM 11 km
NAM AK 45 km
Model inputs
Wind files (1-D, 3-D, 4-D) Grid parameters: dx,dy,dz Grain size distribution, fall velocities
Eruption source parameters: Number of eruptions Time, duration, plume height, erupted volume, Suzuki
constant
Model outputs
Deposit thickness (final, at specified times) Ash cloud elevation & concentration Ash arrival times & thickness at airports & other points of
interest 3-D data in various formats:
ESRI ASCII (For import to Arc products) Kml/kmz (Google Earth) NetCDF Raw binary
Example: Iceland (4-14-2010)24-hours after start of simulation
Resolution = 0.33 degrees
Example: Iceland (4-14-2010)24-hours after start of simulation
Resolution = 0.20 degrees
Example: Iceland (4-14-2010)24-hours after start of simulation
Resolution = 0.10 degrees
Example: Iceland (4-14-2010)42-hours after start of simulation
Resolution = 0.10 degrees
Example: Ensemble simulations
Redoubt event 6
dx,dy=5 kmdz = 1 kmK = 0 km2/hrGrain sizes (1,2,4 m/s)
ESP:Duration = 0.25 hrErup. Vol = 0.007 km3
Plume H = random uniform (6-20 km)
50 realizations
Approximately 90 minutesto run 50 realizations
Probability of 1mm ash deposit Contours at 5%, 50%, 95%
Example: Ensemble simulationsRedoubt event 6
dx,dy=5 kmdz = 1 kmK = 0 km2/hrGrain sizes (1,2,4 m/s)
ESP:Duration = uniform
0.25-0.50 hrErup. Vol = uniform
0.005-0.007 km3
Plume H = normal= 12 km, =3 km
50 realizations
Probability of 1mm ash deposit Contours at 5%, 50%, 95%
Next steps
Finish verification Start validation: compare with field data Automate operational runs for volcanoes in
unrest Aggregation
Further work
Consider plume dynamics as input conditions More realistic initial ash distribution Weak plumes vs strong plumes in presence of
ambient wind
Dusty gas software
Built on clawpack (LeVeque) and authored by Marica Pelanti 2-D axi-symmetric 3-D Cartesian
Thanks!