Ash3d: A new USGS tephra fall model Hans Schwaiger 1 Larry Mastin 2 Roger Denlinger 2 1 Alaska...
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Transcript of Ash3d: A new USGS tephra fall model Hans Schwaiger 1 Larry Mastin 2 Roger Denlinger 2 1 Alaska...
Ash3d:A new USGS tephra fall model
Hans Schwaiger1
Larry Mastin2
Roger Denlinger 2
1 Alaska Volcano Observatory
2 Cascade Volcano Observatory
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
A shfa ll mo delling pro gra m by A .W . H u rs t, N Z - IG N SW ind da ta from N O A A-A R L
0 40 80 12 0 16020K ilo m e ter s
M o u n t S t. H e le n s
A ir p o rts
Modeled Tephra Th ic knes s
Val u e4 m m
0 m m
H y p o th etic a l e r u p tio n o f M o u n t S t. H e le n s V o lc an oV o lu m e = 1 m il lio n c u b ic m ete rs , C o lu m n h e ig h t = 7 km
M M 5 (15 K m ) fo r ec as t w in d s 00 h rs U T C 0 5 J u n 0 7 (17 h rs P D T 04 J u n 0 7)
M o u n t S t . H e le n s
Cla rk
S kam an ia
Cow litz
Mu ltno ma h
Cla ckam as
W a shing ton
Ma rio n
Linn
Co lum bia
Ho odRive r
Wa sco
J effe rson
De schu tes
Crook
Lan e
K lam ath LakeDo ug la s
Coos
Benton
Linco ln
P olk
Yam hill
Tillam oo k
Cla tsop
S he rma n
Gilliam
Mo rrow
Um atilla
Un ion
W h eele rG ra nt
Harn ey
Ma lh eu r
Baker
Wa llo wa
Asotin
G arfield
Co lum bia
W allaWa lla
Fra nklin
Benton
Ada msW h itma n
Linco ln S pokan e
P endO reille
S te vens
Fe rryOkan og an
Doug la s
G rantK ittita s
Ch elan
Y akim a
Lewis
P ierce
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S no homish
Skag it
W h atco m
S anJ ua n
Is land
Cla lla m
Th urs to n
G raysH arbo r
J efferson
Ma son
K itsap
P acific
W a hkiaku m
K lickita t
Bound ary
Bon ne r
K ooten ai
Benew ah
Latah
S ho sho ne
Cle arwate r
Lew is
Ne zP erce
Ida ho
Ada ms
Valley
Wa shington
P ayette
G emBoise
Ca nyo n
AdaE lmoreO w yhee
Lincoln
San de rs
Mine ral
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 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• Uses most 2nd order terms•t = x/u• Increased numerical diffusion
• Conserves mass• Slow• Uses all 2nd order terms•t = x/u• Low numerical diffusion
• Conserves mass only approximately• Fast•t = c x/u• Low numerical diffusion• Accuracy depends on order of interpolation
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)
Types of calculation thatAsh3d can do
Calculation on a sphere Calculation on a plane• Uses lower-resolution Global Forecast System winds
•But, it can model an eruption from any volcano on Earth.
• Uses high-resolution winds from projected models (e.g. NAM, WRF)
•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
Pavolonis
Example: Ensemble simulationsRedoubt: March 24, 2009 (event 6)dx,dy=5 kmdz = 1 kmnx,ny,nz = 140,140,22nt = ~600K = 0 km2/hrgrain sizes (1,2,4 m/s)
ESP:Duration = 15 minErup. Vol = 0.007 km3
Plume H = random uniform (6-20 km)
50 realizations (~90 min)
Example: Ensemble simulations
Redoubt 2009 event 6
ESP:
Plume H uniform 6-20 km
Erup. Vol. 7x10-4 km3
Duration 15 min
Probability of ash deposit > 1mm Contours at 5%, 50%, 95%
Example: Ensemble simulationsRedoubt: March 24, 2009 (event 6)dx,dy=5 kmdz = 1 kmnx,ny,nz = 140,140,22nt = ~600K = 0 km2/hrgrain sizes (1,2,4 m/s)
ESP:Duration = uniform
15-30 minErup. Vol = uniform
0.005-0.009 km3
Plume H = normal= 14 km, =3 km50 realizations (~90 min)
Example: Ensemble simulations
Redoubt 2009 event 6
ESP:
Plume H normal = 14 km=3 kmErup. Vol. uniform 5-9x10-4 km3
Duration uniform 15-30 min
Probability of ash deposit > 1mm Contours at 5%, 50%, 95%
Next steps
Finish verification Start validation: compare with field data Automate operational runs for volcanoes in unrest Sensitivity analysis Adaptive mesh refinement Include Aggregation Topography
Summary
New USGS tephra fall model nearly complete Automated simulations for volcanoes in unrest
coming soon Feedback appreciated on output formats
Simulation output Ensemble output
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 accuracy
tt+t
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
Execution time for different schemes
Circular advection test case
• Smooth boundaries are modeled well
• Sharp boundaries are smoothed by numerical diffusion