Ash3d: A new USGS tephra fall model Hans Schwaiger Larry 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

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

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 Cell Upwind with Dimension Splitting Corner Transport Upwind t+Dt t Semi- Lagrangian

Illustration of advection schemes Donor Cell Upwind with Dimension Splitting Conserves mass Moderately fast Dt = Dx/v Increased numerical diffusion Conserves mass Slow Dt = Dx/v Low numerical diffusion Corner Transport Upwind Conserves mass only approximately Fast Dt = c Dx/v Low numerical diffusion Accuracy depends on order of interpolation Semi- Lagrangian

Illustration of diffusion schemes Explicit Forward Euler Easily implemented First-order accurate Dt = (Dx)2/K t+Dt t Implicit Crank-Nicolson Assumes linearity Requires solving Ax=b Second-order accurate Dt limited only by accuracy t+Dt 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 Linear advection in x,y Linear advection in z Diffusion in x,y,z Circular advection Method of manufactured solutions 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 that Ash3d can do <12-50 km 0.5-2.5 deg. (50-250 km) 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.

Projected Meteorological models used NAM AK 45 km NAM 11 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 ESRI ASCII (For import to Arc products) 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 Probability of 1mm ash deposit Contours at 5%, 50%, 95% Redoubt event 6 dx,dy=5 km dz = 1 km K = 0 km2/hr Grain sizes (1,2,4 m/s) ESP: Duration = 0.25 hr Erup. Vol = 0.007 km3 Plume H = random uniform (6-20 km) 50 realizations Approximately 90 minutes to run 50 realizations

Example: Ensemble simulations Probability of 1mm ash deposit Contours at 5%, 50%, 95% Redoubt event 6 dx,dy=5 km dz = 1 km K = 0 km2/hr Grain sizes (1,2,4 m/s) ESP: Duration = uniform 0.25-0.50 hr Erup. Vol = uniform 0.005-0.007 km3 Plume H = normal m= 12 km, s=3 km 50 realizations

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!