WRF Volcano modelling studies,

NCAS Leeds

Ralph Burton, Stephen Mobbs, Alan Gadian, Barbara Brooks

Why use WRF?

State-of-the-art numerical weather prediction model

Can be run at a variety of scales, from O(100m) to many 10s of kms

Full range of microphysics, boundary layer, radiation, convection, etc. etc. schemes

Open-source – used in over 140 countries

Code is modular

Initialisation fields easily obtained

Runs either on desktop machine or national supercomputer -

scales very well

WRF = Weather Research and Forecasting – NCAR, U.S.

“Ash” is a passive tracer, but is assigned a settling velocity to mimic the effect of mass.

Relative velocities between particle and gas phases: U = V = 0W ≠ 0

Settling velocity is a function of height and density – from Kasten et al. 1968

x

y

z

Time = t

U

I.

x

y

z

Time = t + Δt

U

II.

x

y

zU

II(a).

U’

Time = t + Δt

Leeds implementation: Methodology I.

One-way coupling: ambient atmosphere affects ash, but not vice-versa

U’ = (0,0,-w’)

Up to 7 tracers (or ash species) at the moment. Thus,7 different densities of ash (plus combined field).

Dry Deposition: have included this but not tested it.

(Method: X% of ash is removed at surface. X could dependupon surface type) [X?]

Wet Deposition: have included this but not tested it.(Method: ash is removed when cloud water mixing ratiois greater than Y g/Kg) [Y?]

N.B. no interaction with microphysicsat present

N.B. Grimsvotn 2011?

Leeds implementation: Methodology II.

Leeds implementation: Methodology III.

All ash “species” (i.e. bins) are emitted at same rate.Different emission rates for different densities?

Some key parameters:

Emission rates ? Emission rates for different types of ash ?

Plume height / thermal perturbation ?

Density of ash ?

One-way coupling:Ambient atmosphere affects ash, but not vice-versa

Different applications.

Near-vent: 100m resolution, 141 levels, 25km x 25km

Initialised via GFS / ECMWF or radiosonde profiles

Ash initialised with heat source and point releaseOrder of minutes forecast

Point source,Strong O(100K) thermal perturbation

Updraughts ~ 50m/s

Different formulations of the model I.

Near-vent: 100m resolution, 141 levels, 25km x 25km

Initialised via GFS / ECMWF or radiosonde profiles

Ash initialised with heat source and point releaseOrder of minutes forecast

Plume height depends uponthermal perturbationCan be function of time?(Not implemented)

Emission rateconstant for all ashtypes

Different formulations of the model II.

Column source,No thermal perturbation

Near-vent: 15km resolution, continental scale

Initialised via GFS / ECMWF

Order of 60 hours forecast

Emission rateconstant with heightand forall ashtypes

Different formulations of the model II.

Near-vent: 15km resolution, continental scale

Initialised via GFS / ECMWF

Order of 60 hours forecast

Plume height specified;can be function of time

Output

A) All standard variables, plus tracer concentration

B) netCDF – non-CF compliance

C) A variety of WRF-specific applications to extract,convert data, etc.

Very large files ~50Gb

Some Results. I. Long-range runs

Eyjafjallajökull, May 2010

N.B. both images use the same domain.

from NASA Earth Observatory, 20106th May 12Z

from model: ash + cloud6th May 12Z

Some Results. I. Long-range runs

total integrated column ash

isosurface of ash(Different simulation times)

Some Results. II. Near-vent runsAsh from above

The model is initialised with a sounding from Keflavikurflugvollur (24th April 2010 )

Further work: full multiphase WRF

N + 1 phases: 1 air (gas + liquid and solid water) phase, N particulate phases (size bins)

Fundamentally N + 1 momentum equations, one for each phase, with interaction forces (drag) between them

Integrate N particulate momentum equations plus the combined (summed) momentum equation

There is only one shared pressure field and so the combined momentum equation is simply the usual one in the model, taking account of the contribution of the particles to the density.

All interaction forces between phases are equal and opposite (Newton's 3rd law) so cancel in the combined momentum equation

Drag terms in each particulate momentum equation

Modified equation of state taking account of the compressible fraction (air).

Further Work.

Similar approach adopted by e.g. Neri and Macedonio, “Numerical simulation of collapsingvolcanic columns with particles of two sizes”J. Geophy Res. B4, 8153-8174