1. WRF Volcano modelling studies, NCAS Leeds Ralph Burton, Stephen Mobbs, Alan Gadian, Barbara Brooks

2. 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.

3. “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 = 0 W ≠ 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 z U 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’)

4. 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 depend upon surface type) [X?] Wet Deposition: have included this but not tested it. (Method: ash is removed when cloud water mixing ratio is greater than Y g/Kg) [Y?] N.B. no interaction with microphysics at present N.B. Grimsvotn 2011? Leeds implementation: Methodology II.

5. 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

6. 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 release Order of minutes forecast Point source, Strong O(100K) thermal perturbation Updraughts ~ 50m/s

7. 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 release Order of minutes forecast Plume height depends upon thermal perturbation Can be function of time? (Not implemented) Emission rate constant for all ash types

8. 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 rate constant with height and for all ash types

9. 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

10. 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

11. Some Results. I. Long-range runs Eyjafjallajökull, May 2010 N.B. both images use the same domain. from NASA Earth Observatory, 2010 6 th May 12Z from model: ash + cloud 6 th May 12Z

12. Some Results. I. Long-range runs total integrated column ash isosurface of ash (Different simulation times)

13. Some Results. II. Near-vent runs Ash from above The model is initialised with a sounding from Keflavikurflugvollur (24 th April 2010 )

14. 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 3 rd 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).

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