I. What? ~ II. Why? ~ III. How? Modelling volcanic plumes with WRF Ralph Burton, Stephen Mobbs, Alan Gadian VANAHEIM (Volcanic and Atmospheric Near-to-far-field Analysis of Plumes Helping Interpretation and modelling) PI Stephen Mobbs. Work Package 1 – Near-field plume numerical modelling I. What? ~ II. Why? ~ III. How?

I. What Is it possible to model near-field volcanic plume behaviour using an NWP model? (Eyja, E14, etc. etc. )

II. Why? The near-field influences the far-field. Courtesy Mark Woodhouse, Bristol University From UKMO Website

...Use WRF to model volcanic plumes Application of the Sparks-Mastin curves only implicitly takes into account background temperature profile upstream wind speed moisture content etc ...Use WRF to model volcanic plumes

III. How? Weather Research and Forecasting (WRF), state of the art numerical weather prediction model. Add a continuous thermal perturbation [O(100K)] to surface, co- located with tracer release (arbitrary number of tracers). Settling velocity can be added to tracers, to simulate ash settling of differing densities. Wet / Dry deposition of tracers has been added, but not implemented.

WRF plume model: simple tests WRF configuration: 100m resolution (25km x 25km), 141 vertical levels, 30km top Resting atmosphere – U.S. Standard atmosphere; dry; no ambient wind Different thermal perturbations at “vent” “Circular” vent Results look like plumes, but - Do they follow various theoretical models of plume behaviour

Aspect ratio = 1:1 ~15km 25km

Tests 1. Radial lengthscale, eruption / jet column. 4 3 Height (km) 2 2 gradient ~1/8 Turner, Buoyancy effects in Fluids b = (6/5)αz, b = radial lengthscale α = entrainment constant α = 0.10 (Turner again) gives b ~ z/8 1

Tests II. Height of plume. Theory WRF log H Courtesy Mark Woodhouse, Bristol University gradient = 0.25 H = k (ΔT) 1/4 log ΔT

More complex examples. I . Santorini 100m horizontal resolution, initialised with wind profile derived from averaged JJA ERA40 reanalyses (courtesy S. Sparks et al.) and N = 0.012, using 90m topography data Images show time-averaged concentration at surface (4-hour simulation) Plume height = 0.8km Plume height = 1.8km Plume height = 2.1km Plume height increasing; plume interaction with orography decreasing

Example II. Whirlwind -like structures Under certain circumstances (depending upon upstream wind speed, for fixed heat source), ash is transported downwards along relative vorticity “tubes”, similar to observations of certain cases. -ve (violet) +ve (red) WIND Ash Sparks et al. Volcanic Plumes Relative vorticity Surtsey volcano BAMS Oil tank fire MWR

Summary WRF has been used to simulate the near-field of volcanic plume – can be used to initialise large-scale WRF run Results for idealised cases agree well with theoretical predictions. Can simulate complex (observed) behaviour Ultimate goal: add two-way coupling

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

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).

From Elghobashi (1994) “On predicting turbulent-laden flows”, Applied Scientific Research, 52