Recent plume modelling work – NCAS Leeds Ralph Burton, Stephen Mobbs, Alan Gadian In the following, WRF has been configured with a “volcano” represented by a 200m x 200m vent having An upward jet (50m/s) coupled with Surface heating (2MW/m 2 ) Model configuration: 100m resolution, “large-eddy-simulation”-type run. 25kmx25km domain, U.S. standard atmosphere, no background wind. Simulation times are large (2 hours with output every minute – Tbs of data…) This results in a plume of height ~8km AGL, with level of neutral buoyancy at ~5km. The following slides show examples of wavelike response in the model, together with comparisons of plume spread with recent theoretical work (Bristol.)

t = 0.2ht = 0.6h Vertical velocity response: cross-section through plume LNB Up- and downdraughts, various wavelengths, at many heights - cf. satellite obs. of Okmok eruption: signal of disturbance seen in form of concentric rings emanating from source.

distance from vent (km) edge of plume (solid white) Time-distance plot of vertical velocity at z = 5km (LNB) ΔxΔx Δt1Δt1 ΔxΔx Δt2Δt2 steeper gradient implies slower phase speed FASTER SLOWER vertical velocity N.B. colour scale chosen to highlight lower magnitude W at distances far from vent. Close to the vent, there are much higher magnitudes than these [~O(50m/s)] Atmospheric disturbances can be tracked by following lines of constant W.

ΔxΔx Δt1Δt1 ΔxΔx Δt2Δt2 steeper gradient implies slower phase speed Slower (~5m/s phase speed) wave packet embedded in faster (~10m/s phase speed) wave packet. fast – slow – fast ‘Slow’ packet has lower wavelength. Edge of plume co-located with the edge of the ‘slow’ packet? FASTER SLOWER distance from vent (km) remnants of initial “shock” – travels at speed of sound

Comparison with new theory (WP1) (courtesy of A. Hogg et al., pers. comm. – but shown at EGU) New theory – plume spreads as r ~ t 3/4 [r = radius; t = time] Solid black line is model response Solid red line is r = At 3/4 Reasonable agreement with new theory distance from vent (km)

Surface pressure response to the waves. Similar behaviour shown to that observed at Okmok volcano: Angelis et al. “Evidence of atmospheric gravity waves during the 2008 eruption of Okmok volcano from seismic and remote sensing observations” (2011) GRL 38, L10303 Similar frequency response (observed: 1.7mHz: modelled: 1.6mHz) for duration of “monochromatic” phase. Modelled pressure fluctuations are lower than those observed – but there are many degrees of freedom (plume height, distance of pressure measurement from vent, background wind, stability, etc. ) – however, interesting similarities… Eruption (surface pressure) minus (surface pressure at “infinity”) 2.5km from source MODEL OBS ? km from source (not sure, ~15km?) corresponds to max. pressure fluctuations of ~±0.8hPa

Summary Wavelike motions at a variety of scales are seen. [To be checked against larger-spatial-domain runs to remove any concerns regarding wave reflections at boundaries] Good agreement with Bristol Group theoretical developments for spread of plume Surface pressure perturbations are similar qualitatively (and to some extent quantitatively) to measurements made at an Okmok eruption.