1. 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?

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

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

4. ...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

5. 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.

6. 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

7. Aspect ratio = 1:1
~15km
25km

8. 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

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

10. 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

11. 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

12. 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

13. 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,

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 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).

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