1. Integral models of volcanic plumes in a cross wind Mark Woodhouse 1 with Andrew Hogg 1, Jeremy Phillips 2 & Steve Sparks 2 1 School of Mathematics 2 School of Earth Science University of Bristol

2. Application to Eyjafjallajökull 2010 Application of the mass flux rise height scaling relationships can lead to large and rapid variations in the estimated mass flux. The integral model can used as an inversion tool, to determine source conditions from observations of the rise height with meteorology included. Integral models of volcanic plumes24 July 2013 2

3. Model-derived mass flux estimate Integral models of volcanic plumes24 July 2013 3

4. Beyond single point matching… Matching to a single observation target height gives an estimate of the source mass flux, but the model prediction cannot be assessed. By using additional observational data we can test the ability of the model to capture the detailed plume dynamics. Additional observational data can be obtained from Webcameras test of the entrainment formulation? Volcanic lightning test of the moisture formulation? Integral models of volcanic plumes24 July 2013 4

5. Webcamera at Eyjafjallajökull During the 2010 eruption of Eyjafjallajökull, a webcamera installed by Mila telecommunications recorded images of the volcanic plume every 5 seconds. Integral models of volcanic plumes24 July 2013 5

6. Matching plume model to webcam Integral models of volcanic plumes24 July 2013 6 5 minute period – 60 images From plume edges, the centreline trajectory can be determined. An optimization routine is used to adjust inputs to the integral plume model and match the predicted trajectory to the observation at a series of control points.

7. Matching plume model to webcam Integral models of volcanic plumes24 July 2013 7 2160 snapshots are used to produce 36 averaged images for 0700 to 1000 on 11 th May 2010, and model matching performed. The model matches give estimates of the source mass flux of around 6.4×10 4 kg/s. In comparison, Gudmundsson et al (2012) estimate a mass flux of 1×10 5 – 2×10 5 kg/s on 11 th May.

8. Effect of entrainment coefficient Integral models of volcanic plumes24 July 2013 8

9. Volcanic lightning Lightning is often observed in volcanic plumes. It is thought that lightning occurs due to charging of ash particles that results from fracturing and collisions during transport. Atmospheric conditions can also influence the occurrence of lightning. Integral models of volcanic plumes24 July 2013 9 Volcanic lightning at Eyjafjallajökull (National Geographic)

10. Volcanic lightning at Eyjafjallajökull Integral models of volcanic plumes24 July 2013 10 Lightning discharge data courtesy of Sonja Behnke During the 2010 eruption of Eyjafjallajökull, there was an period of intense volcanic lighting during May. An array of VHF detectors captured the signal from the lightning. The location of lightning flashes gives an indication of the plume trajectory in three-dimensions.

11. Charge structure Sonja Behnke and colleagues at New Mexico Tech. are able to analyse the lightning signal and determine the charge structure of the volcanic plume. Behnke et al suggest the dipole occurs due to ice-formation in the plume and ice-contact charging. (Behnke, S.A., R.J. Thomas, P.R. Krehbiel, W. Rison, and H.E. Edens (2012), Charge Structure and charging mechanisms in the plume of Eyjafjallajo ̈kull, Eos Trans. Am. Geophy. Union, Abstract AE13A-0375; and JGR Atmospheres, in review) Integral models of volcanic plumes24 July 2013 11 Monopole Negative-over- positive dipole 17 th May 12001400 13 th May 22000000

12. Moisture transport in plumes Volcanic plumes can transport large quantities of water vapour high into the atmosphere. On condensation, latent heat is released to the plume, increasing the energy content. For plumes that remain in the troposphere the additional energy can significantly enhance the rise height of the plume. Competition between moisture (enhancing rise height) and wind (reducing rise height). Integral models of volcanic plumes24 July 2013 12

13. Charge structure as a test of the moist plume model Integral models of volcanic plumes24 July 2013 13 17 th May 12001400 13 th May 22000000

14. Charge structure as a test of the moist plume model Integral models of volcanic plumes24 July 2013 14 11 th May 19002100 12 th May 21002300

15. 12 th May 03000500 Radar determined plume height (5.1km) is too lowlightning detected up to 7.6km. Undetermined points above 3.5km are likely to be from negative charge region. Integral models of volcanic plumes24 July 2013 15 Charge structure as a test of the moist plume model Radar determined plume height (7.9km) is too highno lightning detected above 6.3km. Switching between monopole and dipole. Suggests plume top is fluctuating near the level of condensation. 16 th May 14001600

16. Conclusions Integral plumes models incorporating meteorology, in particular wind, can be used to determine estimates of the source mass flux from an observation of the plume height. Additional observational data can be incorporated allowing the model prediction to be assessed. Webcams can provide useful information on plume trajectories and test formulations of the entrainment process. The moisture formulation has been tested using volcanic lightning observations. Integral models of volcanic plumes24 July 2013 16

17. Thanks Funding from NERC VANAHEIM project and FUTUREVOLC. Claire Witham (UK Met Office) for NWP data. Halldor Bjornsson (Icelandic Meteorological Office) and Mila Telecommunications for webcam images. Sonja Behnke (University of South Florida; previously Langmuir Laboratory, New Mexico Tech) for volcanic lightning data. Integral models of volcanic plumes24 July 2013 17