[1] We introduce a novel analytical expression that allows for fast assessment of mass flow rate of both vertically-rising and bent-over volcanic plumes as a function of their height, while first order physical insight is maintained. This relationship is compared with a one-dimensional plume model to demonstrate its flexibility and then validated with observations of the 1980 Mount St. Helens and of the 2010 Eyjafjallajökull eruptions. The influence of wind on the dynamics of volcanic plumes is quantified by a new dimensionless parameter (P) and it is shown how even verticallyrising plumes, such as the one associated with the Mount St. Helens 1980 eruption, can be significantly affected by strong wind. Comparison between a one-dimensional model and the analytical equation gives an R 2 -value of 0.88, while existing expressions give negative R 2 -values due to their inability to adapt to different source and atmospheric conditions. Therefore, this new expression has important implications both for current strategies of real-time forecasting of ash transport in the atmosphere and for the characterization of explosive eruptions based on the study of tephra deposits. In addition, this work provides a framework for the application of more complete three-dimensional numerical models as it greatly reduces the parameter space that needs to be explored.

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25 26A long-standing conceptual model for deep submarine eruptions is that high hydrostatic pressure 27 hinders degassing and acceleration, and suppresses magma fragmentation. The 2012 submarine 28 rhyolite eruption of Havre volcano in the Kermadec arc provided constraints on critical 29 parameters to quantitatively test these concepts. This eruption produced a > 1 km 3 raft of floating 30 pumice and a 0.1 km 3 field of giant (>1 m) pumice clasts distributed down-current from the vent. 31We address the mechanism of creating these clasts using a model for magma ascent in a conduit. 32We use water ingestion experiments to address why some clasts float and others sink. We show 33 that at the eruption depth of 900 m, the melt retained enough dissolved water, and hence had a 34 low enough viscosity, that strain-rates were too low to cause brittle fragmentation in the conduit, 35 despite mass discharge rates similar to Plinian eruptions on land. There was still, however, 36 enough exsolved vapor at the vent depth to make the magma buoyant relative to seawater. 37Buoyant magma was thus extruded into the ocean where it rose, quenched, and fragmented to 38 produce clasts up to several meters in diameter. We show that these large clasts would have 39 floated to the sea surface within minutes, where air could enter pore space, and the fate of clasts 40 is then controlled by the ability to trap gas within their pore space. We show that clasts from the 41 raft retain enough gas to remain afloat whereas fragments from giant pumice collected from the 42 seafloor ingest more water and sink. The pumice raft and the giant pumice seafloor deposit were 43 thus produced during a clast-generating effusive submarine eruption, where fragmentation 44 occurred above the vent, and the subsequent fate of clasts was controlled by their ability to ingest 45 water. 46 3 47

International audienceThe eruption style of silicic magmas is affected by the loss of gas (outgassing) during ascent. We investigate outgassing using a numerical model for one-dimensional, two-phase, steady flow in a volcanic conduit. By implementing Forchheimer's equation rather than Darcy's equation for outgassing we are able to investigate the relative influence of Darcian and inertial permeability on the transition between effusive and explosive eruptions. These permeabilities are defined by constitutive equations obtained from textural analysis of pyroclasts and determined by bubble number density, throat-bubble size ratio, tortuosity, and roughness. The efficiency of outgassing as a function of these parameters can be quantified by two dimensionless quantities: the Stokes number, the ratio of the response time of the magma and the characteristic time of gas flow, and the Forchheimer number, the ratio of the viscous and inertial forces inside the bubble network. A small Stokes number indicates strong coupling between gas and magma and thus promotes explosive eruption. A large Forchheimer number signifies that gas escape from the bubble network is dominated by inertial effects, which leads to explosive behaviour. To provide context we compare model predictions to the May 18, 1980 Mount St. Helens and the August-September 1997 Soufrière Hills eruptions. We show that inertial effects dominate outgassing during both effusive and explosive eruptions, and that in this case the eruptive regime is determined by a new dimensionless quantity defined by the ratio of Stokes and Forchheimer number. Of the considered textural parameters, the bubble number density has the strongest influence on this quantity. This result has implications for permeability studies and conduit modelling

Magma degassing fundamentally controls the Earth's volatile cycles. The large amount of gas expelled into the atmosphere during volcanic eruptions (i.e., volcanic outgassing) is the most obvious display of magmatic volatile release. However, owing to the large intrusive:extrusive ratio, and considering the paucity of volatiles left in intrusive rocks after final solidification, volcanic outgassing likely constitutes only a small fraction of the overall mass of magmatic volatiles released to the Earth's surface. Therefore, as most magmas stall on their way to the surface, outgassing of uneruptible, crystal‐rich magma storage regions will play a dominant role in closing the balance of volatile element cycling between the mantle and the surface. We use a numerical approach to study the migration of a magmatic volatile phase (MVP) in crystal‐rich magma bodies (“mush zones”) at the pore scale. Our results suggest that buoyancy‐driven outgassing is efficient over crystal volume fractions between 0.4 and 0.7 (for mm‐sized crystals). We parameterize our pore‐scale results for MVP migration in a thermomechanical magma reservoir model to study outgassing under dynamical conditions where cooling controls the evolution of the proportion of crystal, gas, and melt phases and to investigate the role of the reservoir size and the temperature‐dependent viscoelastic response of the crust on outgassing efficiency. We find that buoyancy‐driven outgassing allows for a maximum of 40–50% volatiles to leave the reservoir over the 0.4–0.7 crystal volume fractions, implying that a significant amount of outgassing must occur at high crystal content (>0.7) through veining and/or capillary fracturing.

The 2011 Cordón Caulle eruption represents an ideal case study for the characterization of long-lasting plumes that are strongly affected by wind. The climactic phase lasted for about 1 day and was classified as subplinian with plumes between~9 and 12 km above the vent and mass flow rate (MFR) on the order of~10 7 kg s À1. Eruption intensity fluctuated during the first 11 days with MFR values between 10 6 and 10 7 kg s À1. This activity was followed by several months of low-intensity plumes with MFR < 10 6 kg s À1 .Plume dynamics and rise were strongly affected by wind during the whole eruption with negligible upwind spreading and sedimentation. The plumes that developed on 4-6 and 20-22 June can be described as transitional, i.e., plumes showing transitional behavior between strong and weak dynamics, while the wind clearly dominated the rise height on all the other days resulting in the formation of weak plumes. Individual phases of the eruption range between Volcanic Explosivity Indices (VEIs) 3 and 4, while the cumulative deposit related to 4-7 June 2011 is associated with VEIs 4 and 5. Crosswind cloud and deposit dispersal of the first few days are best described by a linear combination of gravitational spreading and turbulent diffusion, with velocities between 1 and 10 m s À1. Downwind cloud velocity for the same days is best described by a linear combination of gravitational spreading and wind advection, with velocities between 17 and 45 m s À1. Results show how gravitational spreading can be significant even for subplinian and small-moderate eruptions strongly advected by wind and with low Richardson number and low MFR.