Insights into coignimbrite plume dynamics from numerical models M. de’Michieli Vitturi 1 , S.L. Engwell 1 *, S. Barsotti 2 , J. Eychenne 3 , T. Eposti Ongaro 1 & A. Neri 1 * Corresponding author (samantha@engwell.com), 1 INGV, Sezione di Pisa, Via della Faggiola 32, 56216 Pisa, Italy 2 Vedurstofa Islands, Iceland Met Office, Bustadavegur 7-9, 150 Reykjavik 3 Dept. Earth Science, University of Bristol, Queens Road, Bristol, BS8 1RJ 1. Introduction Coignimbrite plumes form as ambient air is entrained into the top of propagating pyroclastic density currents (Sparks et al. 1997; PDCs). These plumes transport fine grained ash into the atmosphere, which can then be distributed over thousands of kilometres. While there have been many studies on the formation and dynamics of Plinian plumes, relatively few studies have been conducted on the plumes that loft from the top of PDCs. Here, conditions required for coignimbrite plume formation, and resultant plume dynamics are investigated by applica- tion of steady state models in combination with sensitivity analysis. 2. Ash flow model The steady state ash flow model of Bursik & Woods (1996) is employed to simulate PDC propagation solving equations for conservation of mass (for both mixture and particles of dif- ferent sizes), momentum and energy. Sedimentation is modeled as a function of particle set- tling velocity. The terms of the equations were rearranged such that momentum is calculated 5. Conclusions ⁕ Runout, solid mass fraction, and grainsize of available particles significantly dif- ferent for sub and supercritical flow regimes ⁕ Initial radius, gas mass fraction and height key controls on formation of coignim- brite plume ⁕ Coignimbrite liftoff mostly controlled by gas mass fraction and temperature of flow ⁕ Liftoff temperature and radius dominant controls on coignimbrite plume height ⁕ Coupled model results infer relationship between collapse radius, and gas mass fraction at PDC source and final coignimbrite plume height 4. Coupling the plume and ash flow models The ash flow model was coupled with the plume model to investi- gate the effect of varying ash flow model source conditions on plume height (Figure 9). Only the supercritical model is applied, with the assumption that the runout is equal to the source radius of the coignimbrite plume, i.e. the plume lifts from the whole of ash flow extent, as inferred for the May 18th Mount. St. Helens example (Sparks et al. 1986). Initial vertical velocity and entrainment are as- sumed constant for the plume model, with values of 1 m/s and 0.09 used respectively. Sensitivity analysis show final column height is mainly controlled by the initial ash flow radius (SI 0.51) and gas mass fraction (SI 0.45). 3. Coignimbrite plume height Conditions for coignimbrite plumes are significantly different to those considered when modelling Plinian columns (Figure 5): ⁕ Larger source area ⁕ Smaller initial velocity ⁕ Initial coignimbrite plume density equal to atmosphere. Positive initial buoyancy leads to an increase in velocity resulting in a significant de- crease in column radius to ensure conservation of mass (Figure 5). A modified version of (Bursik 2001) plume model was applied to study the relation between plume height and source conditions. The model (Barsotti et al. 2008) solves equations for conservation of mass, 6. Acknowledgements The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under the project NEMOH, REA grant agreement n° 289976. 7. References Adams, et al. 2013. Sandia Technical Report SAND2010-2183, December 2009. Updated April 2013. ⁕ Barsotti, S, Neri, A, and Scire, JS. 2008. Journal of Geophysical Research, 1 13(B03208). ⁕ Bursik, M. 2001.Geophysical Research Letters, 28(18), 3621–3624, ⁕ Sparks, RSJ, Moore, JG, and Rice, CJ. 1986. Journal of V olcanology and Geothermal Research, 28 (3), 257-274 .⁕ Sparks, RSJ, Bursik, MI, Carey, SN, Gilbert, Jennifer, Glaze, LS, Sigurdsson, H, and Woods, A. Volcanic plumes. Wiley , 1997. ⁕ Woods, AW and Wohletz, K. 1991. Nature, 350(6315), 225–227. ⁕ Woods, AW.1988 Bulletin of Volcanology, 50(3), 169{193). V43E-4942 momentum and thermal energy of bulk mixture with height. Development of the plume is dependent on temperature and gas mass fraction (Figure 6). Multiparametric analysis (Figures 7 & 8) using Dakota software (Adams et al. 2013), identifies initial temperature as the dominant control as a function of the input Richardson number (Ri = (gh(β-α))/βu 2 ), where g is gravitational acceleration, h is flow thickness, β is flow density, α ambient density and u flow velocity). Bursik & Woods (1996) describe two flow end member types, defined by their Richardson number; on maximum column height, while radius and entrainment also play a role. supercritical (Ri < 1) and subcritical flow (Ri > 1; Figure 1). We apply both the sub- and supercritical radial models (Figure 2). Sen- sitivity analysis of model outputs (runout, solid mass fraction and grainsize at liftoff) was conducted with respect to several input parameters. Runout is defined as the distance where flow density reaches ambient, and is as- sumed to be the point at which coignimbrite liftoff occurs. Results show the range of input parameters considered (see Figure 4) results in a large range of runouts, with the subcritical regime tending to greater distances (Figure 3). Limited entrainment in the subcritical flow, means temperature at liftoff is greater than for supercritical flow, despite longer runouts. Final grainsize distributions for the subcritical regimes are much finer than for supercritical regimes. Sensitivity indices (SI; Figure 4) show dominant controls on conditions important for coignimbrite plume formation vary for the two flow regimes studied, however, in both cases, initial radius, height, gas mass fraction and Richardson number are the dominant control on flow characteristics at lift- off. 0.0 0.2 0.4 0.6 0.8 Sensitivity Index Sensitivity Indices Main Total Plume Height Temperature (400 - 800 K) Velocity (1 - 5 m/s) Radius (2 - 10 km) Entrainment (0 - 0.1) Model Inputs 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Gas Mass Fraction 400 500 600 700 800 900 1000 Temperature (K) Buoyant: Plume formation No plume 0 10 20 Plume Height (km) 0 5 10 15 Plume Radius (km) 0 100 200 300 Plume Velocity (m/s) 0 1 2 3 4 5 Density (kg/m 3 ) Plinian Coignimbrite Atmosphere 20 40 60 80 100 Maximum Height (km) 400 500 600 700 800 Initial Temperature (K) 2 4 6 8 10 Initial Radius (km) 0.00 0.05 0.10 Entrainment Coefficient 0 20 40 Maximum Height (km) 1 2 3 4 Initial Radius 0 20 40 Maximum Height (km) 1 2 3 4 Initial Radius 600 800 1000 1200 Initial Temperature (K) 600 800 1000 1200 Initial Temperature (K) 0.1 0.2 0.3 Initial Gas Mass Fraction 0.1 0.2 0.3 Initial Gas Mass Fraction 0 1 2 3 4 5 Flow Thickness (km) 0 20 40 60 Radius (km) 0 20 40 Plume Height (km) 0 20 40 Radius (km) 20 - 77 km Main Sensitivity Index 0.51 Main Sensitivity Index Main Sensitivity Index 0.45 0 1000 2000 3000 Flow thickness (m) 0 1000 2000 3000 Flow thickness (m) 0 20 40 60 80 100 120 140 160 Velocity (m/s) 0 20 40 60 80 100 120 140 160 Velocity (m/s) 700 800 900 1000 Temperature (K) 2 4 6 8 10 12 Runout (km) 700 800 900 1000 Temperature (K) 2 4 6 8 10 12 Runout (km) 2 3 4 2 4 6 8 10 12 Runout (km) 2 3 4 Density (kg/m 3 ) 2 4 6 8 10 12 Runout (km) Supercritical Flow Subcritical Flow 1 2 3 4 Initial Thickness (km) 1 2 3 4 1 2 3 4 Initial Radius (km) 1 2 3 4 0.1 0.2 0.3 Initial Gas Mass Fraction 0.1 0.2 0.3 400 500 600 700 800 900 1000 1100 Final Temperature (K) 0 20 40 60 80 100 Final Runout (km) 400 500 600 700 800 900 1000 1100 0 20 40 60 80 100 0.2 0.4 0.6 0.8 Final Solid Mass Fraction 0 20 40 60 80 100 Final Runout (km) 0.2 0.4 0.6 0.8 0 20 40 60 80 100 3 4 5 Final Mean Grainsize (phi) 0 20 40 60 80 100 Final Runout (km) 3 4 5 0 20 40 60 80 100 Supercritical Flow Subcritical Flow 0.0 0.2 0.4 0.6 0.8 1.0 Main Sensitivity Index 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Total Sensitivity Index 0.0 0.2 0.4 0.6 0.8 1.0 Main Sensitivity Index Response Function 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Total Sensitivity Index Response Function Runout Solid Mass Fraction Grainsize Runout Solid Mass Fraction Grainsize Runout Solid Mass Fraction Grainsize Runout Solid Mass Fraction Grainsize Median Grainsize (-2 - 6 phi) Gas Mass Fraction (0.1 - 0.3) Temperature (600 - 1200 K) Richardson Number Height (0.5 - 4 km) Radius (0.5 - 4 km) Friction (0.001 - 0.02) Supercritical Flow Subcritical Flow Supercritical Flow (0.2 - 1) Subcritical Flow (1.5 - 10) 2 - 98 km Med 3.1 - 3.8 phi 2 - 82 km Med 3.2 - 4.7 phi 0.31 - 0.71 0.47 - 0.75 F in al Runo u t 13 km Fin a l R u n out 33 km Ash Flow Model Inputs Radius Height Temperature Gas Mass Fraction Richardson Number Grainsize Plume Model Inputs Vertical Velocity Entrainment Coefficient Radius Temperature Gas Mass Fraction Grainsize Plume Model Output Maximum Height Grainsize Ash Flow Model Outputs Runout Temperature Gas Mass Fraction Grainsize Figure 1. Schematic for the two regimes to propagating cur- rent (from Woods & Bursik 1996) Figure 5. Comparison of radius, vertical velocity and density profiles for typical Plin- ian (initial mfr 9.4 7 kg/s) versus coignimbrite (initial mfr 8.6 7 kg/s) input conditions. The different initial conditions have a significant affect on the plume dynamics. Figure 7. Control of model inputs on coignimbrite maximum plume height. Each point represents one simulation. Figure 8. Sensitivity indi- ces for relationship be- tween maximum plume height and input param- eters. Figure 9. Flow diagram showing ash flow model outputs used in plume model. Figure 10. Correlation between ash flow model inputs and predicted maximum coignimbrite plume height. Results from highlighted points shown in fur- ther detail in Figure 11. Figure 4. Sensitivity indices for current runout, solid mass fraction and median grainsize at liftoff for each input parameter . Figure 6. Coignimbrite plume formation occurs once neutral buoyancy is attained, controlled by gas mass fraction and mixture temperature. Figure 11. Examples of coupled modelled results, showing current thickness, and plume height for coupled results. Figure 2. (Left) Key differences in current dynamics with distance from source (after Bursik and Woods 1996), Initial radius and height of 2 km, and a magmatic temperature of 1100 K used in both simula- tions. For supercritical case, initial Ri = 0.8 and for subcritical initial RI = 1.2 . Initial velocity calculated as a function of Ri. Figure 3. (Right) Top row: Compilation of final runout versus input parameter for both the subcritical (blue points) and supercritical (red points) flow condition. Bottom Row: Comparison of flow characteristics at final runout, defined as when flow density equals ambient, where each point represents the result from one simulation, see Figure 4 for range of inputs.