Source term (plume models) 28

The description of physical parameters from explosive eruptions is necessary to characterize eruptive behavior of active volcanoes and assess their hazards. In that context, several datasets are for the characterization of eruptive events of the past 10.000 years (e.g. Global Volcanism Program, GVP,

http://www.volcano.si.edu/; LaMEVE database,

http://www.bgs.ac.uk/vogripa/view/controller.cfc?method=lameve). In addition, collaborative efforts are

currently underway to review and restructure the Eruption Source Parameters (ESPs) Database for the world’s volcanoes (Engwell et al., 2016) originally proposed by Mastin et al. (2009).

Accurate characterization of the initial plume height, mass eruption rate (MER) and total grain size distribution (TGSD) is key to characterize the source term and to determine the height at which volcanic plumes spread in the atmosphere. The height to which a volcanic plume (or column; these terms are used interchangeably in this document) may rise is greatly influenced by the surrounding atmospheric characteristics and it is widely investigated for hazard mitigation. Traditionally, simple relationships between the source mass flux and plume height in a wind field have been used to characterize the eruption column. However, such empirical formulations (0-D) can be inaccurate and can underestimate rates in windy conditions (Mastin, 2014). This section focuses on the most recent developments regarding plume modeling.

Noteworthy progress has been reported in the development of new empirical formulations and eruptive plume models. In a recent work, Costa et al. (2016b). compared and evaluated one-dimensional (1-D) and

three-dimensional (3-D) numerical models of volcanic eruption columns in a set of different inter- comparison exercises. Model variability in plume height was estimated to be within ~20% for the weak plume and ~10% for the strong plume (Costa et al., 2016b). Results from this work also suggest that 1D models are considered adequate for weak plumes but recommend the use of more complex 3D models for strong plumes (Fig 4). This section provides a conceptual overview of the existing plume modeling solutions (empirical, 1-D and 3-D) and the most recent developments for each approach. It is worth mentioning that, despite the progress presented by 1-D and 3-D models, recent studies have also highlighted the uncertainty associated to plume models, (e.g. Dioguardi et al., 2016; Macedonio et al., 2016; Mastin, 2014). In light of the above, better understanding of the source conditions and how these affect the development and evolution of eruptive plumes is still required to reduce uncertainties in ash dispersion modeling.

Figure 4. Schematic representation of weak and strong plumes according to eruption size (modified from Costa et al., 2016b)

1.4.1.1 Empirical formulations (0-D)

Historically, empirical formulations provided the relationship between plume height and mass eruption rate based exclusively on field observations (e.g. Mastin et al., 2009). Despite their goodness of fit (Fig. 5), these relationships result in significant uncertainty when used to estimate mass flux in windy conditions (Mastin, 2014). Recent developments have led to explicitly account for the effects of wind. For

example, Degruyter and Bonadonna (2012) and Woodhouse et al. (2013) incorporated the effects of the atmospheric temperature, wind profile, source thermodynamic properties, and values of the entrainment coefficient into this relationship.

More recently, Carazzo et al. (2015) used analogue experiments from strong and weak plumes to account for wind velocity. Despite their advantages, several authors (e.g. Mastin, 2014) have argued that the actual eruption rate could have been 1 to 2 orders of magnitude greater than the empirical relations would suggest, and could be more accurately estimated using one-dimensional plume models.

Figure 5. Column height and MER relationship based on field observations (extracted from Mastin et al. 2009).

1.4.1.2 1-D Plume Models

Despite their simplicity, 1-D models have been remarkably successful at describing buoyant plumes. These employ different applications of the mathematical description of turbulent buoyant plumes (Morton et al., 1956), hereafter referred to as Buoyant Plume Theory (BPT). Most 1-D models use the formulation of Woods (1988) who built his plume theory on Wilson (1976) by assuming ambient pressure and homogeneous mixture of all phases. The inclusion of additional atmospheric processes a few years later,

such as humidity (Mastin, 2007), wind (Bursik, 2001) and profiles in temperature, allowed 1-D models to start reflecting real atmospheric conditions. More recently, models adopted different entrainment coefficients values based on their specific formulations or calibration studies (e.g. Devenish et al., 2010). Finally, Folch et al. (2016a) presented FPlume: a 1-D cross-section averaged plume model which accounts for plume bent over, entrainment of ambient moisture, effects of water phase changes on the energy budget, particle aggregation, particle fallout and re-entrainment by turbulent eddies, as well as variable entrainment coefficients fitted from experiments. FPlume has been implemented in NMMB- MONARCH-ASH. Currently, 1-D models currently offer the best tool for operational use and broad exploratory investigations (Costa et al., 2016b; Devenish, 2013). Table 3 (top) summarizes, in chronological order, 1-D models developed (or updated) in the last 5 years.

1.4.1.3 3-D Plume Models

Three-dimensional (3-D) plume models are designed to resolve the detailed turbulence structure of volcanic plumes using a time-dependent solution of the turbulent Navier–Stokes equations for the conservation of mass, momentum, and energy. Different numerical solutions exist depending on the way models describe the eruptive mixture or solve the governing equations. In any case, to initialize these models it is necessary to provide a description of the flux of volcanic ash and gases into the atmosphere. These multiphase and multicomponent models, while computationally more expensive, have shown to provide critical information on the interaction of the plume with the surrounding atmosphere. Suzuki et al. (2016) provided a thorough inter-comparison of three-dimensional models of volcanic plumes. Table 3 (bottom) summarizes (in chronological order) the most commonly used 3-D models developed (or updated) in the last 5 years.

Table 3. Recent (5 years or less) developments in plume modeling. Top: 1-D models; Bottom: 3-D models (Costa et al., 2016b)

Model (Year) Refs. Model

type Air entrainment Wind

Particle fallout Particle re- entrainment Moisture entrainment Water latent heat

Puffin 2001-2016 1 1D α=0.15 β=1.0 Yes Yes Yes No No

Plumeria 2007-2014 3 1D α=0.09 β=0.5 Yes No No Yes Yes

Degruyter 2012 3 1D α=0.10 β=0.5 Yes No No Yes Yes

PlumeRise 2013 4 1D α=0.09 β=0.9 Yes No No Yes Yes

Devenish 2013 5 1D α=0.10 β=0.5 Yes No No Yes Yes

PPM 2014 6 1D α=f(Ri) β=0.5 Yes Yes No No No

PlumeMoM 2015 7 1D α=0.09 β=0.6 Yes Yes No No No

FpluMe 2016 8 1D α=f(Ri) β=g(Ri) Yes Yes Yes Yes Yes