Dispersal model physics 32

Recent contributions in the physics of ash dispersal models include developments mostly in three fronts: i) experimental and modeling work on aggregation of volcanic ash; ii) description of the gravitational spreading of the umbrella cloud; iii) modeling work on sedimentation processes, and; iv) re-suspension of volcanic ash. This section offers a brief overview of recent contributions on each front.

1.4.2.1 Aggregation processes

A substantial fraction of finer tephra particles (diameters up to 100 μm; fine ash roughly) often falls as different aggregates types. Particle aggregation is a fundamental process that controls the dispersal and sedimentation of ash with diameter <100 μm. Model accuracy is limited by the fact that fine ash aggregates alter patterns of deposition. Experimental work on sedimentation and aggregation of volcanic ash has been (and is being) undertaken by a number of groups. Brown et al. (2012) provided a compressive review on recent volcanic ash aggregation developments during the past few decades. More recently, Mackie et al. (2016) dedicated a chapter to provide an overview of aggregates observed falling out of recent volcanic clouds, aggregates found in deposits, and key formation mechanisms. Since the review of Brown et al. (2012), a significant number of aggregation papers have been published. Some of that progress is highlighted here.

At modeling level, Costa et al. (2010) and Folch et al. (2010) developed a pioneer aggregation model based on a fractal relationship to describe the rate particles are incorporated into ash aggregates. Later, Langmann (2013) reported suitable algorithms for volcanic ash aggregation and wet deposition during long-range transport to be used in standard off-line volcanic ash forecast models. Van Eaton et al. (2015) proposed a mechanism of hail-like ash aggregation, based on previous laboratory experiments (Van Eaton et al., 2012a), that contributes to the anomalously rapid fallout of fine ash and occurrence of concentrically layered aggregates in volcanic deposits. More recently, Mastin et al. (2016) developed a simple, computationally-efficient aggregation parameterization scheme for use in operational model forecasts. The data resulting from these new developments have been included in the IAVCEI Commission for Tephra Hazard Modeling database for ash aggregates and it is currently being used in

ATHAM 1998-2016 10 3D LES Yes Yes Yes Yes Yes

PDAC 2007-2015 11 3D LES No Yes Yes No No

SK-3D 2005-2009 12 3D DNS-LES Yes No No No No

ASHEE 2016 13 3D LES No Yes Yes Yes Yes

Refs: 1—Bursik (2001), Pouget et al. (2016); 2—Mastin (2007, 2014); 3- Degruyter and Bonadonna (2012); 4—Woodhouse et al. (2013); 5—Devenish (2013); 6—Girault et al. (2014);7—De’Michieli Vitturi et al. (2015); 8—Folch et al. (2016a); 9— Cerminara (2015); 10—Oberhuber et al. (1998),(Savre et al., 2016); 11—Esposti Ongaro et al. (2007),Esposti Ongaro and Cerminara (2015); 12—Suzuki (2005),Suzuki and Koyaguchi (2009); 13—Cerminara et al. (2016).

different TTDMs. That same year, Costa et al. (2016a) attempted, for the first time, to assess TGSD on the basis of pivotal physical quantities, such as magma viscosity and plume height. Their proposed empirical strategy represented a valuable step forward towards a better evaluation of ESPs when more rigorous data are not available, e.g. real-time forecasting during volcanic crisis and fast hazard assessments. In addition, several works have illustrated observational and modeling perspectives on aggregation processes for specific recent eruptions – e.g. the 2010 Soufrière Hills eruption - Burns et al., (2017), the 2011 Grímsvötn eruption - Prata et al. (2017), or pre-historical events such as the 25.4 ka Oruanui supereruption from Taupo volcano, New Zealand (Van Eaton and Wilson, 2013).

Despite the significant progress presented above, aggregation processes remain a major source of uncertainty both in ash dispersal forecasting and interpretation of eruptions from the geological record. New integrated observations that combine remote sensing studies of ash clouds with field measurements and lab experiments are required to fill current gaps in knowledge surrounding ash aggregation processes. It is worth mentioning that with the exception of the FALL3D model, no operational model considers aggregation in their forecasts. Instead, aggregation is accounted for by either setting a minimum settling velocity in the code or, in the model input, adjusting particle-size distribution by replacing some of the fine ash with aggregates of a specified density, shape, and size range.

1.4.2.2 Gravitational spreading umbrella cloud

The complex interplay among cloud gravitational spreading, atmospheric diffusion, and wind advection of volcanic clouds have recently been topics of lively debates within the international community. For example, Costa et al. (2013) presented a novel analytical model to describe the radial growth of the umbrella cloud and the conditions when the dominant transport regime is gravity-current, passive, or mixed in terms of the cloud Richardson number. The model was implemented in FALL3D to evaluate the relative importance of gravity current effects during large volcanic eruptions (e.g. comparing model results to satellite imagery showing the 1991 Pinatubo umbrella cloud). In a later work, Mastin et al. (2014) replicated this work in Ash3D by calculating turbulent diffusion through an adjusted Crank- Nicolson formulation to match the observed rate of downwind widening of a deposit or ash cloud in simulations. In that same context, Johnson et al. (2015) suggested the need to re-evaluate the interpretations of Costa et al. (2013) grounded on the assumption that the radius of a continuously supplied intrusion (𝑟!) should grow in time (𝑡) as 𝑟!~𝑡!! rather than 𝑟!~𝑡!!.

More recently, Pouget et al. (2016a) presented a new model for radial, gravity-driven intrusion of volcanic ash and gas into the atmosphere in the umbrella cloud. The model increased the number of regimes described in Costa et al. (2013) to four spreading regimes based on type of resistance force (i.e. buoyancy-inertial or turbulent) and type of release (i.e. instantaneous or continuous).

1.4.2.3 Sedimentation (particle settling velocity)

Particle settling velocity is a complex function of particle size, density, and shape. These parameters control the residence time of tephra in the atmosphere and, consequently, tephra deposition. For simplicity, it is commonly assumed that tephra particles in volcanic clouds settle at their terminal velocity, which is derived from the balance between gravity, buoyancy, and drag forces. The precise determination of the aerodynamic drag forces requires a detailed parameterization of particle shape (e.g., Ganser, 1993). A large amount of experimental aerodynamic data exists for simple regular shapes. However, just a few studies have directly measured the terminal velocities of irregular volcanic particles (non-spherical), which is typical from most volcanic eruptions. In that context, the seminal work of Ganser (1993) has been considered to be the most accurate model available for predicting drag coefficient of non-spherical particles.

A review presented by Alfano et al. (2011) compared and assessed the use of Ganser’s model along with various existing particle settling velocity models considering different morphological characterizations (i.e., 2D and 3D). A couple of years later, Bonadonna et al. (2013) provided a review of the main approaches to model tephra sedimentation from volcanic plumes. This work concluded that more sophisticated numerical models do not necessary provide better accuracy in terms of ground depositions, but they can provide crucial information not possible with analytical models. This review also emphasized that models of all levels of sophistication would benefit from better parameterization of critical sedimentation processes such as particle aggregation and from the quantification of uncertainties associated with input parameters. More recently, Bagheri and Bonadonna (2016) summarized the current state of methods for characterizing size, shape, and aerodynamics of volcanic particles. Their review confirmed that particle shape governs both size parameters and particle aerodynamics (i.e. drag coefficient, settling velocity), and that the spherical approximation of volcanic particles introduces large errors. In a complementary work, Bagheri and Bonadonna (2016b) presented a novel model to predict the drag coefficient of non-spherical solid particles of different shapes (settling in gas or liquid) valid for sub- critical particle Reynolds numbers (i.e. 𝑅𝑒 <  3×10!_{). Finally, Dioguardi et al. (2017) presented new}

drag laws as a function of 3D fractal dimension and 3D sphericity measurements taken with X-ray microtomography.

Despite recent progress, the prediction of the drag coefficient for volcanic particles continues to be a major source of uncertainty. In that context, the seminal work of Ganser (1993) has been considered to be the most accurate model available for predicting drag coefficient of non-spherical particles and it is currently employed in most VATDMs.

Re-suspension of fine ash has long been recognized as an issue for aviation and air quality in some regions of the world (e.g. Alaska, Argentina and Iceland). For the past five years, research groups focusing on re-suspension have worked to classify the source of re-suspended material and identify methodologies to include it as an area source within VATDMs. To define the source term emission schemes for mineral dust have been tested for volcanic ash in Iceland (Leadbetter et al., 2012; Liu et al., 2014); Argentina (Folch et al., 2014; Ulke et al., 2016; Reckziegel et al., 2016; Toyos et al., 2017). In a recent work, Beckett et al. (2016) employed a different approach by using satellite-based measurements in combination with radiative transfer and dispersion modeling to quantify the total mass of ash re- suspended during the 16–17 September 2013 strong surface winds in southern Iceland.