The size range of bubbles that produce ash during explosive volcanic eruptions
- Kimberly Genareau†1, 2Email author,
- Gopal K Mulukutla†3,
- Alexander A Proussevitch†3,
- Adam J Durant4,
- William I Rose5 and
- Dork L Sahagian†1
© Genareau et al.; licensee Springer. 2013
Received: 20 February 2013
Accepted: 1 August 2013
Published: 22 August 2013
Volcanic eruptions can produce ash particles with a range of sizes and morphologies. Here we morphologically distinguish two textural types: Simple (generally smaller) ash particles, where the observable surface displays a single measureable bubble because there is at most one vesicle imprint preserved on each facet of the particle; and complex ash particles, which display multiple vesicle imprints on their surfaces for measurement and may contain complete, unfragmented vesicles in their interiors. Digital elevation models from stereo-scanning electron microscopic images of complex ash particles from the 14 October 1974 sub-Plinian eruption of Volcán Fuego, Guatemala and the 18 May 1980 Plinian eruption of Mount St. Helens, Washington, U.S.A. reveal size distributions of bubbles that burst during magma fragmentation. Results were compared between these two well-characterized eruptions of different explosivities and magma compositions and indicate that bubble size distributions (BSDs) are bimodal, suggesting a minimum of two nucleation events during both eruptions. The larger size mode has a much lower bubble number density (BND) than the smaller size mode, yet these few larger bubbles represent the bulk of the total bubble volume. We infer that the larger bubbles reflect an earlier nucleation event (at depth within the conduit) with subsequent diffusive and decompressive bubble growth and possible coalescence during magma ascent, while the smaller bubbles reflect a relatively later nucleation event occurring closer in time to the point of fragmentation. Bubbles in the Mount St. Helens complex ash particles are generally smaller, but have a total number density roughly one order of magnitude higher, compared to the Fuego samples. Results demonstrate that because ash from explosive eruptions preserves the size of bubbles that nucleated in the magma, grew, and then burst during fragmentation, the analysis of the ash-sized component of tephra can provide insights into the spatial distribution of bubbles in the magma prior to fragmentation, enabling better parameterization of numerical eruption models and improved understanding of ash transport phenomena that result in pyroclastic volcanic hazards. Additionally, the fact that the ash-sized component of tephra preserves BSDs and BNDs consistent with those preserved in larger pyroclasts indicates that these values can be obtained in cases where only distal ash samples from particular eruptions are obtainable.
Explosive volcanic eruptions can result in significant hazards to people and property due to the generation of pyroclastic density currents, emission of ash into the atmosphere, and deposition of ash at great distances from the source volcano. The aviation industry is at particular risk from ash-producing explosive eruptions, as demonstrated by the recent eruptions of Eyjafjallajökull (2010) and Grímsvötn (2011) in Iceland, and Puyehue-Cordón Caulle in Chile (2011). Due to considerable reliance on air transport for global commerce and travel, even relatively small explosive eruptions can have far-reaching consequences, shutting down international and regional airports, altering airline flight paths, and resulting in large economic impacts.
Ash is the finest fraction of volcanic tephra (< 2 mm), formed from a number of different processes that may include: 1) magma-water interaction (e.g., Wohletz 1983; Zimanowski et al. 1986; Zimanowski 2001; Gonnermann and Manga 2007); 2) comminution within the conduit or during the transport of pyroclastic density currents (e.g., Dufek and Manga 2008; Rose and Durant 2009a; Dufek et al. 2012); or 3) the explosive fragmentation of bubbles that nucleate and grow during magma ascent and degassing when the melt portion of the magma becomes oversaturated with dissolved volatiles, primarily H2O (Sparks 1978; Dunbar and Hervig 1992; Gardner et al. 1996; Papale 1999; Sahagian 1999; Zhang 1999; Alidibirov and Dingwell 2000; Wallace 2002; Spieler et al. 2004; Koyaguchi and Mitani 2005). Volcanic ash represents a significant hazard to the airline industry and operation of global commerce (Casadevall 1994; Casadevall et al. 1996; Prata 2009; Durant et al. 2010), water quality (Stewart et al. 2006; Stewart et al. 2009; Wilson et al. 2010), agriculture (Cronin et al. 1997; Wilson et al. 2010), stability of local infrastructure (Wardman et al. 2012a; 2012b; Wilson et al. 2012), and human health (Baxter et al. 1999; Horwell et al. 2003a2003b; Hansell et al. 2006; Hincks et al. 2006; Horwell and Baxter 2006). Because ash can be transported for great distances regardless of the total volume of material actually erupted, it represents one of the farthest reaching volcanic hazards. Analysis of ash helps to assess the pyroclastic hazards and provides virtually the only information available regarding the eruption-driving bubbles that fragmented to produce the ash. By constraining the sizes of the bubbles that burst during fragmentation, it is possible to glean information regarding magma ascent and vesiculation processes, as well as to establish a correlation between eruption style and the proportion of ash generated during eruption. It is toward these goals that this research is directed.
It has been previously demonstrated that explosive volcanic eruptions are driven by the nucleation and growth of exsolved gas bubbles in the magma (Sparks 1978; Proussevitch and Sahagian 1996; 1998; 2005; Sahagian 2005; Gonnermann and Manga 2007) which leads to foam disruption due to instability of inter-bubble films and plateau borders, causing fragmentation (McBirney and Murase 1970; Proussevitch et al. 1993; Alidibirov 1994; Zhang 1999; Alidibirov and Dingwell 2000; Gonnermann and Manga 2007; Castro et al. 2012). Despite the necessity to understand mechanisms of ash production during explosive volcanic eruptions, knowledge is limited due to (1) the disruption of magmatic foams during fragmentation that destroys existing bubbles, and (2) the small size of the ash particles that result from energetic eruptions. Typically, lapilli-sized tephra (2–64 mm) are analyzed using either two-dimensional scanning electron/optical microscopy techniques on sectioned and polished clasts (e.g., Cashman and Mangan 1994; Klug and Cashman 1994; and Toramaru, 1990) or X-ray computed microtomography (e.g., Song et al. 2001; Shin et al. 2005; Gualda and Rivers 2006; Polacci et al. 20062009; Degruyter et al. 2010a2010b). These methods allow examination of entire bubbles that remain preserved in erupted products (the bubbles that did not burst during fragmentation). Until now, analysis of the finest tephra fraction (ash) produced by explosive fragmentation has not been feasible, and any information regarding the bubbles that produced the resultant particles was lost. However, such information is necessary in order to understand bubble nucleation and fragmentation mechanisms that produce volcanic ash during the most energetic eruptions, toward the ultimate goal of mitigating associated immediate and long-term hazards.
In addition to concern about volcanic hazards from erupted ash, a second reason to study ash is that it results from high intensity eruptions and may shed light on the processes that lead to these cataclysmic events. In some cases it may be the only evidence of large-scale explosive eruptions at large distances from source, and it can be safely collected far from the site of the actual eruption following deposition. Although the complete bubble population can be constrained through analysis of larger pyroclasts, in some instances these larger size fractions may not be available at certain collection sites, particularly in very distal locations. As such, analysis of ash as developed here makes it possible to quantify the bubble size population in cases where only the ash-sized tephra component is available for study.
Samples of tephra fall deposits from these eruptions were collected (by others) after deposition, and sieving analyses were performed in order to characterize the tephra granulometry as a function of distance from source. Differences in both the explosivities of the eruptions and the bulk magma compositions allowed a first-order comparison between different types of ash-producing volcanic events to test the viability of the SSEM method in determining the size of the bubbles that burst to produce the ash component of the tephra and helping to characterize individual eruptions. Samples utilized for this study were based on availability, and were not selected in advance due to any specific characteristics.
14 October 1974: Volcán Fuego, Guatemala
The 14 October 1974 eruption of Volcán Fuego, Guatemala was characterized by a quasi-sustained column (rising up to ~14 km above the vent) in conjunction with multiple explosions that erupted a dense rock equivalent (DRE) of 0.021 km3 over a period of 5 hours for an eruption rate of ~3.2 × 106 kg s-1 (Stoiber 1974; Rose et al. 1978; Rose et al. 2008). The tephra dispersal, total time period of the eruption, and quasi-sustained nature of the explosion classifies this particular event as sub-Plinian, as opposed to Vulcanian (Rose et al. 2008). The 14 October sub-Plinian explosion occurred in a longer sequence of events that began on 10 October and ended on 23 October, and samples from 14 October were immediately collected in the days following the eruption (Figure 1a) (Rose et al. 1978; Murrow et al. 1980; Rose et al. 2008). Juvenile tephra from this event was composed of high-Al basaltic (50% SiO2) scoriacious ash and lapilli. Tephra deposition from this eruption included the emplacement of pyroclastic flow deposits (Davies et al. 1978; Rose et al. 2008) and ash dispersal over a total area of ~1600 km2 (Rose et al. 2008). Grain size distribution (GSD) of the tephra fall deposit was unimodal, except in more marginal and distal locations, where the GSD became bimodal, including >10 wt% fine ash (>4 φ; < 63 μm) (Rose et al. 2008).
18 May 1980: Mount St. Helens, Washington, U.S.A.
The eruption of Mount St. Helens, Washington, on 18 May 1980 involved several different phases of activity, including an initial lateral blast followed by a Plinian eruption column and then extensive pyroclastic flows, which produced co-ignimbrite plumes and a significant amount of very fine ash (>5 φ; < 30 μm). The 1980 magma from Mount St. Helens was dacitic (65 wt% SiO2). The main phase of the eruption lasted almost 9 hours and produced an average mass flux of 4.4 × 107 kg s-1 (Carey et al. 1990; Andrews and Gardner 2009), more than an order of magnitude greater than Fuego’s 14 Oct 1974 event. The height of the eruption column was between 13 and 19 km for almost 9 hours (Carey and Sigurdsson 1985; Carey et al. 1990; Andrews and Gardner 2009). Samples of tephra fall from this eruption have been extensively studied (e.g., Sarna-Wojcicki AM et al (1981; Klug and Cashman, 1994; Rose and Durant 2009b). Klug and Cashman (1994) examined pumice clasts and observed two separate bubble size modes depending upon the texture of the analyzed clast. Grey, relatively less vesicular pumice clasts with higher microlite contents displayed a BSD with an equivalent vesicle diameter mode of ~15 μm, while the more vesicular, less crystalline white pumice clasts displayed an equivalent vesicle diameter mode of ~50 μm. Analyses of the ash component of the 1980 MSH tephra showed that 50 wt% of the total GSD was comprised of very fine ash (< 30 μm) (Rose and Durant 2009b). As indicated by these previous studies, explosive eruptions of various styles, with different magma compositions, can produce various proportions of ash and other pyroclasts based on the size and number density of bubbles that control the nature of fragmentation.
Simple and complex ash particle textures
Complex ash particles
Measured characteristics of complex ash particles
Distance from source (km)
No. of Bubbles/Particles
TND (1012 m-3)
TND (1012 m-3)
Bubble size distributions (BSD) and bubble number densities (BND)
Our BSD results from the MSH complex ash samples are consistent with previous measurement of MSH BSDs (Figure ten; Klug and Cashman 1994; Rust and Cashman 2011). Samples from both MSH and Fuego include simple and complex ash particles (see Figures 7 and 8) in all sampled locations, and the abundance of complex ash particles decrease with distance. While the sizes of the modes of the bubbles preserved by ash fragments are markedly different for the basaltic versus the dacitic eruption, many complex ash particles preserve both a larger and smaller population of bubbles. For each eruption, modal bubble size does not vary significantly with distance from the vent, although the fraction of complex ash particles capable of recording the larger bubbles decreases with distance (Figure 9). In addition, the two size modes are clearly differentiable in the MSH complex ash particles, while the Fuego samples show some overlap in the two modes (Table 1; Figure 11).
We now consider how a complex ash particle texture may form in a fragmenting parcel of magmatic foam. If all bubbles are of identical size and evenly distributed, all bubble walls and plateau borders would disrupt simultaneously, producing only simple ash particle textures. At the opposite extreme, if all exsolving volatiles within the volcanic conduit were concentrated in a single bubble, it could burst and leave no bubbly magma behind to make complex ash particles. It is only in the realistic case of a more complex size and spatial distribution of bubbles that complex ash particles are expected to form. We interpret the complex ash particles we observe in both the MSH and Fuego deposits to result from the spatial heterogeneity produced by a later stage nucleation event of smaller bubbles within a pre-existing distribution of relatively larger bubbles.
Although smaller bubbles dominate the BND of both eruptions, MSH shows an even greater fraction of these relatively smaller bubbles than Fuego. From this we infer that the greater viscosity and lower volatile diffusivity of the MSH magma inhibited water from diffusing into pre-existing larger bubbles, thus driving relatively greater nucleation of smaller bubbles that likely formed at a comparatively later stage. Although simple ash particles can be generated from disruption of bubbles of all sizes, only complex ash particles are typically large enough to reliably record a statistically significant population of the larger bubble size mode, and it is those complex ash particles that are examined here.
The ash-sized component of proximal tephra deposits is dominated by complex ash particles, which are more likely to preserve the imprints of larger bubbles that nucleated and grew during magma ascent or formed through bubble coalescence. It is not that disruption of larger bubbles does not produce simple ash fragments, but simply that the radius of curvature of these larger bubbles cannot be distinguished (so cannot be measured) on the majority of simple ash particles due to their relatively smaller size compared to complex ash particles. Thus, it is necessary to collect samples from proximal sites that include many complex ash particles if a statistically significant population of the larger bubbles are sought. Because we are dealing with only the ash-sized portion of the tephra, we are measuring the lower limit of the total BSD (Rust and Cashman 2011). Including the ash-sized component of tephras in the analysis of BSDs now provides an opportunity to evaluate changes in degassing and fragmentation processes between eruptive events, or throughout the course of a long-lived eruption, in order to monitor transitions in activity and potentially contribute to hazard forecasting and mitigation. For example, throughout the course of explosive activity at a particular volcano where only small volumes of ash are generated (ash venting episodes at Soufrière Hills or regular explosions at Santiaguito), if analyses of BSDs from complex ash particles show changes in bubble number densities or shifts in the size of the dominant bubble mode, this may indicate changing degassing dynamics that precede variations in eruptive style. When combined with other lines of evidence, such as seismicity or ground deformation, this information could help to forecast changes in eruptive intensity.
Inferring eruption dynamics from bubble size distributions
When a sample of ash is collected from the field, several processes must be accounted for before it can be used to elucidate eruption dynamics. Vesiculation (nucleation and bubble growth history- which is controlled by magma chemistry, volatile content, magma ascent history, and decompression path) influences the explosivity of eruption. The more viscous, silicic magmas may inhibit rapid bubble growth during ascent and thus result in smaller bubbles with greater overpressure compared to relatively less overpressured (and potentially larger) bubbles formed in more mafic magmas. Magma properties also determine the nucleation dynamics and development of smaller bubbles that form as a result of rapid, late-stage decompression. This, in turn, defines the total BSD, which combines with magma rheology and comminution to determine fragmentation efficiency. Fragmentation efficiency, in addition to comminution processes, then determines the ratio of complex to simple ash particles, which then evolves during atmospheric transport and deposition to yield the distribution collected in the field. A mono-dispersal BSD (all the same size) and homogeneous spatial distribution would produce only simple ash particles because all bubbles would burst simultaneously, while a very broad BSD curve would lead to a maximum number of complex ash particles as the largest bubbles would burst long before the growth of the smallest fraction would produce sufficient overpressure for disruption.
SSEM analysis allows quantification of bubble sizes that are larger than the ash grains on which a portion of the vesicle imprint may be preserved. In fact, a few relatively larger bubbles may be preserved on the much smaller simple ash particle surfaces (see Genareau et al. 2012), but the numbers of larger bubbles are so few relative to smaller bubbles (4 orders of magnitude less) that the few imprints they produce on simple ash particles can be neglected in a total population. Further, the radius of curvature of very large bubbles cannot be measured on simple ash particles due to their small size. Thus, analysis of complex ash particles is required to quantify the size distribution of the larger bubble population preserved in the ash-sized component of tephras, and results acquired from these complex ash particles are consistent with the lower end of the BSD curve acquired from the analyses of larger pyroclasts (Figure 10).
Timing of bubble growth inferred from size subpopulations
Once nucleated, a bubble in a rising magma grows by both diffusive addition of gas to the bubble and decompressive growth due to decrease in ambient pressure (Blank et al. 1993; Proussevitch and Sahagian 1998; Gonnermann and Manga 2007). Consequently, the size of bubbles in a magmatic foam may sometimes be used as a proxy for their age (within the variability of bubble nucleation site density). As such, a bimodal BSD is interpreted to represent at least two separate nucleation events (e.g., Blower et al. 2003). Earlier-nucleated bubbles have more time to grow and are thus larger than later-nucleated bubbles (Proussevitch and Sahagian 1996; 1998; 2005; Sahagian 2005; Gardner et al. 2009). Pre-eruptive coalescence of existing bubbles would grow and broaden the larger size mode (e.g., Klug and Cashman 1994; Gonnermann and Manga 2007; Gardner et al. 2009; Castro et al. 2012). As a parcel of magma rises to shallow levels, it accelerates and rapidly (sometimes explosively) decompresses, leading to another phase of nucleation due to the inability of dissolved water to diffuse sufficiently into previously nucleated bubbles before reaching oversaturation levels needed for nucleation of new bubbles (e.g., Mangan and Sisson 2000; Gonnermann and Manga 2007; Gardner et al. 2009). This late phase of bubble nucleation leads to very high bubble number densities and subsequent explosive fragmentation of a magmatic foam, leading to the generation of both simple (Genareau et al. 2012) and complex ash particles.
The detailed observations of complex ash particles reveal that there is no inflation of bubbles within the interior of ash particles subsequent to fragmentation, although it is apparent that the growth of adjacent bubbles has an influence on the final shape of vesicle walls prior to fragmentation. If post-fragmentation decompression had enabled further bubble growth within complex ash particles, bulges in at least some of the exterior bubble imprints would be expected, but are not observed. Apparently, the bubbles do not continue to expand after the complex ash particle is produced. This confirms that the highly vesiculated magmatic foam was behaving as an elastic solid at the point of fragmentation with insufficient time for viscous relaxation of any overpressure remaining in bubbles that did not burst, and thus, that fragmentation occurred within a narrow time interval that we infer to be caused by late-stage, rapid decompression.
Bubble growth in low versus high silica magma
The two cases considered in this study contrast in their eruption explosivity, and due to the Plinian nature of MSH, the very rapid decompression led to a high number density of late-stage nucleated bubbles. Larger bubbles in the MSH magma were able to expand slightly by diffusion and decompression, but late-stage nucleation of new bubbles dominated due to the low magmatic water diffusivity of dacite relative to basalt, and rate of decompression (0.9-1.6 MPa/s; e.g., Humphreys et al. 2008; Gardner 2009) induced by the preceding landslide and lateral blast, and strengthened by the positive feedback between magma ascent and degassing)). Although the processes in both eruptions were qualitatively similar, quantitatively, MSH had higher energy and greater decompression rate (e.g., Scandone and Malone 1985; Blundy and Cashman 2005), leading to a higher number density of later nucleated, smaller bubbles and higher fraction of simple ash particles than the Fuego eruption. It should be noted that there is no correlation between the average maximum diameter of the particles and the number density of bubbles. This is due to the fact that we are dealing with complex ash particles that settled out of the plume, and represent different locations in the fragmenting magma that contained variable bubble number densities.
Ash transport distance
As would be expected, complex ash particles fall out of the plume closer to the vent due to their greater size and higher settling velocity. This causes the ash fraction composed of complex ash particles to rapidly decrease with distance from source (Figure 9). This distance, and variations in this distance between different eruptions, is presumably controlled by eruption rate differences and cloud characteristics, including GSD, eruptive column height, effectiveness of particle removal (e.g., through aggregation), prevailing wind, humidity, and other atmospheric conditions (Durant and Rose 2009Rose and Durant 2009a2009b). Conversely, travel distance for simple ash particles may be very far-reaching (Genareau et al. 2012), although most simple ash particles fall out quickly and prematurely, governed by microphysical processes which are effective in the first day of atmospheric residence (see Durant et al. 2009; Durant and Rose 2009; Rose and Durant 2009a2009b).
This study demonstrates that the location of the collected ash sample in relation to the overall distance from the vent affects the proportions of bubble populations (larger vs. smaller bubble modes) preserved as vesicle imprints on collected ash grain surfaces. At locations farther from source, there are reduced proportions of complex ash particles, which are more likely to preserve a greater range of bubble size populations, relative to simple ash particles (Figure 9). The MSH samples were all acquired from distal locations (closest location 157 km from the vent), while the Fuego samples were necessarily obtained from more proximal and medial locations (< 60 km). Fuego samples contain not only more complex ash particles, but those complex ash particles are comparatively larger than the MSH complex ash particles and preserve a greater fraction of the relatively larger bubble population. We interpret this to reflect not only a function of sampling location, but also a lower decompression rate of the Fuego eruption, and/or lower viscosity of the Fuego magma that allowed for more rapid diffusive and decompressive growth of existing bubbles, thus reducing the oversaturation of the inter-bubble melt and the number density of later-nucleating bubbles. These results indicate that if tephras are collected at more proximal and medial locations to the vent, larger size populations within the BSD can be examined, but if tephras are only collected at distal locations, BSDs will be dominated by the final stage of bubble nucleation and growth because with greater distance from source the ash particle size decreases far below the size of the larger bubbles.
Explosive volcanism generates two types of morphologically distinct ash particles suitable for the utilization of SSEM imaging in order to calculate bubble volumes. Simple ash particles allow the measurement of only a single vesicle on each observable ash grain surface (Genareau et al. 2012) while relatively larger, complex ash particles preserve the imprints of multiple vesicles for measurement on a single ash grain surface and may also contain complete, unfragmented vesicles in their interiors. Both simple and complex ash particles are produced in eruptions of contrasting style and composition (Fuego: basaltic, sub-Plinian and MSH: dacitic, Plinian). The complete population of simple and complex ash particles escapes the vent, but complex ash particles fall out of the column and plume much more rapidly due to their relatively larger size, causing simple ash particles to dominate in more distal deposits. With the proportion of simple ash particles generated by fragmentation of later-nucleated bubbles increasing with distance from the vent, the apparent fraction of smaller bubbles also increases with distance. Consequently, as samples are collected from more distal deposits relative to source, measured BSDs will reflect the lower end of the total BSD for the entire eruptive unit.
Observed bubble size distributions are bimodal for both the MSH and Fuego eruptions, suggesting at least two bubble nucleation events in the vesiculating magma during ascent and eruption. We interpret the larger of these modes to represent bubbles that nucleated at relatively greater depth within the conduit and grew by diffusive decompression and expansion while the smaller mode nucleated at a relatively later stage of magma ascent and vesiculation.
Number densities of the smaller bubble population in the MSH complex ash particles are greater than those preserved in the Fuego complex ash particles, and the cumulative void fraction (CVF) of the MSH melt (0.864 ± 0.030) was greater than that of the Fuego melt (0.749 ± 0.051), consistent with the expectation that eruptions of greater explosivity should generate a higher number density of smaller bubbles just prior to fragmentation of the magmatic foam (Table 1). These results reflect the higher viscosity resulting from a more volatile-rich and more silicic magma, greater decompression rate, and thus, greater eruption explosivity for the MSH 1980 event. The results presented here demonstrate that SSEM analysis of ash particles can quantify the lower end of the total BSD of a pyroclastic unit, even if distal ash deposits are the only available data source.
Constraints on some outstanding problems regarding eruption dynamics emerge from this study. The first is that vesicles of various sizes are preserved on ash grains, and indicate that bubble nucleation occurs in more than one stage (including one very late in the eruption, just prior to fragmentation). The second is that fragmentation occurs over a short time interval in a highly vesiculated magmatic foam, leading to the production of both complex and simple ash particles simultaneously from a heterogeneous spatial distribution of bubbles. The relative abundance of complex and simple ash particles may be controlled in part by the scale of heterogeneity of bubble nucleation sites and thus the spatial distribution of bubbles and the strength of inter-bubble films and plateau borders. Quantification of this for magmas of various compositions and crystallinities would be a fruitful area for future investigation.
Methodologically, the use of SSEM enables the examination of volcanic tephra and the quantification of vesicle properties that were heretofore unavailable to researchers using previously established methods of particle imaging such as standard two-dimensional SEM examination of sectioned and polished lapilli, and X-ray microtomography of clasts or portions of clasts. SSEM enables direct measurement of the finest tephra component, the ash fraction, and quantification of BSDs for bubbles that burst during eruption and efficiently fragmented the magma as it exited the vent. For explosive eruptions where magma is efficiently fragmented to produce a high proportion of ash, the ability to quantify the ash-producing population of bubbles can reveal syn-eruptive processes of magma vesiculation and fragmentation, which is vital for understanding eruptive dynamics, parameterization of numerical eruption models, and assessment and mitigation of pyroclastic hazards.
The authors thank William Mushock and Robert Keyse for assistance with the SSEM system at Lehigh University. This project was supported by NSF grants #EAR-0838314 and EAR-0838292. These awards were funded under the American Recovery and Reinvestment Act of 2009 (ARRA). Insightful comments from Jacopo Taddeucci, Alain Burgisser, and an anonymous reviewer greatly improved the quality of the manuscript.
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