Using infrasound to constrain ash plume rise
© Lamb et al. 2015
Received: 14 July 2015
Accepted: 3 November 2015
Published: 19 November 2015
Airborne volcanic ash advisories are currently based on analyses of satellite imagery with relatively low temporal resolution, and numerical simulations of atmospheric plume dispersion. These simulations rely on key input parameters such as the maximum height of eruption plumes and the mass eruption rate at the vent, which remain loosely constrained. In this study, we present a proof-of-concept workflow that incorporates the analysis of volcanic infrasound with numerical modelling of volcanic plume rise in a realistic atmosphere. We analyse acoustic infrasound records from two explosions during the 2009 eruption of Mt. Redoubt, USA, that produced plumes reaching heights of 12–14 km. We model the infrasonic radiation at the source under the assumptions of linear acoustic theory and calculate variations in mass ejection velocity at the vent. The estimated eruption velocities serve as the input for numerical models of plume rise. The encouraging results highlight the potential for infrasound measurements to be incorporated into numerical modelling of ash dispersion, and confirm their value for volcano monitoring operations.
Mt. Redoubt, a dome-building volcano located 170 km south-west of Anchorage, Alaska, erupted in March 2009 after approximately 20 years of quiescence. On March 15, a small phreatic explosion marked the onset of the eruption. This was followed by 19 eruptive events between March 23 and April 4, of which at least 16 generated ash plumes with heights of 5–18 km (Schneider and Hoblitt 2013), forcing the grounding of aircraft at Anchorage airport. On April 4, the eruption entered a phase of continuous lava extrusion and dome building at the summit before ending in July 2009.
Mt. Redoubt is one of 50 historically active Alaskan volcanoes located on the busy North Pacific and Far East Russia air traffic corridors along which at least 70 aircraft, collectively carrying approximately 10,000 passengers, fly daily. Between 1953 and 2009, 129 encounters of aircraft with volcanic ash clouds have been documented (Guffanti et al. 2010), including an incident at Mt. Redoubt in 1989 (Casadevall 1994). Rapid growth in air traffic has pushed the scientific and engineering community to increase our ability to detect ash clouds (Prata and Tupper 2009) and constrain the melting characteristics of ash (Song et al. 2014) in order to improve the design of jet engines and mitigate risk (e.g. Drexler et al. 2011). Currently, nine Volcanic Ash Advisory Centers (VAAC) are responsible for issuing warnings of airborne volcanic ash. Advisories are based on satellite imagery and numerical models of atmospheric ash dispersion (Mastin et al. 2009). Whilst numerical models can provide accurate forecasts of atmospheric ash dispersion patterns, they rely on precise knowledge of key eruption parameters such as maximum plume height and mass ejection rates at the vent, which remain loosely constrained.
In recent years the use of acoustic infrasound technology has become commonplace at volcano observatories, in particular to detect eruptions in remote locations (e.g. Caplan-Auerbach and McNutt 2003; De Angelis et al. 2012; Petersen and McNutt 2006) and to measure parameters such as mass eruption rates and plume height (Caplan-Auerbach et al. 2010, Ripepe et al. 2013). A number of studies have focused on estimating gas bubble sizes and gas outflux at the vent during Strombolian-type eruptions (Delle Donne and Ripepe 2012; Firstov and Kravchenko 1996; Gerst et al. 2013; Johnson 2003; Kremers et al. 2013; Ripepe et al. 1996; Vergniolle and Caplan-Auerbach 2006). In contrast, only a handful of eruptions accompanied by atmospheric injection of vigorous, ash-rich plumes have been investigated to date (e.g. Caplan-Auerbach and McNutt 2010; Fee et al. 2013; Mastin et al. 2013; Matoza and Fee 2014; McNutt et al. 2013; Ripepe et al. 2013).
In this paper we combine analyses of infrasound observations with numerical modeling of volcanic plume rise in a realistic atmosphere in order to characterize airborne ash injection during the 2009 eruption of Mt. Redoubt. Our results are confirmed by estimates of plume height obtained from Doppler radar measurements (Schneider and Hoblitt 2013), satellite imagery (Webley et al. 2013), and further validated by field observations of tephra fall deposits (Wallace et al. 2013).
Data and Methods
Infrasound source velocity model
Fluctuations in air pressure recorded at a distance from a volcanic vent are directly related to acoustic power that, in turn, depends on mass outflux at the source (Caplan-Auerbach et al. 2010; Woulff and McGetchin 1976). The relationship between acoustic power and eruptive flux, however, is complicated by uncertainties in the source dynamics. Woulff and McGetchin (1976) introduced, within the framework of linear acoustic theory, relationships between velocity and power for three source types: monopole, dipole, and quadrupole. A monopole source is one in which variations in pressure are due entirely to the rate of change of mass flux, and can be envisioned as an isotropically expanding source. A dipole is often used to describe a directional jet or gas flux that interacts with solid walls. A quadrupole best represents a gas source that generates noise through turbulence, such as a jet engine.
where K m , K d , and K q are empirically derived constants for specific radiation mechanisms (monopole, dipole, and quadrupole respectively), R is the source radius (i.e. volcanic vent radius), u is the velocity of the material at the source, and c is the speed of sound in air. The value of K m is of the order of 1, while K d and K q are approximately 10-2 and 10 −5, respectively (Woulff and McGetchin 1976).
Variables and values used in calculations
Gas velocity modelling
(Calculated, see below)
1.4 kg m-3
Speed of sound
320 m s-1
Dipole source empirical constant
Volcanic vent radius
Vent longitude and latitude
Gas mass fraction
Solid pyroclastic density
1200 kg m-3
No-wind train coefficient
Wind entrainment coefficient
Calculated peak eruption velocities
Event 2: 315 m s-1
Event 17: 251 m s-1
Plume rise model
We use the PlumeRise model of Woodhouse et al. (2013) to estimate the maximum plume height. This model provides a quantitative, 3-dimensional, description of the rise of volcanic ash columns in a moist and windy atmosphere, and is based on the fluid dynamics of turbulent buoyant plumes. The model includes a description of the thermodynamics of heat transfer between hot pyroclasts and the surrounding magmatic and atmospheric gases. PlumeRise allows assessing the effects of a variable atmosphere on volcanic plume rise and includes a description of the thermodynamics of phase changes of water. The effect of a cross wind on the plume ascent is accounted for, using the entrained formulation of Hewett et al. (1971). For atmospheric conditions, we used soundings measured above Anchorage, 168 km north-east of Mt. Redoubt, recorded at intervals of 6 or 12 hours (http://weather.uwyo.edu/upperair/sounding.html; last accessed 21/09/2015). For comparison, we also estimated the plumes using the US Standard Atmosphere (U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976), which is characterized by a piecewise linear temperature profile with height and hydrostatic pressure balance.
For each event analysed, we use the atmospheric sounding measurement taken nearest to the time of the event; additional parameters employed in the plume model along with their sources are listed in Table 1.
We analysed infrasound signals for two explosive events during the eruption of Mt. Redoubt; events 2 and 17 (following the classification of Bull and Buurman 2013; Fig. 1 a, c). Event 2 (7:02 UTC, 23 March) was the first large explosion in the crisis, accompanied by strong seismic and infrasound signals, and a measured plume height of 14 km (McNutt et al. 2013). From the infrasound signal, we calculated a peak mass velocity of 315 m s-1 (Fig. 1 b). Event 17 (23:29 UTC, 28 March) was one of the largest explosions (plume height of 12.5 km) of a group characterised by short durations (3–4 mins). The calculated peak mass velocity for this event was 251 m s-1 (Fig. 1 d).
Numerical models of ash dispersion rely on estimates of initial plume height and mass eruption rates which remain, thus far, poorly constrained. The methods presented here provide a means to infer eruption source parameters from acoustic measurements. Our plume height estimates at Mt. Redoubt expand on previous 1D modelling work by Mastin et al. (2013) for event 5 of the same eruption, who applied a 1D plume rise model assuming a velocity at the vent of 150 m s-1. One fundamental difference between our model and previous work by Mastin et al. (2013) is the value used for mass velocity at the vent. They inferred a mass velocity using mapped erupted mass (Wallace et al. 2013) and measured eruption durations, whereas we used a value based on the analysis of infrasound data. Additionally, our model estimates 3D plume propagation with results in excellent agreement with the mapped distribution of tephra-fall deposits (Fig. 5). Mastin et al. (2013) also successfully mapped the distribution of tephra from event 5, using a 3D tephra and ash dispersal model (Ash3d; Schwaiger et al. 2012). Ash3d parameters include the total erupted mass and the total grain size distribution, which may not be accurately constrained until after the end of an eruptive event.
Our model also differs from previous studies at other volcanoes such as Johnson (2007) and Matoza et al. (2009). The former inferred that a monopole source best described pyroclastic explosions from Karymsky volcano, Russia. The explosions from Karymsky were smaller in time (a few seconds) and scale (plume heights <1 km), suggesting a significantly different source mechanism than at Mt. Redoubt. Matoza et al. (2009) contended that sustained eruption noise has its source in large scale turbulence, favouring a quadrupole source. However, the eruptions described by Matoza et al. (2009) generated infrasound signals with durations of hours whereas those at Mt. Redoubt only last for minutes. The vent for the 2009 activity at Mt. Redoubt lies inside a North-facing collapse scar (Bull and Buurman 2013) which causes infrasound waves to interact with the wall around the vent during eruptions. For this reason a dipole source was deemed the most appropriate approximation for our calculations. Infrasound waveform inversion at Tunguruhua volcano, Ecuador, suggested a dipole source to explain the directivity of the acoustic wavefield (Kim et al. 2012).
One notable feature of the infrasound waveforms recorded at Mt. Redoubt in 2009, are their unusually high amplitudes and relatively short rise times of the initial pulse. Whilst these observations support an explosion source mechanism rather than sustained jetting, they also pose questions on the nature of the flow at the vent. For example, for one event (McNutt et al. 2013) showed clipped waveforms with a peak pressure of 173 Pa and estimated a full-scale pressure of 244 Pa at the DFR site (corresponding to >3000 Pa at the vent). Such high pressures may imply transonic to supersonic flow conditions at the vent, which would make equations (1–4) not applicable. A non-linear formulation should be considered instead (Marchetti et al. 2013). For instance, employing the Rankine-Hugoniot equations for 1D shock wave theory (e.g., Marchetti et al. 2013) and acoustic pressures between 50–200 Pa (i.e. within a range compatible with values measured at Mt. Redoubt), would result in velocities at the vent in excess of 1000 m s-1. However, such high values are not supported by measurements of plume ascent at Mt. Redoubt using Doppler radar (see Fig. 6 in Schneider and Hoblitt 2013). Alternatively, McNutt et al. (2013) suggested that a highly directional flow may provide an explanation for the unusually high infrasound pressures. Furthermore, in the absence of clear observational evidence of supersonic flow, we assume that non-linear dynamics may be restricted to the near-vent region, and consider that the equations of linear acoustics represent a suitable first-order approximation for the purpose of our investigation.
Our calculations are dependent on the assumption that the infrasound source is best described by a pure dipole. To test this assumption, we repeated our workflow using monopole and quadrupole sources instead. The peak velocities for events 2 (107 and 620 m s-1) and 17 (65 and 486 m s-1) using monopole and quadrupole sources are too low or high when compared with values estimated from field observations (e.g. Doppler radar). We acknowledge that the ideal strategy to constrain eruption velocities would be inverting for a multipole source model where monopole, dipole, and quadrupole mechanisms contribute to the radiated acoustic wavefield. Kim et al. (2012) recently proposed a waveform inversion method that represents volcano acoustic sources as the combination of multipole terms (i.e. monopole and dipole) and employs analytical Green’s functions in a half-space to model atmospheric sound propagation. Waveform inversion would allow an accurate estimate of time history of mass outflow at the vent and the systems of forces active at the source. However, this type of inversion requires data from multiple sensors, which were not available during the 2009 eruption at Mt. Redoubt. The most significant limitation of models used to characterise the propagation of volcanic infrasound is the use of equations (2, 3, 4) that are based on simplified Green’s functions for a homogenous and isotropic free space. Calculations based on these relations rely on the implicit assumption that wave amplitude decays as an inverse function of distance from source. In this and previous studies, the effects of variable atmosphere, vent geometry, and the local topography on the propagation of infrasound are neglected. Numerical techniques such as finite-difference time-domain can be employed due to their ability to handle complicated phenomena in infrasound propagation, thus allowing inclusion of the effects of topography (Lacanna and Ripepe 2013; Lacanna et al. 2014; Kim et al. 2015).
Plume heights of the events in 2009 were assessed using satellite imagery (Webley et al. 2013) and Doppler radar measurements (Schneider and Hoblitt 2013). Airborne ash was detected by satellites some time after each event. By tracking cloud top temperatures, Webley et al. (2013) were able to estimate plume heights. Their estimates generally fall below measured heights from radar and our estimates. As these measurements were taken some time after the eruptive event, the ash cloud had undoubtedly begun to disperse and cool, leading to apparently lower cloud-top heights. Our estimates fall close to Doppler radar measurements (Schneider and Hoblitt 2013), demonstrating the strength of the PlumeRise model used. In our calculations, we used parameters calculated a-posteriori for each of the events (Table 1). If the proposed methodology is to be used for near real-time assessment of eruptive plumes during future volcanic crises, a number of parameters (e.g. vent radius, gas mass fraction, source temperature, pyroclast density) will need to be estimated based on previous eruptions.
At other volcanoes, eruptive plume heights have been estimated using other geophysical methods. Using data from Kasatochi and Augustine volcanoes, Alaska, Prejean and Brodsky (2011) demonstrated how the amplitude of explosion-sourced seismicity can be related to the mass ejection rate via force-balance equations. However, the method is limited to using a range of ejection rates and requires clear, noise-free signals from multiple stations located around the eruptive centre. Additionally, due to strong attenuation effects, the method is limited by the size of the explosion and the proximity of the seismometers. In Iceland, real-time GPS and tiltmeter measurements were demonstrated to correlate with plume heights during the 2011 eruption at Grímsvötn (Hreinsdóttir et al. 2014). Again, this method is limited by requiring instruments located close (<10 km) to the eruptive centre as deformation signals can degrade quickly with distance from the pressure source. At present, there is no methodology that provides alone a consistent solution to the problem of estimating mass eruption velocities, or ash plume heights. A multi-parameter, integrated approach should be employed to better constrain eruption dynamics.
A number of simplifying assumptions in our approach mean that we cannot fully replicate the complexity of a natural atmospheric system. However, a workflow based on this relatively simple proof-of-concept would require low computational resources, and results could be available in near real-time. The method proposed here requires few parameters to provide a rapid estimate of ash plume height. Furthermore, recent developments in both infrasound technology and numerical modelling mean that waveform inversion for more complex source mechanisms along with the use of more realistic Green’s functions may soon be commonplace. We surmise that acoustic infrasound holds potential to provide accurate near-real time estimates of eruption source parameters such as mass flux rates and maximum plume height required in risk mitigation strategies.
Infrasound can provide detailed constraints on the timing, duration, and relative intensity of local and remote explosive volcanism, and can be used for early eruption warning. For the aviation industry, a timely issuing of airborne volcanic ash warnings is vital to avoid encounters between aircraft and ash clouds. Whilst numerical models can provide detailed forecasts of atmospheric ash dispersion patterns, they rely on accurate knowledge of key parameters such as initial plume height and mass eruption rates, which remain loosely constrained.
In this study we have presented a proof-of-concept which incorporates the analysis of infrasound data recorded during two explosive events during the 2009 eruption at Mt. Redoubt, USA. Using simple analytical models that describe infrasound radiation at the vent, we have calculated the flux of material ejected from the volcanic vent during each event. The flux measurements were then incorporated into an ash plume rise model, to calculate the maximum height of the eruptive column, and assess its atmospheric dispersal. By comparing the results of our calculations to Doppler radar and satellite measurements, we demonstrated the potential of this and similar methods to obtain accurate estimates of plume heights within seconds of a volcanic explosion. The main implication of our results is that key eruption source parameters can be quickly and accurately quantified. Incorporation of infrasound based eruption source parameters into ash transport modelling workflows holds the potential for more efficient forecasts of volcanic ash cloud dispersion.
We acknowledge the European Research Council for the Starting Grants on ’Strain Localisation in Magmas’ (SLiM, No. 306488). The authors also thank Yousif Al-Sharhan for starting this project during his undergraduate studies. The authors are indebted to colleagues of the Alaska Volcano Observatory, including the U.S. Geological Survey, Alaska Division of Geological and Geophysical Surveys, and the University of Alaska Fairbanks for the combined efforts put into the monitoring and eruption response. Permission to use the infrasound data used in this study was granted by the Alaska Volcano Observatory. Finally, we wish to thank Benoit Taisne, an anonymous reviewer, and the associate editor, Chris Newhall, for their comments which greatly improved the manuscript.
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