re

v, Unchn

x fn oighllecor eac

essfat unprecedented time resolution (1 Hz) and high accuracy (uncertainty of 33%).

measurssmentntury,techniition,

Journal of Volcanology and Geothermal Research 190 (2010) 325336

Contents lists available at ScienceDirect

Journal of Volcanology an

seago (Moffat and Millan, 1971; Stoiber and Jepsen, 1973), numerousground-based, airborne and spaceborne optical remote sensinginstruments and methods have emerged capable of measuring bothvolcanic gas uxes and composition, for individual vents or an entireplume, and with improved temporal resolution (McGonigle andOppenheimer, 2003). As a result, gas geochemistry has increasinglyfound its place among the operational techniques of volcanomonitoring (Oppenheimer, 2003; Galle et al., 2003). Nevertheless,

for gas uxmeasurements is another challenge, since the entire plumeneeds to be captured.

The most widespread method used for measuring volcanic gasuxes is scattered light ultraviolet spectroscopy (see e.g. McGonigleand Oppenheimer (2003) for a review) using correlation spectroscopyor Differential Optical Absorption Spectroscopy (DOAS). The plume isusually proled across its transport direction from below with azenith-viewing telescope, the apparatus being mounted on a movingthe time resolution of gas measurements sroutinely achieved in geophysical studieunderstanding the links between seismicity,sing that are clearly of considerable relev

Corresponding author. Tel.: +44 1223 766561.E-mail addresses: mb632@cam.ac.uk (M. Boichu), co

(C. Oppenheimer), vip20@cam.ac.uk (V. Tsanev), kyle@

0377-0273/$ see front matter. Crown Copyright 20doi:10.1016/j.jvolgeores.2009.11.020eld access can be limitedowever, since the rst(COSPEC), four decades

Strombolian eruptions using the technique of open-path Fouriertransform infrared spectroscopy. This technique enables observationsat a frequency of about 1 Hz. But achieving comparable time resolutionand data streams are often discontinuous. Happlication of the correlation spectrometers1. Introduction

Gas emissions from volcanoes areincluding monitoring, hazard asseenvironmental impact. For over a cebeen studied using in-situ collectionhighly detailed analysis ofuid composshort-term variations of the passive degassing of this volcano renowned for its active lava lake. A cyclicity inux, ranging from about 1124 min, is evident. We propose two physical mechanisms to explain thisdegassing pattern, associated to periodic supply of either gas-rich magma or gas alone into the lake. Thedual-wide eld of view DOAS technique promises better integration of geochemical and geophysicalobservations and new insights into gas and magma dynamics, as well as processes of magma storage and gassegregation at active volcanoes.

Crown Copyright 2009 Published by Elsevier B.V. All rights reserved.

ed for several purposes,, and investigation offumarole chemistry hasques. While these yield

volcano behaviour, especially the transition to explosive activity(Fischer et al., 1994; Watson et al., 2000; Young et al., 2003). Somevolcanoes clearly exhibit rapid changes in gas composition and uxrelated to magmatic activity. For instance, Oppenheimer et al. (2006)and Burton et al. (2007) have demonstrated pronounced composi-tional differences in gas emissions associated with and betweentill lags behind ws, limiting progrdeformation andance for understa

200@cam.ac.uknmt.edu (P.R. Kyle).

09 Published by Elsevcity varying between 1 and 2.50.1 m s . These measurements provide insight into the

During a 2 h experiment on 26 December 2006, SO2 ux varied between 0.17 and 0.890.2 kg s1 with avertical plume velo 1high time resolution gas ux plume velocity and gas uxHigh temporal resolution SO2 ux measu

Marie Boichu a,, Clive Oppenheimer a, Vitchko Tsanea Department of Geography, University of Cambridge, Downing Place, Cambridge CB2 3ENb Department of Earth and Environmental Science, New Mexico Institute of Mining and Te

a b s t r a c ta r t i c l e i n f o

Article history:Received 10 August 2009Accepted 21 November 2009Available online 4 December 2009

Keywords:volcanic degassingDOAS spectroscopy

The measurement of SO2 upurposes, and for evaluatiotechnique for accurate and hspectrometers capable of coplume, obviating the need fin the gas cloud from whichThe method has been succ

j ourna l homepage: www.e lhat isess indegas-nding

ier B.V. All rigments at Erebus volcano, Antarcticaa, Philip R. Kyle b

ited Kingdomology, Socorro, NM 87801, USA

rom volcanoes is of major importance for monitoring and hazard assessmentf the environmental impact of volcanic emissions. We propose here a noveltime resolution estimations of the gas ux. We use two wide eld of view UVting, instantaneously, light from thin parallel cross-sections of the whole gasither traversing, scanning or imaging. It enables tracking of inhomogeneitiescurate evaluation of the plume velocity can be made by correlation analysis.ully applied on Mt. Erebus volcano (Antarctica). It yields estimations of the

d Geothermal Research

v ie r.com/ locate / jvo lgeoresvehicle, or by use of a scanning system (Fischer et al., 2002; Edmondset al., 2003). The ux is then obtained from the product of the gascolumn abundance (integrated across the plume section) and theplume transport speed. The main sources of uncertainty in ux mea-surements made in this way are generally considered to be linked tolight scattering processes (Millan, 1980; Mori et al., 2006; Kern et al.,2009) and to the error in the plume speed estimation (Stoiber et al.,1983;Williams-Jones et al., 2006), which is sometimes taken to be the

hts reserved.

wind speed measured or modelled close to the plume altitude. Buteven if wind speed is measured at the exact plume altitude, it may notrepresent well the plume velocity due to the complex wind-elds thatdevelop downwindof volcanoes due to topography. Differentmethodshave been proposed to enhance plume speed accuracies but are not yetwidely used. One approach is to usemultiple UV spectrometers sited atxed positions some distance apart so as to track the transport ofinhomogeneities in the plume (McGonigle et al., 2005a; Williams-Jones et al., 2006); related approaches use a single instrument carriedbeneath the plume, with optics that enable alternating elds of view,one at zenith, the other inclined (McGonigle et al., 2005b), or simul-taneous measurements in two directions using a double spectrometer(Johansson et al., 2009). Latterly, imaging UV techniques (imagingDOAS or UV cameras combined with appropriate narrow band lters)have been demonstrated (Bobrowski et al., 2006; Bluth et al., 2007;Mori and Burton, 2006), which can achieve a high time resolution onux measurements.

Here we propose an alternative, simple solution which is to use asystem employing two UV spectrometers equipped with wide eld ofview telescopes that instantaneously collect light from two narrowand parallel entire cross-sections of the plume (Fig. 1). This obviatesthe need for either traversing, scanning or imaging. We will use theacronym DW-FOV DOAS (dual-wide eld of view DOAS) to refer tothis technique. By using two spectrometers with elds of viewseparated by a small angle, time-series of retrieved gas amounts can

be correlated to obtain (through knowledge of the viewing and plumegeometry) the plume transport speed through time. Such a system iscapable, therefore, of accurate, highly time-resolved measurements ofvolcanic gas uxes.

The aim of this paper is to describe this new instrumentation andmethodology, and to apply the approach to rapid measurements ofSO2 uxes at Mt. Erebus in Antarctica. Interest in the emissions fromErebus is fuelled by the potential impact of sulfur, halogens and NOxon the pristine atmospheric environment (Radke, 1982; Zreda-Gostynska et al., 1993, 1997; Oppenheimer et al., 2005, 2009a), butalso because the volcano is renowned for its dynamic lava lake andStrombolian activity. This technique provides new possibilities toinvestigate the magma degassing of volcanoes that exhibit short-termvariability in the dynamics of magma transport and degassing, whichare reected in changes in eruptive behaviour (Oppenheimer et al.,

326 M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336Fig. 1. A) Photograph of Erebus volcano from the Lower Erebus Hut showing a buoyantplume. Rectangles illustrate the wide elds of view of the two telescopes. Both arelinked to UV spectrometers and the angle between the upper and lower elds of view isadjusted using a goniometer. B) Sketch of the geometry of the experiment with symbols

used in text.2009b; Harris et al., 2005). Measurements are now also much morecomparable in terms of frequency of data acquisition with observa-tions provided by common geophysical tools such as seismology. AtErebus, interpretation of the observed SO2 variations in terms ofmagma dynamics is simplied by the limited role of hydrothermalscrubbing of emissions (Symonds et al., 2001). Moreover, observa-tions of SO2 ux from the volcano by scanning UV spectroscopy havepreviously suggested a periodicity of 10 min (Sweeney et al., 2008),which we are keen to investigate further.

After a section describing the methodology, we will present thehigh resolution time-series of plume speed and ux obtained at Erebus.Awavelet analysis of theseux observations reveals distinctive patternsin degassing. We will discuss about their interpretation in terms of gasand magma dynamics as well as processes of magma storage and gassequestration. Finally, three appendices include some technical contentand an electronic supplement to this article presents an animationshowing the results in the form of a SO2 uxmeter superimposed onvideo of the plume.

2. Methodology

Note that all mathematical symbols used in the following are listedin Table 1.

2.1. Experiment description

We collected UVDOAS spectroscopicmeasurements at Erebus on 26December 2006 during conditions of clear sky and low wind, such thatthe plume rose approximately vertically from the crater. Spectra wererecorded using two Ocean Optics USB4000 spectrometers spanning awavelength range of about 283440 nm, with a resolution of,respectively, 0.5 and 0.6 nm (FWHM). Hoya lters were used to reducethe amount of stray light. As shown in Fig. 1, each spectrometer wasattached to a telescope consisting of spherical and cylindrical lensesthat provide a horizontal angle of aperture WFOV of 22, giving an

Table 1Symbols used.

Elevation angle of the lowermost eld of view, in NFOV Narrow angle of aperture of the spectrometers elds of view, in Angle of separation between the two elds of view, in dX Long horizontal axis of the eld of view at the plume distance, in m.dY Vertical distance between the two elds of view at the plume distance, in m.D Horizontal distance between observation site and plume, in m.CCF Cross correlation functiont Time step of the gas column amount series, in s. Incremental time step of the correlation analysis, in s.T Duration of correlation sliding windows, in s.t Time, in s. Time shift of the correlation window for the upper spectrometer signal, in s.WFOV Wide angle of aperture of the spectrometer elds of view, in deg.

time shift, giving the absolute maximum of the cross-correlationcoefcients calculated at time t, with varying in [0::max] where represents the incremental time step of the cross correlation (equalto 2 s here) and max the maximum value of associated with theminimum expected plume speed taken equal to 0.1 m s1.

Plume speed is deduced from this time lag according to therelation:

=dYlag

: 2

Because spectrometer's elds of view do not cross perpendicularlythe plume but are slightly inclined, the distance dY separating them atthe entrance of the plume is a bit different than at its exit, dependingon the plume depth (less than 400 m at Erebus which is the crater sizeseen by pointing from Lower Erebus Hut). This uncertainty on dY istaken into account in the estimation of error on the speed, developedin the Results section, by assuming an uncertainty of 50 m on thehorizontal distance D between spectrometers and plume.

2.3.2. Inuence of the correlation window lengthAs shown in Fig. 3A, estimatedplumespeedsdependon the lengthof

the sliding correlation window, compared with the time interval

327M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336elongated horizontal eld of view, and a narrow vertical angle ofaperture NFOV of 0.5 dened by the width of the spectrometer's slitand the focal length of the positive lens. The long axis of the eld of view(dX) was designed so that the projected WFOV footprint (equivalent to810 m at the distance of the plume of 2004 m here) would samplethe entire plume. The long axes of the elds of view were parallel butdisplaced, so that each instrument viewed a different cross-section ofthe plume, determined by the observation geometry.

Spectra from each instrument were recorded in separate laptopcomputers, whose clocks were synchronized using a GPS unit so asto yield a time-stamped series of data. All observations were madefrom Lower Erebus Hut, a horizontal distance D of 1960 m from thesummit of Erebus, and mostly viewed the vertically-rising plumeduring periods with very low winds. The elevation of the lowermosteld of view () was 12 and separation of the two elds of view ()was 2.0, precisely adjusted thanks to a goniometer. The distance dYbetween the two elds of view is then:

dY = D tan180

+

tan 180

h i

1

and was equal to 72 m at the summit. The plume was thus crossed atrespectively 78 and 150 m above the crater. Spectra were collectedwith an exposure time of 130 ms, maximizing their amplitude butavoiding saturation below 350 nm, and 8 spectra were averagedresulting in a time-step of 1 s between measurements. Backgroundand dark spectra were recorded at the start of each set of observations.Background spectra were collected by rotating both spectrometersabout the vertical axis so as to point out of the plume.

2.2. Spectroscopic retrieval

SO2 column amounts were retrieved following differential opticalabsorption spectroscopy (DOAS) procedures (Platt and Stutz, 2008).The reference spectra included in the nonlinear t were obtained byusing WinDOAS convolving high resolution SO2 (293 K, air) (Bogumilet al., 2003) and O3 (246 K, air) (Burrows et al., 1999) cross-sectionswith Gaussian instrumental line shapes estimated using a mercurylamp (FWHM=0.5 and0.6 nm for the lower andupper spectrometers,respectively). A ring spectrum calculated using DOASIS was alsoincluded in the t as well as a third order polynomial to remove broadband structures frommeasured optical densities. The same optimizedtting window (307.6330.0 nm) was selected to analyze data fromboth spectrometers, yielding a near random t residual structure witha minimal standard deviation. As a result, the t residual was betweenten and twenty times smaller than the SO2 t. Spectra recorded withthe upper spectrometer are slightly noisier than those from the lowerone leading to an error of a fewpercent higher on the retrieved columnamounts. The obtained time-series of the SO2 column amounts forboth instruments are shown in Fig. 2.

We are using wide eld of view UV spectrometers capturinginstantaneously whole horizontal plume cross-sections at twodifferent altitudes. Hence, the retrieved gas amount for one W-FOVDOAS instrument can be approximated by the mean column amountalong the different directions inside the wide angle of observation, asshown in Appendix A. The relative error on this approximation(Eq. (A.18)) depends on plume optical densities of the studiedvolcano. As illustrated by Fig. 8, this relative error is of a few percentfor a weak gas emitter like Erebus, and could reach in the worst caseup to 45% for a strong gas emitter like Kilauea volcano (assuming SO2column amounts up to 51018 molec cm2).

2.3. Plume speed retrieval

Inhomogeneities, induced by turbulence or variations in volcanic

degassing rate, give characteristic structures to the plume, whichcan be observable through the time-series of the gas column amountsobtained for each spectrometer. Correlation analysis is used toestimate the transport speed of these structures, representative ofthe spatially averaged plume velocity over the distance separating theelds of view of each spectrometer and of the mean plume speed onthe time window used for correlation.

2.3.1. Principle of the cross-correlation analysisEstimating the plume speed (with a time resolution of1 s) at time

t requires calculation of the cross-correlation coefcients betweensegments of the two column amount time-series selected using aslidingwindow of a given durationT, centred respectively in t for thelower spectrometer and in (t+) for the upper spectrometer, where is the time shift between the two windows (see Fig. 4 for symbols).Cross correlation coefcients CCF(t, , T) consequently depend onthree variables.

The time lag lag between the upper spectrometer signal and thelower one, corresponding to the time for an inhomogeneity to travelfrom the rst to the second instrumental FOV, is a priori equal to the

Fig. 2. Time-series of SO2 column amounts for both upper (blue) and lower (red) wideeld of view spectrometers at Erebus on 26 December 2006 from 20:24 h to 22:02 hUTC. Dashed lines show periods of time when a bend was observable in the plume at aheight less than 200 m above the crater, i.e., below the altitude of the upperspectrometer's FOV.between two structures in the degassing. Velocities are smoothed

328 M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336with a long window, while a narrow window yields estimations closerto the instantaneous plume speed. However, very low velocitiesobtained with the narrow window (close to 0.1 m s1) do not havea physicalmeaning but show the limit of the correlation analysis and theneed for a renement of themethod to remove them. Indeed, recurrentstructures can exist in the observed degassing and lead to a periodicityin the cross-correlation function, relative to the time shift, which ismorepronounced with a narrow window (Fig. 4). In this case, the speedestimated from the absolute maximum of the CCF coefcients, over therange of values, can yield amatch between a structure recorded at therst spectrometer, not with the time-delayed corresponding structureat the second instrument as desired, but with a translated structureresulting from a consecutive inhomogeneity in the plume. An additionalcriterion is thus required to determine a relevant time lag by selectingtherst localmaximumof the CCF function.Moreover, thismaximum isretained only if it presents a signicant amplitude above a giventhreshold, which needs to be determined. If these criteria are notfullled, velocity cannot be estimated. Note that the longer thewindow,the less likely this artifactwill arise, given that secondarypeaks aremoreattened due to the larger number of points taken into account for thecorrelation calculation.

A threshold is imposed on the local maximum in the cross cor-relation function, which has to exceed 0.5 to be retained. Indeed, athreshold of 0.8 removes irrelevant very low velocities of 0.1 m s1,but also some relevant output speed values. With these additionalcriteria (considering a threshold of 0.5), we mainly observe velocitiesranging from 1 to 2.5 m s1, with values very similar for both narrowand longwindows (Fig. 3B). Estimates arenot identical. Narrowwindowspeeds are more dispersed because they represent near instantaneous

Fig. 3. Plume speed vs. time since start of the dataset start at 20:24:48 UTC for (A) different600 and 150 s), (B) a narrow and long sliding window (T=150 and 600 s), using the criteran amplitude above a threshold of 0.5.velocities rather than the averaged ones obtained with the longwindow. Some limits of the correlation analysis using a narrowwindow,associated with characteristics of the gas plume, remain and explainlarge discrepancies with the speeds estimated using a long window.They lead tovelocitiesmostly below0.5 m s1 orhigher than2.5 m s1.These limits in the method are explained in Appendix B.

3. Results

3.1. Time-series of SO2 column amounts

SO2 column amount time-series obtained for both spectrometers(Fig. 2) reveal similar patterns, with a time delay expected for theupper instrument dataset corresponding to the time for an inhomo-geneity to travel from the rst to the second spectrometer FOV. Theslight differences in amplitude between the time-series can resultfrom various processes.

The sensitivity of both instruments can be assumed to have amultiplicative effect on the measured light intensity. Optical depthsand gas column amounts are consequently independent of it. On theother hand, the error in the column amount from the DOAS retrieval,resulting from the tting procedure (Stutz and Platt, 1996; Hausmannet al., 1999), is between 3 and 12% for both instruments. It explains apart of these differences.

Additional errors in the column amount are linked to thescattering of light by air molecules and particles (Millan, 1980; Plattet al., 1997; Mori et al., 2006). The modelling work of Kern et al.(2009) gives a quantication of this effect, including in-plumemultiple scattering and the light dilution effect. Given the low SO2

sliding windows used for correlation analysis (with a duration T of respectively 1200,ion selecting the rst local maximum in the CCF function, relative to the time shift, with

maxaximatchpeakivelr th

329M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336column amounts and aerosol load (with an aerosol extinctioncoefcient assumed to be less than 0.5 km1, as at Etna (Fioraniet al., 2009)), the very limited ash content in the Erebus plume, and

Fig. 4. Example of correlation analysis giving ameaningless speed by selecting the absoluteIndeed, using a narrow correlationwindow of durationT=150 s (on left), the absoluteminside the lower correlation window, which would give the expected time lag. Rather it martifact does not occur with a long window (on right, hereT=600 s) because secondaryshift of the upper spectrometer correlation window. (B) and (C) show signals for, respectobtained time lag. Dashed lines underline correlation windows, centred and xed in t foincreasing until the time lag is found.the distance (2 km) between plume and spectrometers, the error onthe estimated column amount is less than 10% over the wavelengthrange used for retrieval (308330 nm). Nevertheless, the impact ofthe light dilution effect may be underestimated with this study whichdoes not consider a wide spectrometer angle of observation,especially when the plume is far from lling the whole eld of view.More experiments would be required to quantify this phenomenon.Finally, light scattering inuences the absolute amount of gas butshould have a negligible impact on the differences identied betweenspectrometers because they are both pointing at about the samealtitude, equivalent to just 75 m apart when projected to the crater,leading to negligible differences in light path lengths.

The plume studied in this experiment was mainly vertical.Contrary to horizontal plumes, which are principally advected bythe wind, vertical plumes rise due to buoyancy. They can beinuenced by the local wind eld at an altitude where their verticalbuoyancy-induced velocity is smaller than the horizontal componentof the wind. At this stage, they expand laterally forming a bend. If thetwo elds of view intersect such a bend, gas molecules are effectivelycounted more than once, leading to an over-estimation of thecolumn amount. It can explain differences in column amount time-series, the higher spectrometer being potentially the only oneaffected. We checked a video footage recorded during our experimentand observed occasionally a bend in the plume at a height less than200 m above the crater, i.e., below the altitude of the upperspectrometer's FOV. It happened during three time intervals (0939,14641866, and 33543791 s after the start time of 20:24 h GMT),and the column amounts measured with the upper instrument wereonly 210% higher than those obtained with the lower spectrometer(see Fig. 2). Consequently, this issue only weakly affects the results.

An additional process is associated with the presence of stagnant,diffuse SO2 around theplume,which sometimes formsa thin veil as seenon the video. This background pollution is hard to quantify but iscertainly negligible comparedwith thepreviouslymentionedprocesses.

Errors on column amounts (CA) are less than 10% for each

imum(blue) of the cross-correlation function (CCF) and not therst localmaximum(red).um does not correspond to the translation to the second instrument's FOV of the structurees this initial structure with the translated signal of a similar neighbouring structure. Thiss of the CCF are strongly attened. (A) Plot of the cross-correlation function with the timey, the upper and lower spectrometers, from (tT/2) up to (t+lag+T/2), with lag thee lower spectrometer signal, centred in (t+) for the upper spectrometer signal with spectrometer. The main differences between the two CA time-seriesare of highermagnitude and cannot be due to any of these artifacts butresult from atmospheric phenomena to be discussed later. The lowereld of view is likely to present the time variations in column amountthe closest to those of the emission of gas at the magma source. It isconsequently chosen for the ux estimation.

3.2. Plume speed time-series

We have seen in Section 2.3.2 some issues encountered when theplume speed is evaluated with a narrow correlation window (here of2.5 min), due to limits of the correlation analysis method. Whenevaluations are available, estimated speeds are closer to real-time values,which is of considerable interestwhen studying very short-termeruptivebehaviour such as explosions. There was no Strombolian activity duringour experiment, and we are primarily interested in exploring periodicbehaviour with cycles around 10 min. For this reason, the SO2 ux iscalculated from the speed estimatedwith a longer correlationwindow of10 min (Fig. 5B). Cross-correlation coefcients used for wind speeddetermination are shown in Fig. 5C with values most of the timesignicantly higher than the chosen threshold of 0.5. The average plumevelocity varies smoothly over the range 12.5 m s1. By a basicdifferential calculation from Eq. (2), the uncertainty in the speed isestimatedas 0.1 m s1 consideringuncertainties in thedistancebetweenthe two spectrometer's elds of view (dY) and in the time lag betweenthe upper and lower column amount signals (lag) of respectively 9 mand 2 s.dY is dependent on, respectively, the uncertainties in the angle between the two spectrometers'elds of view, taken to be 20.2 (ourgoniometric stage has a precision of 0.1 but the resulting uncertainty isconsidered greater considering imperfections in the structure supportingboth spectrometers); the elevation angle of the lowermosteld of viewwhich is 120.5; and the horizontal distance D between observation

330 M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336Fig. 5. High time resolution (1 s) (A) SO2 ux (in kg s1) from the lower spectrometer,(B) plume speed (in m s1), (C) cross-correlation coefcient used for plume rise speedsite and plume which is 196050m. lag results from the commonwidth of the cross-correlation function maximum, which provides anestimate of the time lag. It is important to note that the obtained velocityrepresents an average value of the plume speed between the twospectrometer FOVs. In reality, a deceleration of the plume rise is expecteddue to a loss of buoyancy with ascent. Moreover, the speed is alsoaveraged over the length of the correlationwindow, used to estimate thetime lag, as mentioned above.

Plume velocities estimated with the DW-FOV DOAS are similar tospeeds evaluated using video techniques. To estimate speed from thevideo, we tracked clearly dened fronts of ascending puffs (on a timescale of 30 s) and used for a distance scale mapped asperities on thecrater rim (clearly visible in the video). Decreasing velocities(averaged at 30 s) were seen, in the range of 2.82.10.4 m s1 foraltitudes ranging from 165 to 230 m above the crater, whichcorrespond approximately to the heights of the spectrometers' eldsof view at 78 and 150 m (note that speeds were estimated withvideo at slightly higher altitudes than spectrometer FOVs, where pufffronts were better dened). The uncertainty in this speed arises fromthe difculty in locating precisely the gas puff front (at 10 m), theerror on the distance scale seen in the video eld of view (estimated at2605 m)beingnegligible by comparison. It is also in agreementwiththeoretical estimations of the rise rate of a buoyant gas puff, which arein the range of 0.63.2 m s1 at Erebus as shown in Appendix C.

3.3. SO2 ux time-series

Given that the gas column amount CAWFOV measured with a wideeld of view spectrometer approximately represents the averagecolumn amount along the different directions in the wide angle of

estimation fullling the two imposed criteria (i.e. corresponding to the rst maximumof the cross-correlation function with the time shift and which has to exceed a value of0.5), vs. time from the data set start at 20:24:48 UTC on 26 December 2006, using a10 min correlation window. Note that the cross-correlation coefcient is articially setto zero when it does not full both required criteria. This results in four gaps in ux dataduring which speeds cannot be calculated from the correlation analysis.observation (see Section 2.2 and Appendix A), the gas ux (in kg s1)estimated with this new technique is obtained from:

= CAWFOV104MNAv

Dcos

WFOV

! ; 3

considering a column amount in molec cm2, M the gas molar massin kg mol1 and NAv Avogadro's number. At Erebus, the SO2 uxmeasured during 1.7 h on 26 December 2006 varies between 0.17and 0.89 kg s1 (Fig. 5A). The uncertainty in the ux is estimated at0.2 kg s1 (33% on the mean ux). This low value represents aconsiderable improvement in the accuracy of ux measurements. Itdepends on the different uncertainties, listed by order of magnitude,linked to the elevation angle of the lowermost FOV, the columnamount (assumed equal to 10%), the plume speed, and the wide angleof FOV aperture (assuming an uncertainty on WFOV of 1 resultingfrom the adjustment of the lensesmounted on the telescopes) leadingeach of them to an uncertainty in the range of 0.030.06 kg s1 on theux. Note that this obtained uxmay include some gas emitted from asecondary vent within the crater known as Werner vent, though nolava was present within it during the experiment.

Estimations of the gas ux with the DW-FOV DOAS are similar toprevious measurements:

(1) Measurements of 0.860.20 kg s1 carried out in December2003 by Oppenheimer et al. (2005) by the traverse methodbeneath a horizontally advected plume travelling at 5.1 m s1

(the plume speed was derived from two DOAS spectrometersaligned along the plume axis).

(2) The mean ux between 1992 and 2005 of 0.70.3 kg s1,estimated by scanning vertical plumes each eld season overtwo to ve days in December, with plume speeds obtainedfrom video methods by Kyle et al. (1994).

The SO2 ux from Erebus is low compared tomany volcanoes but issimilar to Erta 'Ale in Ethiopia, which also hosts a persistent lava lake(Oppenheimer et al., 2004). An animation showing the results in theform of an SO2 uxmeter superimposed on video of the plume, isavailable as an electronic supplement to this article.

3.3.1. Time-series analysis of ux data for ErebusIn view of the likely non-stationarity of SO2 output from Erebus, we

use wavelet analysis to explore any frequencies present in the signal, aswell as their variability with time. Analysis of the ux time-series isachieved here using a continuous transform with a complex Morletwavelet (Fig. 6). Thiswavelet analysis is particularly suitable to study ournon-stationary time-series, where smooth variations in the frequencycontent are expected. Moreover, the Fourier transform of a complexMorlet wavelet presents an analytical expression, simplifying calcula-tions of the wavelet transform. Full details concerning the method ofanalysis are given in Appendix 9. Concerning our time-series, high-frequencies are associated with variations of smaller amplitude of thesignal than lower frequencies, and are consequently less energetic andvisible in the wavelet analysis. We broadly distinguish three populationsof distinctive periods, associated to approximately the same power atboth spectrometers, which can be listed by decreasing energy as follows:

(1) Pattern 1: periods in the range 7001300 s (1122 min) forupper spectrometer; and in the range 8001400 (possiblymore)s (1324 min) for lower spectrometer, which are energeticduring the whole dataset.

(2) Pattern 2: periods in the range 300600 s (510 min) for theupper spectrometer, energetic until 3200 s; periods in therange 400600 s (6.510 min) for the lower spectrometer, lessenergetic than at the upper instrument, present until 2000 s.

(3) Pattern 3: periods in the range 100200 s (1.52.5 min) for

bothspectrometers, appearing irregularlyduring theexperiment.

331M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336Calculating the wavelet transform of both ux signals, to which awhite noise of a chosen amplitude (equal to 0.1 kg s1 here) has beenadded, allows us to test the signicance of the results. The resultingwavelet analysis is slightly different but still shows peaks in powerassociated with the groups of periods mentioned above, including theless energetic Pattern 3 which is consequently well above the noiselevel and consistent. In addition, wavelet analysis was also performedon portions of the data set without gaps (i.e. before 2000 s), verifyingthat these gaps, where linear interpolation was performed, do notinuence the results.

4. Discussion

4.1. Methodology

The basis of the DW-FOV DOAS system to record high temporalresolution ux measurements relies on the estimation of the plumevelocity by following inhomogeneities between the two spectro-meters' elds of view crossing the plume. It is consequently importantto orientate elds of view closely to the perpendicular direction toplume transport in order not to gather dissimilar plume parts in a FOV.

Fig. 6.Wavelet transform (modulus) and time-series of SO2 uxes (in kg s1) for (A) upperand (B) lower spectrometers. Note that ux time-series are linearly interpolated to ll thefew data gaps described in Fig. 5. The three populations of distinctive periods present in thesignal (referenced as Patterns 1, 2, and 3 in the gure) are discussed in the text. The cone ofinuence (white lines) delimits cross-hatched regions, inside which edge effects are non-negligible.The distance between both FOVs also has to be carefully chosen inorder to allow a relevant correlation analysis. It must not be too largesuch that structures recorded by the lower instrument are substan-tially modied or lost by the time they reach the upper spectrometer.The half-life of a turbulent inhomogeneity can be estimated consid-ering the auto-correlation function of the column amount time-serieswhere it corresponds to the width of its rst peak (70 s at Erebus). Alarge distance can also average out variations in plume speed,especially for vertical plumes which typically decelerate. Fields ofview that are too close can also impede identication of elongatedpuffs, which cannot be adequately differentiated during their rise fromthe lower to the upper eld of view to carry out a meaningfulcorrelation. Depending on the plume velocity, the minimum distanceof separation is also dictated by the data sampling frequency, aswell asby the uncertainty of the method of correlation analysis. Furthermore,the travel time of one inhomogeneity to reach the second eld of viewmust be less than any periodicity of the volcanic degassing to avoidirrelevant results of the correlation analysis. As a consequence, theoptimumdistance between the twoelds of view inside the plumewillvary from one volcano to another, depending also on its activity.

Reducing themain sources of uncertainty in the gas ux estimationswill improve the method. In particular, a more accurate estimation ofthe elevation angle of the spectrometer FOVs could be achieved quitestraightforwardly. Concerning the instrument, lenses mounted on thetwo telescopes gave a xed horizontal eld of view width adjusted forthe typical width of the Erebus plume. We have since constructed atelescopic system with adjustable elds of view to adapt to differentsituations. This could be particularly useful for a horizontal plume,which can display more variable dimensions with time depending onthe local wind eld. Vigilance is indeed required to make sure that thewhole plume is captured in the wide angle of observation.

4.2. Interpretation of degassing patterns

Wavelet analysis of the ux time-series identies three patterns inErebus degassing (see Fig. 6 and Section 3.3.1). The most noticeableone, in terms of energy, includes periods in the range of 1124 minwhich are manifest during the whole data set and for both spectro-meters. The second pattern is associated with 510 min cycles, but isonly apparent during the rst half of the experiment. It is relevant tonote that this behaviour is more pronounced, and that the signal isstronger, in data from the upper spectrometer (see Fig. 6). Thissuggests that the signal results from the large scale organization ofturbulence inside the plume developing with height above the crater.This is commonly observed at chimneys expelling a constant gas uxwhere structure develops with altitude. Thus, this part of the signalyields no information about the magma source but rather theatmospheric processes modifying the large gas puffs associated withthe rst pattern of degassing. Further investigation would be requiredto quantify this inuence and its dependence on the distance betweenthe magmatic source and the plume sections crossed by the spectro-meters' elds of view. The third pattern in degassing consists of short-period uctuations of the ux in the range of 1.53 min, which appearseveral times during the experiment. They reveal the exhalations ofsmaller gas puffs covering just one part of the crater, as illustrated inthe video (see electronic supplement). In the next section, we explorethe magmatic processes that can explain the SO2 ux variabilityfocusing on Pattern 1, associated with cycles with 1124 min period.Note that no explosions occurred during our observations according toseismic and acoustic observations.

4.2.1. Periodic gas-rich magma supply to the lava lakePeriodic SO2 degassing could be linked to pulsatory discharge of

gas-rich magma into the lava lake. Such a magma ow could resultfrom different processes. Magma convection in the conduit can

promote the persistence of long-lived lava lakes with sustained

degassing (Francis et al., 1993; Kazahaya and Shinohara, 1994;Stevenson and Blake, 1998). The models assume bi-directional owof a less dense, lower viscosity ascending magma, and a degassed,denser and more viscous descending magma. It has been shown thatthe Erebus lava lake has a sufciently large feeder conduit radius tomaintain this process for assumed viscosity and density contrastsbetween rising and sinking magma (Calkins et al., 2008). Oppenhei-mer et al. (2009b) argued that the viscosity stratication induced bysuch bi-directional magma ow can lead to boudinage of the risinggas-rich magma and explain a pulsatory supply of magma into thelake (Fig. 7A).

Variations in magma viscosity can also lead to periodic magmaow. Wylie et al. (1999) have modelled magma rise dynamicsassuming a constant ux at the base of an elastic conduit. Theyshowed how the dependence of viscosity on volatile content can leadto an oscillating magma ow at shallow depth, given a relevant rangeof model input parameters (Fig. 7B). This model was applied to theandesitic Soufriere Hills Volcano (Montserrat), indicating an unstablemagma ow with oscillation periods of a few hours, but it should bevalid more generally during closed-system degassing. However, noanalytical expression is given for the oscillation frequency. Thus wecannot identify if it reproduces the 1124 min periodic degassingobserved at Erebus, but it does provide a plausible conceptualmechanism. Periodic magma ow could also result from pressuriza-tion feedbacks between magma ascent rate, crystallization, and open

considers the progressive accumulation of a gas foam that grows andbecomes unstable above a critical thickness. The foam then collapses asbubbles coalesce, resulting in expulsion of overpressured gas slugs thatrise to the surface generating explosions. Since therewere noexplosionsat Erebus during theperiodof our experiment,we consider a variationofthis process thatmight result in periodic passive degassing. Rather thanan asperity with sharp boundaries, we consider a continuous, smoothcavity in the conduit walls, as illustrated in Fig. 7C. The gas expelled tothe atmosphere is then a mixture of two sources: one, a continuousdegassing from amagma rising directly from depth to surface; the otherassociated with the accumulation of gas in a smooth conduit cavity,whichdepends on the size of this segregator aswell as the rising gas andmagma uxes. This smooth geometry does not allow the collapse of agas foam but rather the regular retention and extraction of theaccumulating foam. This would permit a continuous passive release ofgas from the lava lake with a periodic pattern depending on the rate ofgas accumulation at some depth in the magmatic system.

4.2.3. Complementary geochemical and geophysical observationsThese two groups of physical processes allow us to interpret not

only the observed periodicux of SO2 but also the diverse geochemicaland geophysical measurements made during other eld seasons atErebus. Unfortunately, when our DW-FOV DOAS spectra wererecorded in December 2006, it was already late in the eld seasonand other instruments (thermal camera and FTIR spectrometer) were

ioddowas s

332 M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336vs. closed-system degassing, which have been proposed as anexplanation for the periodic behaviour of andesitic and silicic domes(Melnik and Sparks, 1999; Barmin et al., 2002).

A further explanation for periodic magma ascent is stick-slipmovement along the conduit walls (Denlinger and Hoblitt, 1999). Thismechanism can be ruled out for Erebus given the absence ofcorresponding seismicitythe few long period earthquakes that arerecorded there are associated with Strombolian explosions (Asteret al., 2003, 2008).

4.2.2. Periodic gas supply to the lava lakeGas segregation at the roof of a magma reservoir (Jaupart and

Vergniolle, 1989) or in asperities such as horizontal intrusions leadingfromamagmaconduit (Menand and Phillips, 2007), has been suggestedto explain intermittent Strombolian explosions. This mechanism

Fig. 7. Cartoon illustrating different processes that can explain periodic degassing. (A) Perow, resulting from shear stresses between the buoyant gas-rich hot rising magma andvolatile-dependent viscosity; and (C) periodic gas supply to the lava lake arising from g

Panel A is modied from (Oppenheimer et al., 2009b).not running; so we cannot explore the correlation between the time-varying behaviour of gasuxwith other parameters. Nevertheless, it isof particular interest to note that a similar periodicity of about 10 minhas been identied in December 2004 from analysis of both thermalimagery of the lava lake and gas composition measured by Fouriertransform infrared spectroscopy (Oppenheimer et al., 2009b). Theseobservations revealed cycles in lava lake convection (surface speedand direction) and heat output with periods of 415 min, that werephase-locked with cyclic changes in gas composition (SO2/CO2 andHCl/CO ratios). Columnamounts of gasesmeasuredbetween the craterrim and the lake surface (a distance of about 300 m) also revealed thesame cyclicity, suggesting that gas uxes were very likely periodic too.Both types of model discussed above can account for these additionalobservations but only gas segregation offers an explanation for theseismicity at Erebus and complementary geochemical measurements.

ic magma supply to the lava lake as a consequence of boudinage of the ascendingmagmanwelling cooler degassed counterpart; (B) periodic rising magma ow resulting fromegregation in smooth cavities in the conduit.

333M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336The stability of oscillatory, very long period signals precedingStrombolian eruptions, over a span of ve years, suggests a stablenear-summit reservoir with multiple sites for gas slug coalescence asVLP sources (Aster et al., 2003, 2008). Shallow magma sequestration isalso proposed to interpret measurements of water and carbon dioxideuxes from Erebus, which reveal that not all the magma that suppliesthe CO2 emitted from the lake can reach the surface, since otherwise theH2Oux should bemuchhigher than observed (Oppenheimer andKyle,2008). Note that the presence of a CO2 rich pre-existing uid phase, nottrapped in melt inclusions, could also explain this observation.

4.3. Further remarks

This study shows the value of accurate high resolution ux data toexplore variability in magma degassing. Our experiment was only ofshort-duration and we only had simultaneous video images asadditional data. This precludes discrimination between the alternativemodels for the periodic degassing behaviour of Erebus that weidentied. However, it paves the way for further investigation, whichwill greatly benet from complementary volcanological observationsincluding thermal imagery, and FTIR spectroscopy to constrain thedepths of gas sources in themagmatic network, themechanisms of gassegregation, and the different modes of gas transport. A betterknowledge of the magma plumbing system with the dimension ofpotential gas storage regions could be explored further throughseismic studies. Eventually, developing physical models from concep-tual mechanismswill help to determine the range of input parameters(including in particular rising gas andmagma uxes, magma rheology,the dimension of gas bubbles, and the geometry and size of gassegregators) that would lead to periodic degassing, and how theexpected periodicity at Erebus could be modelled analytically.

5. Conclusions

We have described the construction of a dual-wide eld of viewUV spectroscopic system designed for the high temporal resolutionmeasurement of volcanic gas uxes (principally of the species SO2).The novelty of the instrumental set up lies in the use of a combinationof spherical and cylindrical lenses, which present an elongated eld ofview that is oriented perpendicularly to the plume transport directionso as to observe all SO2 molecules present simultaneously (withoutthe need for imaging, motion or scanning). Additionally, the two eldsof view are separated by a small angle that permits tracking of plumeinhomogeneities in the time-stamped datasets obtained from eachspectrometer. The data analysis includes DOAS retrieval of gas columnamounts and correlation analysis of the time-varying signals recordedat the two spectrometers, whose angular separation indicates theseparation distance between the two instrument elds of viewprojected to the plume. The deployment of the system is relativelysimple and it can be used, in principle, on any plume rising verticallyor drifting horizontally, where the basic plume and viewing geometrycan be measured with some certainty. Processing of the data couldalso be achieved in real-time, and it would only require limited furtherdevelopment to yield a real-time uxmeter, capable of measurementsat a frequency of 1 Hz or better, with an accuracy of 33% or better.

This method allows the study of short-term variations in volcanicdegassing. We have demonstrated the vigilance required to discrim-inate between uctuations linked to atmospheric processes fromthose resulting from magmatic activity. At Erebus, a particularlynoticeable periodicity in the range of 1124 min is apparent in the SO2degassing rate. Two groups of physical processes can explain thisoscillatory behaviour. The rst involves a periodic supply of gas-richmagma to the lava lake, which may result either from boudinage ofthe rising magma ow due to shear stresses between ascending anddescending magmas in a bi-directional conduit ow, or from a

volatile-dependent viscosity leading to an oscillating magma ow.The secondmechanism is associatedwith periodic supply of gas to thelake arising from gas segregation in smooth cavities in the conduit.Smaller gas puffs, leading to short-period uctuations of the uxlasting a few minutes, are also observed intermittently. A longerexperiment duration, combining ux measurements with othervolcanological data streams, is needed to discriminate between thesuggested source mechanisms for this particular degassing behaviour.This would improve understanding of gas and magma dynamics andstorage in the Erebus plumbing system.

Acknowledgments

We gratefully acknowledge support from the NSF Ofce of PolarPrograms grants (OPP-0229305; ANT-0538414) and the United StatesAntarctic Program. CO also thanks the Leverhulme Trust for a StudyAbroad Fellowship and the EU Framework 6 programme, whichsupported the project NOVAC. MB thanks the European Commissionfor an Intra-European Marie-Curie Fellowship (Project VolcanGas14018), and Olivier De Viron for fruitful discussions concerning signalanalysis. CO and PKwarmly acknowledge their companions in ScienceEvent G-081 and the helicopter pilots, and the staff based at McMurdoStation. They are particularly grateful to Dr. Tom Wagner (then NSFProgram Manager for Antarctic Geology and Geophysics) for hissupport. Finally, we thank Nicole Bobrowski and Michael Burton fortheir reviews which allowed to greatly improve the manuscript.

Appendix A. Meaningof thecolumnamountmeasuredwithDW-FOVDOAS spectrometers

The elemental light power d received from the solid angle d,associated to longitude and latitude , by a lens aperture of surfaceAr is a function of the radiance (or intensity) L:

d = ArL;d: A:1

Considering a small lens aperture surface, the total light powerreceived by a wide eld of view capturing instantaneously the wholehorizontal plume cross-section spectrometer is given by:

= Ar+ NFOV = 2NFOV = 2

+ WFOV = 2WFOV = 2 L;d; A:2

where WFOV and NFOV are, respectively, the wide horizontal andnarrow vertical angles of aperture of the eld of view. The elementalsolid angle can be written in spherical coordinates:

d= cosdd: A:3

The vertical angle of aperture of the wide eld of view spectro-meters NFOV being very small (8 mrad), the radiance can be assumedconstant on the range of considered latitudes . The total light power(Eq. (A.2)) is thus given by:

= ArNFOV+ WFOV = 2WFOV = 2 Ld; A:4

and can be rewritten:

= ArNFOVWFOV L; A:5

with L the mean radiance for 2 [WFOV/2; WFOV/2]. An equivalentequation is valid for the light power received from the background sky

= A L : A:6bg r NFOV WFOV bg

As a consequence, writing Eq. (A.14) from Eqs. (A.15) and (A.16)gives the error made by approximating CAWFOV by

CA:

CAWFOVCA = 1

CAWFOV0 CAWFOVtetdtCA0 CAtetdt

;

A:17

which gives after majoration

jCAWFOVCACA j maxCA: A:18Fig. 8 illustrates the evolution of this relative error according to the

strength of gas emission from the studied volcano.

Appendix B. Cases of failure of the correlation analysis linked toplume characteristics

Correlation analysis is successful when clearly dened structuresare present in the selected window. But failures show up in thefollowing cases:

334 M. Boichu et al. / Journal of Volcanology and Geothermal Research 190 (2010) 325336Combining Eqs. (A.5) and (A.6), we have:

Bg

=L

Lbg: A:7

Moreover, according to the BeerLambert law (simplied hereby not explicitly including low-frequency components), we have:

L = LbgeCA; A:8

where is the cross-section of the considered gas species and CA() itsslant column amount in the direction dened by . Note that the proofis exactly the same with the complete BeerLambert law, merely anadditional step is required to remove the low-frequency component.We would obtain in this case the above equation, where would justbe replaced by its associated differential cross-section. A limiteddevelopment of the exponential is valid for Eq. (A.8) if we have weakoptical depths (i.e. CA()bb1). This is the case at Erebus consideringthe emission of sulfur dioxide, where this product is close to 102,with a SO2 slant column amount of the order of 1017 molec cm2 andSO2 1019 cm2. It follows that:

L Lbg1CA: A:9

If we take the mean of this expression with , assuming that thebackground has been collected for a uniform or clear sky and that Lbgis consequently negligibly dependent on , we nd:

L Lbg1

CA : A:10

Therefore, Eq. (A.7) can be rewritten:

Bg

1CA: A:11

Given again (CAbb1), Eq. (A.11) is approximated by:

bgeCA ; A:12

with

CA =

1WFOV

+ WFOV = 2WFOV = 2 CAd: A:13

Consequently, the column amount measured with the wide eldof view spectrometer CAWFOV represents the mean column amountalong the different directions inside the wide angle of observationWFOV. This result has been proven assuming weak optical depthshere. But it is generally valid, for any optical depth. In this case, wecannot give an analytical expression for the relationship betweenCAWFOV and

CA. But we can estimate the error made when assuming

the equality CAWFOV =CA, that will be used then for gas ux

estimation with this technique. According to Eq. (A.7) and thesimplied Beer Bouguer Lambert law Eq. (A.8), we have:

eCAWFOV =eCA: A:14

Moreover, a rst order Taylor expansion with integral remaindergives:

eCAWFOV = 1CAWFOV + CAWFOV0 CAWFOVtetdt A:15

and

eCA = 1CA +CACAtetdt: A:160(1) When a structure in the degassing is recorded at the rstspectrometer but has faded or completely dissipated by thetime it reaches the second spectrometer.

(2) When there is no structure in the plume. In this case, themaximum of the CCF function which is obtained is notmeaningful due to the presence of a few peaks with similaramplitudes. Checking the video footage recorded simulta-neously with the DOAS measurements, we observed that theselimits in the correlation analysis do occur when the plumeappears less distinct with elongated and very few structuredpuffs, as opposed to smaller puffs with a clearly dened risefront due to a large contrast of density with the surrounding air.

Appendix C. Theoretical estimation of a rise speed of a buoyant puff

According to seismic observations, there were no explosionsduring our period of spectroscopic measurements and degassingconsisted of the passive release of magmatic gases from the lava lake.The rise of these hot gas puffs, or thermals, is consequently mainlydriven by buoyancy and not by an initial source momentum. Theirascent, during which they rapidly entrain colder atmospheric air

Fig. 8. Relative error on the approximation of the mean SO2 column amount (CA) along

the different directions in the wide eld of view by the SO2 column amount measuredwith the DW-FOV DOAS (CAWFOV), according to Eq. (A.18) (for more explanations, seeAppendix A). For calculations, an averaged value of the SO2 cross-section, estimated

19 2over the wavelength range used for t, is considered (10 cm ).

335nd Geothermal Research 190 (2010) 325336through a large organized vortex ring and expand, can be described byuid dynamics. If a fully turbulent regime is assumed, an analyticalsolution of the three coupled equations of mass, momentum andenergy conservation is possible. It is self-similar with distance fromthe source z and for a non-density stratied atmosphere can bewritten as (Morton et al., 1955; Turner, 1979; Sparks et al., 1997;Branan et al., 2008):

r = z C:1

=B0r

30

33

!1=21z

C:2

B =B0r

30

31z3

C:3

with the expression of the buoyancy

B = gapa0

; C:4

where r is the radius of the puff which is assumed spherical, v its verticalvelocity, the entrainment constant (with an empirically determinedvalue of 0.25 for fully turbulent laboratory thermals (Scorer, 1957;Turner, 1979)), g the acceleration due to gravity, p and a the bulkdensity of, respectively, the puff and the surrounding atmospheric air.The subscript 0 refers to the variable value at the source of the puffrelease, which is the lava lake at Erebus.

Note that an idealized point source is an unrealistic initial con-dition. This ow description is consequently not valid very close to thesource. We show that it can be applied at the altitude of the DOASmeasurements, just above the crater rim (220 m above the lake).Indeed, this model predicts spherical puffs with a radius of 55 m,which is consistent with estimates made from available photographsand videowhere it varies between45 and68 m. According to Eq. (C.2.),the puff vertical speed mainly depends on the source radius r0 via anexponent of 3, and at second order on the reduced gravity B0.

An upper value for the source size is the dimension of the lava lakewhose radius is 17.5 m. A better constrained range of estimates canalso be deduced from the dilution coefcient d, dened as the ratio ofthe initial puff volume to the volume at the measurement height,which can be written:

d =r0r

3: C:5

From Fourier Transform Infrared (FTIR) spectroscopy carried outfrom the crater rim along the 300 m path to the lava lake, a meanmixing ratio of 0.001 is evaluated and gives a rough indication of thedilution coefcient which can be assumed to range in 0.010.001.According to photographs, for a puff radius at the measurementaltitude of 4468 m, Eq. (C.5) gives a source radius in the range 4.514.5 m.

The puff consists of a gas mixture (10 kg s1 of water; 15 kg s1 ofCO2, and total gas ux of 27 kg s1) (Oppenheimer and Kyle, 2008),whose density follows the perfect gas law. Its value at the source is0.2 kg m3 for an initial puff temperature of 1273 K, an atmosphericair temperature of 250 K and pressure of 0.63 105 Pa for Erebussummit altitude (3798 m above sea level). From Eq. (C.2), assuming anatmospheric bulk density of 0.88 kg m3, the puff vertical velocity is inthe range 0.63.2 m s1.

Note that the assumption of a turbulent regime can be checkedafterwards. The Reynolds number associated with the puff risedynamics has the expression:

ReP =vzP

; C:6

M. Boichu et al. / Journal of Volcanology aPwhere P represents the gas puff dynamic viscosity (of 5106 Pa saccording to Sutherland's formula describing viscosity variations withtemperature, though this calculation is made outside the calibrationrange for a temperature of 555 K and thus represents an approxima-tion). For a mean vertical speed of 2 m s1, ReP is 107 at themeasurement height, i.e. much greater than 104 and demonstrating afully turbulent ow.

This description of the plume rise does not consider the potentialconvective ux of air that is heated by the surface of the lava lake. Itcan reduce the contrast of temperature between the puff and thesurrounding air, slowing the puff rise. On the other hand, it can alsoentrain the puff and accelerate its ascent. This effect has counter-balancing consequences and is neglected.

Appendix D. Wavelet analysis

A time-series analysis is performed using a complex Morletwavelet with the expression

t = 11=4

e + i0te20 =2et

2=2

: D:1

0 is taken equal to 2 and is consequently superior to 5 in order tosatisfy the wavelet admissibility condition (Farge, 1992). The secondterm of Eq. (D.1) is also thus negligible and the Fourier transform ofthis wavelet is simply a Gaussian function, which facilitates thecalculation of the wavelet transform (Torrence and Compo, 1998). Wechose to express the wavelet analysis as a function of a set of scales alinearly distributed between Tmin and Tmax, which represent theshortest and longest time periods that we can study. They are,respectively, taken as equal to twice the time spacing of the dataset(1 s here) and less than half the duration of the entire data set(4000 s), in order to satisfy the NyquistShannon sampling theorem.Note that the scales associated with aMorlet wavelet are almost equalto Fourier periods for06 (Torrence and Compo, 1998). This analysisis carried out onux time-series that are linearly interpolated toll thefew data gaps in plume speed estimations resulting from the lack ofplume structure, assuming continuous variations of the velocity. Thedomainwhere thewavelet analysis does not suffer from edge effects isdelimited by a cone of inuence. It is associated with a characteristictime equal to

2

pa, which corresponds to the time where the wavelet

power associated to a discontinuity at the edge drops by a factor e2,which ensures that the edge effect is negligible (Torrence and Compo,1998).

Appendix E. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jvolgeores.2009.11.020.

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High temporal resolution SO2 flux measurements at Erebus volcano, AntarcticaIntroductionMethodologyExperiment descriptionSpectroscopic retrievalPlume speed retrievalPrinciple of the cross-correlation analysisInfluence of the correlation window length

ResultsTime-series of SO2 column amountsPlume speed time-seriesSO2 flux time-seriesTime-series analysis of flux data for Erebus

DiscussionMethodologyInterpretation of degassing patternsPeriodic gas-rich magma supply to the lava lakePeriodic gas supply to the lava lakeComplementary geochemical and geophysical observations

Further remarks

ConclusionsAcknowledgmentsMeaning of the column amount measured with DW-FOV DOAS spectrometersCases of failure of the correlation analysis linked to plume characteristicsTheoretical estimation of a rise speed of a buoyant puffWavelet analysisSupplementary dataReferences