A discussion of the mechanisms of explosive basaltic eruptionsruprecht/Site/... · cooled upper surface of a magma column (e.g., Black-burn et al., 1976; Wilson, 1980). In such events,

A discussion of the mechanisms of explosive basaltic eruptions

Elisabeth A. Parfitt

Department of Environmental Science, Lancaster University, Lancaster, LA1 4YQ, UK

Received 3 February 2003; accepted 16 January 2004

Abstract

Two contrasting models of the dynamics of explosive basaltic eruptions are in current usage. These are referred to as the risespeed dependent (RSD) model and the collapsing foam (CF) model. The basic assumptions of each model are examined, and itis found that neither model is flawed in any fundamental way. The models are then compared as to how well they reproduceobserved Strombolian, Hawaiian and transitional eruptive behaviour. It is shown that the models do not differ greatly in theirtreatment of Strombolian eruptions. The models of Hawaiian eruptions are, however, very different from each other. A detailedexamination of the 1983–1986 Pu’u ‘O’o eruption finds that the CF model is inconsistent with observed activity in a number ofimportant aspects. By contrast, the RSD model is consistent with the observed activity. The issues raised in the application ofthe CF model to this eruption draw into doubt its validity as a model of Hawaiian activity. Transitional eruptions have only beenexamined using the RSD model and it is shown that the RSD model is able to successfully reproduce this kind of activity too.The ultimate conclusion of this study is that fundamental problems exist in the application of the CF model to real eruptions.D 2004 Elsevier B.V. All rights reserved.

Keywords: basaltic; explosive; eruption; strombolian; hawaiian; foam; separated flow

1. Introduction

Basaltic volcanism is the dominant mode of vol-canic activity on Earth, the Moon, Mars and Venus(e.g., Cattermole, 1989; Head et al., 1992; Wilson andHead, 1994). On Earth, >80% of the annual volcanicoutput is basaltic with >70% of this occurring beneaththe Earth’s oceans (Crisp, 1984). Basaltic eruptionsare frequently described as effusive because theycommonly generate lava flows. While the term ‘‘ef-fusive’’ is appropriate for basaltic eruptions in whichthe lava oozes passively from the vent, it is a mis-leading term when applied to the majority of subaerialeruptions on Earth, to eruptions on the Moon and

almost certainly to eruptions on Mars (Wilson andHead, 1983, 1994). The presence of dissolved gaswithin basaltic magma results in explosive volcanicactivity unless the exsolution of the gas from themagma is suppressed (as in sufficiently deep sea-floorvolcanism—Head and Wilson, 2003) or the gas is lostfrom the magma prior to eruption. Although explosivebasaltic eruptions are generally much less violent thantheir more silicic counterparts they are, nonetheless,explosive and need to be considered as part of acontinuum of explosive activity that embraces notonly the familiar explosive basaltic eruption styles—Hawaiian and Strombolian—but includes sub-Plinian,Plinian, ultra-Plinian and ignimbrite-forming events.

Our understanding of the mechanisms of explosivebasaltic eruptions has advanced considerably duringthe past f30 years due to the collection and analysis

0377-0273/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jvolgeores.2004.01.002

E-mail address: [email protected] (E.A. Parfitt).

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Journal of Volcanology and Geothermal Research 134 (2004) 77–107

of new field data (e.g., Heiken, 1972, 1978; Walker,1973; McGetchin et al., 1974; Self et al., 1974; Self,1976; Williams, 1983; Walker et al., 1984; Houghtonand Schmincke, 1989; Carracedo et al., 1992; Thor-darson and Self, 1993; Parfitt, 1998), volcano moni-toring (e.g., Richter et al., 1970; Chouet et al., 1974;Blackburn et al., 1976; Swanson et al., 1979; Wolfe etal., 1987, 1988; Neuberg et al., 1994; Vergniolle andBrandeis, 1994, 1996; Ripepe, 1996;Vergniolle et al.,1996; Hort and Seyfried, 1998; Chouet et al., 1999),laboratory studies (e.g., Jaupart and Vergniolle, 1988;Mangan et al., 1993; Mangan and Cashman, 1996;Zimanowski et al., 1997; Seyfried and Freundt, 2000)and through mathematical modelling (Sparks, 1978;Wilson, 1980; Wilson and Head, 1981; Stothers et al.,1986; Vergniolle and Jaupart, 1986; Head and Wilson,1987; Jaupart and Vergniolle, 1988; Woods, 1993;Parfitt and Wilson, 1995, 1999). It is now widelyaccepted that Strombolian eruptions result from theformation and bursting of a gas pocket close to thesurface (e.g., Blackburn et al., 1976; Wilson, 1980;Vergniolle and Brandeis, 1994, 1996), though somedetails of the mechanism are still disputed and arediscussed below. In the case of the dynamics ofHawaiian eruptions, however, a curious situationexists in which two very different models have beendeveloped that are both in common usage. I refer tothese models as the rise speed dependent (RSD)model (Wilson, 1980; Wilson and Head, 1981; Headand Wilson, 1987; Fagents and Wilson, 1993; Parfittand Wilson, 1994, 1999; Parfitt et al., 1995) and thecollapsing foam (CF) model (Vergniolle and Jaupart,1986, 1990; Jaupart and Vergniolle, 1988, 1989;Vergniolle, 1996).

The aims of this paper are to review both models ofexplosive basaltic eruptions, and to present an in-depth examination of the models of Hawaiian activityin which the assumptions and predictions of eachmodel are compared with a wide range of geophysicaland observational data from recent eruptions.

2. Styles of explosive basaltic eruption

Volcanologists have had many opportunities toobserve and monitor explosive basaltic eruptions(e.g., Richter et al., 1970; Blackburn et al., 1976;Swanson et al., 1979; Fedotov et al., 1983; Aramaki et

al., 1986; Bertagnini et al., 1990). Though rare exam-ples of sub-Plinian and Plinian basaltic activity dooccur (Self, 1976; Williams, 1983; Walker et al.,1984), explosive basaltic eruptions resulting fromthe exsolution of magmatic gases alone (rather thanhydromagmatic activity) generally exhibit Hawaiianor Strombolian styles, or behaviour which exhibitscharacteristics of both end-member styles.

2.1. Hawaiian activity

The term ‘‘Hawaiian’’ is used to denote eruptionsthat are continuous in character and that generate lavafountains (Fig. 1), typically tens to hundreds of metresin height (though they can occasionally exceed 1 kmin height: Wolff and Sumner, 2000). As the termsuggests, this type of activity is characteristic of thevolcanoes of the Hawaiian chain but it is commonlyseen on other basaltic volcanoes, e.g., Eldfell (Self etal., 1974), Hekla (Thorarinsson and Sigvaldason,1972), Etna (Bertagnini et al., 1990) and Miyakejima(Aramaki et al., 1986). Hawaiian eruptions havetypical durations of hours to days, during which timea lava fountain of fairly constant height may playabove the vent (e.g., Wolfe et al., 1988). The lavafountain ejects clots of magma ranging in size frommillimetres to about a metre in diameter into the air atspeeds of typically f100 m s!1 (Wilson and Head,1981). The majority of the erupted material lands

Fig. 1. Photograph of a lava fountain at the Pu’u ‘O’o vent. The

fountain is f400 m in height. (Photograph taken by Lionel Wilson,

August 1984).

E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–10778

while still incandescent, and accumulation and coa-lescence of these hot clots generates rootless lavaflows (Head and Wilson, 1989). These flows aretypically still fluid enough to flow many kilometresto tens of kilometres from the vent. For example, a 21-day-long Hawaiian eruption at Mauna Loa in 1984

produced a number of lava flows, the longest of whichreached a length of 27 km (Lockwood et al., 1987).Much material falling from the outer edges of thefountain cools sufficiently during flight that, though itdeforms on landing and is hot enough to weld to thematerial around it, is not hot enough to form rootless

Fig. 2. Hot clots of magma accumulate around vents forming spatter ramparts/cones. (a) A section of a spatter rampart formed during the April

1982 eruption of Kilauea. Individual clots have flattened and flowed upon landing. Each clast is f0.2 m is diameter and is welded to those

above and below them. (Photograph taken by the author). (b) The spatter cone and down-wind tephra blanket formed during the 1959 Kilauea

Iki eruption. Close-up the cone is formed of welded clasts like those in (a). The figure is standing in a collapse pit within the down-wind tephra

blanket. Here, at a distance off0.5 km from the vent, the deposit is composed of centimetre-scale clasts and is unwelded. (Photograph taken by

the author, May 1996).

E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107 79

lava flows and instead accumulates as a spatter conearound the erupting vent (Fig. 2; Head and Wilson,1989). Some even cooler material can accumulate toform a loose cinder cone, and a small proportion ofthe erupted material is carried upwards in a convectiveplume above the fountain and is deposited downwindforming a tephra blanket (Fig. 2b, Parfitt, 1998).

2.2. Strombolian activity

Strombolian activity takes its name from the fre-quent, small-scale, transient explosions exhibited byStromboli, a volcano which forms one of the AeolianIslands north of Sicily. Whereas the term ‘‘Hawaiian’’is well-defined and used in a fairly restricted way, theterm ‘‘Strombolian’’ has been used to denote a widerange of activity, and, thus, caution must be used inunderstanding individual usage of the term. The term‘‘Strombolian’’ is most commonly used (and is usedhere) to denote the relatively mild explosions thatoccur from the accumulation of gas beneath thecooled upper surface of a magma column (e.g., Black-burn et al., 1976; Wilson, 1980). In such events, gasaccumulation causes a raising and up-doming of thesurface of the magma column. This ‘‘blister’’ eventu-ally tears apart allowing the release of the gas and theejection of the magma that formed the skin of theblister. Blackburn et al. (1976) found typical initialvelocities of clasts at Heimaey to be f150 m s!1

whereas at Stromboli initial velocities are generally50–100 m s!1 (Chouet et al., 1974; Blackburn et al.,1976; Weill et al., 1992; Vergniolle and Brandeis,1996). Each explosion usually lasts f1 s and oneexplosion may follow another after anything from afew seconds to several hours. At Stromboli the typicaltime between explosions is between 10 min and 1h (Vergniolle and Brandeis, 1996). The erupted ma-terial is generally cooler prior to eruption than thatproduced in Hawaiian eruptions and also experiencesmore cooling during flight than Hawaiian clasts. Theclasts produced are too cool on landing to weld orcoalescence and so accumulate as a tephra/cinder conearound the vent (McGetchin et al., 1974; Heiken,1978). At Stromboli clasts typically reach heights of<100 m above the vent (Vergniolle and Brandeis,1996) and the plume generated by the explosiongenerally rises to heights of <200 m (Fig. 3, J.Davenport, unpublished data).

Though many Strombolian explosions are mild,discrete events, the term Strombolian is also used todescribe events which can generate sustained eruptionplumes that reach heights of up to 10 km above thevent (e.g., Cas and Wright, 1988). These are events inwhich the individual explosions are so closely spacedin time that they generate a sustained eruption plumeof considerable height rather than the small plumesassociated with truly discrete explosions (e.g., Fig. 3).The 1973 Heimaey eruption in Iceland provides agood example of this type of behaviour. The eruptionproduced explosions every 0.5–3 s with incandescentclasts reaching heights of f250 m above the vent andgenerated a plume that extended to heights of 6–10km above the vent (Self et al., 1974; Blackburn et al.,1976). The eruption simultaneously generated lavaflows. This behaviour is distinctly different from thediscrete explosive events seen at Stromboli andappears, in fact, to represent a type of behaviour

Fig. 3. Photograph of the plume generated during an explosion at

Stromboli. The plume is f200 m in height. (Photograph taken by

the author, September 1996).


which exhibits characteristics of both Hawaiian andStrombolian eruptions: Although the explosions arediscrete, they are so closely spaced in time that interms of the eruption column the activity is continuousas in a Hawaiian eruption. The continuous productionof lava flows is also more characteristic of Hawaiianevents than the mild Strombolian events describedpreviously. Thus, this type of eruption can be viewedas transitional between the Hawaiian and Strombolianend-member eruption styles.

Classification schemes for explosive basaltic activ-ity define Strombolian events as being more ‘‘explo-sive’’ than Hawaiian events (Fig. 4; Walker, 1973; Casand Wright, 1988). Two points are important to noteabout such classification schemes: (1) they are basedon the dispersal in eruptions like the Heimaey erup-tion, not on truly discrete Strombolian explosions likethose occurring with such regularity at Stromboli; and(2) they can lead to misclassification of Hawaiianeruption deposits. The 1959 Kilauea Iki deposits, forexample, would be classified as Strombolian (Fig. 4) insuch a scheme when they were actually depositedduring a classic Hawaiian eruption (Richter et al.,1970; Parfitt, 1998). Thus, it is important to exercisecaution in the use of the terms Hawaiian and Strombo-lian and to recognise that they represent end-membercases while many basaltic eruptions simultaneouslyexhibit facets of both types of activity and are betterdescribed as ‘‘transitional’’ eruptions (Parfitt and Wil-son, 1995).

3. Models of eruption mechanisms

3.1. The rise speed dependent model

The earliest attempt to apply fundamental ideas ofconservation of energy and mass in volcanic eruptionswas made by McGetchin and Ulrich (1973), but theyapplied their model only to eruptions producing maarsand diatremes. The first model to specifically addressthe dynamics of explosive basaltic eruptions wasdeveloped by Wilson (1980) and Wilson and Head(1981). These two papers set out the basic premises ofthe RSD model that have been developed further insubsequent papers (Head and Wilson, 1987; Fagentsand Wilson, 1993; Parfitt and Wilson, 1994, 1995,1999; Parfitt et al., 1995). The essential idea set out inthese papers is that Strombolian and Hawaiian activityrepresent end-members of a continuum of explosivebasaltic activity and that the form of activity thatoccurs depends most fundamentally on the rise speedof the magma beneath the eruptive vent (e.g., Table 1).

Volatiles exsolve from magma as it rises, and thedepth at which exsolution occurs depends on thevolatile species and the amount of dissolved volatilespresent (Wilson and Head, 1981). Gas bubbles thatform within the magma are always buoyant and riseupwards through the magma at a rate that depends onthe size of the bubble and the magma rheology. In theRSD model, it is assumed that if the rise speed of themagma is relatively great then the bubbles do not rise

Fig. 4. Diagram showing Walker’s (1973) classification scheme for explosive volcanic eruptions which is based on the degree of fragmentation

(F) of the magma and the dispersal area (D) of the tephra. The asterisk shows that the deposits of the 1959 Kilauea Iki eruption would be

classified as Strombolian using this scheme even though the deposits were formed during a typical Hawaiian eruption. Redrawn from Cas and

Wright (1988).


far through the overlying magma before the magmaitself is erupted. In effect, the gas bubbles are‘‘locked’’ to the magma in which they formed. Thus,the model assumes homogeneous two-phase flow, inwhich two different fluid phases are present (themagma and gas) but in which the fluids behave as ifthey are a single fluid phase. In this situation, thegrowth of bubbles through diffusion and decompres-sion (Sparks, 1978; Proussevitch and Sahagian, 1996)and the continued formation of bubbles during ascentwill eventually lead to a situation in which the bubblevolume fraction becomes large enough (f60–95%)to cause fragmentation of the magma (e.g., Sparks,1978; Wilson and Head, 1981; Houghton and Wilson,1989; Thomas et al., 1994). The rising gas–magmamixture accelerates as it rises due to the decompres-sion and expansion of the gas (Wilson and Head,1981). After fragmentation, the acceleration becomesmuch more pronounced due to the reduction in wallfriction caused by the fragmentation process andresults in the eruption of a continuous jet of gas andmagma clots at typical speeds off100 m s!1 (Wilsonand Head, 1981). This continuous jet of materialproduces the lava fountains characteristic of Hawaiianeruptions (Fig. 1). As Parfitt and Wilson (1999)pointed out, this proposed mechanism is essentiallythe same as that envisaged as causing Plinian erup-tions (Wilson et al., 1980). The material erupted inHawaiian fountains is, however, very coarse com-pared with that of Plinian eruptions (Parfitt, 1998),and it is this difference in the grain size of the erupting

material that, more than anything, causes the style andproducts of Hawaiian eruptions to differ so greatlyfrom those of Plinian eruptions (see Parfitt and Wil-son, 1999).

The RSD model further proposes that a differenteruption mechanism operates if the rise speed ofmagma is relatively low. In this case, gas bubbleswithin the magma will rise upwards through theoverlying magma and can segregate from the magmain which the bubbles formed (Sparks, 1978; Wilsonand Head, 1981). The magma will contain a popula-tion of bubbles with a range of sizes—bubbles thatformed early will have grown by diffusion and de-compression, while newly formed bubbles will bemuch smaller. As the rise speed of a bubble dependspartly on its size, a runaway situation can be achievedin which an initially larger bubble, rising faster thanthe smaller bubbles, overtakes the smaller bubbles andin doing so coalesces with them. In an extreme case,such coalescence can lead to a single large bubble thatis as wide as the conduit rising through the overlyingmagma (essentially a slug of gas). In the RSD model,Strombolian eruptions are assumed to be the result ofthis bubble segregation and coalescence process.Wilson (1980) simulated these eruptions by consider-ing what would happen in an open system in whichmagma was rising slowly or was static. Cooling at thetop of the magma column causes the development of a‘‘skin’’ with a finite strength. The skin strength willdepend on how much cooling occurs before the arrivalof the large bubbles. If the interval between bubble

Table 1

Rise speeds beneath vents during recent Hawaiian (H), Strombolian (S) and transitional (T) eruptions

Eruption Style Volume flux

(m3 s!1)

Vent area

(m2)

Rise speed at

depth (m s!1)

Reference

Mauna Ulu, 1969 S 0–3 400 0–0.008 Swanson et al. (1979)

Stromboli, 1971 S 8"10!3 2.3 3.5"10!3 Chouet et al. (1974)

Kupaianaha, 1986 S 3 315 0.01 Parfitt and Wilson (1994)

Etna, typical Strombolian activity S <9.1 – 0.0006–0.045 Harris and Neri (2002)

Heimaey, 1973 T* 30 314 0.1 Self et al. (1974), Blackburn et al. (1976)

Kilauea Iki, 1959 H 160 180 0.9 Richter et al. (1970), Eaton et al. (1987)

Mauna Ulu, 1969 H 300 400 0.75 Swanson et al. (1979)

Miyakejima, 1983 H 185 2000 0.09 Aramaki et al. (1986)

Pu’u ‘O’o, 1983–1986 H 100 315 0.3 Parfitt and Wilson (1994)

Rise speeds have been calculated from observed volume fluxes and vent areas.

* The eruption was described as Strombolian both on the grounds of the fall deposit it generated and the intermittent nature of the

explosions. The short intervals (0.5–2 s) between explosions and the generation of fountains and an significant eruption column suggest,

however, that the eruption represents a transitional event as described by Parfitt and Wilson (1995) and in the text.


arrival is short enough, each bubble will updome thethin skin and burst through the top of the magmacolumn with minimal delay. If the interval betweenthe arrival of giant bubbles is longer, the skin will cooland thicken and then more than one bubble may haveto arrive and become trapped before sufficient pres-sure is built up in an accumulating gas pocket to breakthrough the skin. In either case, the short time intervalbetween explosions suggests that the strength of thisskin is never very great. Repeated cycles of coolingand gas accumulation followed by bubble burstinglead to the series of transient explosions characteristicof Strombolian eruptions.

Wilson and Head (1981) presented computer mod-elling to define the rise speed conditions in whichStrombolian and Hawaiian activity would be domi-nant. Parfitt and Wilson (1995) carried out moredetailed simulation of these conditions and discussed

the character of ‘‘transitional’’ eruptions—eruptionsthat show aspects of both Hawaiian and Strombolianeruptions. For typical basaltic eruptions the transitionbetween Hawaiian and Strombolian activity occurs atrise speeds of f0.01–0.1 m s!1 (Parfitt and Wilson,1995). It is expected that Hawaiian eruptions willoccur at rise speeds much greater than this andStrombolian activity will occur at much lower speeds(Fig. 5).

3.2. The collapsing foam model

A series of papers published in the 1980s and1990s (Vergniolle and Jaupart, 1986; Jaupart andVergniolle, 1988; Jaupart and Vergniolle, 1989; Verg-niolle and Jaupart, 1990; Vergniolle, 1996; Vergniolleand Brandeis, 1996) put forward an alternative modelof the mechanisms of basaltic eruptions. The originalpaper (Vergniolle and Jaupart, 1986) challenged theassumption of ‘‘homogeneity’’ (i.e., homogeneoustwo-phase flow) made in the RSD model and pro-posed that both Hawaiian and Strombolian eruptionsare the result of separated, two-phase flow, i.e.,eruptions in which the flow of the magma and gasphases are significantly different. They described thedifferent flow regimes that can prevail during sepa-rated, two-phase flow and proposed that Strombolianeruptions result from slug flow and Hawaiian erup-tions from annular flow (Fig. 6). The model wasdeveloped further by Jaupart and Vergniolle (1988)and Jaupart and Vergniolle (1989), wherein the con-ditions in which slug flow and annular flow candevelop were described.

In the CF model, magma is assumed to be storedwithin some sort of storage area (a magma chamber or

Fig. 5. The controls of magma rise speed and gas content on basaltic

eruption style as predicted by the RSD model. Redrawn from Parfitt

and Wilson (1995).

Fig. 6. Schematic diagram depicting two examples of separated, two-phase flow: (a) slug flow and (b) annular flow.


a dike system) at a depth at which gas can exsolvefrom the magma. The gas bubbles, once formed, riseand accumulate at the roof of the storage area andbecome close-packed into a foam layer. When thefoam layer reaches a critical thickness, it becomesunstable and collapses, the bubbles coalescing to forma gas pocket. The gas pocket then rises up an openvent system and is erupted. In this model, Strombolianeruptions represent repeated partial foam collapseevents, whereas Hawaiian eruptions occur from com-plete, almost instantaneous foam collapse. In a seriesof laboratory experiments, Jaupart and Vergniolle(1988) showed that if the viscosity of the liquid phaseis relatively low then the collapse of the foam is totaland the pocket of gas rises up the open conduit systemas a single body. The observed flow is annular in thiscase and liquid in the annulus around the gas core isdragged upwards with the gas and erupted (Fig. 6).Jaupart and Vergniolle (1988) liken this behaviour tothat of a Hawaiian eruption. If the viscosity of theliquid is higher, the foam collapses only partially andforms a series of smaller gas pockets. These travel upthe conduit system periodically in slug flows andburst at the surface. This behaviour is likened toStrombolian eruptions.

4. Strombolian eruptions

The RSD and CF models do not differ very muchin their view of Strombolian activity. They both treatthese eruptions as occurring when gas segregates fromthe magma and accumulates as a gas pocket that thenbursts at the top of an open magma column producingthe mild explosions characteristic of Strombolianactivity. This behaviour is consistent with directobservations of eruptions (e.g., Vergniolle and Bran-deis, 1994) and studies of the acoustic wave thataccompanies each explosion (Vergniolle and Bran-deis, 1994, 1996; Vergniolle et al., 1996).

The main difference between the models concernswhere gas accumulation occurs within the magmaticsystem. In the RSD model, the gas segregation isconsidered to be progressive, with bubble coalescenceoccurring because the magma rise speed is low. Bycontrast, in the CF model bubbles are assumed toaccumulate at some depth forming a foam layer thatthen partially collapses (or coalesces) and travels up

the open conduit to become trapped by the cool ‘skin’on the top of the magma column prior to bursting. Inthis model, there is no explicit link between magmarise speed and eruption style.

Vergniolle and Jaupart (1986) challenged the as-sumption made in the RSD model that coalescence ofbubbles can occur progressively during magma ascent.The RSD model assumptions are based on the obser-vation that larger bubbles rise faster than smaller ones(Fig. 7) and therefore have the opportunity to overtakeand coalesce with smaller bubbles. Wilson and Head(1981) and Parfitt and Wilson (1995) assume thatbubbles ‘‘which initially lie within their own radiusof the vertical line of ascent of the large bubble willmake geometric contact with it’’ and will be absorbedby the larger bubble. Vergniolle and Jaupart (1986)drew on work by Taitel et al. (1980) that suggests thatcoalescence only occurs when bubbles are rising fastenough to deform during ascent. This work suggestedthat only bubbles larger than f40 mm will be able tocoalesce with smaller bubbles. As bubbles only reachsizes of 10–50 mm by decompression and diffusionVergniolle and Jaupart (1986) argue that bubble coa-lescence cannot occur during ascent, i.e., that the RSDmodel is invalid. More recent work by Manga andStone (1994), however, suggests that bubbles >5 mmradius will deform during ascent and that such bubblesenhance coalescence, i.e., that coalescence can occurwith bubbles of smaller size but that if larger bubblesare present, models such as that of Wilson and Head(1981) will underestimate the amount of coalescencethat occurs. So coalescence can occur for smallerbubbles, but once bubbles have grown to sizes >5mm enhanced coalescence will facilitate runawaycoalescence. Evidence from the study of bubble sizedistributions in lava and tephra supports the idea thatbubble coalescence occurs during magma ascent (e.g.,Mangan et al., 1993).

While the assumptions in Wilson and Head (1981)and Parfitt and Wilson (1995) about whether twobubbles will coalesce are obviously a simplificationof the real situation, the current evidence does suggestthat it is possible for coalescence to occur in risingmagmas as long as the bubbles have the opportunity tomove upwards relative to the magma, i.e., as long asthe magma rise speed is low. A link between explosivebasaltic eruption style and rise speed is evident fromfield observations of recent eruptions (e.g., Table 1).


Furthermore, Parfitt and Wilson (1995) suggested thatfor typical magma volatile contents the transition fromStrombolian to Hawaiian activity occurs between risespeeds of 0.01 and 0.1 m s!1 (Fig. 5). Comparisonwith the examples given in Table 1 show that (a)Strombolian eruptions are indeed associated with low-er rise speeds and (b) that the transition in eruptionstyle occurs within the rise speed range predicted byParfitt and Wilson (1995). This would seem to supporttheir contention that coalescence is progressive anddependent on the magma rise speed.

In contrast to the RSD model, the CF model ofStrombolian eruptions requires that gas segregationand foam formation occurs during storage at depthand thus can only operate under the particular circum-stance where a storage zone exists beneath the vent ata depth at which exsolution of one or more gas phasesis occurring. At Stromboli itself, there is evidence thatmagma storage can occur at depths no greater than afew hundred metres (Giberti et al., 1992). Eachexplosion at Stromboli is associated with a distinct

seismic signal that consists of an initial compressionfollowed by a dilation and further compression (Neu-berg et al., 1994; Chouet et al., 1999). Chouet et al.(1999) have shown that the seismic source varies indepth through the course of the explosion, starting at adepth of 125 m, deepening to a depth of f350 m andthen shallowing again to a depth of around f200 m.They suggest that this seismic event is caused by theuprush of a gas pocket of the sort pictured in the CFmodel, though it has yet to be demonstrated that thedetails of the seismic signal are consistent with theupward passage of a gas slug. There is therefore nodefinitive answer at present as to which gas segrega-tion process operates at Stromboli. In a broadercontext, there is no reason why one model shouldexplain all Strombolian activity. It must be borne inmind, however, that the CF model can only apply in aparticular combination of circumstances—where thereis a suitable storage zone at a depth where one of moregas phase can exsolve—whereas the RSD model isapplicable to any open system.

Fig. 7. The relationship between bubble radius and bubble rise speed through magma. The rise speed, u, was calculated from u=(2(qm–qg)gr2)/

9g where qm and qg are the magma and gas densities, g is the acceleration due to gravity and g is the magma viscosity. Line 1 represents the case

in which the magma is assumed to have a density of 2600 kg m!3 and a viscosity of 10 Pa s. Line 2 represents the case in which the magma is

assumed to have a density of 2000 kg m!3 and a viscosity of 30 Pa s.


Both models assume that shallow bubble burstingcauses the observed explosions so that the samemodel of the bursting process is applicable in eithercase. Wilson (1980) modelled the ejection of clasts inStrombolian eruptions by assuming that the eruptionsresult from the bursting of near-surface bubbles. Themodel links the initial pressure in the bursting bubble,the weight percentage of gas erupted and the maxi-mum velocity achieved by the ejected matter (Fig. 8).Pressures within the bursting bubbles are unlikely toexceed 0.3 MPa (Blackburn, 1977; Sparks, 1978).Observations at Heimaey and Stromboli suggest thatthe weight percentage of gas in typical explosions is10–30 wt.% (Blackburn et al., 1976), althoughChouet et al. (1974) note that some events at Strom-boli can have gas contents as high as 94 wt.%. Directobservations suggest that clasts are ejected in someStrombolian eruptions at speeds of up to 230 m s!1

(Blackburn et al., 1976). At Stromboli itself, speedsare more typically <100 m s!1 (Chouet et al., 1974;Blackburn et al., 1976). Comparison of these valueswith the model results in Fig. 8 shows that there isbroad consistency between the model predictions andfield observations.

5. Hawaiian eruptions

The RSD and CF models present very differentviews of the dynamics of Hawaiian activity. Two fun-damental differences exist between the models. Theseare concerned with the nature of the fluid flow at depthand with the dominant volatile species driving theeruptions. Each difference is considered here in turn.

5.1. Flow regimes in Hawaiian eruptions

The RSD model assumes that homogeneous two-phase flow prevails. By contrast, the CF modelassumes that separated two-phase flow occurs. Thereare a range of flow regimes in which separated two-phase flow can occur, and the CF model assumes thatannular flow (Fig. 6) prevails during Hawaiian erup-tions (Vergniolle and Jaupart, 1986). I now discuss theimplications of, and evidence for, each type of flow.

The assumption of homogeneous two-phase flow isnever strictly valid because gas bubbles are alwaysbuoyant relative to the magma and thus are alwaysrising faster than the magma. However, as statedabove, if the rise speed of the magma is rapid thebubbles do not rise far through the overlying magmabefore the magma is erupted and in effect the gasbubbles are ‘‘locked’’ to the magma, i.e., the assump-tion of homogeneous flow is valid. Thus, it is the risespeed of the bubbles relative to the magma rise speedwhich determines whether flow is homogeneous ornot. The rise speed of a bubble depends on its size,larger bubbles rising faster than smaller ones (Fig. 7).The validity of the assumption of homogeneitydepends, therefore, on the size of the bubbles involvedand on the magma rise speed at depth. Table 1 showsthat rise speeds in Hawaiian eruptions are typically>0.1 m s!1. Fig. 7 shows that only at radii of z0.01 m(10 mm) does the bubble rise speed through themagma become of the same order of magnitude asthe magma rise speed. For bubbles with radii <5 mm,the bubble rise speed is always likely to be more thanan order of magnitude less than the typical magma risespeed in a Hawaiian eruption. Thus, the assumption ofhomogeneity is likely to be valid as long as the bubbleradii are less than f5 mm. So, the crucial issue is thesize of the bubbles within the rising magma.

Bubbles form in magma when the magma becomessupersaturated in the volatile concerned. The depth

Fig. 8. Diagram showing the relationship between bubble pressure

and the maximum ejecta velocity in a Strombolian eruption. The

different curves represent different weight percentages of gas in the

erupted material. The cross-hatched area represents the likely range

of conditions during Strombolian eruptions. Redrawn from Wilson

(1980).


beneath the surface at which bubbles start to formdepends on the amount of dissolved volatiles and thespecies of volatile involved (Wilson and Head, 1981).Bubbles have typical radii of f10 Am when firstformed and then grow by diffusion and decompressionas the magma rises (e.g., Sparks, 1978). Sparks (1978)presented numerical modelling of the growth of bub-bles by diffusion and decompression and found thatmaximum bubble sizes for H2O bubbles exsolvingfrom a basaltic magma depend on the amount ofdissolved water in the magma. For a gas content of0.5 wt.% (a reasonable value for basaltic magmas), themaximum radius is f5 mm. A more recent study byProussevitch and Sahagian (1996) gives maximumbubble radii of 6–8 mm for H2O bubbles in basalticmagma using initial water contents of 1.52% and 3.03wt.%, respectively. The sizes would be smaller formore reasonable initial water contents. Thus, theoret-ical studies suggest that water bubbles forming inrising basaltic magmas would typically have maxi-mum radii of f5 mm for water contents typical ofmost basaltic eruptions. The size of the largest bubbleis not, however, representative of the bubble popula-tion as a whole. Most bubbles will reach an interme-diate size. For instance, Sparks (1978) showed that forbubbles formed in basalt containing 1 wt.% water themaximum radii would bef40 mm but the typical sizewould be 1–10 mm rather than 40 mm. Furthermore,in the modelling studies just described, it is assumedthat bubbles continue growing all the way to thesurface. In practice, though, magma fragmentation willoccur beneath the surface and so the maximum bubblesize will not be achieved. These theoretical studiessuggest then that for typical water contents the typicalsize of bubbles in basaltic magmas will be b5 mm.

Determining the bubble sizes in real magmas isextremely problematic because the fragmentation pro-cess destroys much of the evidence of pre-fragmenta-tion bubble sizes. A number of studies have looked,though, at sizes of bubbles in basaltic scoria and lava(e.g., Cashman and Mangan, 1995; Mangan andCashman, 1996). Bubbles contained in such samplesrepresent bubbles formed in magma clots after frag-mentation but also bubbles which survived the frag-mentation process and continued to grow afterfragmentation. Cashman and Mangan (1995) reportmean bubble radii for quenched lava from Kilaueavolcano of 0.1–0.15 mm and Mangan and Cashman

(1996) report radii for bubbles in basaltic scoria fromthe Pu’u ‘O’o eruption of Kilauea of V2.5 mm. Whilewe cannot know for sure how such sizes relate tobubble sizes prior to fragmentation, certainly suchstudies do not provide any compelling reason to thinkthat bubbles sizes in basaltic magmas exceed the f5mm size predicted by the theoretical studies.

Bearing all these points in mind it seems reason-able to assume that the radii of the majority of H2Obubbles in magma with a water content V0.5 wt.% islikely to be b5 mm. This means that in the case ofH2O bubbles in basaltic magma, the situation consid-ered in all the RSD modelling, the assumption ofhomogeneity is almost certainly valid.

The RSD modelling has only considered the situ-ation of water exsolution. It is important to note,though, that the situation would be different in thecase of CO2 exsolution. CO2 is less soluble in magmathan water and so exsolves and forms bubbles atgreater depths beneath the surface. This means thatCO2 bubbles experience more growth by decompres-sion during ascent than do H2O bubbles. Fig. 9 showsthat for CO2 contents in the range of 0.1–0.5 wt.%(reasonable values for a basaltic magma), bubbles are

Fig. 9. Diagram showing the relationship between final bubble size

and magma rise speed for magma containing 0.1, 0.3 and 0.5 wt.%

CO2. At rise speeds less than f1 m s!1, the bubbles are able to rise

through the overlying magma and in doing so to coalesce. The

resulting bubbles are considerably larger than those developed in

faster rising magma where bubble coalescence is negligible.


likely to experience coalescence at rise speeds of V1m s!1 (and so achieve final diameters anywhere in therange 3 mm to 10 m). So, as coalescence is evidencefor separated flow, and as rise speeds typical ofbasaltic eruptions are generally <1 m s!1 (Table 1),we would expect separated two-phase flow to occurduring ascent. In the case of CO2 exsolution, then, itwould be invalid to assume that homogeneous two-phase flow occurs. As I have stated, however, CO2

has not been considered as the ‘driving’ gas in any ofthe RSD modelling. The issue of which volatile actsas the ‘driving’ gas for Hawaiian eruptions is dis-cussed in detail below.

Vergniolle and Jaupart (1986) argued that homo-geneous two-phase flow does not occur during Ha-waiian eruptions. They based this assertion on anumber of lines of evidence. The first is that thecharacteristic radius of bubbles in Hawaiian eruptionsis 50 mm. Such a bubble would have a rise speedthrough the magma of f1 m s!1 (Fig. 7) and thus aspeed that is comparable to the magma rise speed atdepth (Table 1). In such a situation, the bubbles wouldtend to separate from the magma and the assumptionof homogeneous two-phase flow would break down.As explained above, such bubble sizes are only likelyto be achieved in eruptions in which CO2 is thedriving gas. Thus, as just stated, the crucial issue is:Which gas species ‘drives’ these eruptions? This isdiscussed in more detail below but the initial conclu-sion that can be drawn is that homogeneous flow ispossible in Hawaiian eruptions driven by H2O but notthose driven by CO2.

This bubble size argument is not the only onepresented by Vergniolle and Jaupart (1986) to supporttheir contention that separated rather than homoge-neous two-phase flow occurs during Hawaiian erup-tions. Another argument concerns the volumes of gasand magma present upon eruption. They note thatmagma typically makes up less than f1% of theerupted volume in a Hawaiian lava fountain and arguethat such a situation cannot be achieved in an eruptionin which homogeneous two-phase flow prevails. Thisargument is fundamentally flawed, as can be demon-strated by the following simple calculations.

Consider a basaltic magma exsolving 0.5 wt.%water during ascent. In an eruption with a magmavolume flux of 100 m3 s!1 (the situation treated byVergniolle and Jaupart, 1986) the mass of magma

erupted per second is 2.6"105 kg (assuming a magmadensity of 2600 kg m!3) and so the mass of waterreleased from this magma during ascent is 1300 kg. Atatmospheric pressure this mass of gas occupies 8667m3 (the density of steam at atmospheric pressure andmagmatic temperature is f0.15 kg m!3). So, at thesurface, the volume of the magma compared with thevolume of gas is f 1%, even though there has beenno concentration and segregation of the gas from themagma prior to eruption. It is the mass of magmarelative to the mass of gas erupted that is crucialevidence of segregation or homogeneity, not thevolume.

This point can be further tested using a realexample. Between 1983 and 1986, a series of 47 lavafountaining episodes occurred at Pu’u ‘O’o, a vent onthe flanks of Kilauea Volcano (Heliker and Wright,1991). During a number of episodes, measurementswere made of the mass of CO2 and SO2 released andof the relative volumes of each gas species released ineach eruption (e.g., Greenland et al., 1985; Greenland,1988). By combining these measurements, it is pos-sible to estimate the mass of each gas species releasedduring each episode. As measurements were alsomade of the volumes of lava erupted in each episode(e.g., Wolfe et al., 1988), it is possible to assesswhether the amounts of gas released are in excess ofthat originally dissolved in the magma: If the CFmodel is valid, the gas mass fraction in the eruptedmaterial will be considerably greater than that in themagma at depth. Consider, then, one example fromthis eruption. Episode 16 of the eruption (in March1984) produced H2O at a rate of 40000 tonnes/dayand CO2 at 3200 tonnes/day (Greenland et al., 1985).The eruption lasted for 31 h, so a total of 51700tonnes (5.17"107 kg) of H2O and 4130 tonnes(4.13"106 kg) of CO2 were released during thisepisode. The volume of lava produced was 12"106

m3 (Wolfe et al., 1987), which, assuming a lava bulkdensity of f2000 kg m!3, yields an erupted mass ofmagma of 2.4"1010 kg. This yields gas mass fractionsin the erupted material of 0.22 wt.% of H2O and 0.017wt.% of CO2. Residual gas contents in Kilauean lavasare typically 0.10 wt.% H2O and 0.015 wt.% CO2 forKilauea (Gerlach and Graeber, 1985), which yieldsestimates of the gas content within the magma prior toeruption of 0.33 wt.% H2O and 0.032 wt.% CO2.Similar calculations for other Pu’u ‘O’o episodes


produce similar results. Independent estimates ofvolatile contents based on fluid inclusions studiesgive H2O contents for the Pu’u ‘O’o eruption of0.39–0.51 wt.% for tephra from the high fountainevents and 0.10–0.28 wt.% for spatter from lessvigorous activity (Wallace and Anderson, 1998). Sothe gas released during the eruptions is consistent withthe gas contents contained within the magma prior toeruption, and, thus, there is no evidence to support theidea that gas concentration and separation occurredprior to eruption. The values instead support thecontention of the RSD model that Hawaiian eruptionsresult from homogeneous two-phase flow. It is alsoworth noting that in this eruption, the volume per-centage of the magma in the lava fountain is f0.35%(calculated in the same way as in the example givenabove). This supports my contention that, even in ahomogeneous eruption, the volume percent of magmain the fountain can be <1%, and, thus, that thestatement by Vergniolle and Jaupart (1986) that thisis evidence of separated flow is erroneous.

More fundamentally, Vergniolle andMangan (2000)describe a distinctive pattern of behaviour observedduring the 1959 Kilauea Iki eruption in which magmawas simultaneously erupted in a lava fountain anddrains back around the edges of the vent. They assertthat this observation is evidence for annular flow andthat simultaneous drainback and eruption is not possi-ble during homogeneous flow. Wilson et al. (1995)have previously published a model in which simulta-neous drainback and eruption occurs during homoge-neous flow. This issue has been examined again byLionelWilson (unpublished calculations, 2003) and hisfindings are contained in Appendix A. His treatmentshows that it is perfectly possible to explain theobservation of simultaneous drainback and eruptionat Kilauea Iki in terms of homogeneous flow.

In conclusion, arguments presented as evidencethat separated two-phase flow must occur duringHawaiian eruptions do not stand up to detailed scru-tiny. Existing observational evidence, instead, sup-ports the contention that Hawaiian eruptions occuras the result of homogeneous two-phase flow.

5.2. Dominant volatile species

The other fundamental difference between the twomodels concerns the species of volatile that typically

‘drives’ Hawaiian eruptions. The RSD model as-sumes that the ‘driving’ gas is H2O, whereas theCF model assumes that it is CO2. This issue is crucialbecause, in the situations considered in the publishedmodels, the RSD model is incompatible with thedriving gas being CO2 and the CF model is incom-patible with the driving gas being H2O. It is possible,therefore:

(a) to distinguish between the two models forspecific eruptions provided observational evidenceexists about the species and mass fractions of gasreleased in the eruption (see below); and

(b) that each mechanism could be valid in differentvolcanic situations depending on the gas species, massfraction present in the magma, and the storage historyof the magma as it ascends.

Let us examine why the two models assumedifferent ‘driving’ gas species and then look at whichsituation is most common in actual eruptions.

5.2.1. H2O as the ‘driving’ gasThe RSD model assumes in all cases that the gas

driving Hawaiian eruptions is H2O. This is for twomain reasons:

(1) Water is usually the most abundant volatilepresent within basaltic magmas (e.g., Wallace andAnderson, 2000).

(2) Water only exsolves from basalts at shallowdepths (typically a few hundred metres) beneath thesurface (Sparks, 1978; Wilson and Head, 1981 ). Thismeans that the water will usually have had littleopportunity to exsolve and escape from the magmaas it ascends towards the surface, and thus its exso-lution from the magma near the surface must playsome role in the eruption dynamics.

5.2.2. CO2 as the ‘driving’ gasThe CF model assumes that the driving gas is CO2.

This is because in this model gas bubbles mustaccumulate as a foam layer in a storage area at depthin order for separated two-phase flow to occur. Forthis to be possible, it is necessary that:

(1) Storage occurs at a depth where exsolution ofthe ‘driving’ gas can occur.

(2) The roof of the storage zone has sufficientarea to allow the accumulation of a sufficient volumeof foam to be consistent with observed eruptedvolumes.


The shallow exsolution depths of H2O make itextremely unlikely that these criteria will be met,whereas CO2 exsolves at depths of several kilometresbeneath the surface and thus within zones wherelarge-scale storage often occurs.

Although it is possible for CO2 to be exsolved andstored in the way the CF model suggests, Parfitt andWilson (1994) have pointed out that a problem withthis model is that it neglects the effects of waterexsolution, occurring as the foam ascends, will haveon eruption. Their argument is that, even if theeruption were driven from depth by foam collapse,the magma that is carried up and erupted will stillcontain dissolved water (water being abundant inbasalts). This water will exsolve from the magma asit reaches shallow levels and thus this water must playsome role in driving the eruption. Vergniolle andJaupart (1986) have argued that, though the waterexsolves from the magma as it rises, ‘‘the smallvesicles formed through exsolution in the conduitcannot coalesce and can therefore reach high volumefractions without leading to a change in flow regime’’.In other words, water bubbles do form in the magmaas it rises towards the surface but this exsolution is‘‘passive’’ because it generates magma clots with highvesicularity, but this material does not fragment or inany way drive the eruption. This explanation appearsto be flawed in two ways:

(1) In the example given above, it was shown thatthe volume of the water exsolved from the risingmagma compared with the volume of the magma fromwhich it exsolved is such that at the vent the magmarepresents V1% of the total volume at the vent. If theexsolving water is held, as Vergniolle and Jaupart(1986) suggest, as small bubbles within the magmathis means that the vesicularity of the erupting magmawould have to exceed 99% in all of the eruptedmagma. The most vesicular material generated inHawaiian eruptions, reticulite, has vesicularities rang-ing up to 98% (Thomas et al., 1994) but reticulitemakes up only a small proportion of the materialproduced in Hawaiian eruptions.

(2) If the water is trapped in small bubbles withinthe clasts, then it would not be released in the eruptionplume. Yet, in the Pu’u ‘O’o eruption, which Verg-niolle and Jaupart (1990) and Vergniolle (1996) use asa test case for the CF model, 85% by volume of themeasured volatile release was water whereas CO2

accounted for only 3% of the volatiles released(Greenland, 1984; 1988). It is difficult to accept,therefore, that CO2 is the ‘driving’ gas rather thanH2O.

5.3. Initial conclusions

The RSD and CF models of Hawaiian eruptionsmake fundamentally different assumptions about theflow regime prevailing at depth and about thevolatiles driving the eruptions. Both models couldpotentially apply in different situations depending onthe volatiles species, bubble sizes, storage historyand magma rise speeds concerned. Neither modelappears to have any fundamental flaw. However, theusefulness of a model depends not on its theoreticalvalidity but on how well it reproduces the activitywhich occurs in nature, and in this respect, observa-tional data examined thus far favour the RSD modelover the CF model.

Both models have been used to look at the sametest case—the 1983–1986 Pu’u ‘O’o eruption—andboth models purport to explain the observational datacollected during that eruption. As the two modelsmake fundamentally different assumptions and pre-dictions about Hawaiian activity, it is impossible thatboth models are consistent with the same set ofobservational data. For this reason, I will now exam-ine, in detail, how the models have been tested usingevidence from this eruption.

6. The 1983–1986 Pu’u ‘O’o eruption of KilaueaVolcano

This eruption started in January 1983 with theemplacement of a feeder dike laterally from thesummit magma chamber into Kilauea’s East RiftZone (ERZ) (Klein et al., 1987; Wolfe et al.,1987). The dike fed a fissure eruption on the middleERZ at distances of 14–22 km from the summit.Dike emplacement and eruption were accompaniedby major deflation of the summit magma chamber(Fig. 10). After about a month, during which thesummit magma chamber reinflated (Fig. 10), a neweruptive episode began in the same area of the ERZfed through the same feeder dike (Wolfe et al.,1987). A pattern of activity developed in which


eruptions typically f1 day in duration occurredassociated with deflation of the summit and punctu-ated by repose periods of f3 weeks during whichthe summit reinflated. By the 4th eruptive outbreak,activity had become concentrated at one eruptivevent subsequently named Pu’u ‘O’o (Wolfe et al.,1988). The eruption continued this cyclic patternuntil July 1986 when the location and behaviour ofactivity switched to a vent 3 km further down rift(Heliker and Wright, 1991). Eruption at this newvent, Kupaianaha, was characterised by continuousminor explosive activity and slow outpouring oflava. The eruption was monitored in great detail bythe staff of the Hawaiian Volcano Observatory(HVO) and their observations have been publishedin a number of papers (e.g., Dvorak and Okamura,1985; Wolfe et al., 1987; Greenland, 1988; Okamuraet al., 1988; Wolfe et al., 1988; Heliker and Wright,1991; Heliker et al., 2003). Thus, this is an eruptionfor which there is an exceptionally large and com-plete set of field and geophysical observations withwhich to test the eruption models.

Vergniolle and Jaupart (1990) and Vergniolle(1996), and Parfitt and Wilson (1994), have pre-sented very different, and mutually incompatible,models of this eruption based on the RSD and CFmodels described above. I now compare the twomodels by looking at some of the key character-

istics of the eruption that both models seek toexplain.

6.1. The cyclic character of the eruption

A key feature of the eruption was its repetitive,cyclic character. Each eruption was preceded by arepose period during which slow inflation of thesummit occurred accompanied by minor explosiveactivity at the vent and each eruption was accompa-nied by rapid deflation of the summit in associationwith high lava fountaining and generation of lavaflows (Fig. 10). Dvorak and Okamura (1985) ob-served that the deflation rate increased as the eruptionsequence continued while the duration of each erup-tive episode gradually decreased (Fig. 11). Theysuggested that this behaviour reflected an evolutionof the magma system feeding the eruption. Parfitt andWilson (1994) noted that the deflation during eachepisode showed a characteristic pattern in which therate was initially low, increased to a peak value, andthen declined approximately exponentially (Fig. 12).

Parfitt and Wilson (1994) adopted the interpretationthat inflation and deflation of Kilauea’s summit mag-ma chamber occurs primarily as the result of the inflowand outflow of magma (e.g., Dzurisin et al., 1984;Dvorak and Dzurisin, 1993). The idea is that magma issupplied to the magma chamber from deeper levels at a

Fig. 10. The summit tiltmeter record for Kilauea volcano for 1983. The numbers indicate each eruptive episode of the Pu’u ‘O’o eruption during

1983. Redrawn from Wolfe et al. (1987).


fairly constant rate (estimated at f3 m3 s!1; Dzurisinet al., 1984; Dvorak and Dzurisin, 1993). This leads toslow chamber inflation during times when no highfountaining was occurring. When an eruption occurs,magma is withdrawn and erupted at a rate that exceedsthe inflow rate from the mantle and thus rapid deflationoccurs. Starting with this premise, Parfitt and Wilson(1994) examined the deflation patterns that wouldresult from flow of magma through feeder dikes of

various geometries. By assuming that the dike was ofnon-uniform geometry they were able to reproduce theobserved deflation patterns (Fig. 12), to explain whythe eruptive behaviour was cyclic and to examine thefactors which determined when each episode startedand stopped. In their model, the cyclic nature of theeruption is determined by the details of the subsurfacestorage and movement of magma not by the eruptionstyle (as is the case in the CF model—see below).

Fig. 11. (a) The maximum deflation rate and (b) the duration of each episode during the 1983–86 Pu’u ‘O’o eruption. Data courtesy of the

Hawaiian Volcano Observatory.


Instead, the Hawaiian character of the eruption iscontrolled by the cyclicity because the cycles arerelated to variations in flow rate through the dikesystem and thus to the rise speed of the magma beneaththe vent. The flow rate through the dike system isdirectly correlated with the deflation rate; thus the flowrate rapidly increases as cooled magma is pushedthrough the dike system, reaches a peak and thendeclines exponentially (Fig. 12). Such a pattern is

common in basaltic eruptions where the initial highpressure in the chamber allows high flow rates near thestart of an eruption, flow rate gradually declining as thechamber pressure declines (Wadge, 1981). In the caseof the Pu’u ‘O’o high fountaining episodes, the flowrate through the dike system, and hence the rise speedbeneath the vent, is sufficiently high to allow homo-geneous two-phase flow. During the repose periodsbetween high fountain episodes, the flow rate throughthe dike system becomes negligible and so the risespeed beneath the vent is close to zero. In thissituation, gas segregates from the magma within thevent and rises to the surface giving rise to the minorexplosive activity which characterised the repose peri-ods (Wolfe et al., 1987, 1988).

Vergniolle (1996) interpreted the cyclic pattern ofthe eruption and the associated inflation/deflationpatterns in a very different way. In her model at leastpart of the inflation and deflation is viewed as result-ing from changes in gas volume in the summit magmachamber. Inflation is related to exsolution of CO2

from the stored magma and its accumulation as afoam layer at the roof of the magma chamber. Col-lapse of this foam layer triggers eruption of magmaand deflation of the magma chamber. There are anumber of problems with this model:

(1) As mentioned above, observation shows thatCO2 constitutes an average of only f3% of the totalvolume of gas released in the eruptive episodes(Greenland, 1984; 1988). The majority of the gasreleased is magmatic water (85%), which must playa significant role in the eruption but cannot becollected as a foam prior to these eruptive episodes(see above).

(2) The Vergniolle (1996) model requires that CO2

exsolving within the magma chamber should becometrapped at the chamber roof forming the foam layerthat ultimately causes each fountaining episode. Ger-lach and Graeber (1985), Gerlach (1986) and Gerlachand Taylor (1990) have studied gas release from theKilauea system and show that magmas erupted on therift zones, including the Pu’u ‘O’o magma, aredepleted of CO2 prior to eruption (consistent withPoint 1). They propose that CO2 is lost from themagma chamber during storage and show that themeasured daily release rates of CO2 (1.6 to 3.6"106

kg day!1—Greenland et al., 1985) from the summitregion are consistent with calculated release rates that

Fig. 12. Patterns of summit deflation during the Pu’u ‘O’o eruption.

During each episode the summit deflated at a rate which was

initially slow, increased rapidly to a maximum value and then

declined approximately exponentially until the eruptive episode

ended. The patterns of deflation during two eruptive episodes are

shown—episodes 11 and 31. The bold line shows the actual

deflation rate derived from the summit tiltmeter records kept by the

Hawaiian Volcano Observatory. The dashed lines represent the

modelled deflation rate calculated for each episode using a model

developed by Parfitt and Wilson (1994). The diagram is modified

from Parfitt and Wilson (1994).


are based on the influx of magma into the chamberover a period of decades (f3.7"106 kg day!1—Gerlach and Graeber, 1985). Gerlach and Graeber(1985), Gerlach (1986) and Gerlach and Taylor(1990) conclude that most of the magmatic CO2 islost from the magma chamber through non-eruptivedegassing. So, although CO2 does exsolve in themagma chamber, the observational evidence suggeststhat it is lost from the chamber by degassing ratherthan being trapped at the roof of the chamber toproduce a foam layer as the CF model requires.

(3) The model of Vergniolle and Jaupart (1990) andVergniolle (1996) explains the change in eruptivebehaviour in July 1986 from cyclic fountaining tocontinuous lava outpouring as being the result of adecline in gas volume through time. Values for thedeclining gas release in each episode are shown in Fig.7 in Vergniolle and Jaupart (1990). These data werederived by Vergniolle and Jaupart (1990) from meas-urements of the maximum fountain height recorded foreach episode and the total eruption duration made byHVO staff. The gas volume was calculated by obtain-ing the exit velocity for each episode from the fountainheight and then multiplying this by the vent cross-sectional area and the eruption duration. There areseveral reasons why this is inaccurate way of estimat-ing the gas volume released:

(a) The maximum fountain height is not repre-sentative of the episode as a whole and represents atime when the exit velocity is a maximum. This isclear from time-lapse data collected by HVO, someof which was published in Wolfe et al. (1987,1988).(b) The estimates of large gas volumes during the

early episodes of the sequence, which add greatlyto the impression that gas volume declines throughtime, result from using the long durations of theseepisodes to calculate the volumes. Observationalevidence shows, however, that the vents were notactive throughout the duration of the episode andthus the use of the total durations to calculate thevolumes is inappropriate.(c) Finally, the calculation takes no account of

the expansion of the gas as it rises.That the values of gas volume calculated by Vergniolleand Jaupart (1990) are unreliable can be verified bycomparison with observational data. Their gas vol-umes range from 3.1"109 m3 during the initial stages

of the eruption to 0.6"109 m3 for the last highfountaining episode. Such values are almost an orderof magnitude greater than volumes calculated frommeasurements of gas mass release during the eruptiveepisodes (Table 2). Thus, the data presented in Verg-niolle and Jaupart (1990) as evidence for a decline ingas release through the eruption sequence must betreated with scepticism. Furthermore, observationalevidence does not support the idea that less gas wasbeing released during the continuous phase of activityat the Kupaianaha vent compared with the high foun-taining phases at Pu’u ‘O’o which preceded it. Meas-urements of SO2 emission rates during the Kupaianahaeruption show that the rates are 5–27 times less thanthe emission rates during the high fountaining episodes(Andres et al., 1989). However, eruption rates atKupaianaha are also lower, averaging 0.35"106 m3

day!1 compared with f7.7"106 m3 day!1 during thehigh fountaining episodes (Heliker et al., 2003), i.e.,22 times less than during high fountaining. Thus, thedecreases in emission rates and eruption rates arecomparable. Averaged over time the continuous slowrelease of gas and magma from Kupaianaha actuallyreleased as much gas as the higher rate but short-livedhigh fountaining episodes. Thus, there is no evidence

Table 2

Gas volumes released during episodes 15 and 16 of the Pu’u ‘O’o

eruption

Gas

species

Gas mass

released

per day

(tonnes/day)

Total gas

mass released

during the

episode (kg)

Gas density

(kg m!3)

Gas volume

erupted (m3)

(a) Gas release during episode 15. The episode duration was 19 h

H2O 58,000 4.59"107 0.15 3.06"108

SO2 27,000 2.14"107 0.53 4.03"107

CO2 4700 3.72"106 0.36 1.03"107

HCl 330 2.61"105 0.3 8.71"105HF 200 1.58"105 0.16 9.90"105

Total 3.59"108

(b) Gas release during episode 16. The episode duration was 31 h

H2O 40,000 5.17"107 0.15 3.44"108

SO2 18,000 2.33"107 0.53 4.39"107

CO2 3200 4.13"106 0.36 1.15"107

HCl 220 2.84"105 0.3 9.47"105

HF 140 1.81"105 0.16 1.13"106

Total 4.02"108

Gas masses released are taken from Greenland et al. (1985).


that any less SO2 was being released from the magmaafter the change in eruption style. Though no evidenceis available for release of other volatiles before andafter the change in eruptive character, it seems unlikelythat the overall release rate should decline while theSO2 release rate remains unchanged.

6.2. Fountain heights and exit velocities

Measurements were made by HVO staff of themaximum and average fountain heights for eacheruptive episode (Wolfe et al., 1987, 1988). Wilsonand Head (1981), Head and Wilson (1987) and Parfittet al. (1995) have related fountain heights to theeruption rate and gas content of the erupting magmausing the RSD model by calculating the exit velocityof the erupting mixture and assuming that the largerclasts (which form the main part of the fountain)behave ballistically. When this model is applied tothe Pu’u ‘O’o eruption, it suggests that the observedfountain heights would be produced if the watercontent of the erupting magma is 0.32 wt.%. This isconsistent with independent estimates that range from0.21% to 0.38 wt.% (Gerlach and Graeber, 1985;Greenland et al., 1985; Greenland, 1988).

The CF model (Vergniolle and Jaupart, 1990;Vergniolle, 1996) does not make a prediction of theexit velocities or fountain heights of the eruption.

6.3. Volumes and durations

Observational evidence collected by HVO staff(Heliker and Mattox, 2003) provides constraints onthe volumes of lava produced during each episode (2to 38"106 m3), on the average eruption rates (12 to489 m3 s!1) and on the duration of each episode (5 to290 h). Parfitt and Wilson (1994) used the RSD modelto simulate the Pu’u ‘O’o episodes and the model canadequately explain the observed values of each ofthese parameters. It has never been demonstrated thatthe CF model can explain these observed eruptionvolumes or durations.

6.4. Change in eruption character

A further fundamental difference between the twomodels is highlighted by the change in eruptioncharacter that occurred in July 1986, when the site

and style of eruption changed abruptly. A fissuresystem opened up that extended downrift from Pu’u‘O’o and activity from this system eventually local-ised at a new vent later named Kupaianaha (Helikerand Wright, 1991). The change in locality corre-sponded to the end of the cyclic lava fountainingactivity seen at Pu’u ‘O’o. Instead, the activity be-came continuous and occurred at a much slowereruption rate (f5 m3 s!1). A low lava shield with alava lake at the top gradually developed. Lava withinthe lake circulated and degassed (Fig. 13a) and wascontinually drained from the lake through a complextube system (Mattox et al., 1993). Though somedegassing occurred at Kupaianaha, the bulk of thegas release occurred through the Pu’u ‘O’o vent aswas evident from observation of a plume constantlyrising from the cone (Fig. 13b) and confirmed bydirect measurements (Andres et al., 1989). Thischange in character is similar to ones which occurredduring the 1969–1974 Mauna Ulu eruption (Swansonet al., 1979; Tilling et al., 1987). Vergniolle andJaupart (1990) and Vergniolle (1996) propose thatchanges from high fountaining to continuous eruptionin each of these eruptions represent a change ineruption style from Hawaiian to effusive. Parfitt andWilson (1994) have argued that the change in eruptioncharacter represents a change from Hawaiian toStrombolian. Thus, there is a basic disagreementabout how to interpret the observed activity as wellas a disagreement on the causes of the change. Part ofthe problem arises because of the unusual nature ofgas release during the Kupaianaha eruption. Themagmatic plumbing system established between Pu’u‘O’o and Kupaianaha in July 1986 allowed shallowdegassing of the magma through the Pu’u ‘O’o ventprior to magma eruption at Kupaianaha. This meansthat although there was minor explosive activity atKupaianaha (Fig. 13a), the overflow of the lake can beinterpreted as effusive activity. Parfitt and Wilson(1994) argue, however, that the eruption is Strombo-lian because the observation of significant gas releaseand spattering within the Pu’u ‘O’o cone (Andres etal., 1989; Mangan et al., 1995) shows that gas issegregating in significant quantities and giving rise toexplosive activity at the top of the magma column.Effusive activity corresponds to events where nosignificant gas segregation is occurring. This is moreevident when considering the Mauna Ulu eruption.


Here, after the change from high fountaining tocontinuous activity, eruption was associated domefountaining, gas-pistoning, spattering and low foun-taining, all of which indicate that gas release andminor explosive activity was associated with theproduction of lava (Swanson et al., 1979).

Vergniolle and Jaupart (1990) and Vergniolle(1996) argue that the change in character observedin the Pu’u ‘O’o eruption occurred because of aprogressive decline in the gas accumulation rate in

the magma chamber as the magma became depleted ofgas. As we have seen above, the evidence that the gasrelease rate is smaller after the change in eruptioncharacter is unconvincing. Furthermore, this argumentis based on the idea that the magma chamber is notbeing resupplied with magma. Many studies suggestthat the magma chamber is fairly continuously resup-plied with magma (e.g., Dzurisin et al., 1984; Dvorakand Dzurisin, 1993). Furthermore, if the magmachamber were isolated in this way through the course

Fig. 13. (a) Photograph of the Kupaianaha lava lake. The lava lake is covered with a cooled crust which was constantly moving and overturning.

A large bubble in the process of bursting can be seen near the far wall of the lake. Gas release from the lake was constant and sufficient to

prevent an observer watching the activity for periods of more than a few minutes at a time. (b) The Pu’u ‘O’o cone viewed from Kupaianaha.

The photograph was taken at the same time as that in (a). It is evident from the plume rising from Pu’u ‘O’o that significant quantities of gas

were being released there while eruption occurred from Kupaianaha. (Both photographs taken by the author, February 20, 1988).


of the Pu’u ‘O’o–Kupaianaha eruption this would bereflected in the temperature and chemistry of theerupting lava. Instead, the most recent study of thePu’u ‘O’o–Kupaianaha eruption (Thornber, 2003)reinforces the idea that resupply of magma from themantle has occurred throughout the eruption andshows that what long-term changes have occurred inthe eruption temperature and magma compositionrepresent the increasing involvement of mantle mag-ma—the exact opposite trend to that which would beseen if the magma chamber were isolated. Thus, allthe available evidence contradicts the idea of anisolated magma chamber and a decline in the supplyof gas to the eruption.

Parfitt and Wilson (1994) argued that the change incharacter from intermittent fountaining to continuouseruption represents a long-term evolution of the dikegeometry and thermal state, consistent with the obser-vations and interpretation of Dvorak and Okamura(1985). The change from high fountaining to minorexplosive activity, gas release and lava outpouring isseen as being a result of the decrease in magmaeruption rate and rise speed that accompanied thechange from intermittent to continuous eruption. Thatthe eruption rate was lower during the continuousphase is indisputable. Observations made during thehigh fountaining phases at Pu’u ‘O’o and during lavaoutpouring at Kupaianaha show that the typical vol-ume flux during high fountaining was f7.7"106 m3

day!1 compared with f0.35"106 m3 day!1 atKupaianaha (Heliker et al., 2003). Parfitt and Wilson(1994) used these fluxes to estimate the magma risespeed as being f0.3 m s!1 during the high fountain-ing episodes and f0.01 m s!1 during the Kupaianahaeruption. Parfitt and Wilson (1995) have shown that,for magma gas contents and viscosities observedduring the Pu’u ‘O’o–Kupaianaha eruption, theRSD model predicts that at a rise speed of 0.3 ms!1, the activity should be Hawaiian, and at a risespeed of 0.01 m s!1, the activity should be Strombo-lian, consistent with the observed change in eruptioncharacter.

6.5. Discussion

I have discussed this one eruption in detail forseveral reasons. Both the RSD and CF models havebeen tested using the Pu’u ‘O’o eruption. It is an

excellent test case because the range of data collect-ed during the eruption is exceptional and the qualityof the data is extremely good. The eruption provides,therefore, a unique opportunity to examine a Hawai-ian eruption sequence in great detail. Over the pastf10–15 years, the CF model has come to be themore widely accepted model of the dynamics ofHawaiian eruptions (e.g., Sparks et al., 1994; Verg-niolle and Mangan, 2000). Parfitt and Wilson (1994)pointed out general problems with the model and Ihave detailed in this paper the ways in which the CFmodel is inconsistent with the observations madeduring the Pu’u ‘O’o eruption, the eruption whichthe authors of the CF model elected to use as theirtest case (Vergniolle and Jaupart, 1990; Vergniolle,1996). Furthermore, I have shown that the RSDmodel, when applied to the same eruption, producesresults that are consistent with a wide range ofobservations. My point is not that the CF model isinherently flawed but, instead, that any model hasvalue only if it actually reproduces the key featuresof the system under examination. In the case of theCF model as applied to Hawaiian eruptions, themodel is inconsistent in many ways with the obser-vational evidence.

7. Transitional eruptions

Some basaltic eruptions exhibit behaviour thatappears to display features of both Hawaiian andStrombolian activity and are referred to as ‘‘transi-tional’’ eruptions (Parfitt and Wilson, 1995). The 1973eruption of Heimaey in Iceland is an example of thistype of event (see above). Another example is the 6thto 29th July 1975 stage of the Great Tolbachik Fissureeruption. This eruption is described as Strombolian–Plinian by Maleyev and Vande-Kirkov (1983). Theysay that the eruption ‘‘ejected a continuous streamof pyroclastic material to a height of 8–11 km’’.Tokarev (1983) describes the eruption as a ‘‘non-stopvertical jet of incandescent gases, ash, cinder andvolcanic bombs’’ that reached ‘‘a height of 1–1.5km, while above it, to a height of 6–8 km, rose abillowing cloud of ash blown sideways by the wind’’.Although there were pulsations in the eruption jet,eruption was continuous (Tokarev, 1983). Clasts up to2–3 m in diameter were produced and accumulation


of this material around the vent generated a cindercone but did not produce any lava flows (Maleyev andVande-Kirkov, 1983; Tokarev, 1983). Thus, this erup-tion, like the Heimaey eruption, exhibits character-istics of both Hawaiian and Strombolian activity.

In addition to exhibiting characteristics of bothHawaiian and Strombolian styles, basaltic eruptionsfrequently exhibit rapid transitions between these end-member types of activity. For example, Bertagnini etal. (1990) described such behaviour during the 1989eruption of Etna. They describe how each ‘‘eruptiveepisode began with a weak strombolian activity, withlava clasts thrown just beyond the crater rim.’’ As themagma level rose in the vent, the explosions became‘‘more frequent and more violent’’ until they were‘‘nearly continuous’’. This activity then evolved intoactivity which was ‘‘typically hawaiian, with lavafountains up to 100–200 m in height’’ and whichgenerated lava flows.

Parfitt and Wilson (1995) used the RSD model toinvestigate the nature of transitional eruptions and theconditions which give rise to them. The results of thismodelling (Fig. 5) show that transitional activity isexpected to arise primarily when the magma risespeed is intermediate between that of Hawaiian andStrombolian eruptions (Table 1) and furthermore thatgradual changes in rise speed will give rise to aprogressive change in eruption character from Strom-bolian to Hawaiian or vice versa. The time frame overwhich the eruption character changes is then a func-tion of the rate at which the magma rise speedchanges. The modelling suggests that, for example,as magma rise speed increases the eruption characterwould change from widely spaced Strombolian explo-sions to more frequent explosions with the strength ofthe explosions being fairly constant. Then as the risespeed increases further the explosions will becomemore closely spaced in time still and will rapidlyincrease in violence throwing clasts much higher inthe air. Continued increase in rise speed then givesrise to continuous high lava fountaining activity. Thispattern of behaviour is remarkably similar to thatdescribed above for the 1989 Etna eruption.

The model developed by Parfitt and Wilson (1995)does not explicitly look at the behaviour of the finermaterial ejected in the eruption. A characteristic ofmany transitional eruptions is the high sustainederuption plume they develop. Presumably, this arises

because the short time gap between Strombolianexplosions means that from the point of view of theheat output the activity is continuous and can thusgenerate a sustained plume. The height of the plume ismuch greater than that associated with Hawaiianeruptions and this difference is expected to be relatedto the difference in grainsize of the erupted materialcompared with a pure Hawaiian eruption (Parfitt andWilson, 1999).

The CF model has not been used to look attransitional eruptions or to explain how changes ingas accumulation rates or magma viscosity canaccount for the types of rapid transition in eruptionstyle which are a common feature of basaltic activity.As we have seen, the sudden change in eruptioncharacter which occurred during the Pu’u ‘O’o–Kupaianaha eruption is explained in the CF modelby a gradual change in gas accumulation whichoccurs over a period of years. Changes in characterfrom Strombolian to Hawaiian and back again, likethose described at Etna, can occur on time scales ofonly hours.

8. Conclusions

During the past 20 years, two very differentmodels have been proposed to explain the dynamicsof explosive basaltic eruptions—the rise speed de-pendent model (Wilson, 1980; Wilson and Head,1981; Head and Wilson, 1987; Fagents and Wilson,1993; Parfitt and Wilson, 1994, 1999; Parfitt et al.,1995) and the collapsing foam model (Vergniolle andJaupart, 1986, 1990; Jaupart and Vergniolle, 1988,1989; Vergniolle, 1996). Both models are in currentusage, often without acknowledgement that an alter-native model exists. In this paper, I have examinedthe basic assumptions made in each model andshown that neither model is flawed in any funda-mental way, i.e., that each model could apply in agiven set of conditions. The purpose of a model is,however, to represent some behaviour that we ob-serve in nature. Thus, the value of any modeldepends on how well it can reproduce this realbehaviour. Volcanologists examining explosive ba-saltic activity are at a considerable advantage com-pared with those interested in more violent, silicic,events in that basaltic explosions occur frequently


and are relatively safe to monitor. Thus, large bodiesof literature and data are available to test the twomodels. I have examined the way in which eachmodel has been used to explain Strombolian, Hawaiiand transitional eruption styles, and in doing so havearrived at the following conclusions.

8.1. Strombolian eruptions

Both models agree that Strombolian eruptionsresult from the accumulation and bursting of a gaspocket at shallow depths within an open magmaticsystem. This is consistent with direct observations(e.g., Vergniolle and Brandeis, 1994) and with acous-tic wave studies (Vergniolle and Brandeis, 1994,1996; Vergniolle et al., 1996). The models diverge,however, in the assumptions they make about wherethe gas segregates from the magma. In the RSDmodel segregation is thought to be progressive andoccurs because of the low rise speed of the magmabeneath the eruptive vent. Such a model is consistentwith observational evidence (Table 1) which showsthat Strombolian eruptions are associated with lowmagma rise speeds. The CF model assumes that gassegregation occurs at depth in a magma chamber orstorage zone and that accumulation of this gas as afoam layer and its partial collapse give rise to a slugof gas which rises up through the vent system andbursts through the top of the magma column. Thus,the CF model requires a special set of conditions toexist whereas the RSD model is applicable to anyopen system.

Recent studies of seismicity at Stromboli (Neuberget al., 1994; Chouet et al., 1999) show that earth-quakes are generated in direct association with eachStrombolian explosion. The source of such earth-quakes is located several hundred metres beneaththe surface. It has been suggested that these earth-quakes are caused by the collapse and movement ofthe gas slug at depth. Further modelling work isneeded to show that the seismic waves generated inStrombolian explosions are generated in this way butsuch work provides a potential way to determinewhether gas accumulation and foam formation occursat Stromboli. It should be stressed, though, that thereis no reason why both models should not be applica-ble in different systems and it must be understood thatthe CF model requires a particular set of conditions to

exist beneath the vent in order to operate whereas theprocesses invoked by the RSD model can occur in anyopen system as long as the rise speed of the magma isslow or negligible.

8.2. Hawaiian eruptions

In the case of Hawaiian activity the RSD and CFmodels present very different and mutually exclusiveviews of the eruption dynamics. The models makefundamentally different assumptions about the flowregime which prevails during eruption: The RSDmodel assumes homogeneous two-phase flow andthe CF model assumes segregated two-phase flow.They also assume different ‘driving’ gases—in typicalconditions, the RSD model will only work if H2O isthe dominant gas and the CF model only works if CO2

is the driving gas. My examination of the two modelssuggests that neither model is fundamentally flawedand thus that either might operate in different startingconditions.

Both models have been tested on the same eruption(the 1983–1988 Pu’u ‘O’o eruption of Kilauea vol-cano). I have examined in detail how well each modelfits with the behaviour observed during this eruptionand have shown that the CF model (Vergniolle andJaupart, 1990; Vergniolle, 1996) fails to explain manykey aspects of the eruption. For instance, observationsshow that the dominant gas released in the eruption isH2O (85%) and only 3% of the released gas is CO2

which the CF model assumes is the driving gas.Furthermore, observational evidence does not supportthe contention that gas segregation and concentrationhas occurred at depth prior to eruption but is insteadconsistent with the homogeneous flow assumed in theRSD model. The RSD model can also explain manyother aspects of the eruptive behaviour such as thecharacteristic deflation pattern observed during eacheruption, the long-term changes in the duration anderuption rates observed during the eruption sequence,and the change in eruption character which occurredin 1986.

The problems highlighted by the application ofthe CF model to the Pu’u ‘O’o eruption aresufficiently far-reaching that they draw the validityof the model in its application to other Hawaiianeruptions into serious question. I would thereforeurge considerable caution in the use of this model


in treating the dynamics of Hawaiian eruptions. Itmust also be borne in mind, though, that the modelshave only been tested in detail on this one eruption.While the evidence from the Pu’u ‘O’o eruptionsupports the RSD model as the most valid treat-ment, more testing on other Hawaiian eruptions isneeded to resolve the issue of which model is mostapplicable to Hawaiian eruptions and, indeed, toexplosive basaltic eruptions in general. It should benoted, though, that like with Strombolian eruptionsthe CF model requires a particular set of conditionsto prevail beneath the vent in order to be applicable(a large enough storage zone at a depth where gasis exsolving) whereas the RSD model has no suchlimitations.

8.3. Transitional eruptions

I have noted that some explosive basaltic eruptionsshow features of both Hawaiian and Strombolianeruption styles and these have been denoted ‘‘transi-tional’’ eruptions by Parfitt and Wilson (1995). Inaddition, basaltic eruptions frequently show rapidtransitions in character from Strombolian to Hawaiianand vice versa. The RSD model was used by Parfittand Wilson (1995) to investigate the conditions inwhich transitional eruption styles arise. They sug-gested that transitional eruptions arise when themagma rise speed is too high to yield purely Strom-bolian activity and too low to yield purely Hawaiianbehaviour. For a typical basaltic eruption this transi-tion occurs in the magma rise speed range 0.01–0.1m s!1 (Fig. 5). This is consistent with a range ofobservational data (e.g., Table 1). The model furthersuggests that as magma rise speed progressivelyincreases or decreases, an eruption can rapidly changein character from Strombolian to Hawaiian or viceversa. In the case of increasing rise speed, for exam-ple, it would be expected that Strombolian explosionswill become progressively more frequent but withlittle change in violence until a rapid change occursduring which explosions become very closely spacedin time and much more violent. This behaviour thengives way to continuous lava fountaining. This kindof transition in character is very similar to thatobserved in many real basaltic eruptions. In theRSD model, the primary control on eruption characteris the magma rise speed and thus transitions in

character can occur rapidly in response to changesin rise speed. By contrast, in the CF model, eruptioncharacter is determined by magma viscosity and gasaccumulation rates (Jaupart and Vergniolle, 1988;Vergniolle, 1996), and it is hard to see how the rapidtransitions observed in basaltic eruptions can beexplained by such a model.

Acknowledgements

I thank Christina Heliker for comments on theorigin of data used in Vergniolle and Jaupart (1990). Ialso thank the staff of the Hawaiian VolcanoObservatory, especially Tom Wright, for providingaccess to data used here (and elsewhere) and fordiscussion of many of the issues raised in this paper.Thanks to Andy Harris for comments relating toactivity at Etna. This paper has benefited fromdetailed reviews by Sylvie Vergniolle, Greg Valentineand Roberto Scandone. Finally, thanks to LionelWilson for many, many discussions of these issuesover the years.

Appendix A. Treatment of simultaneous magmaeruption and drainback in conduit flow

A.1. Introduction

It is assumed that all of the magma behaves as aNewtonian fluid with the same viscosity and that forboth upward and downward magma streams there isno variation with depth of the magma density and thepressure gradient driving the motion. There is noguarantee that the pressure gradients in real volcanicconduits are independent of depth. However, asshown by Wilson et al. (1980), Wilson and Head(1981) and Giberti and Wilson (1990), for maficmagmas, there exists a wide range of possible erup-tion conditions in which this condition is approxi-mately satisfied, even when rising magma exsolvessufficient volatiles to undergo fragmentation. Themain restriction on the application of the followingcalculations, therefore, is the assumption of constantmagma densities. There are two cases to be consid-ered. In the first, both the rising and the descendingmagma are unvesiculated and their motions are


laminar. In the second, the rising magma is assumedto have vesiculated to the point of fragmentation intopyroclasts and released gas, and the upward motionis turbulent.

A.2. Laminar upward motion

This analysis can be applied directly to themotion of volatile-poor magma in a conduit wherethere is either net drainback from a lava pond aroundthe vent or net growth of such a pond. It can also beinferred to apply to conditions in which vesiculatingmagma is erupting into a lava fountain whiledegassed magma is draining back into the conduitsystem provided that the values derived are taken torefer to conditions at depths greater than a fewhundred metres, where variations in bulk magmadensity are still small, there is negligible upwardacceleration of the rising magma, and similar viscos-ities can be assumed for both the rising and thesinking magma.

The basic relationship controlling flow of a New-tonian fluid in a circular conduit is:

l du=dr # !$1=2%r$dP=dx%; $A1%

where l is the fluid viscosity, (dP/dx) is the pressuregradient driving the motion in the x direction, r is theradial co-ordinate and u is the local velocity of thefluid. We assume that between r=0 and r=r0, where r0is some intermediate radius, the motion is upward andbetween r=r0 and r=rw, where rw is the radius of theconfining wall, the motion is downward. Thus, u=0 atboth r=r0 and at r=rw.

First, consider the fluid moving upward. Integrat-ing Eq. (A1) between r=0 and a general value of rgives the velocity profile u(r):

u # &$dP=dx%up=$4l%' $r20 ! r2%: $A2%

In this equation and those that follow, (dP/dx)uprepresents the absolute value of the pressure gradient;the driving pressure must of course decrease in thedirection of motion for the velocity to be positive. Themaximum velocity uc occurs at r=0 and is:

uc # &$dP=dx%up=$4l%'r20: $A3%

To find the average velocity uav-up of the upward-moving fluid, we weight the local value of u by therelative volume of fluid with that velocity, (2prdr),so that:

uav!up #Z r0

0

2purdr! "#

Z r0

0

2prdr! "

$A4%

which yields:

uav!up # &$dP=dx%up=$8l%'r20: $A5%

The upward mass flux Mup is then:

Mup # p r20uav!upqup; $A6%

where qup is the bulk density of the upward-flowingfluid.

Next consider the fluid moving downward. Skel-land (1967, Chap. 3) derives equations for flow in anannulus of a Bingham plastic fluid, and by setting theyield strength of such a fluid equal to zero the velocityprofile u(r) is found to be:

u # &$dP=dx%down=$4l%'fr2w ! r2 ( &$r2w ! r20%

=ln$rw=r0%'ln$r=rw%g: $A7%

Note that u is zero at r=rw because then (rw2!r2)=0

and ln(r/rw)=ln(1)=0; also u is zero at r=r0 becausethen ln(r/rw)=ln(r0/rw)=!ln(rw/r0). The maximum ve-locity ua must occur at the radius ra for which du/dr=0. Differentiating Eq. (A7):

du=dr # &$dP=dx%down=$4l%'f!2r ( &$r2w ! r20%=ln $rw=r0%'$1=r%g $A8%

and setting the term in curly brackets in Eq. (A8) tozero gives:

r2a # $r2w! r20%=&2 ln$rw=r0%' # $r2w ! r20%=ln $rw=r0%2:$A9%

The value of the maximum velocity, ua, is given by:

ua # &$dP=dx%down=$4l%'fr2w ! r2a ( &$r2w ! r20%

=ln$rw=r0%'ln$ra=rw%g: $A10%


and the average velocity of the fluid, uav-down, isobtained using the equivalent of Eq. (A4) as:

uav!down # &$dP=dx%down=$8l%'fr2w ( r20 ! &$r2w ! r20%

=ln$rw=r0%'g: $A11%

The downward mass flux Mdown is then:

Mdown # p$r2w ! r20%uav!downqdown; $A12%

where qdown is the bulk density of the downward-flowing fluid.

The final issue is to establish how the boundarybetween the two flows at r=r0 is related to the othervariables. This involves looking at the continuity ofthe overall velocity profile. We have already ensuredthat the velocity itself is continuous by arranging thatu=0 at r=r0 in both Eq. (A2) for the upward velocityand Eq. (A7) for the downward velocity. We nowrequire that the slopes of the two functions also becontinuous. For the upward velocity profile, Eq. (A2)leads to:

du=dr # &$dP=dx%up=$4l%'$!2r% $A13%

and we have already obtained the derivative of thedownward velocity profile as Eq. (A8). Equating thetwo at r=r0 and simplifying:

$dP=dx%up=$dP=dx%down # f&$r2w=r20% ! 1'

=ln$rw=r0%2g! 1; $A14%

so for any choice of the ratio (rw/r0), Eq. (A14) givesthe ratio of [(dP/dx)up/(dP/dx)down] that ensures con-tinuity of the velocity profile. Then taking the ratio ofEqs. (A6) and (A12):

Mup=Mdown # &qup=qdown'&$dP=dx%up=$dP=dx%down'" &r40=f$r2w ! r20%fr2w ( r20 ( &$r2w ! r20%=ln$rw=r0%'gg': $A15%

Thus, given a choice of the density ratio [qup/qdown], the ratio of the mass fluxes can be obtained.Table A1 shows a selection of examples, tabulated asa function of (r0/rw) for [qup/qdown]=0.8. The reasonfor this choice of [qup/qdown] is as follows. Thepressure gradients driving the upward and downwardmovement of the magmatic fluids are by definition

the amounts by which the total pressure gradientsdiffers from the static weights of the magma in eachcase. Assume that the pressure in the magma reser-voir at depth is the hydrostatic weight of the over-lying crust (in practice, the reservoir is likely to beoverpressured relative to the lithostatic load by a fewMPa, but this does not significantly affect thefollowing illustration) and that the upward magmaflow occurs because the magma in the centre of theconduit is positively buoyant. Similarly, the magmain the outer, descending annulus is assumed to benegatively buoyant. If the crustal density is qcrust, wethen have:

$dP=dx%up # g$qcrust ! qup% $A16%

$dP=dx%down # g$qdown ! qcrust% $A17%

Plausible values might be qcrust=2250 kg m!3, qup=2000 kg m!3 and qdown=2500 kg m!3, in which case[qup/qdown]=0.8, as illustrated in Table A1. The tableshows that for the case of pure convection, whereMup/Mdown=1, r0/rw=0.642, which implies thatf41% of the area of the conduit is occupied byrising magma and f59% by descending magma.Clearly, it is necessary that qup is always less thanqdown, and depending on the amount of gas exsolv-ing from the rising magma in the deep part of theconduit, and on the crustal density, likely ranges ofvalues are f0.55 to 0.85 for [qup/qdown] and f0.3to at least 3 for [(dP/dx)up/(dP/dx)down].

Table A1

Values of the ratios of upward to downward pressure gradient,

magma mass flux, maximum fluid velocity and mean fluid velocity

as a function of the fraction of the conduit radius occupied by the

upward flow for the case where the upward motion is laminar and

[qup/qdown]=0.8

r0/rw (dP/dx)up /

(dP/dx)down

Mup /

Mdown

uc /ua uav-up /

uav-down

0.154 10.00 0.092 0.611 0.473

0.232 5.00 0.152 0.870 0.666

0.386 2.00 0.327 1.543 1.169

0.534 1.00 0.621 2.589 1.950

0.642 0.61 1.000 3.892 2.925

0.683 0.50 1.214 4.621 3.471

0.838 0.20 3.007 10.646 7.988

0.910 0.10 6.004 20.656 15.494


A.3. Turbulent upward motion

This treatment applies to the shallow part of aconduit where enough volatile exsolution has oc-curred that magma fragmentation had taken place.Both the viscosity and the density of the magma arevery different in the upward and downward magmastreams. The velocity profile in the outer annulus isthe same as in the previous section but in the centralregion out to radius r0 the velocity profile is of theform (Knudson and Katz, 1958):

u # uc&1! a$r=r0%2 ! b$r=r0%32' $A18%

where a=0.204 and b=0.796. The average velocityuav-up is found from Eq. (A4):

uav!up #Z r0

0

2purdr! "#

Z r0

0

2prdr! "

# &$2uc%=r20' r2=2! ar4=$4r20%

$

! br34#%

Z r0

0

34r320

&"

and so:

uav!up # uc&1! a=2! b=17' # 0:8512 uc: $A19%

The first derivative of the velocity profile is:

du=dr # uc&!2ar=r20 ! 32br31=r320 ' $A20%

and using Eq. (A19) to write this in terms of uav-up,becomes:

du=dr # uav!up&!2ar=r20 ! 32br31=r320 '=&1! a=2! b=17': $A21%

This must now be equated to the first derivative ofthe annulus flow, Eq. (8), at r=r0. It is convenient touse Eq. (A11) to eliminate [(dP/dx)down/(4l)] fromEq. (A8) giving:

du=dr # &2uav!down=fr2w ( r20 ! &$r2w ! r20%=ln$rw=r0%'g' " f!2r ( &$r2w ! r20%=ln$rw=r0%'$1=r%g: $A22%

Equating this to Eq. (A21) with r=r0, takingaccount of the fact that the upward and downwardvelocities have opposite signs:

uav!up=uav!down # f&!2 ln$rw=r0% ( $rw=r0%2 ! 1'" &1! a=2! b=17'g=f&a( 16b'" f&$rw=r0%2 ( 1' ln$rw=r0%! $rw=r0%2 ( 1gg: $A23%

Then taking the ratio of Eqs. (A6–12) and substi-tuting Eq. (A23) for (uav-up/uav-down):

Mup=Mdown # $qup=qdown%&$1! a=2! b=17%

=$a( 16b%'&!2 ln$rw=r0% ( $rw=r0%2

! 1'=ff&$rw=r0%2 ( 1'ln$rw=r0%! $rw=r0%2 ( 1g&$rw=r0%2 ! 1'g: $A24%

Thus, for any choice of the ratio (rw/r0), the ratioof the upward and downward average velocities canbe found from Eq. (A23) and of the upward anddownward mass fluxes can be obtained from Eq.(A24). Some values of (uav-up/uav-down) are given inTable A2. However, in order to specify values of

Table A2

Values of the ratios of upward to downward magma mass flux and

mean magma velocity as a function of the fraction of the conduit

radius occupied by the upward flow for the case where the upward

motion is turbulent and [qup/qdown]=0.024

r0 /rw Mup /Mdown uav-up /uav-down

0.10 0.000011 0.046

0.20 0.000077 0.076

0.30 0.000269 0.113

0.40 0.000738 0.161

0.50 0.001823 0.228

0.60 0.004417 0.327

0.70 0.011349 0.492

0.80 0.035050 0.821

0.90 0.185045 1.808

0.95 0.840210 3.782

0.96 1.345392 4.769

0.97 2.450476 9.702

0.99 23.13130 19.569

0.999 2362.51119 197.171

0.9999 236761.95087 1973.312


(Mup/Mdown), it is necessary to decide on a plausiblevalue of (qup/qdown). The fragmented magma in therising part of the conduit will have a bulk densityqup given by:

$1=qup% # $n=qg% ( &$1! n%=qmelt' $A25%

where n is the mass fraction of exsolved volatile, qgis the gas density and qmelt is the density of unvesi-culated rising magma. Consider a typical basalticmelt having exsolved 0.25 wt.% H2O, i.e., a massfraction n=0.0025; at a typical magmatic temperatureof 1450 K, the density of this gas emerging from thevent, where the pressure is close to atmospheric, isf0.15 kg m!3. Thus, qup is f60 kg m!3. Usingqdown=2500 kg m!3, as before, (qup/qdown)=0.024,and this value is used to generate the values of (Mup/Mdown) in Table A2.

It is much less easy in this case to specify the ratiosof the maximum velocities and the pressure gradients.The normal treatment for turbulent flow is to relate thepressure gradient to the mean velocity by:

r0$dP=dx%up # f qupu2av!up $A26%

where f is a dimensionless friction factor of order 10!3

for the case of motion of a fluid in a pipe with smoothwalls (probably the best assumption in this case).However, Eq. (A26) assumes that there is no acceler-ation of the magma, whereas if the rising magma isfragmenting to form a lava fountain much of theambient pressure decrease is used to accelerate themagma and very little is used to overcome wallfriction. Thus, the value needed for (dP/dx)up in Eq.(A26) would be very much less than the value used inthe slow-speed, laminar flow case and, furthermore,would change with depth below the surface. Noattempt is made to take the analysis further here, butTable A2 shows that a given ratio of Mup/Mdown

occurs much closer to the conduit wall in the caseof turbulent upward flow than in the laminar case.

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Documents

A discussion of the mechanisms of explosive basaltic eruptionsruprecht/Site/... · cooled upper surface of a magma column (e.g., Black-burn et al., 1976; Wilson, 1980). In such events,