Journal of Volcanology and Geothermal Research 134 (2004) 77 – 107
www.elsevier.com/locate/jvolgeores
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 rise
speed dependent (RSD) model and the collapsing foam (CF) model. The basic assumptions of each model are examined, and it
is found that neither model is flawed in any fundamental way. The models are then compared as to how well they reproduce
observed Strombolian, Hawaiian and transitional eruptive behaviour. It is shown that the models do not differ greatly in their
treatment of Strombolian eruptions. The models of Hawaiian eruptions are, however, very different from each other. A detailed
examination of the 1983 – 1986 Pu’u ‘O’o eruption finds that the CF model is inconsistent with observed activity in a number of
important aspects. By contrast, the RSD model is consistent with the observed activity. The issues raised in the application of
the CF model to this eruption draw into doubt its validity as a model of Hawaiian activity. Transitional eruptions have only been
examined 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 volcanic activity on Earth, the Moon, Mars and Venus
(e.g., Cattermole, 1989; Head et al., 1992; Wilson and
Head, 1994). On Earth, >80% of the annual volcanic
output is basaltic with >70% of this occurring beneath
the Earth’s oceans (Crisp, 1984). Basaltic eruptions
are frequently described as effusive because they
commonly generate lava flows. While the term ‘‘effusive’’ is appropriate for basaltic eruptions in which
the lava oozes passively from the vent, it is a misleading term when applied to the majority of subaerial
eruptions on Earth, to eruptions on the Moon and
E-mail address: [email protected] (E.A. Parfitt).
0377-0273/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jvolgeores.2004.01.002
almost certainly to eruptions on Mars (Wilson and
Head, 1983, 1994). The presence of dissolved gas
within basaltic magma results in explosive volcanic
activity unless the exsolution of the gas from the
magma is suppressed (as in sufficiently deep sea-floor
volcanism—Head and Wilson, 2003) or the gas is lost
from the magma prior to eruption. Although explosive
basaltic eruptions are generally much less violent than
their more silicic counterparts they are, nonetheless,
explosive and need to be considered as part of a
continuum of explosive activity that embraces not
only 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 explosive
basaltic eruptions has advanced considerably during
the past f30 years due to the collection and analysis
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E.A. Parfitt / 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; Houghton
and Schmincke, 1989; Carracedo et al., 1992; Thordarson and Self, 1993; Parfitt, 1998), volcano monitoring (e.g., Richter et al., 1970; Chouet et al., 1974;
Blackburn et al., 1976; Swanson et al., 1979; Wolfe et
al., 1987, 1988; Neuberg et al., 1994; Vergniolle and
Brandeis, 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 widely
accepted that Strombolian eruptions result from the
formation and bursting of a gas pocket close to the
surface (e.g., Blackburn et al., 1976; Wilson, 1980;
Vergniolle and Brandeis, 1994, 1996), though some
details of the mechanism are still disputed and are
discussed below. In the case of the dynamics of
Hawaiian eruptions, however, a curious situation
exists in which two very different models have been
developed that are both in common usage. I refer to
these models as the rise speed dependent (RSD)
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 (CF) model (Vergniolle and Jaupart,
1986, 1990; Jaupart and Vergniolle, 1988, 1989;
Vergniolle, 1996).
The aims of this paper are to review both models of
explosive basaltic eruptions, and to present an indepth examination of the models of Hawaiian activity
in which the assumptions and predictions of each
model are compared with a wide range of geophysical
and observational data from recent eruptions.
al., 1986; Bertagnini et al., 1990). Though rare examples of sub-Plinian and Plinian basaltic activity do
occur (Self, 1976; Williams, 1983; Walker et al.,
1984), explosive basaltic eruptions resulting from
the exsolution of magmatic gases alone (rather than
hydromagmatic activity) generally exhibit Hawaiian
or Strombolian styles, or behaviour which exhibits
characteristics of both end-member styles.
2.1. Hawaiian activity
The term ‘‘Hawaiian’’ is used to denote eruptions
that are continuous in character and that generate lava
fountains (Fig. 1), typically tens to hundreds of metres
in height (though they can occasionally exceed 1 km
in height: Wolff and Sumner, 2000). As the term
suggests, this type of activity is characteristic of the
volcanoes of the Hawaiian chain but it is commonly
seen on other basaltic volcanoes, e.g., Eldfell (Self et
al., 1974), Hekla (Thorarinsson and Sigvaldason,
1972), Etna (Bertagnini et al., 1990) and Miyakejima
(Aramaki et al., 1986). Hawaiian eruptions have
typical durations of hours to days, during which time
a lava fountain of fairly constant height may play
above the vent (e.g., Wolfe et al., 1988). The lava
fountain ejects clots of magma ranging in size from
millimetres to about a metre in diameter into the air at
speeds of typically f100 m s!1 (Wilson and Head,
1981). The majority of the erupted material lands
2. Styles of explosive basaltic eruption
Volcanologists have had many opportunities to
observe 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
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) 77–107
while still incandescent, and accumulation and coalescence of these hot clots generates rootless lava
flows (Head and Wilson, 1989). These flows are
typically still fluid enough to flow many kilometres
to tens of kilometres from the vent. For example, a 21day-long Hawaiian eruption at Mauna Loa in 1984
79
produced a number of lava flows, the longest of which
reached a length of 27 km (Lockwood et al., 1987).
Much material falling from the outer edges of the
fountain cools sufficiently during flight that, though it
deforms on landing and is hot enough to weld to the
material 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 of f0.5 km from the vent, the deposit is composed of centimetre-scale clasts and is unwelded. (Photograph taken by
the author, May 1996).
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
lava flows and instead accumulates as a spatter cone
around the erupting vent (Fig. 2; Head and Wilson,
1989). Some even cooler material can accumulate to
form a loose cinder cone, and a small proportion of
the erupted material is carried upwards in a convective
plume above the fountain and is deposited downwind
forming a tephra blanket (Fig. 2b, Parfitt, 1998).
2.2. Strombolian activity
Strombolian activity takes its name from the frequent, small-scale, transient explosions exhibited by
Stromboli, a volcano which forms one of the Aeolian
Islands north of Sicily. Whereas the term ‘‘Hawaiian’’
is well-defined and used in a fairly restricted way, the
term ‘‘Strombolian’’ has been used to denote a wide
range of activity, and, thus, caution must be used in
understanding individual usage of the term. The term
‘‘Strombolian’’ is most commonly used (and is used
here) to denote the relatively mild explosions that
occur from the accumulation of gas beneath the
cooled upper surface of a magma column (e.g., Blackburn et al., 1976; Wilson, 1980). In such events, gas
accumulation causes a raising and up-doming of the
surface of the magma column. This ‘‘blister’’ eventually tears apart allowing the release of the gas and the
ejection of the magma that formed the skin of the
blister. Blackburn et al. (1976) found typical initial
velocities of clasts at Heimaey to be f150 m s!1
whereas at Stromboli initial velocities are generally
50– 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 one
explosion may follow another after anything from a
few seconds to several hours. At Stromboli the typical
time between explosions is between 10 min and 1
h (Vergniolle and Brandeis, 1996). The erupted material is generally cooler prior to eruption than that
produced in Hawaiian eruptions and also experiences
more cooling during flight than Hawaiian clasts. The
clasts produced are too cool on landing to weld or
coalescence and so accumulate as a tephra/cinder cone
around 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 explosion
generally rises to heights of <200 m (Fig. 3, J.
Davenport, unpublished data).
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).
Though many Strombolian explosions are mild,
discrete events, the term Strombolian is also used to
describe events which can generate sustained eruption
plumes that reach heights of up to 10 km above the
vent (e.g., Cas and Wright, 1988). These are events in
which the individual explosions are so closely spaced
in time that they generate a sustained eruption plume
of considerable height rather than the small plumes
associated with truly discrete explosions (e.g., Fig. 3).
The 1973 Heimaey eruption in Iceland provides a
good example of this type of behaviour. The eruption
produced explosions every 0.5– 3 s with incandescent
clasts reaching heights of f250 m above the vent and
generated a plume that extended to heights of 6– 10
km above the vent (Self et al., 1974; Blackburn et al.,
1976). The eruption simultaneously generated lava
flows. This behaviour is distinctly different from the
discrete explosive events seen at Stromboli and
appears, in fact, to represent a type of behaviour
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
which exhibits characteristics of both Hawaiian and
Strombolian eruptions: Although the explosions are
discrete, they are so closely spaced in time that in
terms of the eruption column the activity is continuous
as in a Hawaiian eruption. The continuous production
of lava flows is also more characteristic of Hawaiian
events than the mild Strombolian events described
previously. Thus, this type of eruption can be viewed
as transitional between the Hawaiian and Strombolian
end-member eruption styles.
Classification schemes for explosive basaltic activity define Strombolian events as being more ‘‘explosive’’ than Hawaiian events (Fig. 4; Walker, 1973; Cas
and Wright, 1988). Two points are important to note
about such classification schemes: (1) they are based
on the dispersal in eruptions like the Heimaey eruption, not on truly discrete Strombolian explosions like
those occurring with such regularity at Stromboli; and
(2) they can lead to misclassification of Hawaiian
eruption deposits. The 1959 Kilauea Iki deposits, for
example, would be classified as Strombolian (Fig. 4) in
such a scheme when they were actually deposited
during a classic Hawaiian eruption (Richter et al.,
1970; Parfitt, 1998). Thus, it is important to exercise
caution in the use of the terms Hawaiian and Strombolian and to recognise that they represent end-member
cases while many basaltic eruptions simultaneously
exhibit facets of both types of activity and are better
described as ‘‘transitional’’ eruptions (Parfitt and Wilson, 1995).
81
3. Models of eruption mechanisms
3.1. The rise speed dependent model
The earliest attempt to apply fundamental ideas of
conservation of energy and mass in volcanic eruptions
was made by McGetchin and Ulrich (1973), but they
applied their model only to eruptions producing maars
and diatremes. The first model to specifically address
the dynamics of explosive basaltic eruptions was
developed by Wilson (1980) and Wilson and Head
(1981). These two papers set out the basic premises of
the RSD model that have been developed further in
subsequent papers (Head and Wilson, 1987; Fagents
and Wilson, 1993; Parfitt and Wilson, 1994, 1995,
1999; Parfitt et al., 1995). The essential idea set out in
these papers is that Strombolian and Hawaiian activity
represent end-members of a continuum of explosive
basaltic activity and that the form of activity that
occurs depends most fundamentally on the rise speed
of the magma beneath the eruptive vent (e.g., Table 1).
Volatiles exsolve from magma as it rises, and the
depth at which exsolution occurs depends on the
volatile species and the amount of dissolved volatiles
present (Wilson and Head, 1981). Gas bubbles that
form within the magma are always buoyant and rise
upwards through the magma at a rate that depends on
the size of the bubble and the magma rheology. In the
RSD model, it is assumed that if the rise speed of the
magma 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).
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
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
Stromboli, 1971
Kupaianaha, 1986
Etna, typical Strombolian activity
Heimaey, 1973
Kilauea Iki, 1959
Mauna Ulu, 1969
Miyakejima, 1983
Pu’u ‘O’o, 1983 – 1986
S
S
S
S
T*
H
H
H
H
0–3
8"10!3
3
<9.1
30
160
300
185
100
400
2.3
315
–
314
180
400
2000
315
0 – 0.008
3.5"10!3
0.01
0.0006 – 0.045
0.1
0.9
0.75
0.09
0.3
Swanson et al. (1979)
Chouet et al. (1974)
Parfitt and Wilson (1994)
Harris and Neri (2002)
Self et al. (1974), Blackburn et al. (1976)
Richter et al. (1970), Eaton et al. (1987)
Swanson et al. (1979)
Aramaki et al. (1986)
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.
far through the overlying magma before the magma
itself is erupted. In effect, the gas bubbles are
‘‘locked’’ to the magma in which they formed. Thus,
the model assumes homogeneous two-phase flow, in
which two different fluid phases are present (the
magma and gas) but in which the fluids behave as if
they are a single fluid phase. In this situation, the
growth of bubbles through diffusion and decompression (Sparks, 1978; Proussevitch and Sahagian, 1996)
and the continued formation of bubbles during ascent
will eventually lead to a situation in which the bubble
volume 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 – magma
mixture accelerates as it rises due to the decompression and expansion of the gas (Wilson and Head,
1981). After fragmentation, the acceleration becomes
much more pronounced due to the reduction in wall
friction caused by the fragmentation process and
results in the eruption of a continuous jet of gas and
magma clots at typical speeds of f100 m s!1 (Wilson
and Head, 1981). This continuous jet of material
produces the lava fountains characteristic of Hawaiian
eruptions (Fig. 1). As Parfitt and Wilson (1999)
pointed out, this proposed mechanism is essentially
the same as that envisaged as causing Plinian eruptions (Wilson et al., 1980). The material erupted in
Hawaiian fountains is, however, very coarse compared 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 and
products of Hawaiian eruptions to differ so greatly
from those of Plinian eruptions (see Parfitt and Wilson, 1999).
The RSD model further proposes that a different
eruption mechanism operates if the rise speed of
magma is relatively low. In this case, gas bubbles
within the magma will rise upwards through the
overlying magma and can segregate from the magma
in which the bubbles formed (Sparks, 1978; Wilson
and Head, 1981). The magma will contain a population of bubbles with a range of sizes—bubbles that
formed early will have grown by diffusion and decompression, while newly formed bubbles will be
much smaller. As the rise speed of a bubble depends
partly on its size, a runaway situation can be achieved
in which an initially larger bubble, rising faster than
the smaller bubbles, overtakes the smaller bubbles and
in doing so coalesces with them. In an extreme case,
such coalescence can lead to a single large bubble that
is as wide as the conduit rising through the overlying
magma (essentially a slug of gas). In the RSD model,
Strombolian eruptions are assumed to be the result of
this bubble segregation and coalescence process.
Wilson (1980) simulated these eruptions by considering what would happen in an open system in which
magma was rising slowly or was static. Cooling at the
top of the magma column causes the development of a
‘‘skin’’ with a finite strength. The skin strength will
depend on how much cooling occurs before the arrival
of the large bubbles. If the interval between bubble
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
83
the character of ‘‘transitional’’ eruptions—eruptions
that show aspects of both Hawaiian and Strombolian
eruptions. For typical basaltic eruptions the transition
between Hawaiian and Strombolian activity occurs at
rise speeds of f0.01– 0.1 m s!1 (Parfitt and Wilson,
1995). It is expected that Hawaiian eruptions will
occur at rise speeds much greater than this and
Strombolian activity will occur at much lower speeds
(Fig. 5).
3.2. The collapsing foam model
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).
arrival is short enough, each bubble will updome the
thin skin and burst through the top of the magma
column with minimal delay. If the interval between
the arrival of giant bubbles is longer, the skin will cool
and thicken and then more than one bubble may have
to arrive and become trapped before sufficient pressure is built up in an accumulating gas pocket to break
through the skin. In either case, the short time interval
between explosions suggests that the strength of this
skin is never very great. Repeated cycles of cooling
and gas accumulation followed by bubble bursting
lead to the series of transient explosions characteristic
of Strombolian eruptions.
Wilson and Head (1981) presented computer modelling to define the rise speed conditions in which
Strombolian and Hawaiian activity would be dominant. Parfitt and Wilson (1995) carried out more
detailed simulation of these conditions and discussed
A series of papers published in the 1980s and
1990s (Vergniolle and Jaupart, 1986; Jaupart and
Vergniolle, 1988; Jaupart and Vergniolle, 1989; Vergniolle and Jaupart, 1990; Vergniolle, 1996; Vergniolle
and Brandeis, 1996) put forward an alternative model
of the mechanisms of basaltic eruptions. The original
paper (Vergniolle and Jaupart, 1986) challenged the
assumption of ‘‘homogeneity’’ (i.e., homogeneous
two-phase flow) made in the RSD model and proposed that both Hawaiian and Strombolian eruptions
are the result of separated, two-phase flow, i.e.,
eruptions in which the flow of the magma and gas
phases are significantly different. They described the
different flow regimes that can prevail during separated, two-phase flow and proposed that Strombolian
eruptions result from slug flow and Hawaiian eruptions from annular flow (Fig. 6). The model was
developed further by Jaupart and Vergniolle (1988)
and Jaupart and Vergniolle (1989), wherein the conditions in which slug flow and annular flow can
develop were described.
In the CF model, magma is assumed to be stored
within some sort of storage area (a magma chamber or
Fig. 6. Schematic diagram depicting two examples of separated, two-phase flow: (a) slug flow and (b) annular flow.
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
a dike system) at a depth at which gas can exsolve
from the magma. The gas bubbles, once formed, rise
and accumulate at the roof of the storage area and
become close-packed into a foam layer. When the
foam layer reaches a critical thickness, it becomes
unstable and collapses, the bubbles coalescing to form
a gas pocket. The gas pocket then rises up an open
vent system and is erupted. In this model, Strombolian
eruptions represent repeated partial foam collapse
events, whereas Hawaiian eruptions occur from complete, almost instantaneous foam collapse. In a series
of laboratory experiments, Jaupart and Vergniolle
(1988) showed that if the viscosity of the liquid phase
is relatively low then the collapse of the foam is total
and the pocket of gas rises up the open conduit system
as a single body. The observed flow is annular in this
case and liquid in the annulus around the gas core is
dragged upwards with the gas and erupted (Fig. 6).
Jaupart and Vergniolle (1988) liken this behaviour to
that of a Hawaiian eruption. If the viscosity of the
liquid is higher, the foam collapses only partially and
forms a series of smaller gas pockets. These travel up
the conduit system periodically in slug flows and
burst at the surface. This behaviour is likened to
Strombolian eruptions.
4. Strombolian eruptions
The RSD and CF models do not differ very much
in their view of Strombolian activity. They both treat
these eruptions as occurring when gas segregates from
the magma and accumulates as a gas pocket that then
bursts at the top of an open magma column producing
the mild explosions characteristic of Strombolian
activity. This behaviour is consistent with direct
observations of eruptions (e.g., Vergniolle and Brandeis, 1994) and studies of the acoustic wave that
accompanies each explosion (Vergniolle and Brandeis, 1994, 1996; Vergniolle et al., 1996).
The main difference between the models concerns
where gas accumulation occurs within the magmatic
system. In the RSD model, the gas segregation is
considered to be progressive, with bubble coalescence
occurring because the magma rise speed is low. By
contrast, in the CF model bubbles are assumed to
accumulate at some depth forming a foam layer that
then 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. In
this model, there is no explicit link between magma
rise speed and eruption style.
Vergniolle and Jaupart (1986) challenged the assumption made in the RSD model that coalescence of
bubbles can occur progressively during magma ascent.
The RSD model assumptions are based on the observation that larger bubbles rise faster than smaller ones
(Fig. 7) and therefore have the opportunity to overtake
and coalesce with smaller bubbles. Wilson and Head
(1981) and Parfitt and Wilson (1995) assume that
bubbles ‘‘which initially lie within their own radius
of the vertical line of ascent of the large bubble will
make geometric contact with it’’ and will be absorbed
by the larger bubble. Vergniolle and Jaupart (1986)
drew on work by Taitel et al. (1980) that suggests that
coalescence only occurs when bubbles are rising fast
enough to deform during ascent. This work suggested
that only bubbles larger than f40 mm will be able to
coalesce with smaller bubbles. As bubbles only reach
sizes of 10 –50 mm by decompression and diffusion
Vergniolle and Jaupart (1986) argue that bubble coalescence cannot occur during ascent, i.e., that the RSD
model is invalid. More recent work by Manga and
Stone (1994), however, suggests that bubbles >5 mm
radius will deform during ascent and that such bubbles
enhance coalescence, i.e., that coalescence can occur
with bubbles of smaller size but that if larger bubbles
are present, models such as that of Wilson and Head
(1981) will underestimate the amount of coalescence
that occurs. So coalescence can occur for smaller
bubbles, but once bubbles have grown to sizes >5
mm enhanced coalescence will facilitate runaway
coalescence. Evidence from the study of bubble size
distributions in lava and tephra supports the idea that
bubble 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 two
bubbles will coalesce are obviously a simplification
of the real situation, the current evidence does suggest
that it is possible for coalescence to occur in rising
magmas as long as the bubbles have the opportunity to
move upwards relative to the magma, i.e., as long as
the magma rise speed is low. A link between explosive
basaltic eruption style and rise speed is evident from
field observations of recent eruptions (e.g., Table 1).
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
85
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.
Furthermore, Parfitt and Wilson (1995) suggested that
for typical magma volatile contents the transition from
Strombolian to Hawaiian activity occurs between rise
speeds of 0.01 and 0.1 m s!1 (Fig. 5). Comparison
with the examples given in Table 1 show that (a)
Strombolian eruptions are indeed associated with lower rise speeds and (b) that the transition in eruption
style occurs within the rise speed range predicted by
Parfitt and Wilson (1995). This would seem to support
their contention that coalescence is progressive and
dependent on the magma rise speed.
In contrast to the RSD model, the CF model of
Strombolian eruptions requires that gas segregation
and foam formation occurs during storage at depth
and thus can only operate under the particular circumstance where a storage zone exists beneath the vent at
a depth at which exsolution of one or more gas phases
is occurring. At Stromboli itself, there is evidence that
magma storage can occur at depths no greater than a
few hundred metres (Giberti et al., 1992). Each
explosion at Stromboli is associated with a distinct
seismic signal that consists of an initial compression
followed by a dilation and further compression (Neuberg et al., 1994; Chouet et al., 1999). Chouet et al.
(1999) have shown that the seismic source varies in
depth through the course of the explosion, starting at a
depth of 125 m, deepening to a depth of f350 m and
then shallowing again to a depth of around f200 m.
They suggest that this seismic event is caused by the
uprush of a gas pocket of the sort pictured in the CF
model, though it has yet to be demonstrated that the
details of the seismic signal are consistent with the
upward passage of a gas slug. There is therefore no
definitive answer at present as to which gas segregation process operates at Stromboli. In a broader
context, there is no reason why one model should
explain all Strombolian activity. It must be borne in
mind, however, that the CF model can only apply in a
particular combination of circumstances—where there
is a suitable storage zone at a depth where one of more
gas phase can exsolve—whereas the RSD model is
applicable to any open system.
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
Both models assume that shallow bubble bursting
causes the observed explosions so that the same
model of the bursting process is applicable in either
case. Wilson (1980) modelled the ejection of clasts in
Strombolian eruptions by assuming that the eruptions
result from the bursting of near-surface bubbles. The
model links the initial pressure in the bursting bubble,
the weight percentage of gas erupted and the maximum velocity achieved by the ejected matter (Fig. 8).
Pressures within the bursting bubbles are unlikely to
exceed 0.3 MPa (Blackburn, 1977; Sparks, 1978).
Observations at Heimaey and Stromboli suggest that
the weight percentage of gas in typical explosions is
10 – 30 wt.% (Blackburn et al., 1976), although
Chouet et al. (1974) note that some events at Stromboli can have gas contents as high as 94 wt.%. Direct
observations suggest that clasts are ejected in some
Strombolian eruptions at speeds of up to 230 m s!1
(Blackburn et al., 1976). At Stromboli itself, speeds
are more typically <100 m s!1 (Chouet et al., 1974;
Blackburn et al., 1976). Comparison of these values
with the model results in Fig. 8 shows that there is
broad consistency between the model predictions and
field observations.
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).
5. Hawaiian eruptions
The RSD and CF models present very different
views of the dynamics of Hawaiian activity. Two fundamental differences exist between the models. These
are concerned with the nature of the fluid flow at depth
and with the dominant volatile species driving the
eruptions. Each difference is considered here in turn.
5.1. Flow regimes in Hawaiian eruptions
The RSD model assumes that homogeneous twophase flow prevails. By contrast, the CF model
assumes that separated two-phase flow occurs. There
are a range of flow regimes in which separated twophase flow can occur, and the CF model assumes that
annular flow (Fig. 6) prevails during Hawaiian eruptions (Vergniolle and Jaupart, 1986). I now discuss the
implications of, and evidence for, each type of flow.
The assumption of homogeneous two-phase flow is
never strictly valid because gas bubbles are always
buoyant relative to the magma and thus are always
rising faster than the magma. However, as stated
above, if the rise speed of the magma is rapid the
bubbles do not rise far through the overlying magma
before the magma is erupted and in effect the gas
bubbles are ‘‘locked’’ to the magma, i.e., the assumption of homogeneous flow is valid. Thus, it is the rise
speed of the bubbles relative to the magma rise speed
which determines whether flow is homogeneous or
not. 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 homogeneity
depends, therefore, on the size of the bubbles involved
and on the magma rise speed at depth. Table 1 shows
that 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 the
magma become of the same order of magnitude as
the magma rise speed. For bubbles with radii <5 mm,
the bubble rise speed is always likely to be more than
an order of magnitude less than the typical magma rise
speed in a Hawaiian eruption. Thus, the assumption of
homogeneity is likely to be valid as long as the bubble
radii are less than f5 mm. So, the crucial issue is the
size of the bubbles within the rising magma.
Bubbles form in magma when the magma becomes
supersaturated in the volatile concerned. The depth
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
beneath the surface at which bubbles start to form
depends on the amount of dissolved volatiles and the
species of volatile involved (Wilson and Head, 1981).
Bubbles have typical radii of f10 Am when first
formed and then grow by diffusion and decompression
as the magma rises (e.g., Sparks, 1978). Sparks (1978)
presented numerical modelling of the growth of bubbles by diffusion and decompression and found that
maximum bubble sizes for H2O bubbles exsolving
from a basaltic magma depend on the amount of
dissolved water in the magma. For a gas content of
0.5 wt.% (a reasonable value for basaltic magmas), the
maximum radius is f5 mm. A more recent study by
Proussevitch and Sahagian (1996) gives maximum
bubble radii of 6 –8 mm for H2O bubbles in basaltic
magma using initial water contents of 1.52% and 3.03
wt.%, respectively. The sizes would be smaller for
more reasonable initial water contents. Thus, theoretical studies suggest that water bubbles forming in
rising basaltic magmas would typically have maximum radii of f5 mm for water contents typical of
most basaltic eruptions. The size of the largest bubble
is not, however, representative of the bubble population as a whole. Most bubbles will reach an intermediate size. For instance, Sparks (1978) showed that for
bubbles formed in basalt containing 1 wt.% water the
maximum radii would be f40 mm but the typical size
would be 1– 10 mm rather than 40 mm. Furthermore,
in the modelling studies just described, it is assumed
that bubbles continue growing all the way to the
surface. In practice, though, magma fragmentation will
occur beneath the surface and so the maximum bubble
size will not be achieved. These theoretical studies
suggest then that for typical water contents the typical
size of bubbles in basaltic magmas will be b5 mm.
Determining the bubble sizes in real magmas is
extremely problematic because the fragmentation process destroys much of the evidence of pre-fragmentation 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 and
Cashman, 1996). Bubbles contained in such samples
represent bubbles formed in magma clots after fragmentation but also bubbles which survived the fragmentation process and continued to grow after
fragmentation. Cashman and Mangan (1995) report
mean bubble radii for quenched lava from Kilauea
volcano of 0.1 – 0.15 mm and Mangan and Cashman
87
(1996) report radii for bubbles in basaltic scoria from
the Pu’u ‘O’o eruption of Kilauea of V2.5 mm. While
we cannot know for sure how such sizes relate to
bubble sizes prior to fragmentation, certainly such
studies do not provide any compelling reason to think
that bubbles sizes in basaltic magmas exceed the f5
mm size predicted by the theoretical studies.
Bearing all these points in mind it seems reasonable to assume that the radii of the majority of H2O
bubbles in magma with a water content V0.5 wt.% is
likely to be b5 mm. This means that in the case of
H2O bubbles in basaltic magma, the situation considered in all the RSD modelling, the assumption of
homogeneity is almost certainly valid.
The RSD modelling has only considered the situation of water exsolution. It is important to note,
though, that the situation would be different in the
case of CO2 exsolution. CO2 is less soluble in magma
than water and so exsolves and forms bubbles at
greater depths beneath the surface. This means that
CO2 bubbles experience more growth by decompression during ascent than do H2O bubbles. Fig. 9 shows
that 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.
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
likely to experience coalescence at rise speeds of V1
m s!1 (and so achieve final diameters anywhere in the
range 3 mm to 10 m). So, as coalescence is evidence
for separated flow, and as rise speeds typical of
basaltic eruptions are generally <1 m s!1 (Table 1),
we would expect separated two-phase flow to occur
during ascent. In the case of CO2 exsolution, then, it
would be invalid to assume that homogeneous twophase flow occurs. As I have stated, however, CO2
has not been considered as the ‘driving’ gas in any of
the RSD modelling. The issue of which volatile acts
as the ‘driving’ gas for Hawaiian eruptions is discussed in detail below.
Vergniolle and Jaupart (1986) argued that homogeneous two-phase flow does not occur during Hawaiian eruptions. They based this assertion on a
number of lines of evidence. The first is that the
characteristic radius of bubbles in Hawaiian eruptions
is 50 mm. Such a bubble would have a rise speed
through the magma of f1 m s!1 (Fig. 7) and thus a
speed that is comparable to the magma rise speed at
depth (Table 1). In such a situation, the bubbles would
tend to separate from the magma and the assumption
of homogeneous two-phase flow would break down.
As explained above, such bubble sizes are only likely
to be achieved in eruptions in which CO2 is the
driving gas. Thus, as just stated, the crucial issue is:
Which gas species ‘drives’ these eruptions? This is
discussed in more detail below but the initial conclusion that can be drawn is that homogeneous flow is
possible in Hawaiian eruptions driven by H2O but not
those driven by CO2.
This bubble size argument is not the only one
presented by Vergniolle and Jaupart (1986) to support
their contention that separated rather than homogeneous two-phase flow occurs during Hawaiian eruptions. Another argument concerns the volumes of gas
and magma present upon eruption. They note that
magma typically makes up less than f1% of the
erupted volume in a Hawaiian lava fountain and argue
that such a situation cannot be achieved in an eruption
in which homogeneous two-phase flow prevails. This
argument is fundamentally flawed, as can be demonstrated by the following simple calculations.
Consider a basaltic magma exsolving 0.5 wt.%
water during ascent. In an eruption with a magma
volume flux of 100 m3 s!1 (the situation treated by
Vergniolle and Jaupart, 1986) the mass of magma
erupted per second is 2.6"105 kg (assuming a magma
density of 2600 kg m!3) and so the mass of water
released from this magma during ascent is 1300 kg. At
atmospheric pressure this mass of gas occupies 8667
m3 (the density of steam at atmospheric pressure and
magmatic temperature is f0.15 kg m!3). So, at the
surface, the volume of the magma compared with the
volume of gas is f 1%, even though there has been
no concentration and segregation of the gas from the
magma prior to eruption. It is the mass of magma
relative to the mass of gas erupted that is crucial
evidence of segregation or homogeneity, not the
volume.
This point can be further tested using a real
example. Between 1983 and 1986, a series of 47 lava
fountaining episodes occurred at Pu’u ‘O’o, a vent on
the flanks of Kilauea Volcano (Heliker and Wright,
1991). During a number of episodes, measurements
were made of the mass of CO2 and SO2 released and
of the relative volumes of each gas species released in
each eruption (e.g., Greenland et al., 1985; Greenland,
1988). By combining these measurements, it is possible to estimate the mass of each gas species released
during each episode. As measurements were also
made of the volumes of lava erupted in each episode
(e.g., Wolfe et al., 1988), it is possible to assess
whether the amounts of gas released are in excess of
that originally dissolved in the magma: If the CF
model is valid, the gas mass fraction in the erupted
material will be considerably greater than that in the
magma at depth. Consider, then, one example from
this eruption. Episode 16 of the eruption (in March
1984) produced H2O at a rate of 40 000 tonnes/day
and CO2 at 3200 tonnes/day (Greenland et al., 1985).
The eruption lasted for 31 h, so a total of 51 700
tonnes (5.17"107 kg) of H2O and 4130 tonnes
(4.13"106 kg) of CO2 were released during this
episode. The volume of lava produced was 12"106
m3 (Wolfe et al., 1987), which, assuming a lava bulk
density of f2000 kg m!3, yields an erupted mass of
magma of 2.4"1010 kg. This yields gas mass fractions
in the erupted material of 0.22 wt.% of H2O and 0.017
wt.% of CO2. Residual gas contents in Kilauean lavas
are typically 0.10 wt.% H2O and 0.015 wt.% CO2 for
Kilauea (Gerlach and Graeber, 1985), which yields
estimates of the gas content within the magma prior to
eruption of 0.33 wt.% H2O and 0.032 wt.% CO2.
Similar calculations for other Pu’u ‘O’o episodes
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
produce similar results. Independent estimates of
volatile contents based on fluid inclusions studies
give H2O contents for the Pu’u ‘O’o eruption of
0.39 –0.51 wt.% for tephra from the high fountain
events and 0.10 – 0.28 wt.% for spatter from less
vigorous activity (Wallace and Anderson, 1998). So
the gas released during the eruptions is consistent with
the gas contents contained within the magma prior to
eruption, and, thus, there is no evidence to support the
idea that gas concentration and separation occurred
prior to eruption. The values instead support the
contention of the RSD model that Hawaiian eruptions
result from homogeneous two-phase flow. It is also
worth noting that in this eruption, the volume percentage of the magma in the lava fountain is f0.35%
(calculated in the same way as in the example given
above). This supports my contention that, even in a
homogeneous eruption, the volume percent of magma
in the fountain can be <1%, and, thus, that the
statement by Vergniolle and Jaupart (1986) that this
is evidence of separated flow is erroneous.
More fundamentally, Vergniolle and Mangan (2000)
describe a distinctive pattern of behaviour observed
during the 1959 Kilauea Iki eruption in which magma
was simultaneously erupted in a lava fountain and
drains back around the edges of the vent. They assert
that this observation is evidence for annular flow and
that simultaneous drainback and eruption is not possible during homogeneous flow. Wilson et al. (1995)
have previously published a model in which simultaneous drainback and eruption occurs during homogeneous flow. This issue has been examined again by
Lionel Wilson (unpublished calculations, 2003) and his
findings are contained in Appendix A. His treatment
shows that it is perfectly possible to explain the
observation of simultaneous drainback and eruption
at Kilauea Iki in terms of homogeneous flow.
In conclusion, arguments presented as evidence
that separated two-phase flow must occur during
Hawaiian eruptions do not stand up to detailed scrutiny. Existing observational evidence, instead, supports the contention that Hawaiian eruptions occur
as the result of homogeneous two-phase flow.
5.2. Dominant volatile species
The other fundamental difference between the two
models concerns the species of volatile that typically
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‘drives’ Hawaiian eruptions. The RSD model assumes that the ‘driving’ gas is H2O, whereas the
CF model assumes that it is CO2. This issue is crucial
because, in the situations considered in the published
models, the RSD model is incompatible with the
driving gas being CO2 and the CF model is incompatible with the driving gas being H2O. It is possible,
therefore:
(a) to distinguish between the two models for
specific eruptions provided observational evidence
exists about the species and mass fractions of gas
released in the eruption (see below); and
(b) that each mechanism could be valid in different
volcanic situations depending on the gas species, mass
fraction present in the magma, and the storage history
of the magma as it ascends.
Let us examine why the two models assume
different ‘driving’ gas species and then look at which
situation is most common in actual eruptions.
5.2.1. H2O as the ‘driving’ gas
The RSD model assumes in all cases that the gas
driving Hawaiian eruptions is H2O. This is for two
main reasons:
(1) Water is usually the most abundant volatile
present within basaltic magmas (e.g., Wallace and
Anderson, 2000).
(2) Water only exsolves from basalts at shallow
depths (typically a few hundred metres) beneath the
surface (Sparks, 1978; Wilson and Head, 1981 ). This
means that the water will usually have had little
opportunity to exsolve and escape from the magma
as it ascends towards the surface, and thus its exsolution from the magma near the surface must play
some role in the eruption dynamics.
5.2.2. CO2 as the ‘driving’ gas
The CF model assumes that the driving gas is CO2.
This is because in this model gas bubbles must
accumulate as a foam layer in a storage area at depth
in order for separated two-phase flow to occur. For
this to be possible, it is necessary that:
(1) Storage occurs at a depth where exsolution of
the ‘driving’ gas can occur.
(2) The roof of the storage zone has sufficient
area to allow the accumulation of a sufficient volume
of foam to be consistent with observed erupted
volumes.
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
The shallow exsolution depths of H2O make it
extremely unlikely that these criteria will be met,
whereas CO2 exsolves at depths of several kilometres
beneath the surface and thus within zones where
large-scale storage often occurs.
Although it is possible for CO2 to be exsolved and
stored in the way the CF model suggests, Parfitt and
Wilson (1994) have pointed out that a problem with
this model is that it neglects the effects of water
exsolution, occurring as the foam ascends, will have
on eruption. Their argument is that, even if the
eruption were driven from depth by foam collapse,
the magma that is carried up and erupted will still
contain dissolved water (water being abundant in
basalts). This water will exsolve from the magma as
it reaches shallow levels and thus this water must play
some role in driving the eruption. Vergniolle and
Jaupart (1986) have argued that, though the water
exsolves from the magma as it rises, ‘‘the small
vesicles formed through exsolution in the conduit
cannot coalesce and can therefore reach high volume
fractions without leading to a change in flow regime’’.
In other words, water bubbles do form in the magma
as it rises towards the surface but this exsolution is
‘‘passive’’ because it generates magma clots with high
vesicularity, but this material does not fragment or in
any way drive the eruption. This explanation appears
to be flawed in two ways:
(1) In the example given above, it was shown that
the volume of the water exsolved from the rising
magma compared with the volume of the magma from
which it exsolved is such that at the vent the magma
represents V1% of the total volume at the vent. If the
exsolving water is held, as Vergniolle and Jaupart
(1986) suggest, as small bubbles within the magma
this means that the vesicularity of the erupting magma
would have to exceed 99% in all of the erupted
magma. The most vesicular material generated in
Hawaiian eruptions, reticulite, has vesicularities ranging up to 98% (Thomas et al., 1994) but reticulite
makes up only a small proportion of the material
produced in Hawaiian eruptions.
(2) If the water is trapped in small bubbles within
the clasts, then it would not be released in the eruption
plume. Yet, in the Pu’u ‘O’o eruption, which Vergniolle and Jaupart (1990) and Vergniolle (1996) use as
a test case for the CF model, 85% by volume of the
measured 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 than
H2O.
5.3. Initial conclusions
The RSD and CF models of Hawaiian eruptions
make fundamentally different assumptions about the
flow regime prevailing at depth and about the
volatiles driving the eruptions. Both models could
potentially apply in different situations depending on
the volatiles species, bubble sizes, storage history
and magma rise speeds concerned. Neither model
appears to have any fundamental flaw. However, the
usefulness of a model depends not on its theoretical
validity but on how well it reproduces the activity
which occurs in nature, and in this respect, observational data examined thus far favour the RSD model
over the CF model.
Both models have been used to look at the same
test case—the 1983 – 1986 Pu’u ‘O’o eruption—and
both models purport to explain the observational data
collected during that eruption. As the two models
make fundamentally different assumptions and predictions about Hawaiian activity, it is impossible that
both models are consistent with the same set of
observational data. For this reason, I will now examine, in detail, how the models have been tested using
evidence from this eruption.
6. The 1983 –1986 Pu’u ‘O’o eruption of Kilauea
Volcano
This eruption started in January 1983 with the
emplacement of a feeder dike laterally from the
summit magma chamber into Kilauea’s East Rift
Zone (ERZ) (Klein et al., 1987; Wolfe et al.,
1987). The dike fed a fissure eruption on the middle
ERZ at distances of 14 –22 km from the summit.
Dike emplacement and eruption were accompanied
by major deflation of the summit magma chamber
(Fig. 10). After about a month, during which the
summit magma chamber reinflated (Fig. 10), a new
eruptive episode began in the same area of the ERZ
fed through the same feeder dike (Wolfe et al.,
1987). A pattern of activity developed in which
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
91
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).
eruptions typically f1 day in duration occurred
associated with deflation of the summit and punctuated by repose periods of f3 weeks during which
the summit reinflated. By the 4th eruptive outbreak,
activity had become concentrated at one eruptive
vent subsequently named Pu’u ‘O’o (Wolfe et al.,
1988). The eruption continued this cyclic pattern
until July 1986 when the location and behaviour of
activity switched to a vent 3 km further down rift
(Heliker and Wright, 1991). Eruption at this new
vent, Kupaianaha, was characterised by continuous
minor explosive activity and slow outpouring of
lava. The eruption was monitored in great detail by
the staff of the Hawaiian Volcano Observatory
(HVO) and their observations have been published
in a number of papers (e.g., Dvorak and Okamura,
1985; Wolfe et al., 1987; Greenland, 1988; Okamura
et al., 1988; Wolfe et al., 1988; Heliker and Wright,
1991; Heliker et al., 2003). Thus, this is an eruption
for which there is an exceptionally large and complete set of field and geophysical observations with
which to test the eruption models.
Vergniolle and Jaupart (1990) and Vergniolle
(1996), and Parfitt and Wilson (1994), have presented very different, and mutually incompatible,
models of this eruption based on the RSD and CF
models described above. I now compare the two
models by looking at some of the key character-
istics of the eruption that both models seek to
explain.
6.1. The cyclic character of the eruption
A key feature of the eruption was its repetitive,
cyclic character. Each eruption was preceded by a
repose period during which slow inflation of the
summit occurred accompanied by minor explosive
activity at the vent and each eruption was accompanied by rapid deflation of the summit in association
with high lava fountaining and generation of lava
flows (Fig. 10). Dvorak and Okamura (1985) observed that the deflation rate increased as the eruption
sequence continued while the duration of each eruptive episode gradually decreased (Fig. 11). They
suggested that this behaviour reflected an evolution
of the magma system feeding the eruption. Parfitt and
Wilson (1994) noted that the deflation during each
episode showed a characteristic pattern in which the
rate was initially low, increased to a peak value, and
then declined approximately exponentially (Fig. 12).
Parfitt and Wilson (1994) adopted the interpretation
that inflation and deflation of Kilauea’s summit magma chamber occurs primarily as the result of the inflow
and outflow of magma (e.g., Dzurisin et al., 1984;
Dvorak and Dzurisin, 1993). The idea is that magma is
supplied to the magma chamber from deeper levels at a
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
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.
fairly constant rate (estimated at f3 m3 s!1; Dzurisin
et al., 1984; Dvorak and Dzurisin, 1993). This leads to
slow chamber inflation during times when no high
fountaining was occurring. When an eruption occurs,
magma is withdrawn and erupted at a rate that exceeds
the inflow rate from the mantle and thus rapid deflation
occurs. Starting with this premise, Parfitt and Wilson
(1994) examined the deflation patterns that would
result from flow of magma through feeder dikes of
various geometries. By assuming that the dike was of
non-uniform geometry they were able to reproduce the
observed deflation patterns (Fig. 12), to explain why
the eruptive behaviour was cyclic and to examine the
factors which determined when each episode started
and stopped. In their model, the cyclic nature of the
eruption is determined by the details of the subsurface
storage and movement of magma not by the eruption
style (as is the case in the CF model—see below).
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
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).
Instead, the Hawaiian character of the eruption is
controlled by the cyclicity because the cycles are
related to variations in flow rate through the dike
system and thus to the rise speed of the magma beneath
the vent. The flow rate through the dike system is
directly correlated with the deflation rate; thus the flow
rate rapidly increases as cooled magma is pushed
through the dike system, reaches a peak and then
declines exponentially (Fig. 12). Such a pattern is
93
common in basaltic eruptions where the initial high
pressure in the chamber allows high flow rates near the
start of an eruption, flow rate gradually declining as the
chamber pressure declines (Wadge, 1981). In the case
of the Pu’u ‘O’o high fountaining episodes, the flow
rate through the dike system, and hence the rise speed
beneath the vent, is sufficiently high to allow homogeneous two-phase flow. During the repose periods
between high fountain episodes, the flow rate through
the dike system becomes negligible and so the rise
speed beneath the vent is close to zero. In this
situation, gas segregates from the magma within the
vent and rises to the surface giving rise to the minor
explosive activity which characterised the repose periods (Wolfe et al., 1987, 1988).
Vergniolle (1996) interpreted the cyclic pattern of
the eruption and the associated inflation/deflation
patterns in a very different way. In her model at least
part of the inflation and deflation is viewed as resulting from changes in gas volume in the summit magma
chamber. Inflation is related to exsolution of CO2
from the stored magma and its accumulation as a
foam layer at the roof of the magma chamber. Collapse of this foam layer triggers eruption of magma
and deflation of the magma chamber. There are a
number of problems with this model:
(1) As mentioned above, observation shows that
CO2 constitutes an average of only f3% of the total
volume of gas released in the eruptive episodes
(Greenland, 1984; 1988). The majority of the gas
released is magmatic water (85%), which must play
a significant role in the eruption but cannot be
collected as a foam prior to these eruptive episodes
(see above).
(2) The Vergniolle (1996) model requires that CO2
exsolving within the magma chamber should become
trapped at the chamber roof forming the foam layer
that ultimately causes each fountaining episode. Gerlach and Graeber (1985), Gerlach (1986) and Gerlach
and Taylor (1990) have studied gas release from the
Kilauea system and show that magmas erupted on the
rift zones, including the Pu’u ‘O’o magma, are
depleted of CO2 prior to eruption (consistent with
Point 1). They propose that CO2 is lost from the
magma chamber during storage and show that the
measured daily release rates of CO2 (1.6 to 3.6"106
kg day!1—Greenland et al., 1985) from the summit
region are consistent with calculated release rates that
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
are based on the influx of magma into the chamber
over 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 is
lost from the magma chamber through non-eruptive
degassing. So, although CO2 does exsolve in the
magma chamber, the observational evidence suggests
that it is lost from the chamber by degassing rather
than being trapped at the roof of the chamber to
produce a foam layer as the CF model requires.
(3) The model of Vergniolle and Jaupart (1990) and
Vergniolle (1996) explains the change in eruptive
behaviour in July 1986 from cyclic fountaining to
continuous lava outpouring as being the result of a
decline in gas volume through time. Values for the
declining gas release in each episode are shown in Fig.
7 in Vergniolle and Jaupart (1990). These data were
derived by Vergniolle and Jaupart (1990) from measurements of the maximum fountain height recorded for
each episode and the total eruption duration made by
HVO staff. The gas volume was calculated by obtaining the exit velocity for each episode from the fountain
height and then multiplying this by the vent crosssectional area and the eruption duration. There are
several reasons why this is inaccurate way of estimating the gas volume released:
(a) The maximum fountain height is not representative of the episode as a whole and represents a
time when the exit velocity is a maximum. This is
clear from time-lapse data collected by HVO, some
of 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 greatly
to the impression that gas volume declines through
time, result from using the long durations of these
episodes to calculate the volumes. Observational
evidence shows, however, that the vents were not
active throughout the duration of the episode and
thus the use of the total durations to calculate the
volumes 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 Vergniolle
and Jaupart (1990) are unreliable can be verified by
comparison with observational data. Their gas volumes range from 3.1"109 m3 during the initial stages
of the eruption to 0.6"109 m3 for the last high
fountaining episode. Such values are almost an order
of magnitude greater than volumes calculated from
measurements of gas mass release during the eruptive
episodes (Table 2). Thus, the data presented in Vergniolle and Jaupart (1990) as evidence for a decline in
gas release through the eruption sequence must be
treated with scepticism. Furthermore, observational
evidence does not support the idea that less gas was
being released during the continuous phase of activity
at the Kupaianaha vent compared with the high fountaining phases at Pu’u ‘O’o which preceded it. Measurements of SO2 emission rates during the Kupaianaha
eruption show that the rates are 5– 27 times less than
the emission rates during the high fountaining episodes
(Andres et al., 1989). However, eruption rates at
Kupaianaha are also lower, averaging 0.35"106 m3
day!1 compared with f7.7"106 m3 day!1 during the
high fountaining episodes (Heliker et al., 2003), i.e.,
22 times less than during high fountaining. Thus, the
decreases in emission rates and eruption rates are
comparable. Averaged over time the continuous slow
release of gas and magma from Kupaianaha actually
released as much gas as the higher rate but short-lived
high 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
Gas mass
species released
per day
(tonnes/day)
Total gas
Gas density Gas volume
mass released (kg m!3)
erupted (m3)
during the
episode (kg)
(a) Gas release during
58,000
H2 O
SO2
27,000
CO2
4700
HCl
330
HF
200
Total
episode 15. The episode duration was 19 h
4.59"107
0.15
3.06"108
7
2.14"10
0.53
4.03"107
3.72"106
0.36
1.03"107
5
2.61"10
0.3
8.71"105
1.58"105
0.16
9.90"105
3.59"108
(b) Gas release during
H2 O
40,000
SO2
18,000
CO2
3200
HCl
220
HF
140
Total
episode 16. The episode duration was 31 h
5.17"107
0.15
3.44"108
7
2.33"10
0.53
4.39"107
4.13"106
0.36
1.15"107
5
2.84"10
0.3
9.47"105
1.81"105
0.16
1.13"106
4.02"108
Gas masses released are taken from Greenland et al. (1985).
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
that any less SO2 was being released from the magma
after the change in eruption style. Though no evidence
is available for release of other volatiles before and
after the change in eruptive character, it seems unlikely
that the overall release rate should decline while the
SO2 release rate remains unchanged.
6.2. Fountain heights and exit velocities
Measurements were made by HVO staff of the
maximum and average fountain heights for each
eruptive episode (Wolfe et al., 1987, 1988). Wilson
and Head (1981), Head and Wilson (1987) and Parfitt
et al. (1995) have related fountain heights to the
eruption rate and gas content of the erupting magma
using the RSD model by calculating the exit velocity
of the erupting mixture and assuming that the larger
clasts (which form the main part of the fountain)
behave ballistically. When this model is applied to
the Pu’u ‘O’o eruption, it suggests that the observed
fountain heights would be produced if the water
content of the erupting magma is 0.32 wt.%. This is
consistent with independent estimates that range from
0.21% 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 the
exit velocities or fountain heights of the eruption.
6.3. Volumes and durations
Observational evidence collected by HVO staff
(Heliker and Mattox, 2003) provides constraints on
the volumes of lava produced during each episode (2
to 38"106 m3), on the average eruption rates (12 to
489 m3 s!1) and on the duration of each episode (5 to
290 h). Parfitt and Wilson (1994) used the RSD model
to simulate the Pu’u ‘O’o episodes and the model can
adequately explain the observed values of each of
these parameters. It has never been demonstrated that
the CF model can explain these observed eruption
volumes or durations.
6.4. Change in eruption character
A further fundamental difference between the two
models is highlighted by the change in eruption
character that occurred in July 1986, when the site
95
and style of eruption changed abruptly. A fissure
system opened up that extended downrift from Pu’u
‘O’o and activity from this system eventually localised at a new vent later named Kupaianaha (Heliker
and Wright, 1991). The change in locality corresponded to the end of the cyclic lava fountaining
activity seen at Pu’u ‘O’o. Instead, the activity became continuous and occurred at a much slower
eruption rate (f5 m3 s!1). A low lava shield with a
lava lake at the top gradually developed. Lava within
the lake circulated and degassed (Fig. 13a) and was
continually drained from the lake through a complex
tube system (Mattox et al., 1993). Though some
degassing occurred at Kupaianaha, the bulk of the
gas release occurred through the Pu’u ‘O’o vent as
was evident from observation of a plume constantly
rising from the cone (Fig. 13b) and confirmed by
direct measurements (Andres et al., 1989). This
change in character is similar to ones which occurred
during the 1969 –1974 Mauna Ulu eruption (Swanson
et al., 1979; Tilling et al., 1987). Vergniolle and
Jaupart (1990) and Vergniolle (1996) propose that
changes from high fountaining to continuous eruption
in each of these eruptions represent a change in
eruption style from Hawaiian to effusive. Parfitt and
Wilson (1994) have argued that the change in eruption
character represents a change from Hawaiian to
Strombolian. Thus, there is a basic disagreement
about how to interpret the observed activity as well
as a disagreement on the causes of the change. Part of
the problem arises because of the unusual nature of
gas release during the Kupaianaha eruption. The
magmatic plumbing system established between Pu’u
‘O’o and Kupaianaha in July 1986 allowed shallow
degassing of the magma through the Pu’u ‘O’o vent
prior to magma eruption at Kupaianaha. This means
that although there was minor explosive activity at
Kupaianaha (Fig. 13a), the overflow of the lake can be
interpreted as effusive activity. Parfitt and Wilson
(1994) argue, however, that the eruption is Strombolian because the observation of significant gas release
and spattering within the Pu’u ‘O’o cone (Andres et
al., 1989; Mangan et al., 1995) shows that gas is
segregating in significant quantities and giving rise to
explosive activity at the top of the magma column.
Effusive activity corresponds to events where no
significant gas segregation is occurring. This is more
evident when considering the Mauna Ulu eruption.
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
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).
Here, after the change from high fountaining to
continuous activity, eruption was associated dome
fountaining, gas-pistoning, spattering and low fountaining, all of which indicate that gas release and
minor explosive activity was associated with the
production of lava (Swanson et al., 1979).
Vergniolle and Jaupart (1990) and Vergniolle
(1996) argue that the change in character observed
in the Pu’u ‘O’o eruption occurred because of a
progressive decline in the gas accumulation rate in
the magma chamber as the magma became depleted of
gas. As we have seen above, the evidence that the gas
release rate is smaller after the change in eruption
character is unconvincing. Furthermore, this argument
is based on the idea that the magma chamber is not
being resupplied with magma. Many studies suggest
that the magma chamber is fairly continuously resupplied with magma (e.g., Dzurisin et al., 1984; Dvorak
and Dzurisin, 1993). Furthermore, if the magma
chamber were isolated in this way through the course
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
of the Pu’u ‘O’o – Kupaianaha eruption this would be
reflected in the temperature and chemistry of the
erupting lava. Instead, the most recent study of the
Pu’u ‘O’o – Kupaianaha eruption (Thornber, 2003)
reinforces the idea that resupply of magma from the
mantle has occurred throughout the eruption and
shows that what long-term changes have occurred in
the eruption temperature and magma composition
represent the increasing involvement of mantle magma—the exact opposite trend to that which would be
seen if the magma chamber were isolated. Thus, all
the available evidence contradicts the idea of an
isolated magma chamber and a decline in the supply
of gas to the eruption.
Parfitt and Wilson (1994) argued that the change in
character from intermittent fountaining to continuous
eruption represents a long-term evolution of the dike
geometry and thermal state, consistent with the observations and interpretation of Dvorak and Okamura
(1985). The change from high fountaining to minor
explosive activity, gas release and lava outpouring is
seen as being a result of the decrease in magma
eruption rate and rise speed that accompanied the
change from intermittent to continuous eruption. That
the eruption rate was lower during the continuous
phase is indisputable. Observations made during the
high fountaining phases at Pu’u ‘O’o and during lava
outpouring at Kupaianaha show that the typical volume flux during high fountaining was f7.7"106 m3
day !1 compared with f0.35"106 m 3 day!1 at
Kupaianaha (Heliker et al., 2003). Parfitt and Wilson
(1994) used these fluxes to estimate the magma rise
speed as being f0.3 m s!1 during the high fountaining episodes and f0.01 m s!1 during the Kupaianaha
eruption. Parfitt and Wilson (1995) have shown that,
for magma gas contents and viscosities observed
during the Pu’u ‘O’o – Kupaianaha eruption, the
RSD model predicts that at a rise speed of 0.3 m
s!1, the activity should be Hawaiian, and at a rise
speed of 0.01 m s!1, the activity should be Strombolian, consistent with the observed change in eruption
character.
6.5. Discussion
I have discussed this one eruption in detail for
several reasons. Both the RSD and CF models have
been tested using the Pu’u ‘O’o eruption. It is an
97
excellent test case because the range of data collected during the eruption is exceptional and the quality
of the data is extremely good. The eruption provides,
therefore, a unique opportunity to examine a Hawaiian eruption sequence in great detail. Over the past
f10– 15 years, the CF model has come to be the
more widely accepted model of the dynamics of
Hawaiian eruptions (e.g., Sparks et al., 1994; Vergniolle and Mangan, 2000). Parfitt and Wilson (1994)
pointed out general problems with the model and I
have detailed in this paper the ways in which the CF
model is inconsistent with the observations made
during the Pu’u ‘O’o eruption, the eruption which
the authors of the CF model elected to use as their
test case (Vergniolle and Jaupart, 1990; Vergniolle,
1996). Furthermore, I have shown that the RSD
model, when applied to the same eruption, produces
results that are consistent with a wide range of
observations. My point is not that the CF model is
inherently flawed but, instead, that any model has
value only if it actually reproduces the key features
of the system under examination. In the case of the
CF model as applied to Hawaiian eruptions, the
model is inconsistent in many ways with the observational evidence.
7. Transitional eruptions
Some basaltic eruptions exhibit behaviour that
appears to display features of both Hawaiian and
Strombolian activity and are referred to as ‘‘transitional’’ eruptions (Parfitt and Wilson, 1995). The 1973
eruption of Heimaey in Iceland is an example of this
type of event (see above). Another example is the 6th
to 29th July 1975 stage of the Great Tolbachik Fissure
eruption. This eruption is described as Strombolian –
Plinian by Maleyev and Vande-Kirkov (1983). They
say that the eruption ‘‘ejected a continuous stream
of pyroclastic material to a height of 8 – 11 km’’.
Tokarev (1983) describes the eruption as a ‘‘non-stop
vertical jet of incandescent gases, ash, cinder and
volcanic bombs’’ that reached ‘‘a height of 1 –1.5
km, while above it, to a height of 6 –8 km, rose a
billowing cloud of ash blown sideways by the wind’’.
Although there were pulsations in the eruption jet,
eruption was continuous (Tokarev, 1983). Clasts up to
2– 3 m in diameter were produced and accumulation
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
of this material around the vent generated a cinder
cone but did not produce any lava flows (Maleyev and
Vande-Kirkov, 1983; Tokarev, 1983). Thus, this eruption, like the Heimaey eruption, exhibits characteristics of both Hawaiian and Strombolian activity.
In addition to exhibiting characteristics of both
Hawaiian and Strombolian styles, basaltic eruptions
frequently exhibit rapid transitions between these endmember types of activity. For example, Bertagnini et
al. (1990) described such behaviour during the 1989
eruption of Etna. They describe how each ‘‘eruptive
episode began with a weak strombolian activity, with
lava clasts thrown just beyond the crater rim.’’ As the
magma level rose in the vent, the explosions became
‘‘more frequent and more violent’’ until they were
‘‘nearly continuous’’. This activity then evolved into
activity which was ‘‘typically hawaiian, with lava
fountains up to 100 –200 m in height’’ and which
generated lava flows.
Parfitt and Wilson (1995) used the RSD model to
investigate the nature of transitional eruptions and the
conditions which give rise to them. The results of this
modelling (Fig. 5) show that transitional activity is
expected to arise primarily when the magma rise
speed is intermediate between that of Hawaiian and
Strombolian eruptions (Table 1) and furthermore that
gradual changes in rise speed will give rise to a
progressive change in eruption character from Strombolian to Hawaiian or vice versa. The time frame over
which the eruption character changes is then a function of the rate at which the magma rise speed
changes. The modelling suggests that, for example,
as magma rise speed increases the eruption character
would change from widely spaced Strombolian explosions to more frequent explosions with the strength of
the explosions being fairly constant. Then as the rise
speed increases further the explosions will become
more closely spaced in time still and will rapidly
increase in violence throwing clasts much higher in
the air. Continued increase in rise speed then gives
rise to continuous high lava fountaining activity. This
pattern of behaviour is remarkably similar to that
described above for the 1989 Etna eruption.
The model developed by Parfitt and Wilson (1995)
does not explicitly look at the behaviour of the finer
material ejected in the eruption. A characteristic of
many transitional eruptions is the high sustained
eruption plume they develop. Presumably, this arises
because the short time gap between Strombolian
explosions means that from the point of view of the
heat output the activity is continuous and can thus
generate a sustained plume. The height of the plume is
much greater than that associated with Hawaiian
eruptions and this difference is expected to be related
to the difference in grainsize of the erupted material
compared with a pure Hawaiian eruption (Parfitt and
Wilson, 1999).
The CF model has not been used to look at
transitional eruptions or to explain how changes in
gas accumulation rates or magma viscosity can
account for the types of rapid transition in eruption
style which are a common feature of basaltic activity.
As we have seen, the sudden change in eruption
character which occurred during the Pu’u ‘O’o –
Kupaianaha eruption is explained in the CF model
by a gradual change in gas accumulation which
occurs over a period of years. Changes in character
from Strombolian to Hawaiian and back again, like
those described at Etna, can occur on time scales of
only hours.
8. Conclusions
During the past 20 years, two very different
models have been proposed to explain the dynamics
of explosive basaltic eruptions—the rise speed dependent 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 and
Jaupart, 1986, 1990; Jaupart and Vergniolle, 1988,
1989; Vergniolle, 1996). Both models are in current
usage, often without acknowledgement that an alternative model exists. In this paper, I have examined
the basic assumptions made in each model and
shown that neither model is flawed in any fundamental way, i.e., that each model could apply in a
given set of conditions. The purpose of a model is,
however, to represent some behaviour that we observe in nature. Thus, the value of any model
depends on how well it can reproduce this real
behaviour. Volcanologists examining explosive basaltic activity are at a considerable advantage compared with those interested in more violent, silicic,
events in that basaltic explosions occur frequently
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
99
and are relatively safe to monitor. Thus, large bodies
of literature and data are available to test the two
models. I have examined the way in which each
model has been used to explain Strombolian, Hawaii
and transitional eruption styles, and in doing so have
arrived at the following conclusions.
exist beneath the vent in order to operate whereas the
processes invoked by the RSD model can occur in any
open system as long as the rise speed of the magma is
slow or negligible.
8.1. Strombolian eruptions
In the case of Hawaiian activity the RSD and CF
models present very different and mutually exclusive
views of the eruption dynamics. The models make
fundamentally different assumptions about the flow
regime which prevails during eruption: The RSD
model assumes homogeneous two-phase flow and
the CF model assumes segregated two-phase flow.
They also assume different ‘driving’ gases—in typical
conditions, the RSD model will only work if H2O is
the dominant gas and the CF model only works if CO2
is the driving gas. My examination of the two models
suggests that neither model is fundamentally flawed
and thus that either might operate in different starting
conditions.
Both models have been tested on the same eruption
(the 1983– 1988 Pu’u ‘O’o eruption of Kilauea volcano). I have examined in detail how well each model
fits with the behaviour observed during this eruption
and have shown that the CF model (Vergniolle and
Jaupart, 1990; Vergniolle, 1996) fails to explain many
key aspects of the eruption. For instance, observations
show that the dominant gas released in the eruption is
H2O (85%) and only 3% of the released gas is CO2
which the CF model assumes is the driving gas.
Furthermore, observational evidence does not support
the contention that gas segregation and concentration
has occurred at depth prior to eruption but is instead
consistent with the homogeneous flow assumed in the
RSD model. The RSD model can also explain many
other aspects of the eruptive behaviour such as the
characteristic deflation pattern observed during each
eruption, the long-term changes in the duration and
eruption rates observed during the eruption sequence,
and the change in eruption character which occurred
in 1986.
The problems highlighted by the application of
the CF model to the Pu’u ‘O’o eruption are
sufficiently far-reaching that they draw the validity
of the model in its application to other Hawaiian
eruptions into serious question. I would therefore
urge considerable caution in the use of this model
Both models agree that Strombolian eruptions
result from the accumulation and bursting of a gas
pocket at shallow depths within an open magmatic
system. This is consistent with direct observations
(e.g., Vergniolle and Brandeis, 1994) and with acoustic wave studies (Vergniolle and Brandeis, 1994,
1996; Vergniolle et al., 1996). The models diverge,
however, in the assumptions they make about where
the gas segregates from the magma. In the RSD
model segregation is thought to be progressive and
occurs because of the low rise speed of the magma
beneath the eruptive vent. Such a model is consistent
with observational evidence (Table 1) which shows
that Strombolian eruptions are associated with low
magma rise speeds. The CF model assumes that gas
segregation occurs at depth in a magma chamber or
storage zone and that accumulation of this gas as a
foam layer and its partial collapse give rise to a slug
of gas which rises up through the vent system and
bursts through the top of the magma column. Thus,
the CF model requires a special set of conditions to
exist whereas the RSD model is applicable to any
open system.
Recent studies of seismicity at Stromboli (Neuberg
et al., 1994; Chouet et al., 1999) show that earthquakes are generated in direct association with each
Strombolian explosion. The source of such earthquakes is located several hundred metres beneath
the surface. It has been suggested that these earthquakes are caused by the collapse and movement of
the gas slug at depth. Further modelling work is
needed to show that the seismic waves generated in
Strombolian explosions are generated in this way but
such work provides a potential way to determine
whether gas accumulation and foam formation occurs
at Stromboli. It should be stressed, though, that there
is no reason why both models should not be applicable in different systems and it must be understood that
the CF model requires a particular set of conditions to
8.2. Hawaiian eruptions
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E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
in treating the dynamics of Hawaiian eruptions. It
must also be borne in mind, though, that the models
have only been tested in detail on this one eruption.
While the evidence from the Pu’u ‘O’o eruption
supports the RSD model as the most valid treatment, more testing on other Hawaiian eruptions is
needed to resolve the issue of which model is most
applicable to Hawaiian eruptions and, indeed, to
explosive basaltic eruptions in general. It should be
noted, though, that like with Strombolian eruptions
the CF model requires a particular set of conditions
to prevail beneath the vent in order to be applicable
(a large enough storage zone at a depth where gas
is exsolving) whereas the RSD model has no such
limitations.
8.3. Transitional eruptions
I have noted that some explosive basaltic eruptions
show features of both Hawaiian and Strombolian
eruption styles and these have been denoted ‘‘transitional’’ eruptions by Parfitt and Wilson (1995). In
addition, basaltic eruptions frequently show rapid
transitions in character from Strombolian to Hawaiian
and vice versa. The RSD model was used by Parfitt
and Wilson (1995) to investigate the conditions in
which transitional eruption styles arise. They suggested that transitional eruptions arise when the
magma rise speed is too high to yield purely Strombolian activity and too low to yield purely Hawaiian
behaviour. For a typical basaltic eruption this transition occurs in the magma rise speed range 0.01 –0.1
m s!1 (Fig. 5). This is consistent with a range of
observational data (e.g., Table 1). The model further
suggests that as magma rise speed progressively
increases or decreases, an eruption can rapidly change
in character from Strombolian to Hawaiian or vice
versa. In the case of increasing rise speed, for example, it would be expected that Strombolian explosions
will become progressively more frequent but with
little change in violence until a rapid change occurs
during which explosions become very closely spaced
in time and much more violent. This behaviour then
gives way to continuous lava fountaining. This kind
of transition in character is very similar to that
observed in many real basaltic eruptions. In the
RSD model, the primary control on eruption character
is the magma rise speed and thus transitions in
character can occur rapidly in response to changes
in rise speed. By contrast, in the CF model, eruption
character is determined by magma viscosity and gas
accumulation rates (Jaupart and Vergniolle, 1988;
Vergniolle, 1996), and it is hard to see how the rapid
transitions observed in basaltic eruptions can be
explained by such a model.
Acknowledgements
I thank Christina Heliker for comments on the
origin of data used in Vergniolle and Jaupart (1990). I
also thank the staff of the Hawaiian Volcano
Observatory, especially Tom Wright, for providing
access to data used here (and elsewhere) and for
discussion of many of the issues raised in this paper.
Thanks to Andy Harris for comments relating to
activity at Etna. This paper has benefited from
detailed reviews by Sylvie Vergniolle, Greg Valentine
and Roberto Scandone. Finally, thanks to Lionel
Wilson for many, many discussions of these issues
over the years.
Appendix A . Treatment of simultaneous magma
eruption and drainback in conduit flow
A.1 . Introduction
It is assumed that all of the magma behaves as a
Newtonian fluid with the same viscosity and that for
both upward and downward magma streams there is
no variation with depth of the magma density and the
pressure gradient driving the motion. There is no
guarantee that the pressure gradients in real volcanic
conduits are independent of depth. However, as
shown by Wilson et al. (1980), Wilson and Head
(1981) and Giberti and Wilson (1990), for mafic
magmas, there exists a wide range of possible eruption conditions in which this condition is approximately satisfied, even when rising magma exsolves
sufficient volatiles to undergo fragmentation. The
main restriction on the application of the following
calculations, therefore, is the assumption of constant
magma densities. There are two cases to be considered. In the first, both the rising and the descending
magma are unvesiculated and their motions are
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
laminar. In the second, the rising magma is assumed
to have vesiculated to the point of fragmentation into
pyroclasts and released gas, and the upward motion
is turbulent.
A.2 . Laminar upward motion
To find the average velocity uav-up of the upwardmoving fluid, we weight the local value of u by the
relative volume of fluid with that velocity, (2prdr),
so that:
!Z r0
"#!Z r0
"
uav!up ¼
2purdr
2prdr
ðA4Þ
0
This analysis can be applied directly to the
motion of volatile-poor magma in a conduit where
there is either net drainback from a lava pond around
the vent or net growth of such a pond. It can also be
inferred to apply to conditions in which vesiculating
magma is erupting into a lava fountain while
degassed magma is draining back into the conduit
system provided that the values derived are taken to
refer to conditions at depths greater than a few
hundred metres, where variations in bulk magma
density are still small, there is negligible upward
acceleration of the rising magma, and similar viscosities can be assumed for both the rising and the
sinking magma.
The basic relationship controlling flow of a Newtonian fluid in a circular conduit is:
l du=dr ¼ !ð1=2ÞrðdP=dxÞ;
ðA1Þ
where l is the fluid viscosity, (dP/dx) is the pressure
gradient driving the motion in the x direction, r is the
radial co-ordinate and u is the local velocity of the
fluid. We assume that between r =0 and r =r0, where r0
is some intermediate radius, the motion is upward and
between r =r0 and r =rw, where rw is the radius of the
confining wall, the motion is downward. Thus, u =0 at
both r =r0 and at r =rw.
First, consider the fluid moving upward. Integrating Eq. (A1) between r =0 and a general value of r
gives the velocity profile u(r):
u ¼ ½ðdP=dxÞup =ð4lÞ' ðr02 ! r2 Þ:
ðA2Þ
In this equation and those that follow, (dP/dx)up
represents the absolute value of the pressure gradient;
the driving pressure must of course decrease in the
direction of motion for the velocity to be positive. The
maximum velocity uc occurs at r =0 and is:
uc ¼ ½ðdP=dxÞup =ð4lÞ'r02 :
ðA3Þ
101
0
which yields:
uav!up ¼ ½ðdP=dxÞup =ð8lÞ'r02 :
ðA5Þ
The upward mass flux Mup is then:
Mup ¼ p r02 uav!up qup ;
ðA6Þ
where qup is the bulk density of the upward-flowing
fluid.
Next consider the fluid moving downward. Skelland (1967, Chap. 3) derives equations for flow in an
annulus of a Bingham plastic fluid, and by setting the
yield strength of such a fluid equal to zero the velocity
profile u(r) is found to be:
u ¼ ½ðdP=dxÞdown =ð4lÞ'frw2 ! r2 þ ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'lnðr=rw Þg:
ðA7Þ
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 because
then ln(r/rw)=ln(r0/rw)=!ln(rw/r0). The maximum velocity ua must occur at the radius ra for which du/
dr =0. Differentiating Eq. (A7):
du=dr ¼ ½ðdP=dxÞdown =ð4lÞ'f!2r þ ½ðrw2 ! r02 Þ
=ln ðrw =r0 Þ'ð1=rÞg
ðA8Þ
and setting the term in curly brackets in Eq. (A8) to
zero gives:
ra2 ¼ ðrw2 ! r02 Þ=½2 lnðrw =r0 Þ' ¼ ðrw2 ! r02 Þ=ln ðrw =r0 Þ2 :
ðA9Þ
The value of the maximum velocity, ua, is given by:
ua ¼ ½ðdP=dxÞdown =ð4lÞ'frw2 ! ra2 þ ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'lnðra =rw Þg:
ðA10Þ
102
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
and the average velocity of the fluid, uav-down, is
obtained using the equivalent of Eq. (A4) as:
uav!down ¼ ½ðdP=dxÞdown =ð8lÞ'frw2 þ r02 ! ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'g:
ðA11Þ
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
0.232
0.386
0.534
0.642
0.683
0.838
0.910
10.00
5.00
2.00
1.00
0.61
0.50
0.20
0.10
0.092
0.152
0.327
0.621
1.000
1.214
3.007
6.004
0.611
0.870
1.543
2.589
3.892
4.621
10.646
20.656
0.473
0.666
1.169
1.950
2.925
3.471
7.988
15.494
The downward mass flux Mdown is then:
Mdown ¼ pðrw2 ! r02 Þuav!down qdown ;
ðA12Þ
where qdown is the bulk density of the downwardflowing fluid.
The final issue is to establish how the boundary
between the two flows at r =r0 is related to the other
variables. This involves looking at the continuity of
the overall velocity profile. We have already ensured
that the velocity itself is continuous by arranging that
u=0 at r =r0 in both Eq. (A2) for the upward velocity
and Eq. (A7) for the downward velocity. We now
require that the slopes of the two functions also be
continuous. For the upward velocity profile, Eq. (A2)
leads to:
du=dr ¼ ½ðdP=dxÞup =ð4lÞ'ð!2rÞ
ðA13Þ
and we have already obtained the derivative of the
downward velocity profile as Eq. (A8). Equating the
two at r =r0 and simplifying:
ðdP=dxÞup =ðdP=dxÞdown ¼ f½ðrw2 =r02 Þ ! 1'
=lnðrw =r0 Þ2 g ! 1;
ðA14Þ
so for any choice of the ratio (rw/r0), Eq. (A14) gives
the ratio of [(dP/dx)up/(dP/dx)down] that ensures continuity of the velocity profile. Then taking the ratio of
Eqs. (A6) and (A12):
Mup =Mdown ¼ ½qup =qdown '½ðdP=dxÞup =ðdP=dxÞdown '
" ½r04 =fðrw2 ! r02 Þfrw2 þ r02 þ ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'gg':
ðA15Þ
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 as
a function of (r0/rw) for [qup/qdown]=0.8. The reason
for this choice of [qup/qdown] is as follows. The
pressure gradients driving the upward and downward
movement of the magmatic fluids are by definition
the amounts by which the total pressure gradients
differs from the static weights of the magma in each
case. Assume that the pressure in the magma reservoir at depth is the hydrostatic weight of the overlying crust (in practice, the reservoir is likely to be
overpressured relative to the lithostatic load by a few
MPa, but this does not significantly affect the
following illustration) and that the upward magma
flow occurs because the magma in the centre of the
conduit is positively buoyant. Similarly, the magma
in the outer, descending annulus is assumed to be
negatively buoyant. If the crustal density is qcrust, we
then have:
ðdP=dxÞup ¼ gðqcrust ! qup Þ
ðA16Þ
ðdP=dxÞdown ¼ gðqdown ! qcrust Þ
ðA17Þ
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 table
shows that for the case of pure convection, where
M up /M down =1, r 0 /r w =0.642, which implies that
f41% of the area of the conduit is occupied by
rising magma and f59% by descending magma.
Clearly, it is necessary that qup is always less than
qdown, and depending on the amount of gas exsolving from the rising magma in the deep part of the
conduit, and on the crustal density, likely ranges of
values are f0.55 to 0.85 for [qup/qdown] and f0.3
to at least 3 for [(dP/dx)up/(dP/dx)down].
103
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
A.3 . Turbulent upward motion
This treatment applies to the shallow part of a
conduit where enough volatile exsolution has occurred that magma fragmentation had taken place.
Both the viscosity and the density of the magma are
very different in the upward and downward magma
streams. The velocity profile in the outer annulus is
the same as in the previous section but in the central
region out to radius r0 the velocity profile is of the
form (Knudson and Katz, 1958):
2
32
u ¼ uc ½1 ! aðr=r0 Þ ! bðr=r0 Þ '
ðA18Þ
where a=0.204 and b=0.796. The average velocity
uav-up is found from Eq. (A4):
!Z
uav!up =uav!down ¼ f½!2 lnðrw =r0 Þ þ ðrw =r0 Þ2 ! 1'
" ½1 ! a=2 ! b=17'g=f½a þ 16b'
" f½ðrw =r0 Þ2 þ 1' lnðrw =r0 Þ
! ðrw =r0 Þ2 þ 1gg:
Then taking the ratio of Eqs. (A6 –12) and substituting Eq. (A23) for (uav-up/uav-down):
Mup =Mdown ¼ ðqup =qdown Þ½ð1 ! a=2 ! b=17Þ
=ða þ 16bÞ'½!2 lnðrw =r0 Þ þ ðrw =r0 Þ2
r0
! ðrw =r0 Þ2 þ 1g½ðrw =r0 Þ2 ! 1'g: ðA24Þ
0
and so:
uav!up ¼ uc ½1 ! a=2 ! b=17' ¼ 0:8512 uc :
ðA23Þ
! 1'=ff½ðrw =r0 Þ2 þ 1'lnðrw =r0 Þ
"#!Z r0
"
2purdr
2prdr
0
0
$
¼ ½ð2uc Þ=r02 ' r2 =2 ! ar4 =ð4r02 Þ
#% Z r0
&"
34r032
! br34
uav!up ¼
Equating this to Eq. (A21) with r=r0, taking
account of the fact that the upward and downward
velocities have opposite signs:
ðA19Þ
Thus, for any choice of the ratio (rw/r0), the ratio
of the upward and downward average velocities can
be found from Eq. (A23) and of the upward and
downward mass fluxes can be obtained from Eq.
(A24). Some values of (uav-up/uav-down) are given in
Table A2. However, in order to specify values of
The first derivative of the velocity profile is:
du=dr ¼ uc ½!2ar=r02 ! 32br31 =r032 '
ðA20Þ
and using Eq. (A19) to write this in terms of uav-up,
becomes:
du=dr ¼
uav!up ½!2ar=r02
! 32br
=½1 ! a=2 ! b=17':
31
=r032 '
ðA21Þ
This must now be equated to the first derivative of
the annulus flow, Eq. (8), at r=r0. It is convenient to
use Eq. (A11) to eliminate [(dP/dx)down/(4l)] from
Eq. (A8) giving:
du=dr ¼ ½2uav!down =frw2 þ r02 ! ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'g' " f!2r þ ½ðrw2 ! r02 Þ
=lnðrw =r0 Þ'ð1=rÞg:
ðA22Þ
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
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.95
0.96
0.97
0.99
0.999
0.9999
0.000011
0.000077
0.000269
0.000738
0.001823
0.004417
0.011349
0.035050
0.185045
0.840210
1.345392
2.450476
23.13130
2362.51119
236761.95087
0.046
0.076
0.113
0.161
0.228
0.327
0.492
0.821
1.808
3.782
4.769
9.702
19.569
197.171
1973.312
104
E.A. Parfitt / Journal of Volcanology and Geothermal Research 134 (2004) 77–107
(Mup/Mdown), it is necessary to decide on a plausible
value of (qup/qdown). The fragmented magma in the
rising part of the conduit will have a bulk density
qup given by:
ð1=qup Þ ¼ ðn=qg Þ þ ½ð1 ! nÞ=qmelt '
ðA25Þ
where n is the mass fraction of exsolved volatile, qg
is the gas density and qmelt is the density of unvesiculated rising magma. Consider a typical basaltic
melt having exsolved 0.25 wt.% H2O, i.e., a mass
fraction n=0.0025; at a typical magmatic temperature
of 1450 K, the density of this gas emerging from the
vent, where the pressure is close to atmospheric, is
f0.15 kg m!3. Thus, qup is f60 kg m!3. Using
qdown=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 ratios
of the maximum velocities and the pressure gradients.
The normal treatment for turbulent flow is to relate the
pressure gradient to the mean velocity by:
r0 ðdP=dxÞup ¼ f qup u2av!up
ðA26Þ
where f is a dimensionless friction factor of order 10!3
for the case of motion of a fluid in a pipe with smooth
walls (probably the best assumption in this case).
However, Eq. (A26) assumes that there is no acceleration of the magma, whereas if the rising magma is
fragmenting to form a lava fountain much of the
ambient pressure decrease is used to accelerate the
magma and very little is used to overcome wall
friction. Thus, the value needed for (dP/dx)up in Eq.
(A26) would be very much less than the value used in
the slow-speed, laminar flow case and, furthermore,
would change with depth below the surface. No
attempt is made to take the analysis further here, but
Table A2 shows that a given ratio of Mup/Mdown
occurs much closer to the conduit wall in the case
of turbulent upward flow than in the laminar case.
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