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\DOI{10.5802/crgeos.276}
\datereceived{2024-06-12}
\daterevised{2024-10-09}
\dateaccepted{2024-10-10}
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\dateposted{2024-12-05}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Magma degassing and its impact on the Earth's atmosphere: from magma oceans to lava lakes}
%\def\cdr@specialtitle@french{Impact atmosph\'erique  du d\'egazage magmatique : des oc\'eans de magma aux  lacs de lave}
%\makeatother


\title{Constraining sulphur yields of trachytic and phonolitic volcanic
eruptions: Tambora, Vesuvius, Laacher See and Campi Flegrei}

\alttitle{\'{E}tablir les rendements en soufre des \'{e}ruptions
volcaniques trachytiques et phonolitiques : Tambora, V\'{e}suve,
Laacher See et Campi Flegrei}

\author{\firstname{Bruno} \lastname{Scaillet}\CDRorcid{0000-0003-1561-0226}\IsCorresp}
\address{ISTO, CNRS-Universit\'{e} d'Orl\'{e}ans-BRGM, 1a rue de la F\'{e}rollerie, 45071, Orl\'{e}ans, France}
\email[B. Scaillet]{bscaille@cnrs-orleans.fr}

\author{\firstname{Clive} \lastname{Oppenheimer}\CDRorcid{0000-0003-4506-7260}}
\address{Department of Geography, University of Cambridge, Downing Place, Cambridge, CB2 3EN, UK}

\author{\firstname{Raffaello} \lastname{Cioni}\CDRorcid{0000-0002-2526-9095}}
\address{Earth Sciences Dept., Universita di Firenze, Via La Pira 4 50121 Firenze,  Italy}

\author{\firstname{Stephane} \lastname{Scaillet}\CDRorcid{0000-0002-0731-3451}}
\addressSameAs{1}{ISTO, CNRS-Universit\'{e} d'Orl\'{e}ans-BRGM, 1a rue de la F\'{e}rollerie, 45071, Orl\'{e}ans, France}

\author{\firstname{Yves} \lastname{~Moussallam}\CDRorcid{0000-0002-4707-8943}}
\address{Lamont-Doherty Earth Observatory, Columbia University, New York, USA}
\address{American Museum of Natural History, Department of Earth and Planetary Sciences, NY 10024, New York, USA}

\author{\firstname{Gaelle} \lastname{Prouteau}}
\addressSameAs{1}{ISTO, CNRS-Universit\'{e} d'Orl\'{e}ans-BRGM, 1a rue de la F\'{e}rollerie, 45071, Orl\'{e}ans, France}

\author{\firstname{Joan} \lastname{Andujar}\CDRorcid{0000-0001-5988-0506}}
\addressSameAs{1}{ISTO, CNRS-Universit\'{e} d'Orl\'{e}ans-BRGM, 1a rue de la F\'{e}rollerie, 45071, Orl\'{e}ans, France}

\shortrunauthors

\keywords{\kwd{Eruption}
\kwd{Sulphur}
\kwd{Laacher See}
\kwd{Tambora}
\kwd{Vesuvius}
\kwd{Campi Flegrei}}

\altkeywords{\kwd{\'{E}ruption}
\kwd{Soufre}
\kwd{Laacher See}
\kwd{Tambora}
\kwd{V\'{e}suve}
\kwd{Champs Fl\'{e}gr\'{e}ens}}

\begin{abstract}
Evolved alkaline magmas have fuelled renowned large explosive
eruptions, including that of Tambora in 1815. Very high sulphur yields
to the atmosphere have been suggested for some prominent
phonolite--trachyte eruptions, influencing assessments of their
potential climatic impacts. However, the implications of alkalinity on
volatile abundances in melts remain only partially understood. Here, we
draw on available petrological and thermodynamical constraints,
accounting for uncertainty in pre-eruptive magma redox state, to
quantify pre-eruptive sulphur budgets for several prominent
phonolite--trachyte eruptions. We thereby calculate upper limits for
suphur yields for the 13 kyr calBP Laacher See eruption
(3--15 Tg S), the plinian component of the 39.85 ka
Campanian Ignimbrite \mbox{(2--9 Tg S),} and the 1890 calBCE
``Avellino'' and 79 CE eruptions of Vesuvius. Our findings
demonstrate that alkali-rich magmas do not outstrip dacite or rhyolite
arc compositions in respect of sulphur abundance and can inform both
climate modelling efforts and the search for the eruptions'
signatures in ice core records.
\end{abstract}

\begin{altabstract}
Les magmas alcalins \'{e}volu\'{e}s ont aliment\'{e} de grandes
\'{e}ruptions explosives renomm\'{e}es, dont celle de Tambora en 1815.
Des quantit\'{e}s tr\`{e}s \'{e}lev\'{e}es de soufre inject\'{e}es dans
l'atmosph\`{e}re ont \'{e}t\'{e} sugg\'{e}r\'{e}es pour certaines
\'{e}ruptions de phonolite--trachyte importantes, ce qui a influenc\'{e}
les \'{e}valuations de leurs impacts climatiques potentiels. Cependant,
l'effet de l'alcalinit\'{e} sur l'abondance des volatils dissous dans
les liquides silicat\'{e}s n'est que partiellement compris. Nous nous
appuyons ici sur les contraintes p\'{e}trologiques et thermodynamiques
disponibles, en tenant compte de l'incertitude sur l'\'{e}tat redox du
magma aux conditions pr\'{e}-\'{e}ruptives, afin d'estimer les
quantit\'{e}s de soufre \'{e}mis pour plusieurs \'{e}ruptions
phonolitique-trachytique importantes. Nous calculons ainsi les limites
sup\'{e}rieures des injections atmosph\'{e}riques de soufre pour
l'\'{e}ruption du Laacher See de 13 ka calBP (3--15 Tg S), la composante
plinienne de l'Ignimbrite Campanienne il y a 39,85 ka (2--9 Tg S), et
les \'{e}ruptions du V\'{e}suve d'Avellino (1890 calBCE) et de
Pomp\'{e}i (79 AD). Nos r\'{e}sultats montrent que les magmas
\'{e}volu\'{e}s riches en \'{e}l\'{e}ments alcalins ne sont pas plus
riches en soufre que les magmas d'arc dacitiques ou rhyolitiques. Ces
r\'{e}sultats fournissent des informations utiles pour les mod\`{e}les
climatiques ainsi que pour la recherche des signatures des
\'{e}ruptions dans les archives glaciaires.
\end{altabstract}

\thanks{Labex VOLTAIRE project (ANR-10-LABX-100-01), Equipex PLANEX
(ANR-11-EQPX-0036), NERC grant NE/N009312/1}

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\section{Introduction}

Volcanic eruptions can propel large quantities of radiatively important
and chemically reactive species into the atmosphere 
\citep[e.g.,][]{Robocketal2009,Timmreck2012,Oppenheimer2002,Oppenheimeretal2014,Cadouxetal2015}. 
The atmospheric and climatic consequences have been widely studied drawing
on evidence from direct observations \citep[e.g.,][]{Guoetal2004},
indirect and proxy records \citep[e.g.,][]{Buntgenetal2020} and
modelling efforts  \citep[e.g.,][]{Tooheyetal2019}. While many factors
come into play in influencing the climatic impact of a given eruption,
the primary forcing agent is recognised as stratospheric sulphate
aerosol and thus estimates of sulphur yields for past eruptions are a
first order requirement for efforts to understand their climatic and
societal consequences. Much attention has been given to determination
of stratospheric sulphur yields but significant uncertainties remain in
the estimates  \citep{ScailletOppenheimer2024}. For example, estimates
drawing on evidence from the rock record are sensitive to uncertainties
in tephra mass (eruption magnitude), the abundance and composition of
any vapour phase in the pre-eruptive reservoir, and the behaviour of
volatile elements during storage and eruption
\citep[e.g.,][]{Marshalletal2022,Metcalfeetal2023,Venugopaletal2020,
Schiavietal2020,SchmidtBlack2022,ScailletOppenheimer2023,ScailletOppenheimer2024}.

Sulphur yields can now be estimated with a range of spaceborne sensors
\citep[e.g.,][]{Pardinietal2017,Tayloretal2018}. Despite challenges
in validation, this approach is regarded as the gold standard of
eruptive sulphur yield quantification during an eruption, as it
involves spectroscopic measurement of abundances of sulphur-bearing
gases and aerosol. Sulphur yields of past events are also estimated
from polar ice core records \citep[e.g.,][]{Sigletal2015} drawing on
understanding of global atmospheric dispersion of point source tracer
injections in the stratosphere. This approach also entails substantial
uncertainties, for instance in the case of ice core signals that are
not attributed to a particular volcano (the vast majority), the source
location (and its proximity to the deposition site) is unknown. In
effect, measurement of traces (ppb) of the emitted sulphur is used to
extrapolate to global sulphur yields (Tg). 

The third approach draws on petrological analyses of the erupted rocks
\citep{Devineetal1984} along with petrological arguments 
\citep{Scailletetal2003}. In this case, it is not the emitted sulphur
that is measured but rather the non-emitted sulphur that is evaluated,
based on analyses of sulphur contents in crystal-hosted glass
inclusions and of matrix glass. The difference in these quantities is
then used to estimate syn-eruptive sulphur yields by scaling to the
estimated total eruptive rock mass [which itself typically has high
uncertainty; \citealp{Engwelletal2015,Bonadonnaetal2015}]. Realisation
that this approach failed to yield estimates even close to the
satellite-measured sulphur yields of eruptions, such as those of El
Chich\'{o}n in 1982 and Pinatubo in 1991, fuelled recognition that
volatile-saturated pre-eruptive magmas may already contain an abundant
sulphur-rich gas phase 
\citep[e.g.,][]{Luhretal1984,WestrichGerlach1992,Scailletetal1998,WallaceEdmonds2011}.
This became known as the ``excess sulphur'' problem, and it is
particularly acute for eruptions of evolved magmas, though less so for
basaltic ones  \citep[e.g.,][]{Sharmaetal2004}. The amount of this
sulphur is not captured by the ``petrologic method''
\citep{Devineetal1984}. Rather, it has been inferred from wider
geochemical, petrological and geophysical knowledge of magma bodies
[notably drawing on experimental petrology studies and thermodynamic
calculations, e.g., \citealp{ScailletPichavant2003}]. An alternative
approach uses apatite as a proxy for volatile contents of magmas
\citep[e.g.,][]{Stocketal2016,Humphreysetal2021} but this also requires
assumptions, in particular how to relate the volatile contents of
apatite with those of the coexisting melt and gas, in addition to
apatite occurrence. There remain few and sometimes inconclusive
constraints on S partitioning between apatite and melt/fluid 
\citep[e.g.,][]{Pengetal1997,ParatHoltz2005}. While promising, this
method requires further experimental work.


In general, very few eruptions before the satellite remote sensing era
have been identified with any degree of confidence in ice core records
(this requires geochemical fingerprinting of tephra grains in the ice
cores). Thus, when all we have to go on are the proximal deposits of
large eruptions, estimates of sulphur yield must rely on petrological
and eruption magnitude assessments. While significant progress has been
made in understanding the behaviour of sulphur in silicic magmas 
\citep[e.g.,][]{CarrollWebster1994,Scailletetal1998,Clementeetal2004,ScailletMacdonald2006,Keppler2010,Zajaczetal2012,Masottaetal2016},
permitting estimation of sulphur yields of quartz-oversaturated felsic
arc magmas \citep[e.g.,][]{Scailletetal2003}, for quartz-undersaturated,
or alkali-rich magmas, the constraints are limited. This is despite
recognition that the presence of alkalis increases sulphur solubility
\citep[e.g.,][]{CarrollRutherford1987,Duceaetal1994} and hence sulphur
carrying capacity.


In addition to Tambora 1815 \citep{Oppenheimer2003}, 
renowned eruptions of alkali-rich
phonolite to trachyte magmas include those of Campi Flegrei,
Somma-Vesuvius (Italy) and Laacher See (Germany). In the case of the 
13~kyr calBP \citep{Reinigetal2021} eruption of Laacher See, estimates of
sulphur yield range up to 150~Tg \citep{Schminckeetal1999} influencing
the parameterisation of climate models 
\citep[e.g.,][]{Textoretal2003,Niemeieretal2020} as well as the search
for potential sulphur signatures of the episode in polar ice core
records  \citep{Baldinietal2018,Abbottetal2021}. Our aim here is to
re-assess sulphur yields of Laacher See and other significant
phonolite--trachyte eruptions drawing on improved understanding of
volatile behaviour in alkalic magmas and focusing on eruptions for
which pre-eruptive conditions---pressure ($P$), temperature ($T$),
H\tsub{2}O content and, crucially, redox state---are experimentally
constrained. We use relationships between the fugacities of key
S-bearing species (H\tsub{2}S, SO\tsub{2}) and their concentrations in
phonolite liquids to quantify the partial pressures of corresponding
species in pre-eruptive magma reservoirs. We focus on the more evolved
portions of erupted magmas since they are likely to accumulate
volatiles during reservoir growth. 


\section{Methodology}

We follow \citet{Andersonetal1989} and \citet{ScailletPichavant2003} in
calculating the partial pressures of dissolved volatile species using
thermodynamic models and volatile concentrations measured in melt
inclusions (MI). We consider primarily the role of H\tsub{2}O, CO\tsub{2}
and S-bearing species. For the latter, we use fugacity-concentration
relationships established by \citet{Moncrieff2000}, as reported in 
\citet{Burgisseretal2012}. Since the melt compositions we are concerned
with are broadly phonolitic, we use the water solubility model of 
\citet{CarrollBlank1997}, \mbox{established} using a sodic phonolite. For
CO\tsub{2}, the model used is that of \citet{Burgisseretal2012}, which
is also calibrated on Na-rich phonolite. As shown below, the majority
of eruptions had dissolved CO\tsub{2} contents below detection
({${<}$}20~ppm), indicating partial pressures of CO\tsub{2} below 10~MPa,
the fluid being essentially a mixture of water and sulphur ($+$Cl). For
any species $i$, the relationships between fugacity, $f_{i}$, mole
fraction, $X_{i}$, and partial pressure, $P_{i}$, is given by:
{\begin{eqnarray}\label{eqn1}
f_{i}= \rmSigma \gamma_{i}X_{i}P_{i}
\end{eqnarray}}\unskip
where $\gamma_{i}$ is the fugacity coefficient that describes
departure from ideal gas behaviour. In all cases, we have computed
$\gamma_{i}$ from a Modified Redlich Kwong equation of state using
coefficients from \citet{Holloway1987} and  \citet{FerryBaumgartner1987}. We
treat the gas as an ideal mixture of real gases (Lewis and Randall
rule), i.e., $\gamma_{i}$ is that of the pure species $i$ at given
$P$ and $T$.


The total pressure is given by:
{\begin{eqnarray}\label{eqn2}
\rmSigma P_i= P_{\mathrm{tot}}
\end{eqnarray}}\unskip
which we can recast as:
{\begin{eqnarray}\label{eqn3}
P_{\mathrm{H}_2\mathrm{O}}+P_{\mathrm{CO}_2}+P_{\mathrm{H}_2\mathrm{S}}
+P_{\mathrm{SO}_2}=P_{\mathrm{tot}}
\end{eqnarray}}\unskip

In the results presented below, the retrieved $P_{\mathrm{tot}}$ was
checked against independent phase equilibrium constraints for
pre-eruptive conditions. To accommodate uncertainties in
$f\mathrm{O}_{2}$, we carried out calculations assuming that S is
present either as H\tsub{2}S (reduced, or around the
Quartz-Fayalite-Magnetite buffer, QFM) or SO\tsub{2} (oxidized, i.e.\ 2
log units above QFM). 

Evaluating the S yield related to the release of the gas phase present
in the reservoir requires assessment of the quantity of this phase, a
notoriously challenging task \citep{Wallaceetal1995}. Geochemical
analyses based on trace element behaviour point to proportions ranging
from 1 to 6~wt\% of the gas phase (expressed as bubbles in the magmatic
reservoir) which holds all volatiles, including H\tsub{2}O, CO\tsub{2}
and S-bearing species, the high end corresponding with the apical
portion of evolved magma reservoirs \citep{Wallaceetal1995}. Gas amounts
of 5--6~wt\% are thought to correspond to a percolation threshold,
beyond which bubbles interconnect, preventing accumulation of higher
gas contents \citep{Wallace2001}. Comparison of the sulphur yield of
eruptions for which both petrological constraints and remote sensing,
or ice core constraints on sulphur yield are available shows that, in
most cases, both approaches agree if a gas content in the reservoir of
about 5~wt\% is assumed \citep{Scailletetal2003}. 

Estimation of gas content can also be achieved using the bulk
vesicularity of pumice clasts, as recently shown for the rhyolite of
the Changbaishan (Paektu) Millennium eruption in north Korea 
\citep{ScailletOppenheimer2023}. Here, the bulk gas content of magma at
fragmentation (the sum of dissolved and exsolved volatiles) is restored
assuming equilibrium conditions between gas and melt for both
H\tsub{2}O and CO\tsub{2} volatiles, which represent more than 95~wt\%
of the total volatile complement of evolved magmas. The calculation
uses established solubility laws of H\tsub{2}O and CO\tsub{2} in
phonolitic liquids \citep{CarrollBlank1997,Burgisseretal2012} and a
modified Redlich--Kwong equation of state for describing the fugacities
of corresponding species in the gas phase \citep{Holloway1987}. Once
that bulk H\tsub{2}O and CO\tsub{2} contents are known, the amount of
excess gas, if present, at reservoir conditions can be calculated if
the pre-eruptive pressure is adequately constrained. The calculation
assumes also that the magma retains volatiles during ascent, which has
been shown to hold for felsic eruptions along a significant part of
their ascent path \citep[e.g.,][]{Newmanetal1988}. The lower melt
viscosity of phonolitic magmas \citep{AndujarScaillet2012} may permit
loss of gas during early stages of magma ascent, however. 

An example of such calculation is shown in Figure~\ref{fig1}, using a
bulk vesicularity of 0.75, and pre-eruption $P$--$T$ of 200~MPa and
800~\textdegree C. These $P$--$T$ values are typical for evolved reservoirs,
including for those feeding phonolitic--trachytic eruptions 
\citep{Scailletetal2008, FabbrizioCarroll2008, Andujaretal2010}. We show
the effect of remaining CO\tsub{2} in the matrix glass at
fragmentation, for two H\tsub{2}O contents in matrix glass (0.5~wt\%
and 1~wt\%), on the restored amount of gas in a reservoir holding a
phonolitic melt at 200~MPa and 800~\textdegree C. In Figure~\ref{fig1}, a
magma reaching 10~ppm CO\tsub{2} and 0.5~wt\% H\tsub{2}O in the
residual (matrix) glass at fragmentation yields a gas content of 4
wt\%. Such a magma would have a silicate melt with 1.05~wt\% dissolved
H\tsub{2}O and 434~ppm dissolved CO\tsub{2}. Increasing the residual
H\tsub{2}O content of the matrix glass at fragmentation to 1~wt\%
(orange curve) would increase the gas amount to slightly over 5~wt\%
with the dissolved H\tsub{2}O content increasing to 2.46~wt\% and the
dissolved CO\tsub{2} decreasing to 319~ppm. 


\begin{figure}
\includegraphics{fig01}
\caption{(a) evolution of gas mass fraction in the reservoir with the
residual CO\tsub{2} content in the matrix glass for two H\tsub{2}O
content in the matrix glass: blue 1~wt\% H\tsub{2}O and orange 0.5~wt\%
H\tsub{2}O. Both sets of calculations are performed for a terminal bulk
vesicularity of 0.75. The dissolved H\tsub{2}O (wt\%) and CO\tsub{2}
(ppm) contents of the melt phase in the reservoir are shown along each
curve. (b) Same data as in (a) but showing how the dissolved H\tsub{2}O
and CO\tsub{2}  contents in the melt vary. The red box shows typical
pre-eruptive conditions for phonolitic--trachytic magmas, inferred from
the analyses of dissolved volatiles in crystal-hosted glass
inclusions.\label{fig1}}
\end{figure}


The residual volatiles in the matrix glass at fragmentation are poorly
constrained for phonolitic eruptions, in particular the CO\tsub{2}. For
silicic magmas (rhyolites) available data typically show H\tsub{2}O in
the range 0--2~wt\% and up to 20--30 ppm CO\tsub{2} 
\citep[e.g.,][]{Newmanetal1988,Wadsworthetal2020} and it is likely
that phonolitic magmas display comparable values. In
Figure~\ref{fig1}b, the same calculations are shown but using a
conventional diagram of dissolved H\tsub{2}O--CO\tsub{2} contents in
the silicate melt. The data define a single isobaric trend, showing how
the amount of excess gas varies with residual CO\tsub{2} for two
different residual H\tsub{2}O contents. As in Figure~\ref{fig1}a, increasing
CO\tsub{2} content leads to an increase in the amount of excess gas but
also to an increase in dissolved CO\tsub{2} content at pre-eruptive
conditions. These calculations can be compared with typical
pre-eruptive H\tsub{2}O--CO\tsub{2} contents of phonolitic magmas as
inferred from H\tsub{2}O--CO\tsub{2} analyses in melt inclusions, which
typically reveal elevated water contents (up to 6--7~wt\%) and
CO\tsub{2} contents below detection limit \citep[e.g.][]{Cioni2000}.
Inspection of Figure~\ref{fig1}b suggests that phonolitic magmas have
excess gas contents corresponding with the low end of the range
inferred for silicic magmas \citep{Scailletetal2003,Wallace2005}.

Since we lack precise knowledge of residual volatiles in phonolitic to
trachytic matrix glass at fragmentation, in the following we assume a
gas content in the reservoir of 5~wt\%, bearing in mind that it likely
represents a maximum in most cases. 

A critical aspect in performing calculations of S yields is the
accuracy of melt sulphur contents, which are widely determined by
electron microprobe analyses of glass inclusions in phenocrysts. This
instrument affords relatively low detection limits, of order of 50--200
ppm depending on analytical conditions. Figure~\ref{fig2} illustrates how the
calculated mass of emitted sulphur varies with melt sulphur contents,
based on a notional eruption of $4~\mathrm{km}^{3}$ of DRE magma,
initially stored at 200~MPa, with 5--6~wt\% H\tsub{2}O and 20~ppm
CO\tsub{2} in melt along with sulphur, and coexisting with 5~wt\% of
excess gas. The calculations are shown for both reduced and oxidized
conditions. For the reduced case, taking the case of a magma whose
pre-eruptive S content is at 200~ppm (and 5~wt\% H\tsub{2}O in melt),
produces a yield of about 9.3~Tg S. Varying the S abundance by
${\pm}$50~ppm corresponds to a range in the S yield from 5.3~Tg (150
ppm S) to 14.3~Tg (250~ppm). In other words a typical 50~ppm analytical
uncertainty, equivalent to the standard deviation of that element in a
group of melt inclusions of a single event, propagates into 50\%
uncertainty in the calculated S yield from the gas phase. 

\begin{figure}
\vspace*{-2pt}
\includegraphics{fig02}
\vspace*{-4pt}
\caption{Variation of the sulphur yield with pre-eruptive melt sulphur
content (S in glass) for a phonolitic magma stored at 200~MPa,
760~\textdegree C and with 5~wt\% excess gas, calculated for either
reduced (pyrrhotite-bearing) or oxidized conditions. For reduced
conditions, results are shown for two pre-eruptive melt water contents.
A variation in ${\pm}$50~ppm of sulphur in matrix glass corresponds to
a variation of the calculated sulphur yield of
${\pm}$50\%.\label{fig2}}
\vspace*{-2pt}
\end{figure}



While the situation for oxidized conditions seems less critical, an
uncertainty of order 50\% in S yield still emerges. The two curves
shown for reduced conditions illustrate also that the melt water
content is a critical parameter. An increase of H\tsub{2}O content of 1
wt\% (from 5 to 6~wt\%) for the same magma reduces S yield by around
30\% to 6.3~Tg. It is thus essential to quantify as precisely as
possible pre-eruptive conditions in order to calculate volatile yields
associated with volcanic eruptions.

\vspace*{-2pt}


\subsection{Caveats}

\vspace*{-2pt}

Our method is primarily aimed at estimating the S content of bubbles,
whether in the residual melt or trapped along with a melt inclusion
inside a phenocryst. If at equilibrium, the bubble composition is
independent of its location (inside a melt inclusion within the crystal
or outside the crystal). Methods have been developed to determine the
composition of gas bubbles coexisting with melt inclusions in
phenocrysts
\citep[e.g.,][]{Wallaceetal2015,Wallaceetal2021,Asteretal2016},
including their solid compounds or precipitates 
\citep[e.g.][]{Venugopaletal2020,Schiavietal2020}. These reveal that a
significant part of CO\tsub{2} and S of the MI and coexisting bubble in
basaltic rocks resides in the bubble. What could affect our
calculations is if the bubbles in the melt inclusions are shrinkage
bubbles arising from cooling, or in other words, if exsolution of
volatiles has occurred after entrapment as inferred for mafic
compositions 
\citep[e.g.][]{Wallaceetal2015,Venugopaletal2020,Schiavietal2020},
thereby changing the amount of S (and CO\tsub{2}) dissolved in the melt
inclusion pre-eruptively, which would change the corresponding
fugacities. However, while exsolution during cooling is conceivable for
low viscous mafic melts, the colder and viscous felsic melts we
consider here are much less susceptible. The fact that S contents of
matrix glass are comparable to those of melt inclusions in explosively
erupted felsic magmas \citep[e.g.,][]{WestrichGerlach1992} is direct
evidence for limited exsolution of S before the glass transition
temperature is crossed. 

Conversely, some of the S present in the excess fluid in the reservoir
could condense as a solid phase during eruption (i.e.\ upon cooling)
\citep{Rose1977,SchmaussKeppler2014},
such as shown for the Pinatubo 1991 eruption \citep{Jakubowskietal2002}.
This process would reduce the amount of S released to the atmosphere.
An additional process excluded in our calculations is breakdown of
S-bearing minerals, such as pyrrhotite or anhydrite, during magma
ascent. For ``cold'' magmas, however, this process is kinetically
inhibited, as shown by \citet{Gerlachetal1996} for the 1991 Pinatubo
eruption. 

The preceding discussion illustrates some key sources of uncertainty in
the petrologic method, in addition to uncertainties in eruption
magnitude and proportion of exsolved fluid, which both scale linearly
with S yield. In most cases, eruption magnitude is uncertain at least
to a factor of two \citep{ScailletOppenheimer2024}. While these sources
of uncertainty may seem very large, even spaceborne observations of
eruption yields are subject to comparable uncertainty, as are
extrapolations of ice core S abundances to total S yields to the
stratosphere.

\section{Application}\label{sec3}

The essential figures calculated for each event are listed in
Table~\ref{tab1}, while Figure~\ref{fig3} compares the S content of the
corresponding fluid phase with that estimated for other arc-related magmas.

\begin{figure*}
\vspace*{-4pt}
\includegraphics{fig03}
\vspace*{-4pt}
\caption{The sulphur content of the excess gas phase (in wt\%) in the reservoir
of several volcanic eruptions, calculated using petrologic and
thermodynamic constraints on pre-eruptive $P$--$T$--H\tsub{2}O-$f$O\tsub{2}
conditions. Data for calco-alkaline magmas are from 
\citet{Scailletetal2003}. See text for details of
calculations.\label{fig3}}
\vspace*{-4pt}
\end{figure*}

\begin{table*}
\caption{Volatile contents, fluid phase compositions and calculated
sulphur yields of famous phonolite--trachyte eruptions\label{tab1}}
\fontsize{9}{11}\selectfont
\tabcolsep=2pt
\begin{tabular}{lcccccccccc}
\thead
& \multicolumn{2}{c}{Tambora} & 
\multicolumn{2}{c}{Laacher See}& 
\multicolumn{2}{c}{\parbox[t]{2.6cm}{\raggedright Campanian Ignimbrite~(Plinian)}}\vspace*{2pt}
& \multicolumn{2}{c}{Vesuvius Pompei} &
\multicolumn{2}{c}{Vesuvius Avellino}  \\
\cline{2-3}\cline{4-5}\cline{6-7}\cline{8-9}\cline{10-11}
& Reduced & Oxidised & Reduced & Oxidised & Reduced & Oxidised & Reduced & Oxidised & Reduced & Oxidised \\ 
\endthead
P, bar &  1010 &  800 &  1796 &  1760 &  1950 &  1950 &  1940 &  1920 & 2020 &  1900 \\ 
T, \textdegree C$^{\mathrm{a}}$ & 935 &  935 &  760 &  760 &  760 &  760 &  815 &  815 &  785 \vspace*{4pt} &  785 \\ 
H\tsub{2}O, wt\%$^{\mathrm{a}}$ & 0.030 &  0.030 &  0.056 &  0.056 &  0.060 &  0.060 &  0.063 &  0.063 & 0.060 &  0.060 \\ 
CO\tsub{2}, ppm$^{\mathrm{a}}$ & 20 &  20 &  20 &  20 &  20 &  20 &  20 &  20 &  20 &  20 \\ 
S, ppm$^{\mathrm{a}}$ & 732 &  732 &  270 &  270 &  100 &  100 &  200 &  200 &  560\vspace*{4pt} &  560 \\ 
$f$H\tsub{2}O, bar$^{\mathrm{b}}$ & 510 &  510 &  1209 &  1209 &  1330 &  1330 &  1422 &  1422 &  1330 & 1330 \\ 
$f$CO\tsub{2}, bar$^{\mathrm{c}}$ & 197 &  197 &  197 &  197 &  197 &  197 &  197 &  197 &  197 &  197 \\ 
$f$H\tsub{2}S, bar$^{\mathrm{d}}$ &  331 &  &  45 &  &  6 &  &  25 &  &  194 & \\ 
$f$SO\tsub{2}, bar$^{\mathrm{e}}$ &  &  95 &  &  10 &  &  1 &  &  5 &\vspace*{4pt}  &  52 \\ 
PH\tsub{2}0, bar & 555 &  548 &  1639 &  1633 &  1830 &  1830 &  1799 &  1797 &  1763 & 1748 \\ 
PCO\tsub{2}, bar &  154 &  162 &  122 &  123 &  116 &  116 &  117 &  118 &  114 &  118 \\ 
PH\tsub{2}S, bar &  296 &  0 &  35 &  0 &  5 &  0 &  19 &  0 &  143 &  0 \\ 
PSO\tsub{2}, bar  & 0 &  88 &  0 &  7 &  0 &  1 &  0 &  3 &  0\vspace*{4pt} &  37 \\ 
\multicolumn{11}{c}{Fluid composition, molar} \vspace*{2pt}\\ 
XH\tsub{2}O  & 0.550 &  0.685 &  0.912 &  0.928 &  0.938 &  0.938 &  0.927 &  0.936 & 0.873 &  0.920 \\ 
XCO\tsub{2} &  0.152 &  0.203 &  0.068 &  0.070 &  0.060 &  0.060 & 0.060 &  0.061 &  0.056 &  0.062 \\ 
XH\tsub{2}S &  0.293 &  &  0.020 &  &  0.002 &  &  0.010 &  &  0.071 & \\ 
XSO\tsub{2} &  &  0.110 &  &  0.004 &  &  0.000 &  &  0.002 & \vspace*{4pt} & 0.019 \\ 
\multicolumn{11}{c}{Fluid composition, wt\%}  \vspace*{2pt}\\ 
H\tsub{2}O  &  0.3725 &  0.4355 &  0.8179 &  0.8330 &  0.8621 &  0.8647 &  0.8485 &  0.8569 &  0.7631 &  0.8067 \\ 
CO\tsub{2} &  0.2525 &  0.3151 &  0.1488 &  0.1538 &  0.1337 &  0.1341 &  0.1349 &  0.1373 &  0.1202 &  0.1334 \\ 
H\tsub{2}S  &  0.3750 &  &  0.0333 &  &  0.0042 &  &  0.0166 &  & 0.1167 &  \\ 
SO\tsub{2}   &  &  0.2494 &  &  0.0131 &  &  0.0012 &  &  0.0058 & \vspace*{4pt} & 0.0599 \\ 
S fluid, wt\% &  0.3516 &  0.1247 &  0.0312 &  0.0066 &  0.0039 & 0.0006 &  0.0155 &  0.0029 &  0.1094 &  0.0299 \\ 
Bulk S content, wt\% &  0.352 &  0.125 &  0.156 &  0.033 &  0.020 & 0.003 &  0.078 &  0.015 &  0.547 \vspace*{4pt} &  0.150 \\ 
Fluid, wt\% &  0.01 &  0.01 &  0.05 &  0.05 &  0.05 &  0.05 &  0.05 & 0.05 &  0.05 &  0.05 \\ 
vol magma, km$^{3}$ &  35 &  35 &  4.04 &  4.04 &  23 &  23 &  0.50 & 0.5 &  0.1 &  0.1 \\ 
mass S, Tg &  283 &  100 &  14.5 &  3.1 &  10.3 &  1.6 &  0.89 &  0.17 &  1.26 &  0.34  
\botline
\end{tabular}
\tabnote{$^{\mathrm{a}}$~The pre-eruptive temperature. dissolved 
H\tsub{2}O, S and CO\tsub{2} contents come from: 
Tambora: \citet{Selfetal2004,Pougetetal2023,AndujarScaillet2012};
Laacher See: \citet{Harmsetal2004,Berndtetal2001,HarmsSchmincke2000}; 
Campanian Ignimbrite: \citet{Signorellietal2001, Marianellietal2006}; 
Vesuvius: \citet{Scailletetal2008,Cioni2000,Signorellietal1999}.}
\tabnote{$^{\mathrm{b}}$~$f$H\tsub{2}O~${=}$~10$^{((\mathrm{Log}(\mathrm{wt}\text{\%}\ \mathrm{H}_2\mathrm{O})-\mathrm{Log}(0.0329))/0.7238)}$, from \citet{CarrollBlank1997}.}
\tabnote{$^{\mathrm{c}}$~$f$CO\tsub{2}~${=}$~10$^{((\mathrm{Log}(\mathrm{wt}\text{\%}\ \mathrm{CO}_2)-\mathrm{Log}(0.000005611))/1.112)}$, from \citet{Burgisseretal2012}.}
\tabnote{$^{\mathrm{d}}$~$f$H\tsub{2}S~${=}$~10$^{((\mathrm{Log}(\mathrm{wt}\text{\%}\ \mathrm{S})-\mathrm{Log}(0.004))/0.501)}$, from \citet{Burgisseretal2012}.}
\tabnote{$^{\mathrm{e}}$~$f$SO\tsub{2}~${=}$~10$^{((\mathrm{Log}(\mathrm{wt}\text{\%}\ \mathrm{S})-\mathrm{Log}(0.01))/0.437)}$, from \citet{Burgisseretal2012}.}
\end{table*}



\subsection{Tambora}

We first consider the 1815 eruption of Tambora, for which independent
estimates of sulphur yield are available based on recorded deposition
of sulphur in bipolar ice cores. These indicate a stratospheric
injection of 28~Tg of S \citep{TooheySigl2017}, approximately three
times the amount measured for the Pinatubo emission. A recent
re-evaluation of volatile yields (based on melt inclusions) has
concluded that about 74~Tg~S were emitted from melt degassing 
\citep{Pougetetal2023}. The eruption, with an estimated output of
30--40~km$^{3}$ DRE of magma 
\citep{Selfetal2004, KandlbauerSparks2014}
is around 4--8 times greater in magnitude than that of Pinatubo. From
\citet{Selfetal2004} and \citet{AndujarScaillet2012}, the magma was
stored at a pressure of around 100~MPa, a temperature of
935~\textdegree C, with a melt water content of about 3~wt\% at an
$f\mathrm{O}_{2}$ around QFM$+$2. The average sulphur content of melt
inclusions ranges from 689 to 775~ppm 
\citep{Selfetal2004,Pougetetal2023} and in the following we take a
value midway between these two studies (732 ppm).

For reduced conditions, the fluid phase would have more than 30~wt\%
sulphur, while for oxidised conditions the sulphur content would be
around 11~wt\% (Table~\ref{tab1}, Figure~\ref{fig3}). For a 5~wt\% gas
phase in the reservoir and 35~km$^{3}$ DRE of magma, the upper bounds
for the sulphur released from the excess gas are 1415~Tg (reduced) and
502~Tg (oxidised), the lower value being already more than 10 times the
stratospheric S injection estimated based on ice core records. For 1
wt\% excess gas, the corresponding amounts are 283 and 100~Tg~S,
respectively. Considering the inferred high $f\mathrm{O}_{2}$ 
\citep{Selfetal2004}, the lower bounds of these ranges seem more
appropriate. This suggests that had the reservoir been gas-saturated,
the amount of such a free gas phase was {${<}$}1~wt\%, or {${<}$}0.5~wt\%
considering that a significant part of S yield comes from melt
degassing alone \citep{Selfetal2004,Pougetetal2023}. The low
vesicularity of Tambora pumices [{${<}$}60\%, 
\citealp{Suhendroetal2021}] compared with other plinian eruptions of
felsic magmas [70--80\%, \citealp{Thomasetal1994}], is consistent with
a low pre-eruptive excess gas content. This first example already
illustrates that the assumption of abundant gas in the reservoir may
not be universal, calling for a case by case approach when calculating
past S emissions. Gas loss prior to eruption during magma storage has
been inferred for the so-called Millenium Eruption of Paektu
\citep{ScailletOppenheimer2023} and the 1815 Tambora event may~be an
additional example.

\subsection{Laacher See}

Pre-eruptive conditions have been experimentally determined by 
\citet{Harmsetal2004} and \citet{Berndtetal2001}. These works concluded
that the uppermost part of the magma reservoir, which yielded most 
($4~\mathrm{km}^{3}$ DRE) of the erupted material was comparatively cool
(about 760~\textdegree C), water-rich (5--6~wt\% dissolved H\tsub{2}O) and
possibly gas-saturated, and in the pressure range of 150 to 200~MPa. 
This magma appears to have been relatively oxidised, based on
S\tsup{6+}/S\tsup{2-} ratios in melt inclusions
\citep{HarmsSchmincke2000} and the presence of hauyne in the mineral
assemblage \citep{WornerSchmincke1984,Berndtetal2001}. The sulphur coming from melt
degassing of that part has been estimated at 0.45~Tg 
\citep{HarmsSchmincke2000}. The lowermost, more mafic part of the
erupted magma ($2.3~\mathrm{km}^{3}$ DRE), is thought to have been
gas-free, reflecting its lower water content (4~wt\% H\tsub{2}O).
Accordingly, its contribution to the sulphur yield corresponds to the
sulphur exsolved from melt during decompression, estimated as 1.45~Tg 
\citep{HarmsSchmincke2000}. 

Analyses of melt inclusions from the upper part of the Laacher See
reservoir indicate a pre-eruptive S content average of 270 ppm 
\citep{HarmsSchmincke2000}. Calculations of S-species fugacities and
partial pressures, and the corresponding fluid phase compositions are
reported in Table~\ref{tab1}. The sulphur content of the fluid varies
between 3.1~wt\% (reduced) and 0.7~wt\% (oxidised), falling within the
range estimated for typical arc magmas \citep{Scailletetal2003}
(Figure~\ref{fig3}). Assuming an upper value of gas content in
reservoirs of 5~wt\% (which includes the contribution of all gas
species) and taking a magma DRE \mbox{volume} of $4 ~\mathrm{km}^{3}$, then,
depending on redox state, the Laacher See eruption may have released up
to 1.5~Tg (oxidised) or 13.6~Tg (reduced) sulphur in addition to that
released by the melt [$0.45+1.45 = 1.9$~Tg,
\citealp{HarmsSchmincke2000}]. This amounts to a total release of
sulphur in the range 3--15~Tg. 


\subsection{Campanian ignimbrite}

The 39.85~ka BP \citep{Giaccioetal2017} Campanian Ignimbrite erupted an
estimated 155--265~km$^{3}$ DRE (or 4.1--6.9 $\times$ 10$^{14}$~kg) of
magma \citep{Martietal2016,Sillenietal2020}. Phase equilibrium
constraints show that the upper part of the magma body was stored at
pressures of 140 to 200~MPa, at a temperature of 740--780~\textdegree C,
and at or close to H\tsub{2}O saturation, i.e.\ with dissolved
H\tsub{2}O in the melt of about 6~wt\% \citep{FabbrizioCarroll2008},
the latter consistent with melt inclusion constraints 
\citep{Marianellietal2006}. These temperature estimates are
significantly lower than those based on clinopyroxene-melt thermometry
[900--950~\textdegree C; \citealp{Fornietal2016}], suggesting that
clinopyroxene may record early stages of magma evolution and not later
pre-eruptive conditions. 


The pre-eruptive sulphur content of the melt has been studied in some
detail by \citet{Signorellietal2001} by analysing melt inclusions in
phenocrysts belonging to the early plinian phase of the event, which
ejected an estimated $23~\mathrm{km}^{3}$ DRE of magma 
\citep{Martietal2016}. Melt inclusions in phenocrysts inferred to
record pre-eruptive conditions (salitic pyroxenes) have sulphur
contents below the detection limit of electron microprobe (EMPA)
(approximately 200 ppm for the given analytical conditions). Whole rock
analyses (which are representative of matrix glass analyses owing to
the low crystal content of the rock of about 5\%) indicate values of
110--140~ppm of undegassed sulphur \citep{Signorellietal2001}. Sulphur
measurements made by \citet{Marianellietal2006} of various MI from both
the fallout or ignimbrite deposits range from below 100~ppm for the
H\tsub{2}O-rich MI to over 500~ppm for H\tsub{2}O-poor MI. For our
calculations, we take a pre-eruptive sulphur content of 100~ppm,
assuming that the H\tsub{2}O-rich portion represents the top part of
the reservoir which fueled the plinian column. The prevalence of
pyrrhotite inclusions in pyroxene suggests reduced conditions
\citep{Signorellietal2001}. MELTs simulation of liquid lines of descent
has also suggested that the redox state 
\mbox{during} \mbox{crystallization} was
around QFM  \citep{Fowleretal2007}. Some petrological information on
volatiles is available for both H\tsub{2}O and CO\tsub{2} but not for
sulphur for the voluminous ignimbrite component of the deposit
\citep{Morettietal2019}, precluding evaluation of its pre-eruptive
sulphur budget.


The results (Table~\ref{tab1}) indicate a sulphur content of the gas
phase of 0.4~wt\% under reduced conditions (Figure~\ref{fig3}). For the
$23~\mathrm{km}^{3}$ (DRE) magma erupted in the plinian phase, the
sulphur yield arising from exsolved gas (5~wt\%) in the reservoir under
reduced conditions amounts to 9.7~Tg. This is similar to the 10~Tg~S
erupted by the 1991 Pinatubo eruption which ejected 
$5~\mathrm{km}^{3}$ DRE of magma \citep{Guoetal2004}, underscoring the
fact that alkaline magmas do not necessarily eject more S than
calc-alkaline magmas. Similar calculations performed for oxidised
conditions (all SO\tsub{2}) yield a sulphur fluid content of 0.15~wt\%
(Figure~\ref{fig3}) and a bulk sulphur yield of 0.8~Tg, which is a tenth
of the reduced scenario. Taking the higher estimate inferred for the
plinian phase as representative of the entire erupted magma would imply
a total S yield of order 100~Tg~S. Note, however, that this scaling
implies a constant gas content in the reservoir, which is unlikely
considering the propensity of gas bubbles to migrate upwards, as
demonstrated for the Bishop Tuff \citep{Wallaceetal1995}. It also
assumes that all eruptive components (plinian, ignimbrite) are equally
able to release their volatiles into the atmosphere, which is also
unlikely \citep[e.g.,][]{Pecciaetal2023}.

\subsection{Vesuvius}

The erupted volume of phonolite to tephriphonolite magmas for the
renowned 79 CE eruption is estimated as 1.5~km$^{3}$ DRE
\citep{Cionietal2008}, around a third that of Pinatubo's 1991
eruption. Pre-eruptive conditions of the phonolite magma have been
defined via phase equilibrium and melt inclusion studies 
\citep{Cioni2000,Scailletetal2008} indicating a reservoir pressure of
$200 \pm 20$~MPa, temperature of 815 $\pm$ 10~\textdegree C and water-rich
conditions (6--6.5~wt\%). The sulphur content of phonolitic melt
inclusions was found to be below the EMPA detection limit [200~ppm,
\citealp{Cioni2000}], therefore we take this figure as the maximum
sulphur concentration at the top of the reservoir. Similarly, the
CO\tsub{2} content was found to be below the FTIR analysis detection
limit\unskip\break
\citep{Cioni2000}, and therefore we use a pre-eruptive value of
20~ppm. Redox conditions have been estimated to lie around the NNO
solid buffer, consistent with presence of sulphide globules. 


For these conditions, our calculations indicate that the fluid phase in
the apical portion of the magma body had a sulphur content of 1.6~wt\%
(Table~\ref{tab1}, Figure~\ref{fig3}), if reduced, corresponding to a
sulphur yield for the phonolitic part of the deposit [about 
$0.5~\mathrm{km}^{3}$ DRE, \citealp{Cionietal2008}] of around 0.8~Tg,
comparable to that released by the 1980 El Chich\'{o}n eruption
[Mexico, \citealp{Kruegeretal2008}]. Alternatively, for oxidising
conditions, with SO\tsub{2} prevalent over H\tsub{2}S in the fluid,
then we calculate a sulphur content of the fluid of 0.3~wt\% yielding
0.1~Tg of sulphur to the atmosphere. 


Pre-eruptive conditions for the Bronze Age Avellino plinian eruption,
dated 1890 calBCE \citep{Sevinketal2021}, are similar to those for
the 79 CE ``Pompeii'' eruption in terms of $P$--$T$--H\tsub{2}O 
\citep{Scailletetal2008,BalconeBoissardetal2012}. The sulphur content
appears to have been higher than for the 79 CE eruption, averaging 560
ppm  \citep{Signorellietal1999}. This gives a sulphur content in the
fluid of 11~wt\% for reduced, or 3~wt\% for oxidised, conditions. The
modest magnitude, estimated as $0.9~\mathrm{km}^{3}$ DRE, of which
$0.1~\mathrm{km}^{3}$ were phonolite  \citep{Cionietal2008,
Sulpizioetal2010}, translates into a sulphur yield of less than
1.5~Tg in both cases (1.2--0.17~Tg, respectively).


\section{Discussion}

Our estimated upper limits for the sulphur yields of these renowned
eruptions are comparatively modest, with the possible exception of the
Campanian Ignimbrite. The restored gas+melt S contents (i.e.\ S content
of the magma before eruption, excluding that locked in
sulphide/sulphate minerals, which is not available for degassing) range
from 37 ppm up to 5130 ppm (Table~\ref{tab1}). In detail, considering
the likely redox state (with regard to S) of erupted magmas (oxidized
for Laacher See and sulphide-bearing for the others), the bulk content
of S is in general of order several $10^{2}$ ppm and not several
$10^{3}$ ppm, except for Avellino. This parameter is compared with the
values calculated for calc-alkaline magmas by \citet{Scailletetal2003}
using the same general methodology (Figure~\ref{fig4}).
\looseness=-1


\begin{figure*}
\includegraphics{fig04}
\caption{The calculated bulk sulphur content stored in both melt and
pre-existing gas phases. Data from calco-alkaline magmas are from
\citet{Scailletetal2003}. The values corresponding to L\'{a}scar and
Stromboli volcanoes are beyond the range shown (7 and 36~wt\% sulphur
respectively).\label{fig4}}
\vspace*{-2pt}
\end{figure*}



Excluding the case of Avellino eruption, the bulk S contents of alkaline
magmas appear to be slightly lower than those of arc magmas. This could
reflect the oxidized nature of calc-alkaline magmas which allows
efficient mafic-to-felsic S transfer during fractionation, by
inhibiting extensive sulphide fractionation 
\citep[e.g.][]{ScailletMacdonald2006}. However, the case of Laacher
See, an oxidized yet S-poor magma, does not fit with such a scenario.
The apparent low S content of alkaline felsic magmas may primarily
reflect the source rather than a process but additional data are
clearly needed to furnish a more robust statistical lens on this
question. 

The sulphur yield of alkaline magmas is positively correlated with the
volume (DRE) of magma emitted, falling along the same trend defined by
arc magmas (Figure~\ref{fig5}). At a given volume a dispersion of 1--2
orders of magnitude in sulphur yield is apparent, in particular for
large eruptions, stressing that eruption size alone is not a good guide
to S yield (and potential climate impact).

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig05}
{\vspace*{2pt}}
\caption{Relationship between volume of magma erupted and corresponding
sulphur yield for calco-alkaline (orange) and alkaline (blue) magmas.
The data for calco-alkaline magmas are from
\citet{Scailletetal2003}.\label{fig5}}
{\vspace*{-4pt}}
\end{figure}


Below we consider our S estimates for alkaline magmas in the light of
previous estimates, and discuss their relevance in the context of
climate proxies and modelling efforts.


\subsection{Laacher See}

\citet{Schminckeetal1999} and \citet{HarmsSchmincke2000} estimated
syn-eruptive exsolution and degassing of order 2~Tg~S for the Laacher
See eruption. Drawing an analogy with Pinatubo 1991, 
\citet{Schminckeetal1999} suggested the total yield could have been as
much as 150~Tg~S. Based on more specific consideration of the
mineralogy and petrology of Laacher See's products,
\citet{HarmsSchmincke2000} suggested a total yield of at least 10~Tg~S,
speculating that it may have been ``appreciably more''. A subsequent
work acknowledging the implications of redox state suggested a range of
1.7--49~Tg~S \citep{Textoretal2003}. More recently,
\citet{Baldinietal2018} argued for a release of order 42~Tg~S drawing
on scaling arguments and sulphur emissions data for other non-basaltic
eruptions. This high emission led them to suggest a prominent sulphur
anomaly in the Greenland Ice Sheet Project 2 (GISP2) core might
represent the Laacher See eruption, though this match has been
discounted by subsequent high-precision dating of the eruption
\citep{Reinigetal2021}. They also \mbox{suggested} that with such a high
sulphur yield, the eruption may have played a role in triggering the
Younger Dryas.

A study by \citet{GrafTimmreck2001} presented a simulation of the
climate response to the Laacher See eruption, based on a 7.5~Tg~S
injection. Though not intended as palaeoclimate simulations, work by
\citet{Niemeieretal2020} nevertheless has some bearing on understanding
dispersal of the Laacher See ash and gas emissions and their radiative
effects. They modelled sulphur chemistry and ash dispersion for a range
of scenarios predicated on a ``Laacher See-type'' eruption with 0.75,
7.5 and 50~Tg~S emissions. Based on our upper limit of 3--15~Tg of S,
the lower emission scenarios would be more representative for
understanding the potential climatic impacts of the Laacher See
eruption, and for targeting any search of polar ice core records for
its signature (which will ultimately rest on geochemical fingerprinting
of ash grains). We stress that the oxidised nature of erupted rocks
points to an S yield for the Laacher See event lying at the lower end
of our calculated range, i.e.\ 3~Tg~S.

The 3~Tg~S estimate corresponding to oxidised conditions, as suggested
by petrological arguments, may seem counterintuitive but the lower
sulphur content of the gas phase at high $f$O\tsub{2} is an unavoidable
consequence of the higher solubility of sulphur in silicate melt at
high $f$O\tsub{2} \citep{CarrollRutherford1987}: in other words higher
sulphur contents are achieved with lower $P_{\mathrm{SO}_2}$ relative to
$P_{\mathrm{H}_2\mathrm{S}}$: As readily apparent from Equation
(\ref{eqn1}), a lower $P_{\mathrm{SO}_2}$ translates into a lower mole
fraction of SO\tsub{2} in the coexisting fluid phase, and thus a lower
sulphur\unskip\break content. 


\subsection{Campanian ignimbrite}

Our calculations for the Campanian Ignimbrite allow for a sizeable
sulphur release (up to an order of magnitude greater than that of the
1991 Pinatubo eruption). However, they are not consistent with far
higher estimates, exceeding 1 Pg S [\citealp{Scailletetal2003}, and
reported in \citealp{Fedeleetal2007}]. Meanwhile, \citet{Martietal2016}
estimated a yield of 84--89~Tg~S. Clearly, it is the mass of erupted
magma that makes this event potentially important from the viewpoint of
S yield, not intrinsically high S content of the magma
(Figure~\ref{fig2}).

Curiously, very few data are presently available for S content in MI in
minerals from the different CI deposits. This is probably because most
of the MI have S concentrations below typical EMPA detection limits,
although some data \citep{Websteretal2003} suggest SO\tsub{2} contents
up to 2800~ppm. The genesis of the CI magma is debated, and reflects
complex open-system processes of crystallization, assimilation and recharge
\citep{Fowleretal2007}. Based on MI data,  \citet{Marianellietal2006}
suggested that the plinian phase (corresponding to
${>}20~\mathrm{km}^{3}$ of magma) was fed by magma which had ascended
from the main magma body to a depth of 2--3~km depth. If this is the
case, the presence of a large amount of fluid phase in the deeper
(6--8~km) reservoir could be questioned. Recent work has also suggested
that a large part of the magma erupted derived from thermal
reactivation of a large body of crystal mush in the deeper reservoir
\citep{Fornietal2016, DiSalvoetal2020}. In this scenario, the process by
which a free, S-bearing, fluid phase accumulates in the reservoir is
unclear \citep[see][]{Parmigianietal2016}. Further progress in
estimating the S release to the atmosphere for CI eruption requires
deeper understanding of the petrogenesis of the magma combined with
more comprehensive MI studies. The behaviour of volatiles associated
with ignimbrite formation (i.e., processes accompanying and following
column collapse) also requires further study
\citep[e.g.,][]{Pecciaetal2023}.


\subsection{Vesuvius}

We note that our low estimated yield of sulphur for the 79 CE eruption
is consistent with the lack of a prominent sulphur anomaly in Greenland
ice cores at depths consistent with the age of the 79 CE eruption
\citep{Plunkettetal2022}. 


\section{Concluding remarks}\label{sec5}

Our calculations highlight the important role of redox conditions, with
estimates of sulphur yields for the considered eruptions differing by
an order of magnitude depending on whether reduced or oxidised
conditions apply. Clearly oxidising conditions, which enhance the
solubility of sulphur in silicate melts, limit sulphur partition into
the fluid phase. Other factors being equal, higher temperature should
have the same effect because increasing temperature increases sulphur
solubility in silicate melts \citep[e.g.,][]{Clementeetal2004}. 

The role of chlorine needs to be addressed as well. Experiments have
shown that addition of chlorine increases the solubility of sulphur by
a factor of up to two in rhyodacite melt \citep{Botcharnikovetal2004}.
Phonolite and trachyte magmas are generally Cl-rich 
\citep[e.g.,][]{SignorelliCarroll2000}, hence an abundance of chlorine
may affect sulphur behaviour as well. The results of
\citet{Botcharnikovetal2004} suggest that our calculated sulphur
contents for the gas phase could be overestimated by 50\% or more. We
note however that in the case of Vesuvius, whose mafic melt inclusions
hold up to 2000 ppm S  \citep{Cionietal1995}, the Cl-rich character of
felsic MI (up to 1~wt\% Cl) did not act to sustain high S contents
during magma evolution, possibly because sulphur was continuously
scavenged into the fluid during fractionation. 

Our results clearly discount any suggestion that alkaline magmas, i.e.,
trachytes and phonolites, are special in respect of sulphur emissions
during explosive eruptions. Excluding perhaps the case of Campanian
Ignimbrite, the other eruptions we have considered yield sulphur
emissions comparable with, or even lower than, those associated with
the 1991 Pinatubo eruption. It appears also that there is considerable
variability between alkaline magmas. Without robust petrological
control, simple extrapolation from one case to another (even for
similar chemistries such as with Vesuvius 79 CE and Avellino) is
inadvisable. 

While we restrict our work to only four centres for which
volcanological and petrological knowledge is extensive, we note that
many other alkalic provinces deserve similar attention: oceanic island
volcanoes can erupt voluminous quantities of trachyte or phonolite,
such as manifested in the\unskip\break Canary islands \citep{Andujaretal2008}.
Further prominent examples include the Kenyan flood phonolites, which
comprise more than 50,000~km$^{3}$ of Miocene lavas and tephra deposits
\citep{Macdonald2002}, and alkaline volcanic centres of the West
Antarctic Rift System. More experimental work is needed to quantify the
S behaviour in alkaline undersaturated magmas, in particular in the
presence of a multicomponent fluid phase, in addition to the
requirements for detailed petrological understanding of erupted
products.

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Funding}
This work was partly funded by labex VOLTAIRE project
(ANR-10-LABX-100-01) and equipex PLANEX (ANR-11-EQPX-0036). CO
acknowledges support from NERC grant NE/N009312/1.

\CDRGrant[ANR]{ANR-10-LABX-100-01}
\CDRGrant[ANR]{ANR-11-EQPX-0036}
\CDRGrant[NERC]{NE/N009312/1}

\section*{Acknowledgements}
The manuscript greatly benefited from the constructive comments of two
anonymous reviewers and from the efficient editorial handling of
Francois Chabaux.

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