\makeatletter \@ifundefined{HCode} {\documentclass[screen, CRGEOS, Unicode, Thematic]{cedram} %\usepackage[sort&compress,square,comma,authoryear]{natbib} \usepackage[square,comma,authoryear]{natbib} \renewcommand\bibsection{\section*{\refname}} \newenvironment{noXML}{}{} \def\thead{\noalign{\relax}\hline} \def\endthead{\noalign{\relax}\hline} \def\tsup#1{$^{{#1}}$} \def\tsub#1{$_{{#1}}$} \def\ndash{\mbox{--}} \def\botline{\\\hline} \def\tabnote#1{\vskip4pt\parbox{.98\linewidth}{#1}} \RequirePackage{etoolbox} \usepackage{upgreek} \def\jobid{crgeos20240485} %\graphicspath{{/tmp/\jobid_figs/web/}} \graphicspath{{./figures/}} \newcounter{runlevel} \let\MakeYrStrItalic\relax \def\refinput#1{} \def\back#1{} \def\rmSigma{\Sigma} \def\xsection#1{} \csdef{Seqnsplit}{\\} \DOI{10.5802/crgeos.276} \datereceived{2024-06-12} \daterevised{2024-10-09} \dateaccepted{2024-10-10} \ItHasTeXPublished \makeatletter \g@addto@macro{\UrlBreaks}{\UrlOrds} \gappto{\UrlBreaks}{\UrlOrds} \makeatother } { \PassOptionsToPackage{authoryear}{natbib} \documentclass[crgeos]{article} \usepackage[T1]{fontenc} \def\CDRdoi{10.5802/crgeos.276} \let\newline\break \makeatletter \def\CDRsupplementaryTwotypes[#1]#2#3{} \def\href#1#2{\url{#1}} } \makeatother \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} \maketitle \clearpage \twocolumngrid \end{noXML} \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. \back{} \bibliographystyle{crgeos} \bibliography{crgeos20240485} \refinput{crgeos20240485-reference.tex} \end{document}