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\DOI{10.5802/crgeos.235}
\datereceived{2023-03-15}
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\dateposted{2023-09-26}
\begin{document}

\begin{noXML}

%\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{Hydrogen and hydrogen sulphide in volcanic gases: abundance,
processes, and atmospheric fluxes}

\author{\firstname{Alessandro} \lastname{Aiuppa}\CDRorcid{0000-0002-0254-6539}\IsCorresp}
\address{Dipartimento di Scienze della Terra e del Mare, Universit\`{a}
di Palermo, Palermo, Italy}
\email[A. Aiuppa]{alessandro.aiuppa@unipa.it}

\author{\firstname{Yves} \lastname{Moussallam}\CDRorcid{0000-0002-4707-8943}}
\address{Lamont-Doherty Earth Observatory, Columbia University, New
York, USA}
\email[Y. Moussallam]{yves.moussallam@ldeo.columbia.edu}

\keywords{\kwd{Hydrogen}\kwd{Hydrogen sulphide}\kwd{Volcanic
gases}\kwd{Volcanic gas redox}\kwd{Atmospheric fluxes}}

\begin{abstract}
Hydrogen (H$_{2}$) and hydrogen sulphide (H$_{2}$S) are typically
present at only minor to trace levels in volcanic gas emissions, and
yet they occupy a key role in volcanic degassing research in view of
the control they exert on volcanic gas reducing capacity (e.g., their
ability to remove atmospheric O$_{2}$). In combination with other major
compounds, H$_{2}$ and H$_{2}$S are also key to extracting information
on source magma conditions (temperature and redox) from observed
magmatic gas compositions. Here, we use a catalogue, compiled by
extracting from the geological literature a selection of representative
analyses of magmatic to mixed (magmatic--hydrothermal) gases, to review
the processes that control H$_{2}$ and H$_{2}$S abundance in volcanic
gases. We show that H$_{2}$ concentrations and H$_{2}$/H$_{2}$O ratios
in volcanic gases both exhibit strong positive temperature dependences,
while H$_{2}$S concentrations and H$_{2}$S/SO$_{2}$ ratios are
temperature insensitive overall. The high H$_{2}$ concentrations (and
low H$_{2}$S/SO$_{2}$ compositions, of ${\sim}$0.1 on average) in
high-temperature (${>}$1000~{\textdegree}C) magmatic gases are overall
consistent with those predicted thermodynamically assuming external
redox buffering operated by the coexisting silicate melt, at oxygen
fugacities ranging from ${\Delta}$FMQ $-$1 to 0 (non-arc volcanoes) to
${\Delta}$FMQ 0 to ${+}$2 (arc volcanoes) (where ${\Delta}$FMQ is oxygen
fugacity expresses as a log unit difference relative to the
Fayalite--Magnetite--Quartz oxygen fugacity buffer). Lower temperature
(${<}$1000~{\textdegree}C) volcanic gases exhibit more oxidizing redox
conditions (typically above the Nickel--Nickel Oxide buffer) that are
caused by a combination of (i)~gas re-equilibration during
closed-system (gas-phase only) adiabatic cooling in a gas-buffered
system, and (ii)~heterogenous (gas--mineral) reactions. We show, in
particular, that gas-phase equilibrium in the
H$_{2}$--H$_{2}$S--H$_{2}$O--SO$_{2}$ system is overall maintained upon
cooling down to ${\sim}$600~{\textdegree}C, while quenching of higher
temperature equilibria (at which Apparent Equilibrium Temperatures,
AETs, largely exceed measured discharge temperatures) is more
frequently observed for higher extents of cooling (e.g., at $T <
600$~{\textdegree}C). In such lower temperature volcanic environments,
gas--mineral reactions also become increasingly important, scavenging
magmatic SO$_{2}$ and converting it into H$_{2}$S and hydrothermal
minerals (sulphates and sulphides). These heterogeneous reactions, when
occurring, can also control the temperature dependence of the volcanic
gas H$_{2}$/H$_{2}$O ratios. Finally, by using our volcanic gas dataset
in tandem with recently published global{\pagebreak} volcanic
SO$_{2}$ and CO$_{2}$ budgets, we provide refined estimates for total
H$_{2}$S (median, 1.4~Tg/yr; range, 0.9--8.8~Tg/yr) and H$_{2}$
(median, 0.23~Tg/yr; range, 0.06--1~Tg/yr) fluxes from global subaerial
volcanism.
\end{abstract}

\maketitle
\vspace*{.6pc}

\twocolumngrid

\end{noXML}

\section{Introduction} \label{sec1}

\looseness=-1
At the relatively oxidised redox conditions of present day Earth's
upper mantle \citep[e.g.,][]{FrostMcCammon2008, Stagnoetal2013}, the
magmatic gas phase delivered to the atmosphere by shallow degassing,
mantle-sourced magmas is dominated by oxidised molecular combinations
of the elements H, C, O and S, e.g., by water (H$_{2}$O) carbon dioxide
(CO$_{2}$) and sulphur dioxide (SO$_{2}$)
\citep[e.g.,][]{GerlachNordlie1975, Symondsetal1994, Giggenbach1996,
FischerChiodini2015}. However, volcanoes also release a variety of
reduced gas species such as molecular hydrogen (H$_{2}$) and hydrogen
sulphide (H$_{2}$S) that, while making up a relatively small fraction
of the magmatic gas phase, convey information on a variety of
magma-related topics and processes \citep[e.g.,][]{Moussallametal2019a,
MorettiStefansson2020}. For example, studying the release of
H$_{2}$, H$_{2}$S and other reduced gas species (e.g., carbon monoxide,
CO) from modern subaerial volcanoes helps setting constraints on the
composition of the early atmosphere in the Hadean and the Archean
\citep[e.g.,][]{Kastingetal1993, Gaillardetal2015}, and to predict the
temporal evolution and progressive oxygenation of the atmosphere
through geological time \citep[e.g.,][]{Holland2002, Gaillardetal2011,
GaillardScaillet2014}. Measuring H$_{2}$ and H$_{2}$S in combination
with their oxidised complements H$_{2}$O and SO$_{2}$ brings
information on the redox conditions of magmatic gases 
\citep[e.g.,][]{Ellis1957, Matsuo1962, Gerlach1979, Gerlach1982, Gerlach1993a,
Gerlach1993b, Shinoharaetal1993, Ohbaetal1994, Symondsetal1994,
BurgisserScaillet2007, Oppenheimeretal2018, Moussallametal2019a,
Moussallametal2022}, and can potentially allow
constraining oxygen fugacity of the source magmas. H$_{2}$ and H$_{2}$S
in volcanic gases can also effectively contribute to volcano monitoring
\citep[e.g.,][]{Kernetal2022}. For example, H$_{2}$S is a key component
of the hydrothermal gases released by quiescent, closed-conduit
volcanoes \citep[e.g.,][]{Giggenbach1980}, so that monitoring the
H$_{2}$S/SO$_{2}$ ratio is critical to detecting (and interpreting) the
magmatic unrest that proceeds volcanic activity resumption 
\citep[e.g.,][]{Suronoetal2012, Moussallametal2014b,
StixdeMoor2018, deMooretal2019}, and to distinguish
internally triggered (volcano-related) gas changes from those caused by
external factors (e.g., rainfall and/or water level changes)
\citep{Morettietal2020, Mouneetal2022}. A model for estimating magmatic
variables (temperature and redox) from the combined analysis of
H$_{2}$S/SO$_{2}$ and H$_{2}$/H$_{2}$O ratios in volcanic plumes has
recently been proposed that promises to become a useful volcano
monitoring tool \citep{Moussallametal2022}. Volcano-released H$_{2}$
and H$_{2}$S are dispersed into the atmosphere through volcanic plumes,
where concentrations at ppm levels are typically observed, well in
excess of those typical of ambient air \citep[of respectively
${\sim}$0.5~ppm and ${\sim}$0.1--0.3~ppb;][]{SeinfeldPandis2016}. Such
in-plume H$_{2}$ and H$_{2}$S measurements
\citep[e.g.,][]{Aiuppaetal2005, Aiuppaetal2011} are useful to
interpreting reaction mechanisms and rates, and ultimately lifetime of
reduced compounds, during oxidative atmospheric processing, both
near-vent \citep[e.g.,][]{Martinetal2006, Robertsetal2019} and in the
colder, more distal plumes \citep[e.g.,][]{Aiuppaetal2007}. Although
observations indicate H$_{2}$ and H$_{2}$S are conserved during
atmospheric dispersion over short timescales (seconds to days)
\citep[e.g.,][]{Aiuppaetal2007, Aiuppaetal2011}, these species are
ultimately oxidised directly (by molecular oxygen, O$_{2}$) or
indirectly (via O$_{2}$-derived radicals, such as hydroxyl radicals)
during longer atmospheric transit, thus controlling the reducing power
(e.g., the ability to act as atmospheric O$_{2}$ sinks) of volcanic
gases \citep[e.g.,][]{Stolperetal2021}.

\looseness=-1
Despite their importance in such a variety of subjects, and
notwithstanding that excellent reviews are available on magmatic and
hydrothermal gases in general \citep[e.g.,][]{Giggenbach1980,
Giggenbach1996, Symondsetal1994, ChiodiniMarini1998,
FischerChiodini2015, HenleyFischer2021}, no specific study has so far
been devoted to reviewing abundance and source mechanisms of H$_{2}$
and H$_{2}$S in volcanic gases. Also, estimates of global H$_{2}$ and
H$_{2}$S fluxes from subaerial volcanism remain subject to large
uncertainties, owing to the sparse and limited dataset existing. For
example, although natural (geogenic) H$_{2}$ emissions have received
increasing{\break} attention recently \citep[e.g.,][]{Zgonnik2020},
with Earth degassing being though to sustain a cumulative global
H$_{2}$ flux of 6 \citep{GilatVol2012} to 23 \citep{Zgonnik2020} Tg/yr,
there are only two studies in the literature that specifically address
the quantification of volcanic H$_{2}$ emissions from two persistent
active volcanoes [Etna in Sicily, ${\sim}$0.00065~Tg/yr;
\citealp{Aiuppaetal2011}; and Erebus in Antarctica,
${\sim}$0.001~Tg/yr; \citealp{Moussallametal2012}]. As such, current
inventories of volcanic H$_{2}$ fluxes to the atmosphere [0.2 to
0.7~Tg/yr; \citealp{Warneck1988, Canfieldetal2006, Stolperetal2021}]
are subject to large uncertainties. Likewise, the volcanogenic
contribution to the global natural H$_{2}$S flux (${\sim}$7.7~Tg/yr) is
similarly poorly understood, with most estimates converging at
${\sim}$1~Tg/yr \citep[see review by][]{Watts2000} but with total range
being as large as 1 to 37~Tg/yr \citep{Halmeretal2002}.

Here, we review our current understanding of the processes that govern
H$_{2}$ and H$_{2}$S abundance in volcanic gases. To this aim, we
present an updated volcanic gas composition catalogue that we
have put together from available literature information. We also use
this catalogue, in combination with recently improved global volcanic
SO$_{2}$ and CO$_{2}$ fluxes \citep{Carnetal2017, Aiuppaetal2019,
Fischeretal2019}, to present an improved quantification of global
volcanic H$_{2}$ and H$_{2}$S fluxes.

\section{Dataset} \label{sec2}

We compiled a dataset of 747 gas analyses by complementing recent
\citep{Aiuppa2015, Aiuppaetal2017, Moussallametal2019a,
Moussallametal2022} and older \citep{Symondsetal1994, Giggenbach1997}
volcanic gas catalogues with newly published gas results. This dataset
is not exhaustive, e.g., it is not meant to cover the entire mass of
information present in the geological literature. Yet, we are confident
our dataset is well representative of the compositional range of
volcanic gases globally (see below).

The full dataset is available as Supplementary Tables~1 and~2. The
dataset includes data for both high temperature ($T >
600$~{\textdegree}C; Supplementary Table~1) magmatic gases and
for lower temperature ($T \leq 600$~{\textdegree}C;
Supplementary Table~2) mixed (magmatic--hydrothermal) fluids. The
600~{\textdegree}C threshold, although somewhat arbitrary, is justified
by the statistical distribution of the global volcanic arc gas
population \citep{Aiuppaetal2017}, and is consistent with the threshold
used in similar recent studies \citep{Moussallametal2019a,
Moussallametal2022}. Some hydrothermal (temperature close to boiling)
gas samples are also used but are limited to those volcanoes that have
recently erupted and/or that have detectable SO$_{2}$---this latter gas
is typically absent in hydrothermal fluids ``strictu sensu'', that are
covered by other reviews \citep[e.g.,][]{Giggenbach1980,
Giggenbach1987, ChiodiniMarini1998, FischerChiodini2015,
StixdeMoor2018}. The dataset is further categorised depending
on \mbox{tectonic} setting in arc and non-arc volcanic gases, the
latter including gases released by intraplate and continental rift
volcanism \citep{Aiuppaetal2021}. The Etna magmatic gases are plotted
separately in view of the relatively enigmatic nature of volcanism at
this specific locality.

The dataset combines compositional data for both fumaroles (Sample type
``F'' in Supplementary Tables~1 and~2) and for atmospheric gas plumes
(Sample type ``PL'' in Supplementary Tables~1 and~2). We refer to the
original studies (data sources in Supplementary Tables~1 and~2) for
details on sampling and analytical procedures. Broadly speaking
however, fumarole data (F) have been obtained by direct sampling
(Sample Methodology ``DS'' in Supplementary Tables~1 and~2)
\citep{Symondsetal1994}, in which fumarolic effluents are captured
in-pre-evacuated gas flasks partially filled with a reactive solution
[a NaOH solution in most applications; \citealp{Giggenbach1996}].
Incondensable gases (like H$_{2}$) are concentrated in the head space
(later analysed in the lab. via Gas Chromatography), while condensable
gases (such as H$_{2}$S) trapped by the solution are analysed by wet
chemistry methods (typically by ion chromatography). Uncertainty in
DS-derived gas concentrations is typically low (${<}$5\% in most
studies). Plume results (PL) are based on in-situ, near real-time gas
concentration measurements with the Multi-GAS (Sample Methodology
``MG'' in Supplementary Tables~1 and~2), a widely used multi-sensor
unit that analyses H$_{2}$ and H$_{2}$S (among other species) with
specific electrochemical sensors \citep{Aiuppaetal2005,
Shinohara2005}.
In such a case, the Multi-GAS measured in-plume concentrations have
been converted in air-free gas concentrations listed in Supplementary
Tables~1 and~2. Typical associated uncertainty is
${\leq}$15--20\%.\looseness=-1 

It is important to remind that, where available, magmatic gas
compositions are reported in the form of ``restored'' magmatic gas
compositions at equilibrium temperature (identified by Sample type ``F,
R'' in Supplementary Table~1). These restored gas compositions have
been extracted mostly from \citet{Symondsetal1994}, and have been
obtained by the authors by applying (to measured fumarolic gas
compositions) the procedure introduced by \citet{Gerlach1993a}. This
numerical procedure (i)~identifies the causes of disequilibrium in
volcanic gases (often due to sampling/conservation artefacts; e.g., air
addition and oxidation), and (ii)~iteratively removes the cause(s) of
disequilibrium until an restored equilibrium gas (at a given
equilibrium temperature) is obtained \citep{Gerlach1993a,
Symondsetal1994}.

Our dataset, illustrated in a H$_{2}$O/10--CO$_{2}$--5${\cdot}$S$_{{T}}$
space (where S$_{{T}}$ is total sulphur, or $\text{SO}_{2} +
\text{H}_{2}\text{S}$) (Figure~\ref{fig1}), demonstrates the large
heterogeneity of volcanic gas compositions found in previous
inventories \citep[e.g.,][]{Symondsetal1994, Aiuppa2015}, and
represents well the well-established \citep[e.g.,][]{Symondsetal1994,
Gerlach1982} chemical diversity between arc and within-plate/rift
magmatic gases, with the former being typically more hydrous
\citep[e.g.,][]{Fischer2008, TaranZelenski2015} and the latter
extremely variable in terms of their CO$_{2}$/S$_{{T}}$ signatures
\citep[e.g.,][]{Aiuppaetal2021}. The two magmatic gas populations
exhibit some overlap, as previously found \citep[e.g.,][]{Aiuppa2015}.
The lower temperature ($T \leq 600$~{\textdegree}C) mixed gases are
even more compositionally heterogeneous (Figure~\ref{fig1}), and while
many gas samples overlap with the magmatic gas range, many others plot
in the CO$_{2}$-rich, S-poor compositional domain (top left portion of
Figure~\ref{fig1}), indicating some extent of sulphur loss [scrubbing;
\citealp{Symondsetal2001}] during gas--water--rock hydrothermal
interactions in the subsurface
\citep[e.g.,][]{Aiuppaetal2017}.\looseness=-1

\begin{figure}[t!]
\includegraphics{fig01}
{\vspace*{-.3pc}}
\caption{\label{fig1}Triangular plots illustrating the compositional
variability in the gas catalogue used (data from Supplementary Tables~1
and~2).}
{\vspace*{-.7pc}}
\end{figure}

\section{Results} \label{sec3}
\subsection{Hydrogen and hydrogen sulphide{\hfill\break} abundances in
volcanic gases} \label{sec3.1}

H$_{2}$ and H$_{2}$S are usually minor (${<}$1~mol\%) to trace
(${<}$0.1~mol\%) components of volcanic gases
\citep[e.g.,][]{Giggenbach1996}, although H$_{2}$ concentrations
exceeding 10~mol\% have occasionally also been reported \citep[see
review of][]{Zgonnik2020} and H$_{2}$S becomes increasingly important
(e.g., a major species, ${>}$1~mol\%) in low temperature hydrothermal
steam samples \citep[e.g.,][]{Giggenbach1980, Giggenbach1997}.

In our volcanic gas catalogue, H$_{2}$ and H$_{2}$S concentrations span
several orders of magnitude, from ultra-trace (${<}10^{-6}$~mol\%) to
major (${>}$1~mol\%) levels (Supplementary Tables~1 and~2). In
Figures~\ref{fig2}a and~b, the whole H$_{2}$ and H$_{2}$S
concentration dataset (in mol\%) is illustrated as a function of
measured gas outlet temperature.

\begin{figure}[t!]
\includegraphics{fig02}
\caption{\label{fig2}Scatter plots illustrating the dependence of
(a)~H$_{2}$ and (b)~H$_2$S concentrations on measured discharge
temperature (data from Supplementary Tables~1 and~2). Symbols as in
Figure~\ref{fig1}. In this and following figures, error bars are not
shown as smaller than the data symbols.}
{\vspace*{-.4pc}}
\end{figure}

Figure~\ref{fig2}a shows that volcanic gas H$_{2}$ concentrations
exhibit a marked temperature dependence, particularly at $T >
600$~{\textdegree}C. H$_{2}$ concentrations are the highest (0.49--3.1\%
levels) in the hot ($T > 1000$~{\textdegree}C) magmatic gases
\citep{Gerlach1979, Gerlach1980, Gerlach1982, Gerlach1993a,
Gerlach1993b, Symondsetal1994} from within-plate (e.g., Kilauea) and
continental rift (e.g., Nyiragongo, Erta Ale) volcanoes. In arc
magmatic gases, H$_{2}$ concentrations decrease with decreasing
temperature, from 0.1--1.7~mol\% at 800--1100~{\textdegree}C to
0.002--0.38~mol\% at ${\sim}$600~{\textdegree}C. Etna's magmatic gases
plot at the boundary between arc and non-arc gases (H$_{2}$ range:
0.14--2.1~mol\%). The temperature dependence is more scattered in
mixed (magmatic--hydrothermal) gases, in which H$_{2}$ varies from as
low as $4 \times 10^{-6}$~mol\% to as high as 0.867~mol\%.
Close-to-boiling fumaroles ($T < 100$~{\textdegree}C) are especially
diverse in their H$_{2}$ contents that span more than 5 orders of
magnitude.

H$_{2}$S concentrations show no obvious temperature dependence in the
global volcanic gas catalogue (Figure~\ref{fig2}b). The
H$_{2}$S-richest samples are again found in the ``restored'' magmatic
gas analyses from within-plate and continental rift volcanoes (H$_{2}$S
range: 0.04--3.2~mol\%; mean $0.9 \pm 0.55$~mol\%). The range of
H$_{2}$S concentrations in arc magmatic gases is vast, from 0.00016 to
3.3~mol\%. The mean arc gas H$_{2}$S concentration ($0.25 \pm
0.55$~mol\%) is lower than for non-arc volcanic gases ($0.9 \pm
0.55$~mol\%), but given the large spread of values the two populations
are essentially overlapping. Colder ($T \leq 600$~{\textdegree}C)
magmatic--hydrothermal gases exhibit an even larger range of values,
including the lowest (0.000028~mol\%) and highest (14~mol\%) values
of the entire dataset. As for arc magmatic gases, no obvious pattern
with temperature is observed (Figure~\ref{fig2}a). 
{\vspace*{-.3pc}}

\section{Discussion} \label{sec4}
\subsection{Ratios between redox couples} \label{sec4.1}

A standard practise used when interpreting volcanic gas H$_{2}$ and
H$_{2}$S concentrations is to normalise them to their oxidised
counterparts H$_{2}$O and SO$_{2}$ \citep{Gerlach1980, Giggenbach1996,
Giggenbach1987}. This practise developed on since early demonstrations
\citep{Ellis1957, Matsuo1962} that high temperature volcanic gases
approach a state of thermodynamic equilibrium, in which ratios between
redox couples are controlled by equilibria:
{\begin{eqnarray}
&& \label{eq1} \text{H}_{2} + \tfrac{1}{2}\text{O}_{2}=
\text{H}_{2}\text{O}\Seqnsplit
&& \label{eq2} \text{H}_{2}\text{S} + \tfrac{3}{2}\text{O}_{2}=
\text{SO}_{2} + \text{H}_{2}\text{O}
\end{eqnarray}}\unskip\noindent
In a set of seminal articles, Gerlach and co-workers
\citep{Gerlach1979, Gerlach1980, Gerlach1993a, Gerlach1993b,
Symondsetal1994} confirmed that the assumption of ``full'' equilibrium
among all the different species in a volcanic gas mixture holds at
magmatic temperatures. A useful concept introduced to test this full
equilibrium state hypothesis was that of the so-called Correspondence
Temperature (CT), the temperature at which the measured (in a specific
volcanic gas sample) and equilibrium concentrations of a gas species
match one another. As the CTs of the different gas species were found
to converge to within a very narrow range in many high temperature gas
samples \citep{Gerlach1979, Gerlach1980, Gerlach1993a, Gerlach1993b},
the full equilibrium hypothesis could be proved.

However, as demonstrated in later work by \citet{Giggenbach1987,
Giggenbach1996}, the full equilibrium assumption is unlikely to hold in
lower temperature gas samples, where different extents of
re-equilibrations of the different redox couples (e.g., reactions~(\ref{eq1})
and~(\ref{eq2})), as well as admixing with external (meteoric, atmospheric)
fluids \citep{TaranZelenski2015} and reaction with wall-rocks
\citep{HenleySeward2018, HenleyFischer2021}, become likely
eventualities. In such conditions, a conservative approach is to deal
with specific redox reactions individually, e.g., to use plots that
compare, for each specific redox couple, the analytically determined
and equilibrium ratios. This approach, initially elaborated by
\citet{Giggenbach1987, Giggenbach1996} and \citet{Chiodinietal1993}, is
followed below, where we update their results and corroborate their
conclusions using the more complete, today available gas catalogue
(Supplementary Tables~1 and~2).

At discharge conditions ($P = 1$~bar), and at equilibrium, reactions
(\ref{eq1}) and~(\ref{eq2}) imply that ratios between redox couples
will exhibit the following dependences on redox (as expressed by oxygen
fugacity, $f\text{O}_{2}$) and temperature (in~K):
{\begin{eqnarray}
&&\label{eq3} \log\frac{\text{H}_{2}}{\text{H}_{2}\text{O}}=
-\frac{\text{12,707}}{{T}} + 2.548-\frac{1}{2}\log f\text{O}_{2}
\qquad\Seqnsplit
&&\label{eq4} \log\frac{\text{SO}_{2}}{\text{H}_{2}\text{S}}=
\frac{\text{27,377}}{{T}} - 3.986+\frac{3}{2}\log f\text{O}_{2}-
\log X_{\mathrm{H}_{2}\mathrm{O}}\qquad
\end{eqnarray}}\unskip\noindent
These equations are obtained by re-arranging the equilibrium constants
K$_{1}$ and K$_{2}$ of~(\ref{eq1}) and~(\ref{eq2}) [we use
thermodynamic data from Chase and National Institute of Standards and
Technology (U.S.), \citeyear{ChaseNISTUS1998}] and assuming ideal gas
behaviour (fugacity coefficients $\gamma = 1$).

The presence of redox sensitive elements in either the silicate
melt/rock matrix (where iron is typically available in both ${+}$2 and
${+}$3 valence states) or in the gas phase (where sulphur is present in
sufficient amounts in both ${-}$2 and ${+}$4 valence states) has long been
proposed \citep[e.g.,][]{Giggenbach1987, Gerlach1993a}
to act as a buffer for oxygen fugacity in volcanic gases
\citep[see][for examples of recent reviews]{MorettiStefansson2020,
Moretti2021, MorettiNeuville2021}. \citet{Gerlach1993a, Gerlach1993b}
proposed that gas speciation in high temperature
(${>}$900~{\textdegree}C) magmatic gases is buffered by equilibrium
redox exchange between gas and coexisting silicate melt. The same
buffers can also operate at sub-solidus conditions, e.g., if gas reacts
and equilibrates with the host rock matrix in which iron is present in
minerals with two distinct oxidation states
\citep[e.g.,][]{Giggenbach1987}. It was however found that, in such
lower temperature conditions, the buffering role of sulphur in the gas
phase (where H$_{2}$S and SO$_{2}$ are simultaneously present) becomes
increasingly effective \citep[e.g.,][]{Giggenbach1987, Giggenbach1996},
although the competing roles of homogeneous (gas-only) and heterogenous
(gas--mineral) reactions in controlling the volcanic gas redox budget
remained debated \citep[e.g.,][]{HenleyFischer2021} (see below).

Irrespective of the buffering medium (either melt, rock, or gas),
$f\text{O}_{2}$ in~(\ref{eq3}) and~(\ref{eq4}) can conveniently be
replaced by the temperature dependences imposed by the redox buffers
\citep[e.g.,][see recent reviews by \citet{Cicconietal2020,
MorettiNeuville2021}]{Eugster1977, Frost1991}. The predicted
(\ref{eq3}), mineral-buffered or gas-(H$_{2}$S/SO$_{2}$) buffered,
H$_{2}$/H$_{2}$O ratios are graphically illustrated in
Figure~\ref{fig3}a. The same mineral buffered SO$_{2}$/H$_{2}$S ratios
are illustrated in Figure~\ref{fig3}b. These model trends implicate
that, in mineral-buffered conditions (e.g., when gas redox is buffered
by heterogeneous redox budget exchanges with either the melt or the
host rocks), H$_{2}$ is expected to become increasingly abundant
(relative to H$_{2}$O), and H$_{2}$S increasingly depleted (relative to
SO$_{2}$), with increasing temperature (Figure~\ref{fig3}). At fixed
temperature, H$_{2}$/H$_{2}$O ratios are expected to decrease (and
SO$_{2}$/H$_{2}$S to increase) as redox evolves from more reducing
(e.g., redox buffered at the Fayalite--Magnetite--Quartz (FMQ) mineral
buffer) to more oxidised (as expressed by the hematite--magnetite (HM)
mineral buffer) conditions. Results of a comparison between modelled
and measured (volcanic gases) ratios are summarised below
(Figure~\ref{fig3}).

\begin{figure}[ph!]
\includegraphics{fig03}
\bcaption{\label{fig3}\fontsize{10}{11.93}\selectfont
Temperature dependence of (a)~H$_{2}$/H$_{2}$O
and (b)~SO$_{2}$/H$_{2}$S molar ratios in our volcanic gas catalogue
(data from Supplementary Tables~1 and~2). Symbols as in
Figure~\ref{fig1}. The thick coloured lines are the predicted
temperature dependences of the ratios imposed (at 1~bar) by the most
common mineral and gas buffers. These are obtained by using
Equations~(\ref{eq3}) and~(\ref{eq4}) and oxygen fugacity buffered by
either the melt/rock matrix or sulphur species in the gas phase. The
mineral buffer \citep[see][for the relevant $f\text{O}_{2}$--$T$
relationships]{Frost1991} curves illustrated are: HM: 
Hematite--Magnetite; NNO: Nickel--Nickel Oxide; 
FMQ: Fayalite--Magnetite--Quartz;
GB: FeO--FeO$_{1.5}$ buffer \citep{Giggenbach1987}. The dashed line in~(a)
labelled H$_{2}$S/SO$_{2}$ corresponds to the sulphur gas buffer of
\citet{Giggenbach1987}, and is obtained by solving Equation~(\ref{eq6})
(at 1~bar) assuming equimolar amounts of H$_{2}$S and SO$_{2}$
($\text{H}_{2} \text{S/SO}_{2} = 1$) (a similar line at fixed
H$_{2}$S/SO$_{2}$ of 0.1 is also shown in panel~(b)). The DP line is
for gas ratios predicted using the empirically derived $f\text{O}_{2}$
versus temperature dependence typical of hydrothermal systems
\citep[e.g.,][]{DAmorePanichi1980}. Thin light blue curves labelled
H\&F are the gas ratios predicted by the gas--mineral reactions of
\citet{HenleyFischer2021} (the model runs illustrated in their
original Figure~5 are shown).}{2}{ The majority of the mixed
(magmatic--hydrothermal; $T < 600$~{\textdegree}C) gases plot in
panel~(a) along a compositional array (grey dashed area) that overlaps
with both (i)~the H$_{2}$S/SO$_{2}$ buffer lines, and (ii)~the
heterogenous (gas--mineral) equilibria of \citet{HenleyFischer2021}.
Many gas samples have higher H$_{2}$/H$_{2}$O ratio compositions than
predicted by either homogenous \citep{Giggenbach1987} or heterogeneous
\citep{HenleyFischer2021} reactions, likely indication preservation
(quenching) of higher-$T$ equilibria. High-$T$ magmatic gases plot in
between the NNO and FMQ mineral buffers, suggesting buffering from
source silicate melt. See text for discussion.\looseness=-1}
\vspace*{-.3pc}
\end{figure}

\subsubsection{High-temperature magmatic gases} \label{sec4.1.1}

The measured volcanic gas H$_{2}$/H$_{2}$O ratios, as derived from the
analytically determined gas concentrations, are illustrated in
Figure~\ref{fig3}a (and listed Supplementary Tables~1 and~2).
Comparison with modelled compositions (see above) shows that the hot
($T > 900$~{\textdegree}C) non-arc magmatic gases
\citep{Gerlach1980, Gerlach1993b,
Symondsetal1994} have ``restored'' gas compositions that
convert into H$_{2}$/H$_{2}$O (and SO$_{2}$/H$_{2}$S ratios; see
Figure~\ref{fig3}b) overlapping those predicted at equilibrium
(\ref{eq3}) and~(\ref{eq4}) in a melt-buffered gas system at
${\sim}$FMQ, see Figures~\ref{fig3} and~\ref{fig4}. As previously found
\citep{Gerlach1980, Gerlach1993a, Gerlach1993b} therefore, the H$_{2}$
and H$_{2}$S contents of such gases appear to be controlled by
heterogeneous (melt--gas) redox exchanges. High temperature ($T >
900$~{\textdegree}C) arc magmatic gases likewise approach the
melt-buffered model lines, but the majority of them plot at lower
H$_{2}$/H$_{2}$O (and higher SO$_{2}$/H$_{2}$S) ratios relative to
non-arc magmatic gases, close to the NNO (Nickel--Nickel-Oxide) mineral
buffer model line (Figure~\ref{fig3}). This apparent more oxidised
(lower H$_{2}$/H$_{2}$O ratios) signature of arc gases is also well
represented in Figure~\ref{fig4}, and we will return to this point in later
sections (cf. Section~\ref{sec4.3}). \looseness=-1

\begin{figure*}[t!]
\includegraphics{fig04}
{\vspace*{-.15pc}}
\caption{\label{fig4}(a)~Scatter plot of SO$_{2}$/H$_{2}$S versus
H$_{2}$/H$_{2}$O molar ratios in our volcanic gas catalogue (data from
Supplementary Tables~1 and~2). Symbols as in Figure~\ref{fig1}. The
thick coloured lines are the predicted gas molar ratios (from
Equations~(\ref{eq3}) and~(\ref{eq4})) for $f\text{O}_{2}$s calculated
using the temperature dependences imposed by the FMQ, NNO, GB and HM
mineral buffers (calculations are run over a range of temperatures, as
expressed by the isotherms: dashed lines, in~{\textdegree}C). The DP
line is derived by using (for $f\text{O}_{2}$ in Equations~(\ref{eq3})
and~(\ref{eq4})) the empirical $f\text{O}_{2}$ versus $T$ dependence in
hydrothermal systems \citep{DAmorePanichi1980}; thin light blue curves
labelled H\&F are the gas ratios predicted by the gas--mineral
reactions of \citet{HenleyFischer2021} (the model runs illustrated in
their original Figure~5 are shown). (b)~An expanded version of~(a)
illustrating the nominally SO$_{2}$-free field of hydrothermal steam
samples (in the 100--350~{\textdegree}C temperature range). The
magmatic to mixed (magmatic--hydrothermal) samples in our catalogue,
having detectable SO$_{2}$, plot to the right of the hydrothermal
field. Their SO$_{2}$/H$_{2}$S versus H$_{2}$/H$_{2}$O population is
well reproduced by both homogenous \citep[gas-phase only; dashed black
lines;][]{Giggenbach1987} or heterogeneous \citep{HenleyFischer2021}
reactions. However, the H\&F models predict progressively decreasing
SO$_{2}$/H$_{2}$S ratios at increasing mineral--gas reactions (and with
decreasing temperatures), while the majority of the gas samples define
a vertical array that is more consistent with gas oxidations (e.g.,
decreasing H$_{2}$/H$_{2}$O ratios) during closed-system gas cooling in
a S gas-buffered regime \citep[dashed vertical back line, the
H$_{2}$S/SO$_{2}$ gas buffer of][]{Giggenbach1987}.}
{\vspace*{-.45pc}}
\end{figure*}

\subsubsection{Mixed magmatic--hydrothermal gases} \label{sec4.1.2}

Lower temperature magmatic gases ($600~\text{{\textdegree}C} < T <
900$~{\textdegree}C) and mixed (magmatic--hydrothermal) gases ($T <
600$~{\textdegree}C) overall identify a compositional tendency of
decreasing H$_{2}$/H$_{2}$O ratios with decreasing temperature
(Figure~\ref{fig3}a). This trend (qualitatively identified by the grey
shaded region of Figure~\ref{fig3}a) is manifestly steeper than the
temperature dependences imposed by any of the mineral $f\text{O}_{2}$
buffers (solid lines). \citet{Giggenbach1987, Giggenbach1996} took this
as evidence of a marginal (if any) control exercised by redox budget
exchanges between gases and silicate melts (in the supra-solidus
regions) and/or with wall rocks (in the sub-solidus region). Rather,
\citet{Giggenbach1987, Giggenbach1996} proposed that the
H$_{2}$/H$_{2}$O ratios versus temperature dependence exhibited by
volcanic gas samples (Figure~\ref{fig3}a) can satisfactory be explained
by homogeneous (gas-phase only) redox reactions taking place during gas
expansion and cooling, according to reaction:
{\begin{equation}\label{eq5}
3\text{H}_{2} + \text{SO}_{2} = 2\text{H}_{2}\text{O} +
\text{H}_{2}\text{S}
\end{equation}}\unskip\noindent
from which:
{\begin{equation}\label{eq6}
\text{Log}\frac{\text{H}_{2}}{\text{H}_{2}\text{O}}=-\frac{1}{3}
\text{Log}\,K_{5} + \frac{1}{3}\text{Log}\frac{\text{H}_{2}\text{S}}
{\text{SO}_{2}} - \frac{1}{3}f_{\mathrm{H}_{2}\mathrm{O}}
\end{equation}}\unskip\noindent
The basic principle behind Equations~(\ref{eq5})--(\ref{eq6}) is that
the gas H$_{2}$/H$_{2}$O ratio will re-adjust (re-equilibrate) as
temperature decreases (e.g., during gas ascent and adiabatic expansion
from source (magma) to atmospheric discharge) in a gas-buffered regime
in which H$_{2}$S--SO$_{2}$ coexistence will control the gas redox
budget. Equation~(\ref{eq6}), at 1~bar and for equimolar amounts of
H$_{2}$S and SO$_{2}$ ($\text{H}_{2}\text{S}/\text{SO}_{2} = 1$),
resolves into what \citet{Giggenbach1987, Giggenbach1996} referred as
the H$_{2}$S/SO$_{2}$ gas buffer (Figure~\ref{fig3}). 

The resulting model-derived (Equation~(\ref{eq6})) temperature dependence of the
H$_{2}$/H$_{2}$O ratios (dashed line labelled H$_{2}$S/SO$_{2}$;
Figure~\ref{fig3}a) nicely reproduces the volcanic gas compositional
array (grey band). Notably, this ability of coexisting H$_{2}$S and
SO$_{2}$ to buffer gas phase redox is entirely consistent with the
temperature invariant, analytically determined SO$_{2}$/H$_{2}$S ratios
(Figure~\ref{fig3}b). \citet{Giggenbach1987} concluded that the
conversion of SO$_{2}$ to H$_{2}$S during gas cooling, as implicated by
the mineral buffer curves (Figure~\ref{fig3}b), is inhibited by the
rapid transit of magma sourced gases through host rocks, preventing
gas--rock reactions to become effective (to achieve equilibrium).
The temperature-invariant, measured SO$_{2}$/H$_{2}$S gas compositions
in our dataset (Figure~\ref{fig3}b) indeed suggest that sulphur
speciation is little affected by gas--mineral reactions during cooling,
although data align along a nearly horizontal trend at
SO$_{2}$/H$_{2}$S of ${\sim}$10 (H$_{2}$S/SO$_{2}$ of ${\sim}$0.1)
rather than ${\sim}$1 [as implicated in the original H$_{2}$S/SO$_{2}$
gas buffer of \citealp{Giggenbach1987, Giggenbach1996}]
(Figures~\ref{fig3}b, \ref{fig4}).

An alternative view to that of \citet{Giggenbach1987} has recently been
proposed by \citet{HenleyFischer2021}. The authors, based on field
evidence arising from rock alteration assemblages found at extinct (now
eroded) andesitic volcanoes \citep{HenleyBerger2011, Henleyetal2015},
proposed that gas H$_{2}$/H$_{2}$O and SO$_{2}$/H$_{2}$S ratios are
controlled by heterogeneous (mineral--gas) rather than homogenous
(gas-only) reactions. The authors presented a comprehensive
multi-component thermochemical modelling of gas--solid equilibria of
magmatic SO$_{2}$ reaction with primary rock-forming minerals. The key
reaction invoked by the authors is:
{\begin{eqnarray}
&& \text{CaAl}_{2}\text{Si}_{3}\text{O}_{8(s)} + 2\text{SO}_{2(g)} +
2\text{H}_{2(g)}\nonumber\\
&&\quad  = \text{CaSO}_{4(s)}+ \text{Al}_{2}\text{SiO}_{5(s)}
+ \text{SiO}_{2(s)} + \text{H}_{2}\text{O}_{(g)} + \text{H}_{2}
\text{S}_{(g)} \label{eq7} \nonumber\\
\end{eqnarray}}\unskip\noindent
in which magmatic SO$_{2}$ disproportionate into both oxidised
(anhydrite) and reduced (H$_{2}$S) sulphur forms while plagioclase is
converted into a \mbox{secondary} Al-bearing hydrothermal mineral. Similar
\mbox{reactions} can be written to account for the reaction of magmatic
SO$_{2}$ with ferromagnesian minerals, such as ferrosilite (Fe-rich
pyroxene) \citep{HenleyFischer2021}:{\vspace*{-.2pc}}
{\begin{equation}\label{eq8}
\text{FeSiO}_{3(s)} + \text{SO}_{2(g)} + 3\text{H}_{2(g)} =
\text{FeS}_{(s)} + 3\text{H}_{2}\text{O}_{(g)} + \text{SiO}_{2(s)}
\end{equation}}\unskip\noindent
This reaction nicely accounts for the pervasive precipitation of iron
sulphides (e.g., pyrite and pyrrhotite) in hydrothermal systems. 

The equilibrium constant of reaction (\ref{eq7}):
{\begin{equation}\label{eq9}
K_{7}=\frac{\text{H}_{2}\text{S}}{\text{SO}_{2}} \cdot \frac{1}
{\text{SO}_{2}} \cdot \frac{1}{\text{H}_{2}\text{O}} \cdot \frac{1}
{\left(\frac{\text{H}_{2}}{\text{H}_{2}\text{O}}\right)^{2}}
\end{equation}}\unskip\noindent
was rearranged by \citet{HenleyFischer2021} to obtain:{\vspace*{-.2pc}}
{\begin{eqnarray}
\text{Log}\frac{\text{H}_{2}\text{S}}{\text{SO}_{2}} &=& \text{Log}\,
K_{7} + 2\,\text{Log}\frac{\text{H}_{2}}{\text{H}_{2}\text{O}} +
\text{Log}\,\text{S}_{T}\nonumber\\
&& -\; \text{Log}\left(K_{5}\cdot
\left(\frac{\text{H}_{2}}{\text{H}_{2}\text{O}}\right)^{3}
P_{\mathrm{tot}} + 1\right) \label{eq10}
\end{eqnarray}}\unskip\noindent
Equation~(\ref{eq10}) demonstrates that SO$_{2}$-mineral reactions can
control both gas composition and redox state (e.g., H$_{2}$/H$_{2}$O
and SO$_{2}$/H$_{2}$S and Total gas phase sulphur, S$_{T}$) at a given
total pressure ($P_{\mathrm{tot}}$). Figures~\ref{fig3} and~\ref{fig4}
illustrate examples of such gas--mineral reaction paths (light blue
lines labelled H\&F). The plotted model curves \citep[we illustrate the
example runs shown in the original Figure~5 of][]{HenleyFischer2021}
are representative of closed-system multi-component (mineral--gas)
equilibrium runs in a range of pressures (either~1 or 100~bars),
gas--mineral ratios (either 10 or~100) and temperatures
(400--1000~{\textdegree}C), and highlight the expected gas
compositional changes in such gas--mineral reaction environments. The
model reaction paths derived by \citet{HenleyFischer2021} indicate
that, as reaction progresses (e.g., while gases increasingly react with
host-rock minerals during their ascent, expansion and cooling), the
H$_{2}$/H$_{2}$O, SO$_{2}$/H$_{2}$S and S$_{T}$ are all expected to
decrease in the residual gas phase (\ref{eq8}). The H\&F model lines
satisfactorily reproduce the observed (volcanic gas) H$_{2}$/H$_{2}$O
temperature dependence (Figure~\ref{fig3}a). In the models, the
predicted SO$_{2}$/H$_{2}$S ratios are relatively invariant in the
1000--600~{\textdegree}C temperature range, but then drop at
${<}$600~{\textdegree}C as SO$_{2}$ is increasingly converted into
H$_{2}$S and sulphates/sulphides (\ref{eq8}) and~(\ref{eq9})
(Figures~\ref{fig3}b and~\ref{fig4}). 

If either homogeneous (gas-only; Equation~(\ref{eq5})) or heterogenous
(gas--mineral; Equations~(\ref{eq7})--(\ref{eq8})) \mbox{reactions}
prevail (during ascent and cooling of magmatic gases from source to
surface) cannot be unambiguously resolved from our model versus natural
samples comparison. In principle, there is no reason to exclude both
reaction mechanisms can indeed co-operate in a volcanic system in space
and time. The heterogeneous (gas--mineral) reactions satisfactorily
explain the transition of magmatic gases into nominal SO$_{2}$-free
hydrothermal gases (dashed light blue arrows in Figure~\ref{fig4}b),
and are expected to prevail in mature hydrothermal systems where the
transit of gas is sufficiently slow to insure gas--mineral titration
effectively takes place, leading to SO$_{2}$-to-H$_{2}$S conversion and
sulphur loss to hydrothermal minerals. In more active magmatic systems,
vice versa, it is well possible that gas transit through the host rocks
is fast enough to prevent large SO$_{2}$ scavenging from reactions with
minerals. Our mixed (magmatic--hydrothermal) gases all contain
detectable SO$_{2}$, and the SO$_{2}$/H$_{2}$S ratios are relatively
temperature invariant (Figures~\ref{fig3}b and~\ref{fig4}a,b), implying
the gas may remain closed to reactions with host rocks in many cases,
in which case reaction (\ref{eq5}) would keep a major control on gas
chemistry and redox.

Neither homogeneous nor heterogenous reactions can explain the high
H$_{2}$/H$_{2}$O ratio signature of many relatively low-temperature
($T < 400$~{\textdegree}C) gas samples (Figure~\ref{fig3}a). These
H$_{2}$-rich compositions imply that re-equilibration (upon gas
cooling) may eventually not take place at all, causing the surface
discharge of relatively cold gases to preserve quenched,
higher-temperature equilibrium conditions (see arrow labelled
``quenching'' in Figure~\ref{fig3}). Ultimately, the extent of (gas or
gas--mineral) re-equilibration will range from minimal to total in
natural systems, depending on the local conditions and specific
ascent/cooling histories of gases, as on their route to the surface.
\vspace*{-.6pc}

\subsection{Use of hydrogen and hydrogen sulphides as geothermometers}
\label{sec4.2}\vspace*{-.15pc}

The strong temperature dependence of H$_{2}$ concentrations
(Figure~\ref{fig2}a) and H$_{2}$/H$_{2}$O ratios (Figure~\ref{fig3}a),
combined with relatively temperature-invariant SO$_{2}$/H$_{2}$S ratios
(Figures~\ref{fig3}b, \ref{fig4}a,b), suggest that gas chemistry and
redox are often internally buffered (by the gas-phase
reaction~(\ref{eq5})). One possible way to test if/to what extent
fast-reacting H$_{2}$ rapidly attains equilibrium in an internally
buffered volcanic gas phase (e.g., whose redox is controlled by the
H$_{2}$S--SO$_{2}$ gas buffer) is to use Equation~(\ref{eq5}) to
estimate Apparent Equilibrium Temperatures [AETs; e.g., 
\citealp{Matsuo1962,Ohbaetal1994, Moussallametal2019a,
Moussallametal2022}], and compare these with measured (discharge)
temperatures. Deriving such AETs from measured H$_{2}$, H$_{2}$O,
SO$_{2}$ and H$_{2}$S compositions \citep[e.g.,][]{Moussallametal2019a,
Moussallametal2022} is especially important at open-vent
volcanoes \citep{Shinoharaetal2011, Shinoharaetal2015,
Shinoharaetal2018}, in which gas observations are typically taken in
``cold'' atmospheric volcanic gas plumes, whose source vents are
inaccessible to direct temperature measurements [this contrasts with
closed-conduit volcanoes in which gas venting temperatures are measured
concurrently with gas sampling at the fumarolic outlet; e.g.,
\citealp{Ohbaetal1994}]. Such information on magma source temperatures
can be recorded in the composition of the plume at condition that
gas-melt equilibria (i)~are established at magma $T$--$P$-redox
conditions, and (ii)~conserved during gas cooling and mixing during
atmospheric dispersion. Assumption~(ii) is indeed verified by
observations/models that suggest quenching of magmatic gas composition
in volcanic plumes [in which source H$_{2}$/H$_{2}$O and
SO$_{2}$/H$_{2}$S ratios are conserved during plume aging;
\citealp{Aiuppaetal2007, Aiuppaetal2011}].\looseness=-1

Our gas catalogue here offers an opportunity to test condition~(i)
above and, ultimately, to verify if internal (gas-phase) redox
buffering prevails in magmatic systems (over heterogeneous reactions).

We initially illustrate in Figure~\ref{fig5}a the temperature
dependence of the equilibrium constant of reaction~(\ref{eq5})
(expressed in the form of $\text{Log}\,K_{5}$), as derived from
thermodynamic data in \citet{Ohbaetal1994}. This equilibrium line
(solid black line in Figure~\ref{fig5}a) is contrasted against
analytical values of $\text{Log}\,K_{5}$, as derived by solving (for
each sample in Supplementary Tables~1 and~2) Equation~(\ref{eq6}) using
analytically determined H$_{2}$/H$_{2}$O and H$_{2}$S/SO$_{2}$ ratios
(water fugacity, $f{\mathrm{H}_{2}\mathrm{O}}$, is calculated from
measured $X_{\mathrm{H}_{2}\mathrm{O}}$ and assuming 1~bar total
pressure and ideal gas behaviour). This comparison shows that the
``restored gas analyses'' output analytical $\text{Log}\,K_{5}$ values
that perfectly overlap with the equilibrium curve: this merely reflects
the accuracy of the gas restoration procedure of
\citet{Gerlach1980}. More significant is the observation that{\break}
unrestored magmatic gases ($600~\text{{\textdegree}C} < T <
1100$~{\textdegree}C) have analytically determined $\text{Log}\,K_{5}$
that match closely equilibrium $\text{Log}\,K_{5}$ values: for these
samples, approach to equilibrium is proved by the close match between
measured (discharge) temperatures and AETs (Figure~\ref{fig5}b). Some
mixed hydrothermal-magmatic gases also plot along (or at least very
close to) the model equilibrium curve (Figure~\ref{fig5}a), indicating
that equilibrium conditions can still be achieved during gas cooling at
temperatures of ${<}$600~{\textdegree}C (and as low as
${\sim}$200~{\textdegree}C; Figures~\ref{fig5}a, b). However,
in such a temperature range, and increasing number of samples output
analytically derived $\text{Log}\,K_{5}$ that diverge from the
equilibrium line (Figure~\ref{fig5}a): in these samples, AETs exceed
measured (discharge) temperatures by several hundred degrees in some
cases, again indicating quenching of higher temperature (magmatic)
conditions, and or disequilibrium conditions. These are the same
samples that in Figure~\ref{fig3}a diverge from the main
compositional-temperature array (grey band) toward higher
H$_{2}$/H$_{2}$O ratios.

\begin{figure*}[t!]
{\vspace*{2pt}}
\includegraphics{fig05}
{\vspace*{2pt}}
\caption{\label{fig5}(a)~Temperature dependence of the equilibrium
constant of reaction (\ref{eq5}) (expressed in the form of
$\text{Log}\,K_{5}$), as derived from thermodynamic data in
\citet{Ohbaetal1994}. The equilibrium line (solid black line) is
contrasted against analytical values of $\text{Log}\,K_{5}$, as derived
by solving (for each sample in Supplementary Tables~1 and~2)
Equation~(\ref{eq6}) using analytically determined H$_{2}$/H$_{2}$O and
H$_{2}$S/SO$_{2}$ ratios (water fugacity, $f$H$_{2}$O, is calculated from
measured XH$_{2}$O and assuming 1~bar total pressure and ideal gas
behaviour). (b)~Apparent equilibrium temperatures (AET) 
\citep{Matsuo1962,
Ohbaetal1994, Moussallametal2022} derived from
Equation~(\ref{eq6}) and analytically determined H$_{2}$/H$_{2}$O and
H$_{2}$S/SO$_{2}$ ratios for individual gas samples. High-temperature
gases plot along the 1:1 line, e.g., they match closely measured
discharge temperature ($x$-scale), implying equilibrium conditions.
(c)~The difference between Apparent equilibrium temperatures (AET) and
measured temperatures (MT) approach 0 in high-$T$ gas samples, while
AETs exceed MTs at lower temperatures (implying quenching of higher-$T$
equilibria. (d)~A~magnified version of~(c), demonstrating AET and MT
differ by ${<}$ ${\pm}$20\% at $T > 600$~{\textdegree}C.}
{\vspace*{1pt}}
\end{figure*}

The conclusion we can take is that, as previously shown by
\citet{Moussallametal2019a} (see their Figure~S1), at magmatic
temperatures (${>}$600~{\textdegree}C), gas compositions can allow
estimating AETs that are within ${\pm}$20\% of actual venting
temperatures (Figure~\ref{fig5}d). It is very interesting to realise
however that even at lower (${<}$600~{\textdegree}C) gas venting
temperatures, quenching of higher temperature compositions, or
disequilibrium conditions, is indeed common.

The calculations above do not necessarily imply that gas--mineral
reactions (\ref{eq7})--(\ref{eq8}) are altogether unimportant.
Reactions between gas and host-rocks \citep[e.g.,][]{Symondsetal2001,
HenleyFischer2021} are central to the formation of SO$_{2}$-poor
hydrothermal steam samples \citep[e.g.,][]{Giggenbach1980}. In the
$\text{600~{\textdegree}C} < T < 1200$~{\textdegree}C temperature range
however, the fraction of SO$_{2}$ loss via reaction~(\ref{eq7})
and~(\ref{eq8}) is overall a limited fraction (of the total S load in
the gas phase), thus exercising little to no effect on gas equilibria
(Figure~\ref{fig5}).
\vspace*{-.6pc}

\subsection{Use of hydrogen and hydrogen sulphides to estimate oxygen
fugacity} \label{sec4.3}

A matter that has remained debated for years is if, and to what extent,
volcanic gas compositions reflect (and can therefore allow deriving)
the redox conditions (oxygen fugacities) of the source magmas.

\citet{Gerlach1982} found that their ``restored'' magmatic gas analyses
from tholeiitic and alkaline \mbox{intraplate} volcanoes allow
calculating gas oxygen fugacities that vary from ${\sim}10^{-8.5}$ to
${\sim}10^{-12}$~bar. He also found these $f\text{O}_{2}$ values to be
strongly temperature dependent, and to overall define a
$f\text{O}_{2}$-collection temperature trend parallel to the
$f\text{O}_{2}$--$T$ dependence{\break} imposed by the
Fayalite--Magnetite--Quartz (FMQ) and Nickel--Nickel Oxide (NNO) redox
buffers \citep{Eugster1977, Frost1991}. From this, he concluded that
``{\ldots} \textit{lavas tend to buffer the O}$_{2}$ \textit{fugacities
of their associated gases}''. Confirmation to this hypothesis came from
later studies \citep{Gerlach1993a, Gerlach1993b} in which the
$f\text{O}_{2}$ values for (restored) magmatic gases from Kilauea were
found to match the measured/calculated $f\text{O}_{2}$ values of
Kilauea basalts. Again, \citet{Gerlach1993a} concluded that
``\textit{the evidence discussed above indicates that subaerial lavas
buffer volcanic gas compositions emitted by Kilauea basalt along
consistent} $f\text{O}_{2}$-\textit{T trend from molten to subsolidus
temperatures}''. A strong temperature dependence of volcanic gas
$f\text{O}_{2}$ values was also found in the global compilation of
\citet{Symondsetal1994}.

\looseness=-1
This ``melt-buffering'' hypothesis has recently been challenged in a
series of studies by \citet{Oppenheimeretal2018} and 
\citet{Moussallametal2019a, Moussallametal2022}
using evidence from novel gas
plume observations, either in-situ or remote. Using results from Open
Path Fourier Transform Infra-Red (OP-FTIR) spectroscopy observations of
lava lake degassing at Kilauea volcano, \citet{Oppenheimeretal2018}
found that gas composition varies with activity style and temperature.
They found, in particular, that the volcanic gas phase becomes
progressively oxidised as gas temperature progressively drops (below
magmatic temperature), at a rate that is inconsistent with that
predicted by external gas redox buffering by the coexisting silicate
melt. They proposed that magmatic gas redox ($f\text{O}_{2}$) is
controlled by homogeneous (gas-phase only) redox re-equilibration upon
adiabatic gas cooling. Using evidence from a global volcanic gas
dataset, \citet{Moussallametal2019a}
generalised the conclusions of \citet{Oppenheimeretal2018}, showing
that the temperature dependence of volcanic gas $f\text{O}_{2}$ is
different (less steep) than that imposed by external melt redox
buffers. Rather, they found that volcanic gas redox scales with the
extent of gas cooling experienced by gases (as indicated by temperature
difference between gas and the source melt). In this interpretation
therefore, volcanic gas redox decouples from that of the melt, i.e.,
the melt redox information is altered in the gas during its adiabatic
cooling (as gas bubbles separately rise within---and ultimately burst
out of---the silicate melt). To capture this concept,
\citet{Moussallametal2022} proposed the use of the formulation
``apparent oxidation state'' or AOS which is the oxidation state of the
gas mixture at its apparent equilibrium temperature.
\citet{Moussallametal2022} showed that if the magma temperature is
known then the gas AOS can be restored to its true $f\text{O}_{2}$ at
equilibrium with the magma (i.e., the oxidation state of the magma can
be calculated from the AOS).

Hydrogen and hydrogen sulphide are inherently central to this
discussion, as Equations~(\ref{eq3}) and~(\ref{eq4}) can conveniently
be re-arranged to estimate AOS from measured/apparent temperature and
either H$_{2}$/H$_{2}$O or SO$_{2}$/H$_{2}$S ratios. Figure~\ref{fig6}a
is a plot of derived $f\text{O}_{2}$ values for gas samples in our
catalogue, as derived from Equation~(\ref{eq3}) using measured
H$_{2}$/H$_{2}$O ratios and AETs. $f\text{O}_{2}$s obtained by
SO$_{2}$/H$_{2}$S ratios (and Equation~(\ref{eq4})), also listed in
Supplementary Tables~1 and~2, agree well with those derived from
H$_{2}$/H$_{2}$O ratios. The whole volcanic gas population defines in
Figure~\ref{fig6}a a roughly linear temperature-$f\text{O}_{2}$ array
which slope is manifestly less steep than that of any mineral buffer
line. Overall, the volcanic gas population span from redox conditions
between the NNO and FMQ buffers at temperatures of 900~{\textdegree}C
or more, to redox close to the Hematite--Magnetite (HM) buffer at the low
temperature (${<}$400~{\textdegree}C) end of the population. Our
results thus corroborate the results of 
\citet{Moussallametal2019a,Moussallametal2022}
that volcanic gases become increasingly
oxidised with decreasing temperatures. The high temperature ($T >
600$~{\textdegree}C) magmatic gas field is magnified in
Figure~\ref{fig6}b.

\begin{figure*}[t!]
\includegraphics{fig06}
\caption{\label{fig6}The temperature dependence of volcanic gas oxygen
fugacities (a)~apparent oxygen fugacities of individual gas samples
(data from Supplementary Tables~1 and~2), as derived using
Equation~(\ref{eq2}) from measured H$_{2}$/H$_{2}$O ratios and
estimated Apparent Equilibrium Temperatures (AET; same as
Figure~\ref{fig5}). Calculated $\text{Log}\,f\text{O}_{2}$ values vary
linearly with 1/AET, but the slope of the linear function is manifestly
less steep than the $\text{Log}\,f\text{O}_{2}-1/T$ dependence imposed
by the most common mineral redox buffers [HM: Hematite--Magnetite; NNO:
Nickel--Nickel Oxide; FMQ: Fayalite--Magnetite--Quartz; WM:
Wustite--Magnetite; IW: Iron--Wustite; QFI; Quartz--Fayalite--Iron; see
\citealp{Frost1991, MorettiNeuville2021}]; (b)~a magnified version
of~(a) comparing the $\text{Log}\,f\text{O}_{2}-1/T$ dependence for
high-temperature (${>}$600~{\textdegree}C) volcanic gases. The dashed
lines illustrate the gas evolution predicted from closed-system (gas
cooling) calculations. The closed system model lines suitably reproduce
the compositional trend (increasingly oxidised conditions upon cooling)
described by natural samples.}
\end{figure*}

We modelled the closed-system cooling of three gas compositions from
Erta' Ale \citep{LeGuernetal1979}, Satsuma-Iwojima
\citep{Shinoharaetal1993} and Etna \citep{Aiuppaetal2011}. The
calculation method is detailed in 
\citet{Moussallametal2019a,Moussallametal2022} and results are shown in
Figure~\ref{fig6}b. This shows that even at low
(${<}$600~{\textdegree}C) temperature the oxidation state of volcanic
gases having suffered limited interaction with the hydrothermal system
can be explained by closed system cooling from magmatic temperature.
This is an astonishing and very fortunate finding as it means that
volcanic gases with AET as low as a few hundred degrees might preserve
information of the oxidation state and/or temperature of the magma from
which they escaped by simply applying the gas restoration calculations
described in \citet{Moussallametal2022}. For example, we can perform
the same calculations but this time starting with the measured gas
composition from Kawa Ijen volcano collected by Allard 1985 at a
measured temperature of 244~{\textdegree}C but with an AET of
${\sim}$343~{\textdegree}C and at an AOS at QFM+5. Restoring
\citep[using][]{Moussallametal2022} the volcanic gas composition back
to a magmatic temperature (arbitrarily set to 1000~{\textdegree}C for
the purpose of demonstration) would lead to a restored gas composition
with an oxidation state and magmatic temperature of{\break} QFM+0.3.

The link between volcanic gas and silicate melt (magma) redox is more
fully analysed in Figure~\ref{fig7}. Figure~\ref{fig7}a is a frequency
distribution diagram of derived (Equation~(\ref{eq3})) apparent oxygen fugacities
for magmatic gases (temperature ${>}$ 600~{\textdegree}C). The figure
demonstrates distinct redox conditions for non-arc and arc volcanic
gases. In spite of some overlap, most arc volcanic gases have apparent
$f\text{O}_{2}$s (as expressed as $\Delta\text{FMQ} = \log
f\text{O}_{2(\mathrm{sample})} - \log
f\text{O}_{2(\mathrm{FMQ~at~AET})}$) at $\Delta\text{FMQ} \geq 0$, and
as high as $\Delta\text{FMQ} + 4$; whilst non-arc volcanic gases are
generally more reduced $\Delta\text{FMQ} \leq 0.2$, and as low as
$\Delta\text{FMQ} - 1.2$. This diversity is largely explained by the
arc gas dataset containing many fumarole \mbox{samples} in the
600--900~{\textdegree}C temperature range, which have therefore cooled
significantly below source magma temperatures, ultimately having become
more oxidised during closed-system reactions [see Figure~\ref{fig6} and
related discussions and see Figure~1 in \citealp{Moussallametal2022}
showing the oxidation state of arc gases restored to magmatic
temperature]. However, arc gases sampled at close to magmatic
temperatures ($T > 900$~{\textdegree}C) still plot at higher redox than
non-arc magmatic gases (Figure~\ref{fig7}a; see also Figures~\ref{fig4}
and~\ref{fig6}b), implying that the volcanic gas $f\text{O}_{2}$
difference is likely to reflect some distinct redox conditions at
source. Intraplate (Figure~\ref{fig7}b) and arc (Figure~\ref{fig7}c)
melts have previously been shown to exhibit distinct redox
\citep{Cottrelletal2022}. We conclude, therefore, that these diverse
magma $f\text{O}_{2}$s are well preserved in volcanic gases, provided
adiabatic cooling and re-equilibration have not occurred (e.g., at $T
\gg 900$~{\textdegree}C). It is important to remember, however, that
melt redox has been found to vary upon magma de-compressional ascent
and degassing, progressively becoming more reduced
\citep[e.g.,][]{Moussallametal2014a, Moussallametal2016,
Moussallametal2019b, Brounceetal2017, Helzetal2017} at low pressure
[when S(IV) is lost to gas as SO$_{2}$, leading to an overall decrease
of the magma redox budget; \citep{Evans2012}]. As such, magmatic gas
may, at some conditions (limited adiabatic cooling), reflect redox of
shallow, surface-emplaced magma; however, it is unlikely to provide
information on deep magma (and source mantle) redox
\citep{MorettiStefansson2020}.

\subsection{Atmospheric fluxes} \label{sec4.4}

Upon their atmospheric release from subaerial volcanoes, volcanogenic
H$_{2}$ and H$_{2}$S act as primary electron donors (e.g., as reducing
compounds) in the \mbox{atmosphere} \citep[e.g.,][]{Holland2002,
Canfieldetal2006}. As these volcanic gas species thus contribute
largely to the reducing power (e.g., the ability to remove atmospheric
O$_{2}$) of volcanic gases, understanding their volcanic atmospheric
fluxes is central to reconstructing the oxygenation history of the
early atmosphere and the present atmospheric oxygen budget
\citep{Holland2002, Canfieldetal2006, Stolperetal2021}.

\clearpage

\onecolumngrid
\vspace*{-1pc}

\begin{sidewaystable}[p!] %tab1
\fontsize{8}{10}\selectfont
\caption{\label{tab1}Global volcanic H$_{2}$S and H$_{2}$ fluxes (in
Tg/yr) revisited}
\begin{tabular}{ccccccccccccccccccccccc}
\thead
&& Mean & SD && Mean & SD && 50\% & 25\% & 75\% && 50\% & 25\% & 75\%
&& 50\% & 25\% & 75\% && 50\% & 25\% & 75\%\\
\endthead
&& \multicolumn{2}{c}{SO$_{2}$ flux} && \multicolumn{2}{c}{CO$_{2}$
flux} && \multicolumn{3}{c}{H$_{2}$S/SO$_{2}$} &&
\multicolumn{3}{c}{H$_{2}$S flux} &&
\multicolumn{3}{c}{H$_{2}$/SO$_{2}$} && \multicolumn{3}{c}{H$_{2}$
flux}\\
\cline{3-4}\cline{6-7}\cline{9-11}\cline{13-15}\cline{17-19}\cline{21-23}
$S_{\mathrm{vge}}$\raisebox{1pc}{} & Magmatic & \textbf{24.9} & 2.3 &&
\textbf{36} & 2.4 && 0.1 & 0.06 & 0.6 && \textbf{1.3} & 0.8 & 8.3 &&
0.3 & 0.1 & 1.3 && \textbf{0.23} & 0.06 & 1.0{\vspace*{10pt}}\\
&& \multicolumn{2}{c}{SO$_{2}$ flux} && \multicolumn{2}{c}{CO$_{2}$
flux} && \multicolumn{3}{c}{H$_{2}$S/CO$_{2}$} &&
\multicolumn{3}{c}{H$_{2}$S flux} &&
\multicolumn{3}{c}{H$_{2}$/CO$_{2}$} && \multicolumn{3}{c}{H$_{2}$
flux}\\
\cline{3-4}\cline{6-7}\cline{9-11}\cline{13-15}\cline{17-19}\cline{21-23}
$W_{\mathrm{vge}}$\raisebox{1pc}{} & Magmatic & - & - && \textbf{11.6}
& 3.9 && 0.008 & 0.006 & 0.043 && \textbf{0.08} & 0.05 & 0.4\0 && 0.002 &
0.0005 & 0.012 && \textbf{0.0012} & 0.0002 & 0.0062\\
$W_{\mathrm{vge}}$ & Hydrothermal & - & - && \0\textbf{3.7} & 1.2 &&
0.008 & 0.006 & 0.043 && \textbf{0.02} & 0.02 & 0.12 && 0.002 & 0.0005
& 0.012 && \textbf{0.0004} & 0.0001 & 0.0020{\vspace*{10pt}}\\
&& \multicolumn{2}{c}{SO$_{2}$ flux} && \multicolumn{2}{c}{CO$_{2}$
flux} &&&&&& \multicolumn{3}{c}{H$_{2}$S flux} &&&&&&
\multicolumn{3}{c}{H$_{2}$ flux}\\
\cline{3-4}\cline{6-7}\cline{13-15}\cline{21-23}
Total\raisebox{1pc}{} & This study ($S_{\mathrm{vge}} +
W_{\mathrm{vge}}$) & \textbf{24.9} & 2.3 && \textbf{51.3} & 7.5 &&&&&&
\textbf{1.4} & 0.9 & 8.8 &&&&&& \textbf{0.23} & 0.06 & 1.0\\
Total & \citet{Canfieldetal2006} &&&&&&&&&&&
\multicolumn{3}{c}{\0\textbf{1.4--2}} &&&&&&
\multicolumn{3}{c}{\textbf{0.2--0.7}}\\
& \citet{Stolperetal2021} &&&&&&&&&&&
\multicolumn{3}{c}{\textbf{0.05--4}} &&&&&&
\multicolumn{3}{c}{\textbf{0.07--0.44}}
\botline
\end{tabular}
\tabnote{These are obtained by multiplying the global volcanic SO$_{2}$
and CO$_{2}$ fluxes of \citet{Fischeretal2019} by the median (molar)
gas ratios in our catalogue (Supplementary Tables~1 and~2). See text.
Uncertainty is quantified using 25 and 75 percentiles. We distinguish
three volcano categories ($S_{\mathrm{vge}}$, magmatic
$W_{\mathrm{vge}}$ and hydrothermal $W_{\mathrm{vge}}$) as in 
\citet{FischerAiuppa2020}. 
Total fluxes are calculated by summing together the
three flux contributions. Previous flux inventories by
\citet{Canfieldetal2006} and \citet{Stolperetal2021} are shown for
comparison.}
\end{sidewaystable}

\twocolumngrid

\begin{figure}[t!]
\includegraphics{fig07}
\caption{\label{fig7}(a)~Frequency distribution diagram of derived
(Equation~(\ref{eq3})) 
apparent oxygen fugacities for magmatic gases (temperature
${>}$ 600~{\textdegree}C), expressed as $\Delta\text{FMQ} = \log
f\text{O}_{2(\mathrm{sample})}\break - \log
f\text{O}_{2(\mathrm{FMQ~at~AET)}}$. The figure demonstrates distinct
redox conditions for non-arc and arc volcanic gases in the same range
and magnitude as seen for intraplate (panel~b) and arc (panel~c) melts
[redrawn from \citealp{Cottrelletal2022}].}
\vspace*{-.8pc}
\end{figure}

As for the more abundant
CO$_{2}$ \citep{Aiuppaetal2019, Werneretal2019, Fischeretal2019}, the
volcanic H$_{2}$ and H$_{2}$S fluxes to the atmosphere cannot be
measured directly by remote sensing, as no specific observational
technique exists for this aim. Therefore, although some rare direct
in-situ flux measurements exist \citep{Aiuppaetal2013, Allardetal2014,
Tamburelloetal2019, Mouneetal2022},{\break} most applications rely on
the indirect approach \citep{Aiuppaetal2019, Fischeretal2019,
Werneretal2019} of scaling gas ratios (H$_{2}$/SO$_{2}$ and
H$_{2}$S/SO$_{2}$ ratios in this specific case) in volcanic emissions
to the global volcanic SO$_{2}$ flux budget
\citep[e.g.,][]{Carnetal2017, Fischeretal2019}, which is well
understood thanks to abundant UV spectroscopy observations from both
ground \citep{Arellanoetal2021} and space \citep{Carnetal2016}. The
operation is, however, complicated by the large spread of
H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$ ratios in volcanic gas emissions
(Figure~\ref{fig8}a--d), which has traditionally hampered the
derivation of robust global estimates \citep{Halmeretal2002,
Canfieldetal2006}.

\begin{figure*}[p!]
\includegraphics{fig08}
\caption{\label{fig8}(a--d)~Scatter plots of H$_{2}$S and H$_{2}$
concentrations (data from Supplementary Tables~1 and~2) versus major
species' concentrations (either SO$_{2}$ or CO$_{2}$). All
concentrations in mol\%. (e--h)~Frequency distribution diagrams of
volatile (molar) ratios used for flux calculations. See text, symbols
as in Figure~\ref{fig2} except green crossed \citep[hydrothermal steam
samples from][]{ChiodiniMarini1998}.}
\end{figure*}

The two most recent attempts to estimate the H$_{2}$ and H$_{2}$S
fluxes from global subaerial volcanism are from
\citet{Canfieldetal2006} and \citet{Stolperetal2021}
(Table~\ref{tab1}). 

\citet{Canfieldetal2006} compiled 21 high quality volcanic gas analyses
from volcanoes in a variety of geological context, including
rift-related, hot-spot related, and in subduction zones related. They
found volcanic gas H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$ ratios to
vary widely even in such a limited dataset, total ranges being
respectively of 0.02--24 and 0.007--2.7. The median volcanic gas
H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$ ratios in their subset of
volcanic gas samples are 0.8 (H$_{2}$/SO$_{2}$) and 0.3
(H$_{2}$S/SO$_{2}$). Ultimately, by using most representative ratio
ranges in combination with a global SO$_{2}$ flux estimate 
\citep{Halmeretal2002}
they quantified the global volcanic H$_{2}$ and H$_{2}$S fluxes at
0.2--0.7~Tg/yr and 1.4--2.0~Tg/yr, respectively (Table~\ref{tab1}).

\citet{Stolperetal2021} also based their H$_{2}$ and H$_{2}$S flux
estimates on major species' global budgets---they used the more updated
global volcanic SO$_{2}$ and H$_{2}$O flux inventories of
\citet{Fischeretal2019}. However, they adopted a different methodology
for deriving best-estimates for H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$
ratios in ``globally averaged volcanic gas emissions''. Instead of
averaging results from measured H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$
ratios in volcanic gas samples, they relied on thermodynamically
derived H$_{2}$/SO$_{2}$ and H$_{2}$S/SO$_{2}$ ratios, calculated (from
relations similar to Equations~(\ref{eq3}) and~(\ref{eq4}) presented
above) at temperature, pressure and redox ($f\text{O}_{2}$) conditions
of the source silicate melt. For example, they quantified the global
volcanic H$_{2}$ flux at 0.07--0.44~Tg/yr (Table~\ref{tab1}) by
combining the global volcanic H$_{2}$O flux of \citet{Fischeretal2019}
with the thermodynamically derived (Equation~(\ref{eq3}))
H$_{2}$/H$_{2}$O ratios at equilibrium with melt,{\break} using $T$,
$P$, $f\text{O}_{2}$ values relevant to modern subaerial magmas.
Likewise, their global volcanic H$_{2}$S flux range of 0.05--4~Tg/yr
was inferred from the global SO$_{2}$ inventory of
\citet{Fischeretal2019} and the thermodynamically estimated
Equation~(\ref{eq4}) equilibrium (at melt $T$, $P$, $f\text{O}_{2}$)
H$_{2}$S/SO$_{2}$ ratios (Table~\ref{tab1}). It is necessary to
remember that \citet{Stolperetal2021} implicitly assume that surface
volcanic gas emissions are controlled (buffered) by heterogenous
equilibrium with the coexisting silicate melt. However, this
assumption, as previously discussed (cf. Section~\ref{sec4.3}), likely holds
only for the very few cases of gases emitted at magmatic temperature,
but not for the many, lower temperature gas emissions seen at the vast
majority of the active volcanoes worldwide (see Figures~\ref{fig3},
\ref{fig4}, \ref{fig6}). For example, the range of estimated
equilibrium H$_{2}$/H$_{2}$O ratios of \citet{Stolperetal2021} is 0.01
to 0.024, and therefore captures only the upper class (the ``magmatic''
range) of measured H$_{2}$/H$_{2}$O ratios in volcanic gases
(Figures~\ref{fig3}a and~\ref{fig5}); the majority of the
surface-emitted volcanic gases will be far more H$_{2}$-poor because of
re-equilibration during homogenous (closed-system) gas cooling
(cf. Section~\ref{sec4.3}). As magmatic gas H$_{2}$S/SO$_{2}$ are overall
preserved during gas cooling (Figures~\ref{fig3}b, \ref{fig5}), their
estimated range (0.000012--0.28) is representative of the measured gas
composition range (Figure~\ref{fig8}b).

We here attempt at a refined H$_{2}$ and H$_{2}$S volcanic flux
inventory (Table~\ref{tab1}) by using our more complete volcanic gas
catalogue (Supplementary Tables~1 and~2). 

Our calculations stand on the approach developed in the most recent
volcanic gas flux quantification efforts \citep{Fischeretal2019,
FischerAiuppa2020}, 
 in which three categories of subaerial volcanoes
are distinguished and separately treated (Table~\ref{tab1}). A first
category of Volcanic Gas Emitters ($S_{\mathrm{vge}}$) includes the
strongly degassing volcanoes whose SO$_{2}$ emissions can
systematically be detected by satellites \citep[e.g.,][]{Carnetal2017,
Fischeretal2019}. These volcanoes typically release high-temperature,
SO$_{2}$-rich gases, often from open-vent persistently degassing vents,
and are believed to dominate the volcanic SO$_{2}$ and CO$_{2}$ flux
inventories \citep[e.g.,][]{Aiuppaetal2017, Aiuppaetal2019,
Carnetal2017, Fischeretal2019, Werneretal2019, FischerAiuppa2020}. 
 Our high-temperature ($T > 600$~{\textdegree}C; Supplementary Table~1),
S$_{T}$-rich (Figure~\ref{fig1}) magmatic gases are inherently the most
representative of\vadjust{\vspace*{.7pt}\pagebreak} such emission
category. These have \mbox{median} H$_{2}$S/SO$_{2}$
(Figure~\ref{fig8}a--e) and H$_{2}$/SO$_{2}$ (Figure~\ref{fig8}b--f)
ratios of respectively 0.1 and 0.3 (25\%--75\% percentiles: 0.06--0.6
and 0.1--1.3, respectively; Table~\ref{tab1}). From these, and scaling
to the global volcanic flux SO$_{2}$ of \citet{Fischeretal2019}
(24.9~Tg/yr), we infer the $S_{\mathrm{vge}}$ contribution to the
global (subaerial) volcanic H$_{2}$ and H$_{2}$S flux at 1.3~Tg/yr
(confidence interval, 0.8--8.3) and 0.23~Tg/yr (confidence interval,
0.06--1). The other two categories correspond to the Weak Gas Emitters
($W_{\mathrm{vge}}$) \citep{Fischeretal2019, FischerAiuppa2020} 
 that include both (a)~recently active (but now
dormant) volcanoes whose SO$_{2}$ emissions are too small to be
resolved from space (the ``magmatic'' $W_{\mathrm{vge}}$), or
(b)~quiescent volcanoes in hydrothermal stage of activity (the
``hydrothermal'' $W_{\mathrm{vge}}$) that do not release SO$_{2}$ at
all, and in which sulphur is essentially released in H$_{2}$S form. For
$W_{\mathrm{vge}}$, we therefore cannot rely on a SO$_{2}$ flux proxy.
Rather, we use the CO$_{2}$ flux estimates of \citet{Fischeretal2019},
in combination with H$_{2}$S/CO$_{2}$ (Figure~\ref{fig8}c--g) and
H$_{2}$/CO$_{2}$ (Figure~\ref{fig8}d--h) ratios. Our mixed
(magmatic--hydrothermal), lower temperature ($T \leq
600$~{\textdegree}C; Supplementary Table~2) volcanic gas population
exactly corresponds to the category of ``magmatic'' $W_{\mathrm{vge}}$,
and exhibits H$_{2}$S/CO$_{2}$ and H$_{2}$/CO$_{2}$ ratios of 0.008
(0.006--0.043) and 0.002 (0.0005--0.012) (Table~\ref{tab1}).
Hydrothermal $W_{\mathrm{vge}}$ are not explicitly covered by our
review, but their compositions \citep[see data
from][]{ChiodiniMarini1998} overlap with the magmatic''
$W_{\mathrm{vge}}$ compositional range (Figures~\ref{fig8}g
and~h), so we can use the composition of the latter. In
summary, therefore, we infer that $W_{\mathrm{vge}}$ contribute
$\sim$0.1~Tg H$_{2}$S and $\sim$0.0016~Tg H$_{2}$ yearly. It is
important to stress that the population of $W_{\mathrm{vge}}$ spans
orders of magnitude in terms of H$_{2}$S/CO$_{2}$ and H$_{2}$/CO$_{2}$
(Figures~\ref{fig8}c--d and~g--h) ratios, so our flux
estimates for this specific category are very poorly constrained.
However, this has limited impact on our estimated total fluxes of
H$_{2}$S (1.4~Tg/yr; 0.9--8.8) and H$_{2}$ (0.23~Tg/yr; \mbox{0.06--1})
fluxes, which are by far dominated by $S_{\mathrm{vge}}$. We conclude
that, while thus $W_{\mathrm{vge}}$ are important volcanic CO$_{2}$
sources [Table~\ref{tab1}; \citealp{Fischeretal2019, FischerAiuppa2020}], 
 their contribution to global volcanic subaerial
fluxes of reduced, hydrogenated compounds is irrelevant. This reflects
the H$_{2}$-poor signature of low temperature gas emissions
(Figures~\ref{fig2}, \ref{fig3}, \ref{fig5}, \ref{fig8})---caused by
gas oxidation during cooling (Figure~\ref{fig6})
(cf. Section~\ref{sec4.3})---and the removal of water-soluble sulphur during
magmatic gas \mbox{interactions} with liquid-dominated hydrothermal
systems \citep[e.g.,][]{Aiuppaetal2017}, which determines the
prevailing low H$_{2}$S/CO$_{2}$ compositions (Figures~\ref{fig1},
\ref{fig8}g). Our estimated total volcanic H$_{2}$S and H$_{2}$ fluxes
are at the lower range of the estimates of \citet{Canfieldetal2006},
and at the very middle of the flux range of \citet{Stolperetal2021}
(Table~\ref{tab1}).

Our results indicate that global volcanism contributes little
($\sim$1\%; range 0.3--4.3\%) to the cumulative (global) geogenic
H$_{2}$ flux \citep[$\sim$23~Tg/yr;][]{Zgonnik2020}. For comparison,
anthropogenic H$_{2}$ emissions
\citep[$\sim$11~Tg/yr;][]{EhhaltRohrer2009} are 1 to 2 orders of
magnitude higher than volcanic emissions. In contrast, our
best-estimate for the volcanic H$_{2}$S flux (1.4~Tg/yr) implies
volcanoes do make up a non-trivial ($\sim$18\%) fraction of the global
natural H$_{2}$S flux \citep[${\sim}$7.7~Tg/yr;][]{Watts2000}. Volcanic
degassing contributes nearly 3 times less H$_{2}$S than today
anthropogenic emissions \citep[3.3~Tg/yr;][]{Watts2000}.

\section{Summary and conclusions} \label{sec5}

We have reviewed our present understanding of the processes that govern
the abundance of reduced hydrogenated compounds in volcanic gases. Our
review shows that the apparent oxygen fugacities of high-temperature
volcanic gases range from ${\Delta}$FMQ $-$1 to 0 (for non-arc
volcanoes) to ${\Delta}$FMQ 0 to $+$2 (for arc volcanoes), and are
therefore comparable to the redox conditions of the source silicate
melts. A variety of processes can alter gas composition and redox state
(H$_{2}$/H$_{2}$O and H$_{2}$S/SO$_{2}$ ratios) as the gases expand
within the melt and cool, and/or after they separate from magma on
their route to the surface. Data in our catalogue, when interpreted in
the context of existing models of homogeneous (gas) or heterogeneous
(gas--mineral) reactions, suggest that in many cases the fast-reacting
H$_{2}$/H$_{2}$O couple rapidly re-equilibrates during cooling (e.g.,
in low temperature gas environments) in a gas-buffered system which
redox is controlled by coexisting H$_{2}$S and SO$_{2}$ (which
H$_2$S/SO$_2$ ratio is ultimately conserved at ${\sim}$0.1 on average).
This gas-phase (closed-system) re-equilibration upon cooling causes the
gas to become more oxidised than the original (source) magma
\citep{Oppenheimeretal2018, Moussallametal2019a}.
Conversion of magmatic SO$_{2}$ to hydrothermal H$_{2}$S (and
precipitation of sulphates/sulphides) is instead favoured by slower
transit of the gas through the host~rocks, causing more prolonged
gas--water--rock interactions to occur. This condition
\citep{HenleyFischer2021} certainly prevails in more mature,
liquid-dominated, and stable (less magma fed) hydrothermal systems
\citep{ChiodiniMarini1998}. Our volcanic gas dataset, combined with
recently published global volcanic SO$_{2}$ and CO$_{2}$ budgets,
implies total H$_{2}$S and H$_{2}$ fluxes from global subaerial
volcanism of 1.4~Tg/yr (range, 0.9--8.8~Tg/yr) and 0.23~Tg/yr (range,
0.06--1~Tg/yr), respectively.

\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*{Acknowledgements}

This research received financial support from the Ministero
dell'Universit\`{a} e Ricerca (Italy, Grant n.~2017LMNLAW), from the
Dipartimento della Protezione Civile and the INGV (under grant
``Sviluppo del sistema unico (INGV-Universit\`{a}) di monitoraggio
vulcanico e rilevamento precoce dei maremoti e delle esplosioni
parossistiche di Stromboli''), and from the PNRR PE Project ``Return''.
This work was initially inspired by participation of AA to the
International School ``Understanding Oxygen fugacity in Geoscience''
5--9 September 2022, Trieste, Italy
(\url{https://fo2school.units.it/}), and the organisers of the school
(Luca Ziberna and Vincenzo Stagno especially) are warmly thanked.

\CDRGrant[Ministero dell'Universit\`{a} e Ricerca]{2017LMNLAW}

\section*{Supplementary data}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crgeos-235-suppl.pdf}}
\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{Table-S1.xlsx}}
\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{Table-S2.xlsx}}

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