Photochemical box modelling of volcanic SO2 oxidation: isotopic constraints

. The photochemical box model CiTTyCAT is used to analyse the absence of oxygen mass-independent anomalies (O-MIF) in volcanic sulfates produced in the troposphere. An aqueous sulfur oxidation module is implemented in the model and coupled to an oxygen isotopic scheme describing the transfer of O-MIF during the oxidation of SO 2 by OH in the gas-phase, and by H 2 O 2 , O 3 and O 2 catalysed by TMI in the liquid phase. Multiple model simulations are performed in order to explore the relative importance of the various oxidation pathways for a range of plausible conditions in volcanic plumes. Note that the chemical conditions prevailing in dense volcanic plumes are radically different from those prevailing in the surrounding background air. The ﬁrst salient ﬁnding is that, according to model calculations, OH is expected to carry a very

Abstract. The photochemical box model CiTTyCAT is used to analyse the absence of oxygen mass-independent anomalies (O-MIF) in volcanic sulfates produced in the troposphere. An aqueous sulfur oxidation module is implemented in the model and coupled to an oxygen isotopic scheme describing the transfer of O-MIF during the oxidation of SO 2 by OH in the gas-phase, and by H 2 O 2 , O 3 and O 2 catalysed by TMI in the liquid phase. Multiple model simulations are performed in order to explore the relative importance of the various oxidation pathways for a range of plausible conditions in volcanic plumes. Note that the chemical conditions prevailing in dense volcanic plumes are radically different from those prevailing in the surrounding background air. The first salient finding is that, according to model calculations, OH is expected to carry a very significant O-MIF in sulfur-rich volcanic plumes and, hence, that the volcanic sulfate produced in the gas phase would have a very significant positive isotopic enrichment. The second finding is that, although H 2 O 2 is a major oxidant of SO 2 throughout the troposphere, it is very rapidly consumed in sulfur-rich volcanic plumes. As a result, H 2 O 2 is found to be a minor oxidant for volcanic SO 2 . According to the simulations, oxidation of SO 2 by O 3 is negligible because volcanic aqueous phases are too acidic. The model predictions of minor or negligible sulfur oxidation by H 2 O 2 and O 3 , two oxidants carrying large O-MIF, are consistent with the absence of O-MIF seen in most isotopic measurements of volcanic tropospheric sulfate. The third finding is that oxidation by O 2 /TMI in volcanic plumes could be very substantial and, in some cases, dominant, notably because the rates of SO 2 oxidation by OH, H 2 O 2 and O 3 are vastly reduced in a volcanic plume compared to the background air. Only cases where sulfur oxidation by O 2 /TMI is very dominant can explain the isotopic composition of volcanic tropospheric sulfate.
Among all the compounds emitted, volcanic sulfur gases and in particular SO 2 , are considered to be the most effective in affecting climate. Climatic perturbations from volcanic emissions are principally caused by conversion of sulfur gases into sulfate aerosols, which can then interact with solar and terrestrial radiation via scattering and absorption (Stocker et al., 2013). Once injected into the troposphere, volcanic SO 2 is converted in few days typically to H 2 SO 4 by a range of gas-phase and liquid-phase reactions taking place in volcanic plumes and clouds (Chin and Jacob, 1996;Stevenson et al., 2003a). In the atmosphere, depending on the oxidation pathway, H 2 SO 4 is produced either in the gas phase or liquid phase. When generated in the gas-phase, volcanic H 2 SO 4 condenses very rapidly onto pre-existing particles, or it may even form very small sulfate particles by nucleation. In the boundary layer, sulfate aerosols have a residence time much shorter than a week because of the fast wet and dry depositions. However, at higher altitudes, such as in the free troposphere, removal is much slower; consequently, volcanic sulfate aerosols can have a much longer residence time of up to a few weeks (Stevenson et al., 2003b, a;Kristiansen et al., 2016). In addition, the residence time of volcanic aerosols in the stratosphere can reach lifetimes of about a year (Thomason and Peter, 2006).
Nowadays, anthropogenic SO 2 emissions outweigh those from natural sources (Smith et al., 2011). Volcanic quiescent degassing and eruptions is an important natural source of SO 2 , notably to the free troposphere (Bates et al., 1992;Graf et al., 1998). Volcanic emissions release about 10-13 Tg y −1 of SO 2 to the atmosphere (Andres and Kasgnoc, 1998) and contribute to up to 10 % of total sulfur emissions to the atmosphere (Stevenson et al., 2003a). Remarkably, volcanic emissions also have a bigger impact on the tropospheric aerosol burden than other sulfur sources (Graf et al., 1998) because volcanoes tend to emit SO 2 at higher altitudes than most other surface sulfur emissions, where the lifetime is longer.
Most of the tropospheric sulfate is generated in the liquid phase (Alexander et al., 2009) via oxidation of aqueous SO 2 by dissolved oxidants of the atmosphere, such as H 2 O 2 , O 3 , O 2 catalysed by transition metal ions (Fe(III) and Mn(II)) and, possibly, HOBr and HOCl (Vogt et al., 1996;von Glasow et al., 2002;Stevenson et al., 2003a;Berglen et al., 2004;Park et al., 2004;Alexander et al., 2009;von Glasow and Crutzen, 2013;Chen et al., 2016). Note that the importance of the halogen oxidation pathway remains unclear. A significant amount of tropospheric H 2 SO 4 is formed in the gas phase via the termolecular reaction between SO 2 and hydroxyl radicals (OH) (Calvert et al., 1978). In presence of liquid water and for typical pH values of atmospheric water droplets (3.0 < pH < 5.6), SO 2 is quickly oxidized by dissolved H 2 O 2 , and the two species rarely coexist in liquid phases (Gervat et al., 1988;Chandler et al., 1988;Daum et al., 1990;Zuo and Hoigne, 1993;Laj et al., 1997). At acidic pH values, synergism among transition metal ions (TMI) enhances the rate of SO 2 oxidation by dissolved O 2 (Brandt et al., 1994;Brandt and van Eldik, 1995), which can thus compete with the other SO 2 oxidation channels. Particular attention has been paid recently to this heterogeneous oxidation pathway, since its contribution could have been underestimated in previous budget assessments of sulfate production in the troposphere (Alexander et al., 2009;Goto et al., 2011;Harris et al., 2013). During eruptive events, volcanoes emit large quantities of ash and coarse material rich in ironminerals (mainly glass, and in lesser extents magnetite and hematite), which can easily dissolve in water because of the high acidity reached in volcanic cloud droplets and aerosols (Ayris and Delmelle, 2012;Hoshyaripour et al., 2015;Maters et al., 2016). As a consequence, the O 2 /TMI heterogeneous oxidation reaction may be more significant than previously thought.
Quantifying the importance of the different SO 2 oxidation pathways is challenging. It requires the quantification of, among other things, the rates of the different oxidation processes. Conventional methods rely mostly on models that are evaluated and constrained with atmospheric concentration measurements of oxidants, because there is no direct means of measuring chemical fluxes associated with individual reactions . Simultaneous measurements of SO 2 oxidants in both the gas-and liquid phases in the atmosphere, let alone specifically in a volcanic plume, would be experimentally challenging. Alternative approaches need to be considered to reduce the uncertainty in the relative contributions from the different oxidation pathways. Isotopic approaches can provide such constraints (Brenninkmeijer et al., 2003;. Isotopic ratios, indeed, provide direct insights into the nature and importance of individual oxidation fluxes Morin et al., 2008;Martin et al., 2014).
Thanks to peculiar distribution of isotopes among its three oxygen atoms, ozone and its chemistry provides a useful tool of investigation for atmospheric processes using isotopic signatures. Ozone bears a very significant non-mass dependent (also called mass-independent) isotopic fractionation, which is due to its formation mechanism (Heidenreich III et al., 1986;Krankowsky et al., 1995;Marcus, 2013). Since oxygen atoms in tropospheric oxygen-bearing species sometimes originate directly or indirectly from ozone via multiple photochemical reactions, a variety of atmospheric species carry anomalous isotopic mass-independent fractionations (MIFs Thiemens, 2006). For oxygen-bearing species, the anomalous oxygen MIF ( 17 O, O-MIF) is calculated with respect to a reference standard: Where δ 17 O and δ 18 O represent deviations to the reference standard isotopic ratios (R std ): Ozone is a key chemical reactive species of the troposphere. Its isotopic anomaly is intrinsically generated (through photolysis and recombination reactions) instead of being inherited by isotopes transfer like for most atmospheric species (Marcus, 2013). Other oxygen-bearing species in the atmosphere can gain excess-17 O by transfer of this ozone anomaly via reactions with ozone itself, reactions with species that have already inherited the ozone anomaly or via anomalous kinetic isotopic effect (Röckmann, 1998;Lyons, 2001;Michalski et al., 2003). As a consequence, transfer of oxygen MIF among atmospheric species is process-specific and can be used as a signature to trace the chemistry of species as they react with specific oxidants. Once the isotopic anomalies of the oxidants are characterized, the resulting 17 O of an end-oxidation product is simply a linear combination of the isotopic signatures of all the oxidation channels weighted by their respective contributions, to the total production of the end-oxidation products. During the last decade, there has been an increasing number of studies that have used O-MIF oxygen anomalies in oxidation products to constrain oxidation channels, often coupling isotopic measurements and photochemical isotopic modelling (Michalski et al., 2003;Alexander et al., 2005;Morin et al., 2008;Gromov et al., 2010;Michalski and Xu, 2010).
The isotopic signature in sulfates generated in the troposphere, the so-called secondary sulfate (by opposition to sulfate directly emitted in the atmosphere, the so-called primary sulfate) reflects the competition within different oxidation channels. In the liquid phase, sulfate oxygen MIF is produced during sulfur oxidation by transfer of isotopic anomalies from ozone and H 2 O 2 , whereas sulfate with O-MIF very close to 0 ‰ is produced in the liquid phase via O 2 /TMI oxidation (i.e. −0.08 ‰). Mass-dependent (MIF anomaly = 0 ‰) sulfate is generally produced via OH oxidation in the gas-phase (Savarino and Thiemens, 1999a, b;Savarino et al., 2000;Martin et al., 2014).
Most present-day tropospheric sulfates have O-MIF anomalies ( 17 O), typically of the order of 1 ‰ . However, there is some variability. For instance, O-MIF of sulfate aerosols generated in marine environments are higher compared to isotopic anomalies found in continental sulfates (Alexander et al., 2005). Very significant 17 O have also been found in volcanic sulfates collected from ash deposits dating back to the Miocene and the Oligocene, whose values reach 3.5 ‰-5.8 ‰. These peculiar isotopic anomalies have been linked to a different oxidative state of the atmosphere at that time (Bao et al., 2000(Bao et al., , 2003. Tropospheric volcanic sulfates of the present era distinguish themselves from other tropospheric sulfates by having a 17 O often close to 0 (within the measurement error of about 0.1 ‰). This feature is found all over the world in sulfates collected from volcanic ashes of small and medium-size tropospheric explosive eruptions, independent of location or geology of ash deposits (Bao et al., 2003;Bindeman et al., 2007;Martin et al., 2014) (see Table 1). Notably, this is often the case for volcanic sulfate extracted from ash deposits which are found very far from volcanoes, where secondary sulfate is expected to dominate. The only exception is volcanic sulfates in ice cores originating from very large volcanic eruptions. This sulfate had formed and transited through the stratosphere Baroni et al., 2007).
The question is why tropospheric volcanic sulfate from volcanic ash deposits does not appear to carry some isotopic O-MIF as is the case for other types of tropospheric sulfates. One might expect part of sulfate produced by tropospheric oxidation of volcanic SO 2 to carry some MIF isotopic anomaly because the dominant SO 2 oxidants in the troposphere are thought to be species carrying O-MIFs (O 3 and H 2 O 2 ) with some contribution from O 2 /TMI (Martin et al., 2014). An important difference between volcanic sulfur and most other sources of sulfur is that it is often emitted within dense volcanic plumes whose chemical compositions are radically different from the background air. The purpose of the present box-modelling study is to explore in detail the oxidation and fate of volcanic sulfur in dense volcanic clouds and the resulting isotopic MIF signature in volcanic sulfate. The objective is to see to what extent the chemical environment of dense volcanic plumes may affect sulfur dynamics and pathways of oxidation and, hence, sulfate isotopic composition. The focus here is on volcanic clouds that are rich in sulfur but poor in halogens, such in the case of intra-plate and rifting plate volcanoes (e.g. Nyarogongo in Congo, Erta'ale in Ethiopia, Kīlauea in Hawai'i) (Aiuppa, 2009;Oppenheimer et al., 2013).Volcanic eruptions with remarkable low halogens to sulfur emissions are the Holuhraun (Bárðarbunga) eruption of 2012-2014 in Iceland (Ilyinskaya et al., 2017;Stefánsson et al., 2017), and the Kīlauea eruption of 2008 in Hawai'i (Mather et al., 2012). In particular, HCl/SO 2 ratios of the order of 10 −2 have been observed for the Kīlauea eruption of 2008 (i.e. HCl ≈ 10-50 ppbv).
The second section of this work describes the photochemical model, including its sulfur heterogeneous chemistry scheme and the associated oxygen isotopic scheme. The mass balance equations used to evaluate the transfer of MIF oxygen anomaly from ozone to volcanic sulfate via different oxidation pathways are also presented. The third section is devoted to the study of individual and combined oxidation pathways and the resulting isotopic signatures in numerical experiments for this work standard volcanic plume conditions. The fourth section covers sensitivity model studies, investigating how different parameters in volcanic plumes affect the final isotopic anomaly in sulfate. Dominant oxidation pathways are identified and the ability of the model to reproduce observed isotopic signatures of volcanic sulfate is assessed.  Martin (2018) for a more extensive description regarding oxygen isotopic anomalies measured in tropospheric volcanic sulfate of present and past geological eras.

Modelling approach
The photochemical box model used during simulation is the Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a photochemical box model developed to simulate tropospheric chemistry (Evans et al., 2000;Sander et al., 2006;Real et al., 2007;Pugh et al., 2012). It describes the standard gas-phase photochemistry accounting for kinetics of tropospheric species (bimolecular, termolecular and photodissociation reactions), and deposition of gases and particles. Photolysis reaction rates are evaluated using the Fast-J code . Kinetic data are taken from JPL's data sheets (Sander et al., 2006). CiTTyCAT had already been used with success to constrain seasonal pathways of reactive nitrogen species in the troposphere, through the implementation of its chemical scheme with an isotopic transfer scheme accounting for 17 O production in nitrates . We have extended the capabilities of the model by including parameterizations of the transfer of soluble species between liquid and gas phases, of SO 2 heterogeneous chemistry, of pH in the liquid phase and of MIF of oxygen atoms in sulfates.

General continuity equations
The model resolves differential coupled mass balance equations (continuity equations) describing the time evolution of species concentrations in the troposphere. For given initial (e.g. initial concentrations of species) and environmental conditions (e.g. pressure, temperature), mass balance equa-tions are solved for each species, accounting for production and loss as follows: where C i is the concentration of species i, P i the sum of physical and chemical production rates for i, and L i the sum of the physical and chemical loss rates of i. Production and loss terms are calculated using chemical reaction kinetics, where time evolution of concentrations of chemical species depends on the relevant rate constants (k i ) and on concentrations of reactants. They also include liquidgas transfer and deposition. In addition, mixing of air between the volcanic sulfur cloud and the outside background air is also accounted for. It is parameterized by a simple linear relaxation scheme resulting in an exponential decay of plume concentrations towards background concentrations (Methven et al., 2006;Arnold et al., 2007).
where K mix is a first-order mixing rate coefficient representing all the processes mixing volcanic air with the background atmosphere and C (i,bck.) is the concentration of species i in the background air. K mix is set to 0.1 d −1 , a value typical of low mixing in the free troposphere and corresponding to a characteristic mixing timescale of 10 days (Methven et al., 2006;Arnold et al., 2007).

Liquid-gas mass transfer
Concentrations of relevant soluble species are calculated taking into account its partition between the gas and liquid phases. The transfer in both directions (evaporation, condensation) is dynamically computed. At each time step, rates of transfer are defined as follows: where C (i) is gaseous concentration of species i far from liquid droplets, C (i,s) is the gaseous concentration of species i at the surface of droplets (which is assumed to be the equilibrium saturation vapour of i over the liquid) and J i is the coefficient of condensation (from gas phase to liquid droplet) for species i, which is calculated using the Dahneke's expression (Dahneke, 1983) to cover mass-transfer from the continuum to the kinetic regime (see pg. 502 of Seinfeld and Pandis, 2016). Throughout all the model simulations, droplets are assumed to be very large, with a radius of 5.0 µm. The sensitivity of the results to the assumed amount of liquid phase is explored varying the concentration of water droplets (and hence the liquid water content) instead of varying the size of droplets. It is also possible that emitted water condenses onto ash particles. Our treatment does not discriminate between liquid droplets and liquid phases at the surface of solid particles.

Gaseous and heterogeneous sulfur chemistry
The model already describes the SO 2 gas-phase chemistry. Since SO 2 is a mildly soluble species undergoing acid-base equilibrium in the liquid phase, we have added the gas-liquid transfer and the chemical reactions and equilibrium associated with its presence in the liquid phase (see Table 2). The extent of SO 2 dissolution into water droplets is controlled by the pH. The oxidation of S(IV) species (HSO − 3 , SO 2− 3 , SO 2(aq.) ) by reactions with H 2 O 2 , O 3 or O 2 in the liquid phase pushes the gas-liquid partition towards dissolution of gaseous SO 2 . A diagram of the sulfur chemical model is presented in Fig. 1. Since the model CiTTyCAT resolves continuity equations for species with gas-phase concentration units, liquid phase concentrations (e.g. M) and rate constants have to be expressed into gas-phase units in the code in order to be treated by the CiTTyCAT chemistry solver (Seinfeld and Pandis, 2016).
The species involved in the acid-base equilibriums of SO 2 and H 2 SO 4 are often grouped together according to their oxidation state: In these equations, dissolved H 2 SO 4 is assumed to be totally dissociated. Ultimately, S(VI) in droplets ends up deposited at the Earth's surface. In the model, the amount of sulfate deposited is evaluated as a variable. The pH of volcanic water droplets is also a prognostic variable because sulfur species reaction rates and partitioning are pH dependent (Seinfeld and Pandis, 2016). It is dynamically calculated considering the most significant species dissolved in droplets: The main aqueous equilibrium reactions and S(IV) oxidation reactions added to the chemical scheme are summarized in Table 3. The final continuity equation for single SO 2 oxidation channels can be expressed as follows: where k OH+SO 2 is the rate constant of the gas-phase reaction between OH and SO 2 (Sander et al., 2006), k j the rate constant of the aqueous reaction between SO 2 and species C j , whose concentration in the aqueous phase is expressed as [C j ] aq. . Similar continuity equations can easily be derived for all the sulfur species. The continuity equation for atmospheric sulfate S(IV) can be determined by summing all the individ- Table 2. Sulfur aqueous equilibria. Beilke and Gravenhorst (1978); b Redlich (1946); c Graedel and Weschler (1981). Table 3. Sulfur chemistry scheme.
ual continuity equations of S(IV) species: where k j the rate constant of the aqueous reaction between oxidant C j and relevant [S(IV)] species (see the list of aqueous oxidation reaction in Table 3), and k d is the deposition coefficient of dissolved sulfur species. Dry deposition as such is not expected to be important in the plume itself compared to wet deposition for our cloudy conditions. Since only wet deposition is considered, only species dissolved in water phases such as aqueous S(IV) (SO 2(aq.) + HSO − 3 + SO 2− 3 ) and S(VI) (HSO − 4 + SO 2− 4 ) species are deposited in the model. The deposition is treated as a first order loss with k d = 2 × 10 −6 s −1 , equivalent to a characteristic time scale of 5.7 days (Stevenson et al., 2003b).
The same approach can be used for S(VI) and deposited S(VI): where S(VI) dep. is the sulfate deposited at the surface.

Oxygen isotope signatures in sulfur oxidation
The mass-balance equation describing the production of S(VI) species is coupled to an oxygen isotope transfer scheme in order to track the evolution of 17 O in sulfates in water droplets and in sulfates deposited at the surface. Therefore, the specific isotopic anomaly acquired by a S(VI) molecule (produced by the oxidation of a S(IV) molecule by a specific oxidant) is first derived using isotopic transfer  equations. New S(VI) isotopes tracers are then created in order to monitor the amount of isotopic anomaly carried out by sulfates in water droplets and deposited at the surface. They are defined as anomaly products ( 17 O × [S(VI)]), and introduced in the model on the basis of the following continuity equation (Morin et al., , 2011: where 17 O(S(VI)) is the isotopic anomaly of atmospheric sulfate, 17 O(S(VI) prod. ) j is the O-MIF anomaly transferred to sulfate through the specific oxidation channel j , and P j is the oxidation rate of channel j . 17 O(S(VI) prod. ) j is fixed for ozone, H 2 O 2 and TMI oxidation pathways but it is a prognostic variable for OH (see Table 4). As deposited sulfate is a variable in the model (S(VI) dep. ), the transfer of isotopic anomaly during deposition is also monitored following a similar equation, The value of oxygen isotopic anomaly (O-MIF) in sulfate depends on the relative importance of individual SO 2 oxidation pathways (P j ) and their respective transfer of O-MIF ( 17 O(S(VI)) j ). Note that the continuity equations of S(VI) and S(VI) dep. isotopes tracers are integrated with a 4th order Runge-Kutta method algorithm instead of using the CiTTy-CAT chemistry solver with the oxidation rates (i.e. P j in 11) kept constant over a time step . This approach allows keeping the chemistry module totally independent from the oxygen isotopic module. The external integration tool does not affect significantly the results. Throughout this study, it is assumed that both SO 2 and water vapour (H 2 O) are not carrying any initial O-MIF. The isotopic composition of magmatic SO 2 , indeed follows mass-dependent fractionations and no significant 17 O, 34 S and 36 S have been measured so far (Eiler, 2001). Measurements show that tropospheric H 2 O does not carry any O-MIF (Uemura et al., 2010), and the same is found for atmospheric SO 2 (Holt et al., 1981). It is therefore assumed that the O-MIF found in sulfates only originates from the transmission of isotopic anomaly during the aforementioned reactions of sulfur oxidation.
In order to constrain individual SO 2 oxidation pathways from isotopic information, it is first necessary to characterize the specific O-MIFs they transfer to sulfate using isotopic transfer equations.

Oxidation by ozone
The few isotopic measurements of tropospheric ozone indicate values of 17 O (O 3bulk ), ranging from 20 ‰ to 40 ‰ with a mean value of about 25 ‰ (Krankowsky et al., 1995;Johnston and Thiemens, 1997;Vicars and Savarino, 2014). The location of oxygen isotopes within the structure of ozone is not uniform and heavier isotopes are mostly located at the extremities of the molecule (Janssen, 2005;Bhattacharya et al., 2008). Indeed, molecules that have asymmetrical geometrical structures, and bearing heavier oxygen isotopes on terminal sites, are more energetically stable than their symmetric counterparts (Marcus, 2013). This enrichment in heavy oxygen isotopes at terminal locations of ozone is confirmed by laboratory measurements . Ozone does not always react with other molecules via terminal oxygen atoms, although this reaction mechanism is energetically favourable since it requires the breaking of only one molecular bond. During the oxidation of reactive nitrogen leading to production of atmospheric nitrate, most of the oxygen atoms involved in the reaction are from terminal sites . Multiple studies found a similar selective reactivity indeed, as during photochemical reactions or for reactions of ozone on solid substrates (Sheppard and Walker, 1983;Bhattacharya et al., 2008). Considering the mean bulk O-MIF and terminal isotopic enrichments, a mean reactive ozone O-MIF ( 17 O (O * 3 )) of 36 ‰ has been derived Savarino et al., 2008;Morin et al., 2007). This value is used throughout this study, since it is in accordance with parametrizations used in previous successful model simulations (Michalski et al., 2003;Alexander et al., 2002;Morin et al., 2007;Alexander et al., 2009;Morin et al., 2011).
The value of O-MIF in sulfates generated during the aqueous oxidation by ozone is determined by identifying the origins of each oxygen atom in sulfate during the reaction of oxidation. Ozone transfers to sulfate only one oxygen atom during aqueous sulfur oxidation, while another oxygen atom derives from the water molecule forming aqueous S(IV). The equation describing the transfer of O-MIF to sulfate during oxidation by ozone is as follows: This equation can be simplified because the O-MIF anomalies in SO 2 and H 2 O are negligible: Therefore, the isotopic anomaly in atmospheric sulfates produced in the model during the oxidation of dissolved SO 2 through O 3 is 17 O (S(VI)) O 3 +SO 2 = 9 ‰ (Morin et al., , 2011.

Oxidation by hydroxyl radical
In the atmosphere, OH radicals are formed as a result of ozone photolysis in presence of water vapour. In particular, ozone photodissociation can produce an O 1 (D) radical, which react with a water molecule to produce two OH radicals. Tropospheric OH radicals are thought not to carry O-MIF anomaly because the exchange of oxygen atoms with water vapour is so fast that it erases any inherited isotopic anomaly in OH. Recall that tropospheric H 2 O does not carry any O-MIF because the tropospheric H 2 O cycle is entirely controlled by physical processes (condensation, evaporation) and not by chemical processes involving ozone. As a result, the O-MIF signature in OH radicals is expected be 0 ( 17 O (OH) = 0.0 ‰ Morin et al., 2011). However, when the humidity and hence H 2 O levels are very low (e.g. upper troposphere), the rate of isotopic exchange between OH radicals and H 2 O molecules decreases so much that freshly produced OH radicals may have time to react with other molecules before losing their isotopic anomaly by isotopic exchange with H 2 O . Under those conditions, when the OH loss reactions and cycling compete with the isotopic exchange with H 2 O, some of the initial O-MIF originating from ozone is still present in reacting OH. It is also possible for OH loss to compete with the H 2 O isotopic exchange when the rate of OH loss is highly enhanced instead of having a reduced rate of H 2 O isotopic exchange. This may be the case in volcanic plumes, when SO 2 levels are so high that the SO 2 + OH reaction become the dominant chemical loss (Bekki, 1995), accelerating the OH cycling. In order to account for this possibility, instead of assuming a null O-MIF for OH, the O-MIF in the steady-state OH ( 17 O (OH)) is calculated explicitly using the approach developed by Morin et al. . 17 O (OH) is simply derived from the competing balance between the O-MIF erasing isotopic exchange and the total OH loss, typically the reactions with CO and CH 4 in the troposphere. Since we consider sulfurrich volcanic plumes and clouds, the reaction between OH and SO 2 is also taken into account.
Considering all the transfers of oxygen atoms, the isotopic mass-balance equation for the OH pathway can be expressed as follows: The O-MIF of OH can be derived using the following equation and where k * OH+H 2 O is the rate constant for the oxygen atoms exchange reaction between OH and H 2 O, and k OH+CH 4 and k OH+CO are the reaction rate constants for the gas phase reaction of OH with CH 4 and CO, respectively.
In this approach x represents the competition between the O-MIF erasing effect of isotopic exchange and the O-MIF retaining effect of OH chemical loss; only important loss reactions for tropospheric OH are considered here.
17 O(OH * prod. ) is the O-MIF of the OH radical freshly produced, and it is assumed that OH is mostly formed by the photolysis of ozone followed by the reaction of O 1 (D) with H 2 O.

Oxidation by hydrogen peroxide
In the troposphere, H 2 O 2 can quickly dissolve into liquid water phases . In a volcanic plume, these phases can be either water droplets or water condensed on solid particles, typically on ash particles. Once in the aqueous phase, H 2 O 2 oxidizes SO 2 by nucleophilic displacement, and its two oxygen atoms are transmitted to the produced sulfate molecule (McArdle and Hoffmann, 1983;Brandt and van Eldik, 1995 (Savarino and Thiemens, 1999a, b). Using this mean value, sulfate produced by the H 2 O 2 oxidation is assumed to carry a 17 O(S(VI)) H 2 O 2 +SO 2 = 0.87 ‰ (Savarino et al., 2000).

Oxidation by O 2 /TMI
Isotopic measurements of atmospheric O 2 indicate that its O-MIF anomaly is rather small (Luz et al., 1999;Barkan and Luz, 2003). Kinetic isotope fractionation associated to the Dole effect (Dole, 1936) Miller, 2002). This value is chosen because it gives a reasonably good agreement between isotopic measurements (Martin et al., 2014) and models (Miller, 2002;Young et al., 2002;Pack et al., 2007). In addition, it has to be kept in mind that there are large uncertainties associated with the exact reaction mechanism of SO 2 oxidation catalysed by TMI. We assume that only one oxygen atom of O 2 is transmitted to sulfate during the SO 2 oxidation (Brandt and van Eldik, 1995;Herrmann et al., 2000).
With these assumptions, the isotopic mass-balance equation for SO 2 oxidation by O 2 /TMI is given by Since volcanic SO 2 is thought to carry no significant O-MIF, we can assume that initial S(IV) species do not carry any O-MIF. Consequently, the isotopic signature associated to this oxidation pathway can be simplified: 17 O (O 2 ) being taken as −0.34 ‰ (see above), sulfate produced through this pathway carries a O-MIF ( 17 O(S(VI)) O 2 +SO 2 ) almost null, of about −0.09 ‰ (Savarino et al., 2000). The O-MIF signatures of all the S(IV) oxidation pathways used in the model are summarized in Table 4.
3 Box model set-up 3.1 Standard case: initial conditions All simulations are run for springtime conditions and start at 08:00 at tropical latitudes (8.3 • N). In order to reach stable chemical compositions, notably for medium-and short-lived reactive species, the model is run for 3 days before injecting SO 2 , then, the evolution of the chemical composition is followed for 7 days. This timescale corresponds approximately to the lifetime of a plume in the free troposphere, in occurrence of low turbulence and low wind shear .
Since most of volcanoes are situated in remote areas with their peaks close to the free troposphere, or, at least, with volcanic plumes often ending up in the free troposphere, the environmental conditions are chosen to be representative of the lower free troposphere with temperature set at 283.15 K, and pressure fixed at 640 mbar (about 3 km altitude). Since we consider cloudy conditions, the relative humidity is set to 100 %.
Furthermore, concentrations of reactive species are also set to typical levels found in the tropical lower free troposphere: O 3 = 45 ppbv and H 2 O 2 = 0.1 ppbv. Finally, initial SO 2 is set to a mean volcanic plume concentration of 1 ppmv, a value typical of volcanic plumes during degassing (Robock, 2000;Herrmann et al., 2000;Wardell et al., 2004;Mather et al., 2006;Roberts et al., 2012;De Moor et al., 2013;Voigt et al., 2014). The initial pH of the aqueous phase is set to 4.5. It has no impact on the overall model results because the pH is almost immediately driven by SO 2 uptake and sulfur oxidation. Preliminary simulations have shown that the initial SO 2 concentration is a critical input.
Due to the large amounts of water that can be injected during explosive eruptions, in our simulations it is assumed that volcanic water vapour is largely in excess compared to relative humidity of the free troposphere. Moreover, due to low temperature and pressure of the lower free troposphere, for our simulations it is assumed that volcanic water vapour would mostly condense to produce cloud droplets or to coat ash particles. Therefore, throughout this study relative humidity (RH) inside volcanic plumes is set at 100 %, the water saturation point corresponding to the pressure and temperature of the background atmosphere. The Liquid Water Content (LWC) parameterizes the amount of liquid water within plumes. High levels of LWC can be reached, indeed, within volcanic plumes from explosive eruptions. Modelling sim-ulations suggest that LWC as high as 1.6 g m −3 could be reached at the core of water-rich volcanic clouds condensing in the troposphere . It is possible that, during the first stages of medium-size eruptions, LWC within the plume could be at least comparable to LWC values of growing cumulus clouds. For all the simulations LWC is set to 1.0 g m −3 , a value between experimental measurements (e.g. meteorological clouds) and modelling studies of water-rich volcanic plumes reaching the upper troposphere (Tabazadeh and Turco, 1993;Hoshyaripour et al., 2015). Like SO 2 , LWC is found to be a critical model input.
TMI concentrations in the liquid phase are set to [Fe(III)] = 0.5 µM and to [Mn(II)] = 0,05 µM. These values are at the lower end of typical tropospheric measurements with [Fe(III)] concentrations ranging between 0.5 and 2 µM (Martin, 1984;Martin and Good, 1991;Parazols et al., 2006). Because of uncertainties associated with iron dissolution in volcanic plumes, our TMI concentrations are lower than concentrations found in dust-rich polluted conditions where [Fe(III)] can reach concentrations of around 5 µM (Herrmann et al., 2000;Parazols et al., 2006). TMI concentrations follow the same relation throughout the whole study and for each simulation [Mn(II)] = 0.1 × [Fe(III)] (Martin and Good, 1991).

Model experiments
The objective of the first set of numerical experiments is to assess the competition among oxidation pathways in SO 2rich plumes/clouds for the standard case. Three simulations (S1-S3) are run with oxidation schemes of increasing complexity. They simulate oxidation of SO 2 : (S1) by OH in gas phase, (S2) by OH in gas phase, and H 2 O 2 and O 3 in aqueous phase, and (S3) by OH in gas phase, and H 2 O 2 , O 3 and O 2 /TMI in aqueous phase.
Since initial SO 2 levels, LWC and TMI concentrations in volcanic plumes are relatively uncertain and are key model inputs, the sensitivity of the results to varying conditions within plausible ranges is also explored in additional simulations. Isotopic anomaly transfers are investigated for atmospheric concentrations stretching from passive degassing and quiescent conditions to sulfur-rich volcanic clouds with varying levels of TMI. The intervals used for the different sensitivity studies are summarized in Table 5.
The first set of sensitivity simulations is devoted to the sensitivity of results to initial SO 2 levels in the case of the S1 simulation. It is designed to explore not only the impact of varying SO 2 levels on sulfate O-MIF produced by the OH oxidation pathway, but also on OH isotopic signature itself. Recall that the OH isotopic signature ( 17 O (OH)) is generally assumed to be 0 in the literature (see Sect. 2.4.2).
It is widely recognized that SO 2 is the compound emitted by volcanic activity which causes the largest climatic impacts through its conversion into sulfate aerosols (Graf et al., 1998;Robock, 2000;Textor et al., 2004;Langmann, 2014). Emis- sions of volcanic SO 2 have been measured both in proximity of volcanic vents and in aged plumes. It is possible to constrain a range of concentrations, considering age of plumes and distance from points of emissions. During the first stages of plume development concentrations of SO 2 in the range of 10-50 ppmv can be reached right in proximity of volcanic vents (Aiuppa et al., 2005(Aiuppa et al., , 2006aRoberts et al., 2012), while concentrations in the range of 0.1-1 ppmv can be found in aged plumes at longer distances from points of emissions (Delmelle, 2003;Carn et al., 2011). These results are confirmed by modelling simulations which can constrain volcanic emissions by accounting for quick dilution after plume ejection from the vent (Gerlach, 2004;Aiuppa et al., 2007;Roberts et al., 2009). Consequently, based on atmospheric simulations and on in situ measurements, the SO 2 concentration is set to 1.0 ppmv in the standard case, and is varied from 0.1 to 10 ppmv in the sensitivity simulations. LWC plays a crucial role in aqueous oxidation of volcanic SO 2 . The range of LWC considered has been chosen based on LWC observed for different cloud typologies such as mean saturated clouds (0.1 g m −3 ), water-rich cumulus clouds (0.5-1 g m −3 ), and cumulonimbus clouds (1-2 g m −3 ) (Laj et al., 1997;Rosenfeld and Lensky, 1998;Pruppacher et al., 1998;Korolev et al., 2007;Carey et al., 2008). LWC is set to 1 g m −3 in the standard case and is varied from 0.1 to more extreme values of 2.5 g m −3 for sensitivity simulations (Tabazadeh and Turco, 1993;Aiuppa et al., 2007).
Aqueous concentrations of iron ([Fe(tot)] = [Fe(II)] + [Fe(III)]) can peak to 9-10 µM in the troposphere (Desboeufs et al., 1999(Desboeufs et al., , 2001 with [Fe(III)] concentrations between 2.0 and 5.0 µM in polluted conditions if photochemical cycling between [Fe(II)]-[Fe(III)] is inhibited (Parazols et al., 2006). Volcanic eruptions inject large quantities of solid material into the atmosphere in the form of ash. As a result, volcanic plumes/clouds are characterized by high concentrations of ash and minerals (Mather et al., 2003). Ash particles have sizes as large as few mm and they are mainly composed of silica and crystalline minerals of magmatic origin. Glass, olivine, magnetite, hematite and fayelite are among the most common minerals injected during eruptions (Rose and Durant, 2009;Langmann, 2014;Hoshyaripour et al., 2015). These minerals are composed in different proportions by Fe(II) and Fe(III), which are entrapped in the crystalline structure of rocks in different morphologies and compositions. Since large quantities of water are also injected during eruptions, water can condense on mineral particles, especially as the volcanic Atmos. Chem. Phys., 18, 17909-17931, 2018 www.atmos-chem-phys.net/18/17909/2018/ Figure 2. Evolution of the gas-phase concentrations of atmospheric species during the S1 simulation (see text). The simulation starts at 08:00 and SO 2 is injected after 3 days. During the S1 simulation the concentration of injected SO 2 drops from 1.5 ppmv to a final value of 1.27 ppmv.
column reaches higher altitudes and lower temperatures in the troposphere (Tabazadeh and Turco, 1993;Hoshyaripour et al., 2015). Once mineral particles are coated by water, dissolution of iron from the solid mineral surface to the thin liquid water film may take place depending on the acidity of the aqueous phase (Ayris and Delmelle, 2012;Langmann, 2014;Maters et al., 2016). Acidic conditions (pH < 2.0) due to H 2 SO 4 condensation or formation within the liquid phase favour the solubility of minerals containing iron and dissolution of [Fe(III)] (Solmon et al., 2009;Ayris and Delmelle, 2012). Up to a third of total Fe at the ash surface can dissolve into the liquid phase coating volcanic particles (Hoshyaripour et al., 2014) depending on rock composition and gases in the volcanic clouds. Laboratory experiments on dissolution in acidic water of iron from volcanic ashes suggest that [Fe(III)] concentrations of up to 2 µM can be reached quickly in the liquid phase when pH reaches ∼ 2 (Maters et al., 2016). Concentrations as high as [Fe(III)] = 3 µM could be reached if pH reaches 1 (Maters et al., 2016). Mobilization of iron ions from ashes could be enhanced for plumes reaching the upper troposphere and undergoing ice formation (Jeong et al., 2012;Shi et al., 2012). High concentrations of [Fe(III)] might persist in the liquid phase depending on the lifetime of water droplets, notably driven by evaporation and condensation cycles (Desboeufs et al., 2001;Langmann, 2014). Cloud properties are affected by evaporation and condensation cycles changing the pH, the size and number of droplets, while formation of insoluble salts at the surface of ash particles entrapped in cloud droplets can affect mobilization of ions (Ayris and Delmelle, 2012;Langmann, 2014). Therefore, lower acidity combined with the presence of insoluble salts may result in a reduced availability of dissolved TMI in volcanic clouds as the volcanic cloud ages. Over the long term, these conditions can lead to concentration of Fe(III) in water droplets of volcanic clouds which can be lower than typical concentrations found in tropospheric clouds (Desboeufs et al., 1999(Desboeufs et al., , 2001. In this study, [Fe(III)] is set to 0.5 g m −3 in the standard case and is varied from 0.1 to 3 µM in the sensitivity simulations to cover the wide range of possible [Fe(III)] concentrations.
The resulting model 17 O(S(VI)) (i.e. from standard and sensitivity simulations) are compared to sulfate O-MIF found in tropospheric volcanic sulfates extracted from ash deposits of small and medium-size tropospheric explosive eruptions of the present geological era (Bindeman et al., 2007;Martin et al., 2014;Bao, 2015), or in sulfate aerosols collected at volcanic vents, almost certainly primary sulfate .

Results and discussion
4.1 Isotopic constraints on individual oxidation pathways of volcanic SO 2 4.1.1 Gaseous oxidation by OH S1 simulates the O-MIF transfer to sulfate in the absence of aqueous oxidation for standard conditions; H 2 SO 4 is only produced by the reaction between hydroxyl radicals and SO 2 in the gas phase. As soon as SO 2 is injected, it reacts with OH to produce gaseous H 2 SO 4 . Figure 2 shows the decay of SO 2 levels from 1.5 to 1.26 ppmv after 7 days. As expected, gas-phase concentrations of other SO 2 oxidants (i.e. O 3 and H 2 O 2 ) are not substantially affected by the SO 2 injection. Since H 2 SO 4 is very soluble, once produced in the gas phase, it ends up dissolved in the liquid phase where it shifts the pH towards acidic values because of its quasi-complete dissociation. The concentration of atmospheric sulfate (S(VI)) is driven by the gas-phase production and deposition. Sulfate production follows a diurnal cycle because of the diurnal production of OH. There is no significant production of S(VI) during night-time. declines very slowly to +0.9 ‰ after 7 days. Since SO 2 is only oxidized by OH, the evolution of 17 O(S(VI)) reflects the evolution of the OH isotopic signature ( 17 O (OH)). Unexpectedly, it is found to be very different from 0. Usually, the exchange of oxygen atoms with water vapour is so fast in the troposphere that it erases any inherited isotopic anomaly in OH. However, in our standard conditions, SO 2 levels are so high that the SO 2 + OH reaction become the overwhelmingly dominant loss (Bekki, 1995) the OH cycling accelerating greatly. Under those conditions, the OH loss is so enhanced that the reaction competes with the isotopic exchange with H 2 O. Therefore, OH radicals can react before their isotopic anomaly is entirely erased by the isotopic exchange, Figure 5. Time evolution in the gas-phase concentrations of SO 2 , its tropospheric oxidants and produced and deposited sulfates during S2. During the S2 simulation the concentration of injected SO 2 drops from 1.5 ppmv to a final value of 1.2 ppmv. and they maintain a significant positive signature. As SO 2 concentration decreases slowly, the rate of OH loss decreases and, as expected, so is 17 O(S(VI)). The evolution of deposited sulfate O-MIF somewhat follows the evolution of the atmospheric sulfate O-MIF but with the time lag which is related to the characteristic timescale of the atmospheric sulfate deposition specified in the model (5.7 days). The final O-MIF of deposited sulfate (resulting from the cumulative effect of sulfate deposited since the SO 2 injection) is 0.92 ‰, which is distinctively higher than most measurements from volcanic sulfate sampled in volcanic ash deposits (see Table 1).

Isotopic signature of OH: dependence on initial SO 2
Since 17 O(OH) is sensitive to the SO 2 level, additional S1 simulations are carried out with SO 2 concentration differing by 3 orders of magnitude. Figure 4 shows the time evolution of OH and sulfate O-MIF for two different initial SO 2 concentrations (i.e. 1 ppbv and 1 ppmv). The upper plot shows the time evolution of OH for the two SO 2 cases. As soon as the SO 2 is injected, OH concentration drops sharply in the high SO 2 case, whereas it remains unaffected in the low SO 2 case. At such high SO 2 concentrations, the reaction between OH and SO 2 becomes the main OH loss. As a result, OH concentration OH lifetime drop and OH cycling is much faster. The lower plot of Fig. 4  Eq. (17), the competition between OH loss channels and the isotopic exchange with water is represented by the x ratio.
In the simulation with 1 ppmv of initial SO 2 , 17 O(OH) decreases from 10.8 ‰ to 7.6 ‰, whereas the variation is very small in the simulation with 1 ppbv of initial SO 2 .These results suggest that OH could have a positive O-MIF in volcanic sulfur-rich plumes and clouds which is subsequently transferred to the produced sulfate. Since most isotopic measurements indicate that O-MIF in volcanic sulfate is very close to zero, at least typically within the measurement errors of about 0.1 ‰, other oxidation pathways that are mostly mass-dependent (i.e. null O-MIF) have to contribute very significantly to the formation of volcanic sulfate. The other known oxidation pathways of SO 2 are heterogeneous.

Gaseous and heterogeneous oxidation by O 3 and H 2 O 2
The S2 simulation is the same as S1 except that it also includes the aqueous oxidation of SO 2 by H 2 O 2 and O 3 . Figure 5 shows evolving concentrations of atmospheric species as oxidation takes place. Almost as soon as SO 2 is injected, the H 2 O 2 concentration drops from about 20 ppbv to less than a pptv. At the same time, as in S1, the pH quickly drops to less than 3 (see Fig. 6). Just after the injection, H 2 O 2 is initially the overwhelmingly dominant oxidant (Martin et al., 2014). The contribution of oxidation by O 3 is almost negligible under acidic conditions and the oxidation by OH in the gas phase is initially much slower than aqueous oxidation by H 2 O 2 . However, as the SO 2 concentration vastly exceeds the H 2 O 2 concentration (by 3 orders of magnitude), H 2 O 2 is very quickly consumed by reaction with SO 2 in the liquid phase; recall for each molecule of SO 2 oxidized by H 2 O 2 , one molecule of H 2 O 2 is consumed. The difference in concentration between SO 2 and H 2 O 2 is such that, as soon as a molecule of H 2 O 2 enters the liquid phase, it is consumed. The sharp drop in H 2 O 2 concentration is thus limited by H 2 O 2 gas phase diffusion to the surface of the liquid phase, which is followed by its quick reaction with S(IV). After the initial drop, the H 2 O 2 concentration stays very low with very large diurnal variations. The daytime concentration approaches pptv levels because the loss to the liquid phase is balanced by gas-phase photochemical production. After the drop in H 2 O 2 , most of the SO 2 is oxidized by OH in the gas-phase. As shown in Fig. 6, the pH in S2 follows a trend similar to the one in S1. The sulfate O-MIF in S2 is higher than in S1. In the first phase, sulfate is produced with a rather high O-MIF signature because the contribution of O 3 to SO 2 oxidation is significant with an initial pH set to 4.5 (i.e. as high as 50 % of SO 2 is oxidized by O 3 within the first hours  [15][16][17][18][19][20]. This explains why 17 O(OH) decreases from 4 ‰ to roughly 3 ‰ by the end of the simulation, resulting in produced sulfates with O-MIF of 1 and 0.75 ‰, respectively. The value of O-MIF on deposited sulfates produced in this simulation is still much higher than most O-MIF measurements in tropospheric volcanic sulfates (see Table 1). In order to produce mass-dependent sulfates without O-MIF ( 17 O = 0.0 ± 0.1 ‰), another oxidant needs to be dominant and it has to carry a small or null O-MIF anomaly.

Gaseous and heterogeneous oxidation by O 3 , H 2 O 2 and O 2 /TMI
Simulation S3 includes all the major pathways of oxidation involved during formation of sulfate in SO 2 -rich clouds (i.e. without significant halogens concentrations compared to sulfur species). Figure 7 shows the evolution of the chemical species concentrations. In S3, H 2 O 2 is very quickly depleted  just after the SO 2 injection as in S2. However, there is much less SO 2 left at the end of the run in S3 than in S2 and S1 and conversely there is more S(VI) produced in S3 than in S2 and S1. With the TMI catalysed oxidation added to the S2 chemical scheme, heterogeneous chemistry becomes competitive with the gas-phase oxidation by OH and lead to faster formation of S(VI). The pH is also lower (see Fig. 8), confirming that more sulfates are in aqueous solution. The final O-MIF in deposited sulfates is about 0.3 ‰. This value is lower than the values calculated in simulations S1 and S2 and closer but still higher than the range of isotopic measurements carried out on volcanic sulfate (see Table 1). This result suggests  Table 6.
that heterogeneous SO 2 oxidation by O 2 /TMI is the only pathway able to explain sulfate isotopic measurements with the current chemical scheme. Sensitivity studies are however needed to test the responses of the system to varying conditions of heterogeneous oxidation. Consequently, we conduct further simulations to probe the effects of LWC and TMI aqueous concentrations on the final MIF in deposited sulfate and assess the robustness of the overall results.

Influence of SO 2 on sulfate O-MIF
In the first set of sensitivity simulations (Z1), the response of the system to various concentrations of SO 2 is tested for the standard conditions with all the oxidation channels included in the model. Figure 9 shows the time evolution of O-MIF in the produced sulfate for different initial SO 2 concentrations. The initial concentration of volcanic SO 2 is varied from 10 ppbv to 10.0 ppmv. LWC is set to 1.0 g m −3 and [Fe(III)] = 0.5 µM. The response of the system and, in particular, of produced sulfate O-MIF to varying SO 2 levels is complex and not at all linear. In Table 6 Hoffmann, 1983). Above 100 ppbv, instead of decreasing, sulfate O-MIF increases at higher initial SO 2 concentration, with 10 ppmv being the maximum SO 2 concentration considered here. This inversion in the evolution of 17 O(S(VI)) with increasing SO 2 concentration originates from the change in 17 O(OH). Up to 100 ppbv of SO 2 , 17 O(OH) is more or less negligible and consequently the OH oxidation produces sulfate with insignificant O-MIF. However, at 300 ppbv of initial SO 2 , 17 O(OH) is equal to 0.8 ‰ at the start of simulation and is still greater than 0.3 ‰ at the end of the run. The higher SO 2 concentration is, the higher 17 O(OH) is. At 10 ppmv of SO 2 , 17 O(OH) = 11.5 ‰. Recall that the maximum possible value of 17 O(OH) is 18.0 ‰, corresponding to conditions where the rate of the isotopic exchange is negligible compared to the rate of OH chemical loss. Interestingly, the overall contribution of OH to the sulfur oxidation peaks at 69 % for initial SO 2 equal to 300 ppbv. At higher concentrations, the OH contribution decreases reaching 33 % for the simulation with 10 ppmv of initial SO 2 . At the same time, the contribution of O 2 /TMI oxidation (the only channel with a negligible O-MIF signature) increases sharply becoming even dominant (58 %) for the simulation with 10 ppmv of initial SO 2 . Nonetheless, the very large increase in 17 O(OH) is the main driver of 17 O(S(VI)) for high SO 2 levels, because the OH contribution remains important even for the simulation with 10 ppmv of initial SO 2 . Note that the H 2 O 2 contribution declines all the way with increasing initial SO 2 (from 10 ppbv to 10 pmmv) which is the inverse of the O 2 /TMI contribution evolution.
Overall, the model-calculated contribution of the OH pathway to volcanic sulfur oxidation does not drop below 30 % for the standard conditions considered here. As a result, the O-MIF of deposited sulfate O-MIF is expected to depend strongly on the amount of SO 2 injected, via the dependency of OH isotopic signature on SO 2 concentration. Since volcanic SO 2 usually reaches ppmv levels during the first stages of volcanic plume (Roberts et al., 2009(Roberts et al., , 2012Oppenheimer et al., 2013;Voigt et al., 2014), our results suggest that volcanic sulfate should carry positive O-MIF anomalies that exceed isotopic measurement uncertainties (≈ 0.1 ‰). This is not supported by atmospheric measurements of volcanic sulfate isotopic composition which mostly lie close to zero within measurement uncertainties. Other environmental conditions or reaction mechanisms have to be considered to explain the lack of O-MIF in volcanic sulfate

Influence of LWC on sulfate O-MIF
The second set of sensitivity runs (Z2) tests the influence of the LWC amount on model results, notably the final sulfate O-MIF. Fe(III) aqueous concentration is fixed to 0.5 µM, and the initial concentration of SO 2 is set to 1.5 ppmv. Figure 10 shows the evolution of 17 O(S(VI), dep.) for varying LWC. Unlike the influence of SO 2 , sulfate O-MIF is a monotonic function of LWC. The higher the LWC is, the lower the sulfate O-MIF is. Higher values of LWC favours higher dissolution rate of SO 2 in droplets and push the dynamics of oxidation towards liquid phase reactions. Also, at high LWC, H 2 O 2 is more quickly depleted from the gas-phase because of faster uptake in the liquid phase. Overall, higher LWC favors the O 2 /TMI oxidation pathway since lower acid concentration promotes the dissolution of SO 2 in the aqueous phase. Higher LWC does not directly affect the vapour pressure of the system, because it is assumed that cloud droplets are formed at high water saturation. Therefore, changes in cloud LWC do not affect the isotopic composition of produced OH. For the range of LWC considered here (from 0.1 to 3 g m −3 ), the final O-MIF of deposited sulfate varies from 0.8 ‰ to 0.2 ‰. The results show that, in volcanic clouds and plumes, sulfate O-MIF is affected by the LWC value. However, high LWCs alone do not appear to be sufficient to reproduce most of the isotopic measurements in volcanic sulfate.

Influence of TMI on sulfate O-MIF
The third and last set of sensitivity runs (Z3) tests the influence of TMI concentrations on model results, notably the final sulfate O-MIF. Laboratory experiments on iron mobilization from ash indicate that an average concentrations of [TMI] = 3 µM could be reached within the first hour of ash exposure to very acidic water in the case of silica ashes (Maters et al., 2017). According to the measurements, concentration of dissolved [Fe(III)] generally varies in the range of 0.1 to 2 µM depending on the mineral composition (Hoshyaripour et al., 2015;Maters et al., 2016Maters et al., , 2017. However, there is a lot of uncertainty on the typical concentrations According to the laboratory experiments, these high Fe(III) concentrations require a pH below pH ≤ 2, enhancing the mobilization of [Fe(III)]. In the simulations, the pH is close to this threshold value (see Fig. 8). In conclusion, the model simulations suggest that deposited sulfate with very low O-MIF values, consistent with most isotopic measurements of volcanic secondary sulfate (less than 0.1 ‰), can only be achieved with highly enhanced Fe(III) mobilization.

Conclusions
We use the tropospheric photochemical box model CiTTy-CAT to analyse why most oxygen isotopic measurements of tropospheric volcanic sulfate indicate that volcanic sulfates are essentially mass-dependent (i.e. O-MIF anomalies lying close to zero within measurement uncertainties of ±0.1 ‰ typically). This is also observed for volcanic sulfate collected very far from volcanoes where secondary sulfate (produced by oxidation of volcanic sulfur precursors, mostly SO 2 ) is expected to vastly dominate. This lack of O-MIF in volcanic sulfate is rather intriguing because secondary sulfates originating from other sources exhibit significant O-MIF. A major difference between volcanic sulfur and other sources is that it is often emitted within very dense volcanic plumes whose chemical compositions are radically different from Atmos. Chem. Phys., 18, 17909-17931, 2018 www.atmos-chem-phys.net/18/17909/2018/ background air. The chemical environment of the plumes may affect the oxidation pathways and hence sulfate isotopic composition.
A new sulfur isotopic O-MIF scheme is implemented in the model in order to monitor the transfer of O-MIF from oxidants to sulfate during the oxidation of volcanic SO 2 . A range of simulations are performed in order to explore in details the different pathways of SO 2 oxidation (gas-phase oxidation by OH and aqueous oxidation by O 3 , H 2 O 2 and O 2 /TMI) and, more importantly for O-MIF, their relative importance for a range of possible volcanic conditions. The first salient finding is that, according to the model calculations, OH should carry a very significant O-MIF in sulfurrich volcanic plumes. This implies that, when volcanic sulfate is produced in the gas phase via SO 2 oxidation by OH, its O-MIF should have a very significant positive value. Since most isotopic measurements of volcanic sulfate do not indicate the presence of O-MIF, the OH oxidation pathway cannot be the dominant channel for volcanic sulfur. Nonetheless, uncertainties in the rate constant of the isotopic exchange between OH and H 2 O (Dubey et al., 1997) and, more generally, on photochemical modelling are substantial (Ridley et al., 2017). It would be useful for this unexpected model predictions of O-MIF in OH, and hence volcanic sulfate produced in gas phase, to be tested in a controlled environment, ideally with laboratory experiments of SO 2 oxidation with a well constrained OH chemical budget, especially in relation to the loss processes. The second important finding from these simulations is that, although H 2 O 2 is a major oxidant of SO 2 throughout the troposphere, it is very rapidly consumed in sulfur-rich volcanic plumes. Since H 2 O 2 produced within the plume and the entrainment of H 2 O 2 from the atmospheric background also represent relatively weak sources, H 2 O 2 is found to be a minor oxidant for volcanic SO 2 whatever the liquid water content. According to the simulations, oxidation of SO 2 by O 3 is negligible because volcanic aqueous phases are too acidic. The model predictions of minor or negligible sulfur oxidation by H 2 O 2 and O 3 , two oxidants carrying large O-MIF, are consistent with the lack of O-MIF seen in isotopic measurements of volcanic tropospheric sulfate. The third finding is that oxidation by O 2 /TMI in volcanic plumes could be very substantial and, in some cases, dominant, notably because the rates of SO 2 oxidation by OH, H 2 O 2 , and O 3 are vastly reduced in a volcanic plume compared to the background air. Only cases where sulfur oxidation by O 2 /TMI is very dominant can explain the isotopic measurements of volcanic tropospheric sulfate. We stress that oxidation by O 2 /TMI is poorly constrained in model simulations because of the lack of measurements of TMI aqueous concentrations in volcanic plumes. It is worth pointing out that our model results are only applicable to cloudy volcanic plumes. Nonetheless, water clouds do not always form in volcanic plumes, notably during passive degassing. It would be interesting to also consider cloud-free plumes where the condensed phase is concentrated sulfuric acid within sulfate aerosols. In particular, these particles have a chemical reactivity radically different from water droplets.
A potentially significant limitation of the model simulations is the omission of volcanic halogens. Indeed, volcanic halogens are known to undergo multi-phase chemistry, resulting in ozone depletion and possibly impacting the oxidation of volcanic SO 2 (Bobrowski et al., 2003;Millard et al., 2006;Roberts et al., 2009;von Glasow, 2010;Roberts et al., 2014;Jourdain et al., 2016). Halogen species such as HOBr may also directly oxidize SO 2 in the aqueous phase (Chen et al., 2017), but this oxidation pathway has not been quantified yet for volcanic plumes. Overall, the present simulations might only be representative of degassing or eruptions with extremely low halogen emissions, typically originating from intraplate and rift volcanic activity. It is certainly worth exploring the potential impact of halogens in the case of halogenrich eruptions, notably for volcanic plumes where water does not condense and hence only sulfate aerosols are present. Since the heterogeneous conversion of halogen halides into radicals is known to be fast on sulfate aerosols Roberts et al., 2009;von Glasow, 2010;von Glasow and Crutzen, 2013), halogens might significantly impact the plume chemistry and the isotopic composition of secondary sulfate for halogens rich conditions. Data availability. The CiTTyCAT data and model used in this study are archived at LATMOS, and available on request from the lead author (galeazzo.tommaso@latmos.ipsl.fr; tommaso.galeazzo@gmail.com).