Modelling SO 2 conversion into sulphates in the mid-troposphere with a 3D chemistry-transport model: the case of Mount Etna’s eruption on April 12, 2012.

. Volcanic activity is an important source of atmospheric sulphur dioxide ( SO 2 ), which, after conversion into sulphuric acid, induces impacts on, among others, rain acidity, human health, meteorology and the radiative balance of the atmosphere. This work focuses on the conversion of SO 2 into sulphates ( SO 2 − 4(p) , S(+VI) ) in the mid-tropospheric volcanic plume emitted by the explosive eruption of Mount Etna (Italy) on Apr. 12, 2012, using the CHIMERE chemistry-transport model. Since volcanic plume location and composition depend on several often poorly constrained parameters, using a chemistry-transport 5 model allows us to study the sensitivity of SO 2 oxidation to multiple aspects such as volcanic water emissions, transition metal emissions, plume diffusion and plume altitude. Our results show that in the mid-troposphere, two pathways contribute to sulphate production, the oxidation of SO 2 by OH in the gaseous phase (70 %), and the aqueous oxidation by O 2 catalyzed by Mn 2+ and Fe 3+ ions (25 %). The oxidation in aqueous phase is the faster process, but in the mid-troposphere, liquid water is scarce, therefore the relative share of gaseous oxidation can be important. After one day in the mid-troposphere, about 0.5 % 10 of the volcanic SO 2 was converted to sulphates through the gaseous process. Because of the nonlinear dependency of the kinetics in the aqueous phase to the amount of volcanic water emitted and on the availability of transition metals in the aqueous phase, several experiments have been designed to determine the prominence of different parameters. Our simulations show that during the short time that liquid water remains in the plume, around 0.4 % of sulphates manage to quickly enter the liquid phase. Sensitivity tests regarding the advection scheme have shown that this scheme must be chosen wisely, as dispersion will 15 impact both oxidation pathways explained above. This shows to better several parameters that we have be crucial in the representation of the chemical behavior of plumes in the atmosphere. have better estimates the H 2 O / SO 2 ratio in an We also the box-model suggest the of transition metals in liquid-phase oxidation of volcanic SO is better 10 volcanic emissions of Fe(III) and Mn(II) in the atmosphere and their subsequent repartition between volcanic ash and aqueous phase. The present study also highlights the need to ﬁnd ways to reduce numerical diffusion in chemistry-transport models, through not only using better numerical strategies as shown here, but also by examining other approaches such as adaptative mesh reﬁnement in both the horizontal and vertical dimensions.


Introduction
Sulphate aerosols resulting from the conversion of volcanic sulphur dioxide (SO 2 ) have substantial effects on air quality, meteorology, rain acidity and the radiative balance of Earth atmosphere at local-to-global spatial scales, depending on the While contributing to the air quality on a local-to-regional scale, the sulphate aerosols produced as a result of explosive volcanic activities represent an important natural radiative forcing as well and are therefore significant for climate studies. Pattantyus et al. (2018) give an extensive review of the oxidation processes of SO 2 in the Marine boundary layer for the case of Mount Kilaueaa, and list two main oxidation paths for this species, oxidation by hydroxyl radical (OH) in gas phase, and oxidation in liquid phase (including oxidation by H 2 O 2 , O 3 and catalytic oxidation via O 2 ). However, its fate in volcanic 15 plumes in the free troposphere still remains poorly understood, in part due to the difficulty of measuring these events. Multiple efforts have been carried out to understand and model sulphates formation within volcanic plumes, mostly at first phases of eruption events (Hoshyaripour et al., 2014(Hoshyaripour et al., , 2015Roberts et al., 2019). Heard et al. (2012) have modelled the plumes from Kasatochi in 2008, Mt. Sarychev in 2009, and Eyjafjallajökull in 2010 with the NAME dispersion model, with encouraging results in reproducing the observed plumes of SO 2 and sulphates. Specific modelling work has been carried out using a 0D 20 model (Galeazzo et al., 2018), and brought interesting insights into main oxidation pathways of SO 2 : these authors highlight on the potential importance of the catalytic oxidation of SO 2 by O 2 with transition metals as catalysts. Pianezze et al. (2019) have explored the role of volcanic aerosols as Cloud Condensation Nuclei (CCN) and the evolution of their size distribution.
In the free troposphere, volcanic particle size distribution is evolving to a coarser distribution as time goes by, and particles can serve as CCN far from the vent (Sahyoun et al., 2019;Pianezze et al., 2019). 25 Regarding mid-tropospheric eruptions, the issue of aqueous chemistry, with the potential contribution of volcanic water emissions to the formation of an aqueous phase needs to be considered since there is the possibility that these emissions have an impact on sulphate formation for this portion of the atmosphere. In the case of boundary layer eruptions and passive degassing, the quantity of water vapour emitted by the volcano is typically much smaller than the background water vapour at that level, while for stratospheric eruptions temperatures are too cold to allow the presence of liquid water. In particular, the 30 question of sensitivity of sulphate formation to the volcanic emissions of water vapour is unanswered as of yet. In addition, the 0D study of Galeazzo et al. (2018) argues that aqueous oxidation of SO 2 catalyzed by transition metals may be a substantial, or even dominant, oxidation pathway, and that explosive eruptions themselves emit water vapour (possibly contributing to the formation of an atmospheric liquid phase) and transition metals. Another effect, not taken into account in the present study, is the potential depletion of OH radicals due to its consumption by atmospheric halogen. Jourdain et al. (2016) conducted a modelling study on the volcanic plumes of the Ambrym volcano (Vanuatu). They conclude that when taking into account halogen emissions, the lifetime of SO 2 relative to oxidation by OH increases by 36% compared to the same simulation without halogen emissions; the authors attribute this change to OH depletion.
Various pathways can lead to SO 2 [S(+IV)] oxidation to SO 2− 4 [S(+VI)]. In the gaseous phase, SO 2 can react with the OH photochemically produced from ozone and water vapour: Gas-phase conversion of SO 2 by OH follows reactions R3-R5 (Seinfeld and Pandis, 2006): Reaction R3, the limiting step in this mechanism, is relatively slow (the decay rate of SO 2 through this mechanism is estimated at 2.9 ± 2.1 %h −1 during daytime for the remote marine conditions around Mt. Kilauea), therefore in presence of an aqueous phase liquid-phase conversion tends to dominate gas-phase conversion.
Since SO 2 is a soluble gas, aqueous-phase oxidation is also a possibility; the balance between liquid-phase and gas-phase 15 concentrations being governed by the Henry's law: where [SO 2 ] aq is the concentration of dissolved SO 2 in the aqueous phase, p SO2 the partial pressure of SO 2 in gas phase and H SO2 is Henry's law constant for SO 2 , for which the expression and numerical parameters can be found in e.g., Sander (2015): Aqueous SO 2 solution behaves like a weak acid, known as "sulfurous acid": with with a weak acidity constant of pK H2SO3 a = 1.81.
For the sake of completeness, it should also be mentioned that sulfurous acid can have a second acidic dissociation: with pK HSO − 3 a = 7.21, but for pH values below 6 usually occurring in the atmosphere, this second dissociation hardly has an impact. In typical atmospheric conditions (including those found in volcanic plumes) with a pH between 2 and 7, aqueous 5 S(+IV) is seen mainly in the form of HSO − 3 (Seinfeld and Pandis, 2006). One pathway for oxidation of S(+IV) to S(+VI) in aqueous phase is reaction of HSO − 3 with hydrogen peroxyde H 2 O 2 (e.g. Shostak et al. (2019)): However, in situations resembling volcanic plumes where SO 2 is abundant, the availability of H 2 O 2 is a limiting factor for R8 10 and hence other reaction pathways become dominant (Pattantyus et al., 2018). In such cases, oxidation of HSO − 3(aq) by O 3 can become an important pathway (reaction R10; Lagrange et al., 1994;Seinfeld and Pandis, 2006;Pattantyus et al., 2018): Finally, oxidation of HSO − 3(aq) by O 2 with Fe 3+ and Mn 2+ as catalysts is another process that can be relevant in our case: (reaction R11; Connick and Zhang, 1996). 15

HSO
The aim of this work is to estimate the sensitivity of SO 2 conversion through these pathways in a volcanic plume to several parameters that remain poorly constrained.
In Section 2, we present the data used in the current study and the modelling choices that have been made. Section 3 presents the simulation outputs and their interpretation in terms of comparison to observations and in terms of sensitivity to multiple 20 parameters. Finally, Section 4 draws conclusions and examines new perspectives that are not covered by the present study.
2 Material and methods

IASI instrument
The Infrared Atmospheric Sounding Interferometer (Clarisse et al., 2014, IASI) instrument onboard of Metop-A-C satellite series, the instrument is orbiting 817 km above the surface and provides a daily coverage of the earth with a pixel resolution 25 of 12 km of diameter. IASI retrievals are widely used to observe and study the SO 2 in the Earth's atmosphere Clarisse et al. (2012), including in volcanic plumes Carboni et al. (2012Carboni et al. ( , 2016. This instrument has also been recently used to measure the Aerosol optical depth (AOD) of tropospheric volcanic sulphate particles (Guermazi et al., 2021).

CHIMERE model
The modelling work has been performed using v2020r1 version of the CHIMERE CTM (chemistry-transport model) (derived from v2020r1; Mailler et al., 2017;Menut et al., 2021)  istry, SO x chemistry , OH chemistry and more (Derognat et al., 2003;Menut et al., 2013). Gaseous oxidation pathways and 20 aqueous oxidation through O 3 and H 2 O 2 are included in this mechanism, and no modifications were made on this aspect of the chemistry mechanism. Oxidation of SO 2 by O 2(aq) catalyzed by Fe and Mn is also available in the model; the evaluation of [Fe 3+ ] and [Mn 2+ ] have been adapted for the present study as discussed in Section 2.5.

Modelling Volcanic eruption emissions
The time and altitude profiles for the injection of SO 2 into the atmosphere (Table 1) were obtained using SO 2 emission flux 25 rate measurement data from the ground-based DOAS FLAME (Differential Optical Absorption Spectroscopy FLux Automatic MEasurements) scanning network (e.g. Salerno et al., 2018). This method measures SO 2 fluxes during passive degassing, effusive and explosive eruptive activity using plume height inverted via an empirical relationship between plume height and wind speed (Salerno et al., 2009). In explosive paroxysmal events, such as in our case study, the plume is ejected to higher altitudes and the linear height-wind relationship explained above cannot be utilized; therefore mass flux is retrieved in post- Volcanic emissions from explosive activities are more likely to be described with a skewed Gaussian profile (equation 6). In range. The entry for eruptive material in CHIMERE, before it is adapted to CHIMERE vertical grid, is displayed on Figure 1.
Water, Fe and Mn are emitted with the identical vertical distribution.

Volcanic water emissions
Volcanic eruptions inject significant amounts of water in the atmosphere, particularly when considering the ambient humidity in the mid and upper troposphere. In the experiments containing volcanic water emissions, H 2 O is emitted similarly to SO 2 emissions, with identical time and vertical profiles as described in Section 2.3; To estimate the specific amount of the emitted  Addition of volcanic water in the mid-troposphere can imply supersaturation. Consequently, in the model, water is added as water vapour until the partial pressure of water vapour reaches 105 % of the saturation vapour pressure P sat H2O . Remaining water emitted from the eruptive activity is added as liquid water or ice, depending on ambient temperature. Several studies 10 have focused on the phase state of water in the upper troposphere (Textor et al., 2003;Hu et al., 2010;Kärcher and Seifert, 2016) and it is generally agreed that liquid water is virtually inexistent below the temperature of 235 K. Based on CALIOP measurements, Komurcu et al. (2014) has evaluated the supercooled liquid water fraction in clouds. Based on their Fig. 7, Eq. 7 gives a parabolic dependance of the supercooled liquid water fraction H 2 O (s) on temperature, to be used between 235 and 273K (function is plot on Figure A2, in the appendix): the ash surface can dissolve into the liquid phase coating volcanic particles, mostly in Fe(II) oxidation state (Galeazzo et al., 2018;Hoshyaripour et al., 2015). In our experiments, we consider 5 % of the total Iron and Manganese in the plume to be dissolved in the liquid phase (if clouds are produced) and therefore are available as catalysts for Reaction R11. In the case of liquid water in the plume, the Iron concentration in droplets (mol.L −1 ) is calculated following the equation :

Simulations conducted and their purpose
Simulations have been organized into groups, to explore various parameters of interest. First, the simulations focused on the 10 significance of gas phase conversion, aqueous phase conversion and transition metals as catalysts are gathered (Table 2). Then, we focused on the impact of volcanic water emitted during volcanic activity (Table 3). Next series of simulations focuses on evaluating initial parameters, such as the volcanic plume height of injection (Table 4). Finally, we have evaluated the plume chemistry sensitivity to transport modelling parameters, comparing two vertical advection schemes. These schemes are described and tested in Lachatre et al. (2020b), however, the aforementioned article did not analyze their impact on the 15 chemistry of the modelled plume.
Simulations underlined and labelled "Background" in Table 2,3,4,5 are simulations carried out without emissions originating from volcanic events; while they do not appear in figures themselves, these simulations are necessary to separate background information from our other sensitivity tests. In addition, to better understand the impact of ambient conditions alone on volcanic SO 2 and SO 2− 4(p) production, "Dry" simulations have been conducted in several cases. These simulations only include SO 2 as 20 volcanic emissions; neither volcanic water nor metals are considered in these cases. For better readability of the results, a unique simulation labelled "Reference" is retained in every panel of simulations.
3 Results and Discussion

Reference simulation compared to IASI instrument
The background simulation has been used to exclude non-volcanic information from the Reference simulation and compare to 25 the time-step surrounding IASI sounding for SO 2 (Figure 2). Although we have limited data, it is possible to extract several useful information from the comparison of IASI observations and CHIMERE simulations. Although the positioning of the plume on the simulation grid is not accurate in the simulations, other aspects of it, such as its thin shape and the concentration gradient seem to match the observations. These characteristics can be used to assess the quality of emissions data, while the small discrepancies seen in the horizontal localisation of the plume can be linked to various parameters (meteorological fields, 30 plume injection height, transport modelling scheme).  In the first group of tests (Table 2), the objective is to estimate the impact of various chemical pathways of SO 2 conversion.

Sensitivity tests for chemistry parameters
As mentioned in Section 2.6, Background and Dry simulations have also been conducted. For these simulations, since volcanic water is not emitted, super cooled water cannot be formed in the model; therefore, the table has been filled with "not applicable" for relevant cases (e.g. volcanic clouds). The simulation No SCLW is slightly different. In this simulation, volcanic water is 5 emitted, but SCLW is not formed from this water, therefore only the additional water vapour from the volcanic water is considered in the model chemistry and only gaseous pathway is evaluated. The next experiment, labelled as No TM aq (No Transition Metals in aqueous phase) is to evaluate the SO 2 conversion into liquid phase, without considering the pathway of oxidation by O 2 and catalyzed by Fe and Mn; this is presented by Galeazzo et al. (2018) to be the main pathway of SO 2− 4(p) production. The Reference simulation is considered to be the most realistic simulation performed in this work, in which SO 2 emissions   Table 2. Figure 3 shows the hourly evolution of a) the volcanic sulphates mass, b) of volcanic SCLW, d) the minimum volume containing 25 % of SO 2− 4(p) mass, c) consequently, the AOD corresponding to the plume following the volume selection and e) the mass of hydroxyl radical. It can be seen that when 5 volcanic water is added (simulations No TM (aq) ; Reference) SCLW is formed in the mid-troposphere which is a necessary element to evaluate aqueous chemistry paths. The Dry simulation allows us to evaluate the production of sulphates from reaction to background OH, and appears to be the main oxidation pathway in our experiment (70 %). The addition of volcanic water vapour without formation of SCLW did not significantly increase the conversion of SO 2 to SO 2− 4(p) . The same can be said about the addition of SCLW without TM (No TM (aq) simulation). However, the Reference simulation, which includes volcanic TM significantly increases the conversion of SO 2 (25 %). This additional formation of SO 2− 4(p) is produced in a very small volume containing the volcanic cloud, which significantly change the optical properties of the plume (and eventually its radiative forcing generated) as it is shown by the evolution of plume's AOD. The comparison of the simulations conducted to understands the impact of the various chemical pathways has shown that the conversion of SO 2 mainly occurs in gas phase from reaction with the ambient OH (70 %) and then as a second pathway from the oxidation with O 2 catalyzed by TM in the 15 aqueous phase (25 %).  and WV400 respectively. The aforementioned ratios are considered as threshold values for paroxysmal eruptions. The water apportionment between its various physical states is displayed on Figure B1, in the appendix. Figure 4 summarizes the results 5 of simulations conducted in Table 3. As the cloud generation is a threshold process, the amount of SCLW from volcanic eruption is not linearly linked to the volcanic water vapour emissions. In the WV300 scenario 1.3 kt SCLW is formed at peak time interval (around 12/04 at 12h), against 2.9 kt SCLW and 0.5 kt SCLW in the WV400 and WV200 scenarios respectively. The formation of sulphate with WV400 is 80 % stronger than in the simulation with no volcanic water, and 40% stronger than in the simulation with WV200. This results in an increase of sulphates production; however, this is not a linear process either since the concentrations of SO 2 and the TM are different in the aqueous phase in each of the three cases. Thus, the amount of volcanic water impacts the optical properties of the plume, as the plume's AOD significantly increases following SCLW mass. This aspect is highlighted in the Figure 5 , which displays AOD spatial distribution and summarizes what is shown in     Next, to evaluate the impact of the surrounding environment (Table 4), we have conducted sensitivity tests on the plume's injection height. In our reference simulation, the plume injection is centered around 8.0 km.a.s.l.. A sensitivity test with the injection centered around 8.5 km.a.s.l. has been realized. This second test will provide an environment with a lower atmospheric pressure, lower temperature, dryer atmosphere and different wind speed and direction. Figure 6 summarizes the results of simulations described in Table 4. Comparing simulations Dry 8.0 km and Dry 8.5 km show differences in the results. In the 5 Dry 8.5 km case, less SCLW is generated because of lower humidity, nonetheless more SO 2 are converted to sulphates. This is explained by the higher diffusion of the plume at higher altitude, as it can be seen that the minimum volume occupied by 25 % of the sulphate mass is bigger than in the Dry 8.0 km. Consequently, this higher dispersion allows a more efficient conversion from OH which is the limiting reactant in the gas phase oxidation.  Finally, we investigate the impact of the plume dispersion on the computed chemistry (Table 5) Table 5. It was expected to see a larger spread of the plume in the sensitivity test with VL77 compared to the Reference simulation using the Després and Lagoutière (1999) vertical advection scheme. Indeed, the volume of the plume has significantly increased, as it is displayed on Figure 7d). Consequently, less SCLW 10 has been generated, but on the other hand, more sulphates were produced. This is due to higher conversion from the ambient OH, as it can be seen that more radical has been consumed ( Figure 7e). It can also be noted that Reference VL's AOD is lower than Reference DL's AOD, due to the significantly larger spreading of Reference VL plume. This result was slightly unexpected as gaseous oxidation appeared to be linear at first; still, this new observation makes sense since more OH were mobilized to react with the volcanic SO 2 in excess. In this study we aimed to investigate volcanic plume chemistry in the mid-troposphere region using the CHIMERE CTM. With the assistance of the IASI instrument's SO 2 sounding, we have determined that the CHIMERE model is able to reproduce a realistic structure for the plume as well as a correct intensity in terms of SO 2 columns after a number of assumptions were made. Because of these encouraging preliminary observations, we gained confidence in the subsequent results. We have then 5 analyzed the impact of various oxidation pathways by selectively shutting down these pathways to evaluate their contribution.
For our study case, these sensitivity tests suggest that the main oxidation pathway is gas-phase oxidation by OH (about 70 %), followed by liquid-phase catalyzed oxidation by O 2 (about 25%). The fact that liquid-phase oxidation is dominated by TMcatalyzed oxidation is in line with the results of Galeazzo et al. (2018) and quantity of volcanic water vapour potentially has a strong impact on sulphate formation: in our case study, the formation of sulphate with H 2 O/SO 2 = 400/1 is 80 % stronger than in the simulation with no volcanic water, and 40% stronger than in the simulation with H 2 O/SO 2 = 200/1; therefore, in some cases such as mid-tropospheric plumes, including volcanic water may be necessary to correctly represent the conversion of volcanic SO 2 into sulphate aerosols. Apart from the above-mentioned change in the overall quantity of sulphates formed, the localized formation of a liquid-containing volcanic plume may generate 20 strong maxima in the sulphate AOD (∼0.1 in our case study), while in the case devoid of volcanic water sulphate AOD never exceeds ∼0.005, far from any instrumental detection threshold. These sensitivity tests suggest the strong sensitivity of liquidphase SO 2 oxidation to the injection height of the plume: if the plume is too low, then due to warm ambient temperature, volcanic water input may not be sufficient to reach saturation, but if the plume is too high, temperatures will be too cold to permit the formation of a liquid aqueous phase. Therefore, our conclusion on the strong sensitivity of SO 2 oxidation to the 25 H 2 O/SO 2 ratio may hold only for mid-tropospheric plumes such as the one in our case study. This does not mean that the impact of volcanic water on chemistry is not relevant at higher altitudes: on the contrary, the influence of gas-phase volcanic water vapour may still be of interest in the case of upper tropospheric or stratospheric plumes, where an additional input of water vapour would enhance the formation of the OH.
Apart from the sensitivity to uncertainties concerning the physico-chemical processes and the forcings that we have dis- 30 cussed above, representation of SO 2 oxidation in volcanic plumes is also sensitive to the discretization strategies and to the numerical schemes that are used. For example, our sensitivity tests show that reducing excessive numerical diffusion by using an antidiffusive transport scheme such as Després and Lagoutière (1999) can change the structure of the modelled plume strongly, and in a complex way. In our case, reducing diffusion leads to a reduction in total production of sulphates, but with sharper gradients and stronger peaks in concentration and AOD. Due to chemical nonlinearities (e.g the reduced availability of OH in the plume), reducing numerical diffusion can change the quantitative and qualitative properties of the resulting sulphate plume in a much more subtle way than just spreading the plume over a greater volume, as observed in Lachatre et al. (2020b) for an inert tracer. This confirms that chemistry-transport modellers should pay attention to reduce numerical diffusion in their model, not only because excessive numerical diffusion will affect the spread of the plumes, but also, as we have shown here, 5 because it will affect chemistry in a non-linear way, which in turn affects the AOD and therefore the radiative effect of particles.
This study shows the need to better constrain several parameters that we have shown to be crucial in the representation of the chemical behavior of volcanic plumes in the atmosphere. For example, it is critical to have better observational estimates of the H 2 O/SO 2 ratio in an eruptive context. We also confirm the box-model results of Galeazzo et al. (2018), which suggest that the impact of transition metals in liquid-phase oxidation of volcanic SO 2 is substantial. This highlights the need to better constrain 10 volcanic emissions of Fe(III) and Mn(II) in the atmosphere and their subsequent repartition between volcanic ash and aqueous phase. The present study also highlights the need to find ways to reduce numerical diffusion in chemistry-transport models, through not only using better numerical strategies as shown here, but also by examining other approaches such as adaptative mesh refinement in both the horizontal and vertical dimensions.