Role of Criegee intermediates in the formation of sulfuric acid at a Mediterranean (Cape Corsica) site under influence of biogenic emissions

Reaction of stabilized Criegee intermediates (SCIs) with SO₂ was proposed as an additional pathway of gaseous sulfuric acid (H₂SO₄) formation in the atmosphere, supplementary to the conventional mechanism of H₂SO₄ production by oxidation of SO₂ in reaction with OH radicals. However, because of a large uncertainty in mechanism and rate coefficients for the atmospheric formation and loss reactions of different SCIs, the importance of this additional source is not well established. In this work, we present an estimation of the role of SCIs in H₂SO₄ formation at a western Mediterranean (Cape Corsica) remote site, where comprehensive field observations including gas-phase H₂SO₄, OH radicals, SO₂, volatile organic compounds (VOCs) and aerosol size distribution measurements were performed in July–August 2013 as a part of the project ChArMEx (Chemistry-Aerosols Mediterranean Experiment). The measurement site was under strong influence of local emissions of biogenic volatile organic compounds, including monoterpenes and isoprene generating SCIs in reactions with ozone, and, hence, presenting an additional source of H₂SO₄ via SO₂ oxidation by the SCIs. Assuming the validity of a steady state between H₂SO₄ production and its loss by condensation on existing aerosol particles with a unity accommodation coefficient, about 90 % of the H₂SO₄ formation during the day could be explained by the reaction of SO₂ with OH. During the night the oxidation of SO₂ by OH radicals was found to contribute only about 10 % to the H₂SO₄ formation. The accuracy of the derived values for the contribution of OH + SO₂ reaction to the H₂SO₄ formation is limited mostly by a large, at present factor of 2, uncertainty in the OH + SO₂ reaction rate coefficient. The contribution of the SO₂ oxidation by SCIs to the H₂SO₄ formation was evaluated using available measurements of unsaturated VOCs and steady-state SCI concentrations estimated by adopting rate coefficients for SCI reactions based on structure–activity relationships (SARs). The estimated concentration of the sum of SCIs was in the range of (1–3) × 10³ molec. cm⁻³. During the day the reaction of SCIs with SO₂ was found to account for about 10 % and during the night for about 40 % of the H₂SO₄ production, closing the H₂SO₄ budget during the day but leaving unexplained about 50 % of the H₂SO₄ formation during the night. Despite large uncertainties in used kinetic parameters, these results indicate that the SO₂ oxidation by SCIs may represent an important H₂SO₄ source in VOC-rich environments, especially during nighttime.

1 Introduction

Sulfuric acid, H₂SO₄, is an important atmospheric component identified as playing a key role in formation of secondary atmospheric aerosol through new particle formation processes (Dunne et al., 2016; Paasonen et al., 2010; Sipilä et al., 2010; Weber et al., 1997). H₂SO₄ is considered to be a major precursor of newly formed atmospheric nucleation-mode particles and may play a significant role in their subsequent growth (Boy et al., 2005; Smith et al., 2005; Zhang et al., 2012). It is therefore important to understand well the atmospheric mechanisms determining the H₂SO₄ concentrations in different atmospheric environments.

Until recently it was generally accepted that the dominant atmospheric source of H₂SO₄ is the reaction of OH radicals with SO₂ (Reaction R1) presenting a rate-limiting step leading in the troposphere to fast production of H₂SO₄ in the presence of water vapour and oxygen via Reactions (R2)–(R3) (Finlayson-Pitts and Pitts, 2000). It was assumed that H₂SO₄ atmospheric concentrations are determined predominantly by this source and the loss of sulfuric acid on the surface of existing particles, with the loss rate depending on the efficiency of H₂SO₄ uptake.

$$\begin{array}{}\text{(R1)}& {\displaystyle }\mathrm{OH}+{\mathrm{SO}}_{\mathrm{2}}\to {\mathrm{HSO}}_{\mathrm{3}}\text{(R2)}& {\displaystyle }{\mathrm{HSO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\to {\mathrm{SO}}_{\mathrm{3}}+{\mathrm{HO}}_{\mathrm{2}}\text{(R3)}& {\displaystyle }{\mathrm{SO}}_{\mathrm{3}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}(+{\mathrm{H}}_{\mathrm{2}}\mathrm{O})\to {\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\end{array}$$

Another possible atmospheric source of H₂SO₄ via oxidation of SO₂ by stabilized Criegee intermediates (SCIs), compounds formed by ozonolysis of unsaturated organic compounds, was suggested by Cox and Penkett (1971) and discussed first in view of its atmospheric importance by Calvert and Stockwell (1983). For a long time the reactions of SO₂ with SCIs were considered to be too slow to represent an important atmospheric source of H₂SO₄, until in the more recent study of Welz et al. (2012) a rate constant of (3.9±0.7) × 10⁻¹¹ cm⁻³ molec.⁻¹ s⁻¹ was derived for the reaction of SO₂ with the simplest SCI, formaldehyde oxide (CH₂OO), which is significantly larger than previous estimates of around $\mathrm{4}\times {\mathrm{10}}^{-\mathrm{15}}$ cm⁻³ molec.⁻¹ s⁻¹ for the reactions of SO₂ with CH₂OO (Hatakeyama et al., 1986) and for the reactions of SO₂ with other SCIs (Johnson and Marston, 2008). The importance of this additional source of H₂SO₄, which is still under discussion, depends on the atmospheric SCI concentrations and the kinetics and mechanisms of the SCI reactions with SO₂.

Criegee intermediates (CIs), also known as carbonyl oxides, (R₁)(R₂)COO, with R₁ and R₂ representing different substituents, are produced via ozonolysis of alkenes by cycloaddition of an ozone molecule on a double bond forming a primary ozonide (POZ), a highly energized compound containing an O–O–O group. Subsequent rapid cleavage of either of the O–O bonds leads to the formation of a carbonyl compound and chemically activated CIs, which can undergo either prompt dissociation or thermal stabilization, leading to the formation of the SCIs (Criegee, 1975; Criegee and Wenner, 1949; Donahue et al., 2011; Johnson and Marston, 2008; Vereecken and Francisco, 2012; Vereecken et al., 2012).

Atmospheric concentrations of SCIs depend on their production rates by the ozonolysis of alkenes and their loss rates, predominantly via unimolecular decomposition and reactions with water monomers and dimers (Vereecken et al., 2017). However, the kinetic parameters and the reaction mechanisms of these processes are not well known.

The SCI production rate is determined by the ozonolysis reaction rate constants and corresponding speciated yields of different SCIs. The speciated SCI yield depends on a relative yield of two different CIs formed by decomposition of the POZ and a yield of SCI produced by the CI collisional stabilization depending on the CI structure and its energy content. For most of atmospherically relevant alkenes, the total SCI yields were not studied directly, while for those for which multiple studies are available there is in many cases a large data scatter. The data on the speciated SCI yields are available only for a few of alkenes (see e.g. Vereecken et al., 2017, and references therein).

For the loss of SCIs via unimolecular decomposition and reactions with water monomers and dimers, the results of experimental and theoretical studies show that the corresponding rate coefficients may vary by orders of magnitude depending on the SCI substituents and conformers (see e.g. Vereecken et al., 2017, and references therein). In recent years experimental studies of these reactions with direct detection and generation of specific SCIs were performed for several among the simplest of them, such as formaldehyde oxide (CH₂OO) (Chao et al., 2015; Lewis et al., 2015; Sheps et al., 2017; Smith et al., 2015; Stone et al., 2018), acetaldehyde oxide (CH₃CHOO) (Li et al., 2020; Lin et al., 2016; Sheps et al., 2014) and acetone oxide ((CH₃)₂COO) (Chhantyal-Pun et al., 2017; Fang et al., 2017; Huang et al., 2015; Lester and Klippenstein, 2018; Smith et al., 2016). Very recently the decomposition rate and an estimation of the rate coefficients for the reaction with water vapour were obtained for the first time in direct kinetic studies for syn methyl vinyl ketone oxide (syn-MVK-oxide) and anti methacrolein oxide (anti-MACR-oxide), four-carbon unsaturated Criegee intermediates derived from the ozonolysis of isoprene (Barber et al., 2018; Caravan et al., 2020; Lin et al., 2021). For other large SCIs, only estimations based on theoretical and indirect studies are available for their reactions with water vapour and their thermal decomposition.

The result of Welz et al. (2012) about the fast reaction of SO₂ with formaldehyde oxide was extended in later direct and indirect studies, where similarly fast reactions with SO₂ were confirmed for CH₃CHOO, (CH₃)₂COO, Z-nopinone oxide (product of β-pinene ozonolysis), syn-MVK-oxide and anti-MACR-oxide (Ahrens et al., 2014; Caravan et al., 2020; Lin et al., 2021; Vereecken et al., 2017, and references therein), with rate coefficients in the range of (3–16) × 10⁻¹¹ cm³ molec.⁻¹ s⁻¹. Reactions of other SCIs with SO₂ were suggested to be similarly fast on the basis of theoretical results (Kurtén et al., 2011).

Theoretical analysis suggests that the reaction of SCI with SO₂ proceeds via a barrierless cycloaddition of SO₂ to SCI forming a sulfur-bearing secondary ozonide (SOZ) which can either be stabilized or decompose to form SO₃ or other products (Kurtén et al., 2011; Kuwata et al., 2015; Vereecken et al., 2012). For smaller SCIs, e.g. formaldehyde and acetone oxides, the theory predicts negligible SOZ stabilization and about unity yield of SO₃ (Kuwata et al., 2015). These results are supported by experimental studies for CH₂OO (Berndt et al., 2014a; Wang et al., 2018) and (CH₃)₂OO, CH₃CHOO (Berndt et al., 2014b). For larger SCIs with expected longer SOZ lifetimes, the SO₃ yield may depend on the SOZ fate in the atmosphere with respect to its decomposition or further reactions, e.g. with H₂O (Kuwata et al., 2015; Vereecken et al., 2012), although a large yield of sulfur trioxide exceeding 80 % was observed by Ahrens et al. (2014) for the large SCIs formed during the ozonolysis of β-pinene.

Estimations based on the available or evaluated kinetic parameters show that the atmospheric SCI concentrations vary by orders of magnitude depending on conditions specific to different environments, such as the concentrations and composition of alkenes, ozone concentration or humidity. Using chemistry-transport global modelling, the highest SCI concentrations of the order of 10⁴–10⁵ molec. cm⁻³ were inferred for the regions with the highest isoprene and terpene emissions, e.g. above the tropical forest (Chhantyal-Pun et al., 2019; Khan et al., 2018; Newland et al., 2018; Vereecken et al., 2017; Novelli et al., 2017). Estimated using steady-state calculations, the concentration of SCI ranges from 2.3 × 10³ molec. cm⁻³ at a rural site to 5.5 × 10⁴ molec. cm⁻³ in an urban polluted environment (Vereecken et al., 2017). The estimated contribution of SCI to H₂SO₄ formation is also highly variable: about 7 % in rural environments and up to 70 % over tropical regions (Vereecken et al., 2017). At the global scale, the contribution of SCI to SO₂ oxidation was estimated to be negligible, contributing less than 1 % (Newland et al., 2018). The uncertainty associated with the predicted SCI concentrations was estimated to be 1 order of magnitude (Vereecken et al., 2017) due to poorly defined SCI formation and loss rates. Even a higher uncertainty may be expected for the estimated contribution of SCIs to SO₂ oxidation considering not well-defined reaction rate coefficients for the reaction of different SCIs with SO₂.

The adequacy of the mechanism treating the SO₂ oxidation by OH as a predominant source of the atmospheric H₂SO₄ was tested in a number of field campaigns where simultaneous measurements of OH and H₂SO₄ were conducted (Table S1 in the Supplement). A selected ion chemical ionization mass spectrometry (CIMS) technique for simultaneous measurements of OH and H₂SO₄ was first introduced by Eisele and Tanner (1993), and since then it has been used in a number of field measurements in different environments. In these studies the measurements of OH, H₂SO₄, SO₂ and aerosol surface area were used to compare the rate of H₂SO₄ production in Reaction (R1) and the rate of H₂SO₄ loss on aerosol particles assuming a steady-state condition between these processes. In a number of measurement campaigns the H₂SO₄ budget was found to be closed using the uptake coefficient of unity corresponding to the upper limit of the H₂SO₄ loss rate on existing particles. This was observed in different environments including remote marine (Weber et al., 1997), forested rural (Birmili et al., 2000; Boy et al., 2013) and forested remote sites (Eisele and Tanner, 1993; Weber et al., 1997). However, in other field studies conducted in various environments, the H₂SO₄ condensation sink calculated using an uptake coefficient of unity was found to significantly exceed its formation rate via SO₂ oxidation by OH, indicating either an H₂SO₄ uptake efficiency lower than unity or the presence of sources of H₂SO₄ other than Reaction (R1) (Bardouki et al., 2003; Berresheim et al., 2002, 2014; Boy et al., 2013; Jefferson et al., 1998; Mauldin III et al., 2012; Petäjä et al., 2009). Several additional H₂SO₄ gas-phase sources were suggested, such as the oxidation of DMS or DMDS in remote coastal environments, proceeding with SO₃ formation (Berresheim et al., 2002, 2014; Jefferson et al., 1998) or SO₂ oxidation by SCIs in the boreal forest and in moderately polluted environments (Boy et al., 2013; Kim et al., 2015; Mauldin et al., 2012). A heterogeneous formation of gas-phase H₂SO₄ via the catalytic oxidation of SO₂ on the surface of black carbon aerosols has also recently been shown to be important under polluted conditions (Yao et al., 2020).

In this work, we present an evaluation of the role of SCIs in H₂SO₄ production at a remote site on Cape Corsica near the northern tip of Corsica (Ersa station, western Mediterranean). In July–early August 2013, comprehensive field observations including gas-phase (OH radicals, H₂SO₄, VOCs, NO_x, SO₂, others) and aerosol-size distribution measurements were conducted at this site in the framework of the SAFMED (Secondary Aerosol Formation in the Mediterranean) campaign as part of the summer 2013 experimental effort of project ChArMEx (Chemistry-Aerosols Mediterranean Experiment). During the field campaign, the site was strongly influenced by local emissions of biogenic volatile organic compounds, including isoprene and terpenes, forming different SCIs in reactions with ozone and, hence, potentially representing an additional source of H₂SO₄ via reactions of SCIs with SO₂. We use the OH, H₂SO₄ and SO₂ measurements to estimate an upper limit for the contribution of H₂SO₄ sources other than Reaction (R1). Using available measurements of unsaturated VOCs and adopting rate coefficients for SCI reactions based on structure–activity relationships (SARs) from Vereecken et al. (2017), we estimate steady-state SCI concentrations. These SCI concentrations are used for the estimation of the rate of H₂SO₄ formation in the reactions of SCIs with SO₂ and its comparison with OH + SO₂ source resulting from the OH and H₂SO₄ measurements.

2 Methods

2.1 Field site

Measurements were performed at the Ersa site from 18 July to 5 August 2013 during the ChArMEx/SAFFMED field campaign (Dulac et al., 2021). The Ersa station (42.969^∘ N, 9.380^∘ E) is located at Cape Corsica on the northern edge of Corsica (Michoud et al., 2017; Zannoni et al., 2017). It is situated at an altitude of 533 m above sea level on the top of a hill dominating the northern part of the cape. On its eastern, northern and western sides it is a few kilometres away from the coast and has a direct view of the sea. The measurement site is isolated by a mountain range from the closest large city, Bastia, situated about 30 km south of the site. The site is surrounded by widespread vegetation such as scrubland typical of the Mediterranean areas, responsible for biogenic VOC emissions (Debevec et al., 2021; Zannoni et al., 2015).

2.2 Experimental methods

2.2.1 OH and H₂SO₄ measurements

Concentrations of OH radicals and H₂SO₄, as well as total peroxy radicals (HO₂ + RO₂, not discussed here), were measured using chemical ionization mass spectrometry (CIMS) (Berresheim et al., 2000; Eisele and Tanner, 1991). A detailed description of the instrument is presented elsewhere (Kukui et al., 2008, 2012). Here we briefly present the measurement technique and essential details about the setup and performance of the instrument during the ChArMEx/SAFMED campaign. A detailed description of the calibration system used during the campaign, which was not presented before, is given in Sect. S3 in the Supplement.

OH was detected by conversion of the sampled OH with isotopically labelled ³⁴SO₂ to form H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄ in a chemical conversion reactor (CCR) in the presence of ambient water vapour and oxygen. The isotopically labelled H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄ and ambient H₂SO₄ were detected by mass spectrometry as H³⁴SO${}_{\mathrm{4}}^{-}$ and H³²SO${}_{\mathrm{4}}^{-}$ product ions. The product ions were produced by chemical ionization with a NO${}_{\mathrm{3}}^{-}$ reagent ion in an ion-molecule reactor (IMR) following the CCR. The reagent ions were generated in a corona NO₂/air discharge ion source (CD). A scheme of the reactor is presented in Fig. S2 in the Supplement.

Ambient air was sampled at a volumetric flow rate of 10 SLM (standard litre per minute), creating turbulent flow in the chemical conversion region of the reactor. The turbulent flow conditions minimize possible influence of wind speed on the measurements and ensure fast mixing of reactants. The reactants used for the chemical conversion (³⁴SO₂ for OH conversion into sulfuric acid and NO for peroxy radical conversion into OH and their subsequent detection as OH) and the radical quencher (NO₂) are introduced into the reactor through a set of injectors. NO₂ used as a scavenger removes not only the OH radicals, but also peroxy radicals, converting them into HO₂NO₂ and RO₂NO₂ peroxy nitrates. Switching the reactant flows between the different injectors allows measurements in four different modes: the background mode, two different OH radical measurement modes and the peroxy radical measurement mode (Fig. S1). The two OH measurement modes differ by the times used for the chemical conversion, 4 and 20 ms. The ratio of the signals with the short and long conversion times may be used as an indicator of an artificial OH formation in the reactor (Kukui et al., 2008).

Measurements were performed by monitoring the peak intensities at $m/z=\mathrm{62}$ (NO${}_{\mathrm{3}}^{-}$), $m/z=\mathrm{97}$ (H³²SO${}_{\mathrm{4}}^{-}$), and $m/z=\mathrm{99}$ (H³⁴SO${}_{\mathrm{4}}^{-}$) with the CIMS, respectively, denoted I₆₂, I₉₇, and I₉₉ hereafter. Every measurement of OH was derived from 1 min of an OH ion signal count and two 30 s background ion signal counts before and after the OH signal measurement. Peroxy radicals were measured at the end of the OH detection sequence by switching on the NO flow to the corresponding injector for a duration of 2 min. To avoid any possible influence of traces of NO on the OH measurements, a time delay of 6 min was imposed after switching off the NO flow and before starting the next OH measurement sequence in order to ensure flushing of the CCR. The OH and the H₂SO₄ data were averaged, resulting either in a sequence of three points with a step of 7 min separated by a time gap of 15 min or yielding a sequence with a time step of about 90 min. The latter was used to match the time resolution of the VOC measurements (Table S4).

The concentrations of OH and H₂SO₄ were derived from the measured ratios of the H³²SO${}_{\mathrm{4}}^{-}$, H³⁴SO${}_{\mathrm{4}}^{-}$ and NO${}_{\mathrm{3}}^{-}$ ion peak intensities, $I_{\mathrm{97}}/I_{\mathrm{62}}$ and $I_{\mathrm{99}}/I_{\mathrm{62}}$: $\left[R\right]=C_R\times I^R$, where R corresponds to OH or H₂SO₄, I^R is a combination of $I_{\mathrm{97}}/I_{\mathrm{62}}$ and $I_{\mathrm{99}}/I_{\mathrm{62}}$ ratios corresponding to OH or H₂SO₄ accounting for isotopic composition of SO₂ used for the chemical conversion (99 % isotopic enrichment of ³⁴S, Eurisotop, Cambridge Isotope Laboratories, Inc.) and sulfur isotope natural abundance (³²S (95.02 %) and ³⁴S (4.21 %); Hoefs, 2018), and C_R is a calibration coefficient determined in calibration measurements by production of OH or H₂SO₄ in a turbulent flow reactor using photolysis of water vapour at 184.9 nm and quantified by chemical actinometry using photolysis of N₂O (Faloona et al., 2004). A detailed description of the calibration system with definitions of C_R and I^R is given in Sect. S3.

The overall accuracy of the calibration coefficients was estimated taking into account uncertainties of all parameters used for calculation of the radical concentrations in the photolysis reactor and the precision of the measurements of the ratios $I_{\mathrm{97}}/I_{\mathrm{62}}$ and $I_{\mathrm{99}}/I_{\mathrm{62}}$. The overall estimated calibration uncertainty (1σ) was 30 % for OH, 32 % for H₂SO₄ and 8 % for a ratio of [H₂SO₄] to [OH], (Table S3). Accounting for the calibration uncertainties and the measurement precision, the overall 1σ uncertainty of the 14 min-averaged measurements of OH, H₂SO₄ and the ratio of [H₂SO₄] $/$ [OH] was estimated to be around 32 %, 34 % and 16 % during the daytime and 42 %, 44 % and 40 % during the nighttime, respectively. During the ChArMEx/SAFMED campaign the observed level of the OH background signal was significantly higher than the typical OH background found during calibration or field measurements in air with low VOC concentrations (see Fig. 7 and the discussion in Sect. 4.4). Accordingly, the lower limits of detection at a signal-to-noise ratio of 2 and a 15 min integration time were 2×10⁵ molec. cm⁻³ for H₂SO₄ and 5×10⁵ and 2×10⁵ molec. cm⁻³ for OH daytime and nighttime measurements, respectively.

During the ChArMEx/SAFMED campaign the instrument was installed in a dedicated container with the CCR fixed to the roof of the container via an interface cap covered with a PTFE sheet. The sampling aperture of the reactor (3 mm diameter) was positioned 50 cm above the roof and about 3 m above the ground.

To avoid possible contamination of ambient air by the SO₂, NO and NO₂ reactants added to the CCR, a trap was set up at the pump exhaust by using two 100 L cylinders containing zeolites. The cylinders were refilled several times during measurements. A flexible exhaust tube of 30 m length was always placed downwind from the container.

2.2.2 Complementary measurements

The aerosol particle size distribution was measured using a scanning mobility particle sizer (SMPS TSI 3080, associated with a CPC TSI 3010) in the range from 10.9 to 495.8 nm and with an aerodynamic particle sizer (APS, TSI 3321) in the range from 542 nm to 19.48 µm. As the SMPS measurements were made with dehydrated particles, the particle diameters were corrected to ambient humidity using a particle growth factor (GF) of 1.5 at 90 % determined with a volatility hygroscopic–tandem differential mobility analyser (VH-TDMA) (Villani et al., 2008). The dependence of the GF on relative humidity (RH) was calculated using the one-parameter approximation from Rissler et al. (2006). Estimated uncertainties of measured particle number densities and GF-corrected particle diameters were 10 % and 15 %, respectively.

SO₂ concentration was measured by UV fluorescence (Thermo Environmental Instruments (TEI), model 43C-TLE) with an estimated accuracy of 20 %, a lower detection limit of 0.05 ppb and a time resolution of 5 min.

Ozone concentration was measured by means of a CraNOx II (Eco Physics) NO_x and O₃ monitor with an estimated accuracy of 10 %.

A detailed description of VOC measurements during the ChArMEx/SAFMED campaign is given in Michoud et al. (2017). The measurements of 23 unsaturated VOCs, including alkenes, aldehydes, ketones, isoprene and monoterpenes, were used in this work for estimation of SCI concentrations. Employed measurement techniques and concentration ranges for measured unsaturated VOCs are given in Table S4 together with associated time resolution, limit of detection and uncertainties. The data were averaged or interpolated with a time step of 90 min.

Wind speed and direction, relative humidity, temperature and photolysis rates were also measured throughout the campaign.

2.3 Estimation of H₂SO₄ steady-state concentrations

Concentrations of H₂SO₄ produced via SO₂ oxidation by OH and sum of SCIs, H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ and H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$, respectively, were calculated assuming validity of a steady state between the H₂SO₄ production and its loss (see discussion in Sect. 4.1),

$$\begin{array}{}\text{(1)}& {\displaystyle }{\left[{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}\right]}^{\mathrm{OH}}={\displaystyle \frac{k_{\mathrm{1}}\cdot \left[\mathrm{OH}\right]\cdot \left[{\mathrm{SO}}_{\mathrm{2}}\right]}{\mathrm{CS}}},\text{(2)}& {\displaystyle }{\left[{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}\right]}^{\mathrm{SCI}}={\displaystyle \frac{\left\{\sum _i{k}_{{\mathrm{SO}}_{\mathrm{2}}}^i\cdot \left[{\mathrm{SCI}}^i\right]\right\}\times \left[{\mathrm{SO}}_{\mathrm{2}}\right]}{\mathrm{CS}}}.\end{array}$$

Here [OH] and [SO₂] are measured concentrations, [SCIⁱ] are estimated concentrations of speciated SCIs, and CS, a condensation sink, is a rate of H₂SO₄ loss by its condensation on aerosol particles which is assumed to be the predominant H₂SO₄ loss process, while the dry deposition on macroscopic surfaces is neglected considering a long associated lifetime estimated of about 1 d using a typical deposition velocity of 1 cm s⁻¹ (Seinfeld and Pandis, 2016) and a boundary-layer depth of 1 km. Considering the CS to be a major sulfuric acid loss process, the median value of H₂SO₄ lifetime was 2.7 min (2.2–3.7 min interquartile range, Figs. 1, 2). The rate coefficient for the reaction of OH with SO₂, $k_{\mathrm{1}}=\mathrm{8.06}\times {\mathrm{10}}^{-\mathrm{13}}$ cm³ molec.⁻¹ s⁻¹ (at 760 torr and 298 K) was taken from the IUPAC 2004 recommendation (Atkinson et al., 2004) (see Sect. 4.2). Production of H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$ is calculated as a sum of contributions from different speciated SCIⁱ reacting with SO₂ with rate coefficients $k_{{\mathrm{SO}}_{\mathrm{2}}}^i$ (Table S5). It is assumed here that the H₂SO₄ yield in reaction of SCIs with SO₂ is a unity for all SCIs, giving an upper limit for the contribution to H₂SO₄ formation of accounted SCIs.

Figure 1 Time series of the observations during the ChArMEx summer 2013 campaign: OH radicals and O₃ (a); sulfuric acid observed, H₂SO${}_{\mathrm{4}}^{\mathrm{mes}}$, and calculated assuming only an SO₂+OH source, H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ (see Sect. 2.3) (b); SO₂ and condensation sink (CS) (c); total monoterpenes and isoprene (left axis) and EVK (right axis) (d). For clarity, a comparison of the measured H₂SO${}_{\mathrm{4}}^{\mathrm{mes}}$ and calculated H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ concentrations is presented in (b) using two plots, with logarithmic and linear scales on the y axis.

Figure 2 Median diel profiles of calculated [H₂SO₄] produced in OH + SO₂ (H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$), observed [H₂SO₄], [OH] and photolysis rate J(O¹D) (a), CS and [SO₂] (b), [O₃] and concentrations of selected VOCs (c), and relative humidity (RH) and temperature (T) (d). Shaded areas represent the 25th/75th percentiles.

The CS was calculated using measured particle size distributions and number concentrations by calculating diffusional flux to the aerosol particles assuming an accommodation coefficient of unity (Hanson, 2005) and using a Fuchs–Sutugin transition correction (Jefferson et al., 1998; Seinfeld and Pandis, 2016). A diffusion coefficient of H₂SO₄ was estimated using its dependence on relative humidity from Hanson and Eisele (2000), giving 0.077 cm² s⁻¹ at an RH of 60.6 % (median value). Without considering an uncertainty in the accommodation coefficient, the accuracy of the calculated CS of 20 % was assessed, accounting for the uncertainties in particle measurements given in Sect. 2.2.2 and an uncertainty in the H₂SO₄ diffusion coefficient of 5 %.

Concentrations of speciated SCIs, [SCIⁱ], were calculated assuming steady-state conditions considering their production by ozonolysis of the measured unsaturated VOCs and their loss by thermal decomposition and in reactions with water vapour (with H₂O and (H₂O)₂):

$$\begin{array}{}\text{(3)}& \left[{\mathrm{SCI}}^i\right]={\displaystyle \frac{\left\{\sum _X{k}_{X+{\mathrm{O}}_{\mathrm{3}}}\cdot {\mathit{\alpha }}_X^i\cdot Y_X^i\cdot \left[X\right]\right\}\times \left[{\mathrm{O}}_{\mathrm{3}}\right]}{K^i+k_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^i\cdot \left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]+k_{{\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)}_{\mathrm{2}}}^i\cdot \left[{\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)}_{\mathrm{2}}\right]}},\end{array}$$

where X denotes a specific VOC, $k_{X+{\mathrm{O}}_{\mathrm{3}}}$ is a rate coefficient for the reaction of X with O₃, ${\mathit{\alpha }}_X^i$ is a yield of stabilized SCIⁱ from CIⁱ, $Y_X^i$ is a specific yield of CIⁱ in the reaction X+O₃, and Kⁱ, $k_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^i$, and $k_{{\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)}_{\mathrm{2}}}^i$ are rate coefficients for the thermal decomposition, the reaction with H₂O, and the reaction with water dimer for the specific SCIⁱ, respectively. Concentration of (H₂O)₂ was calculated using an equilibrium constant for water dimer formation and its temperature dependence from Ruscic (2013).

The rate coefficients and the yields ${\mathit{\alpha }}_X^i$ and $Y_X^i$ for 36 SCIs derived from the ozonolysis of 23 measured VOCs are presented in Tables S4 and S5. Apart from a few rate coefficients and yields available from more recent experimental and theoretical studies, most of the parameters in Eqs. (2) and (3) are taken from recommendations of Vereecken et al. (2017), which are based either on an analysis of available experimental data or derived from theory-based structure–activity relationships (SARs). For the 36 SCIs listed in Tables S4 and S5, we have adopted the SCI naming convention from Vereecken et al. (2017). Using this approach, uncertainty in the SCI concentrations is estimated in Vereecken et al. (2017) to be of an order of magnitude, mainly due to the uncertainties in CI speciation and the SCI decay rates.

3 Results

3.1 Observed data

Time series and median diel profiles of observed concentrations of OH, H₂SO₄, SO₂, O₃, selected VOCs and a calculated condensation sink of H₂SO₄ are presented in Fig. 1 (time series) and Fig. 2 (median diel cycles, also including J(O¹D), T, RH, and CS data). The nighttime OH and H₂SO₄ measurements on 26 and 28–30 July were influenced by a strong fog event deteriorating the accuracy of the corresponding OH and H₂SO₄ data.

OH and H₂SO₄ concentrations reached around midday, with maximum values of 4.3 × 10⁶ and 8.5 × 10⁶ molec. cm⁻³ (mean values for daytime hours from 11:00 to 13:00 local time (= GMT+2 h)), respectively, with nighttime concentrations around 1 × 10⁵ and 5 × 10⁵ molec. cm⁻³ for OH and H₂SO₄, respectively, close to the detection limit.

Comparing the present observations (Fig. 2) with previous measurements in the Mediterranean region, the mean peak OH concentration during the noon hours was close to the peak OH levels observed during the CYPHEX campaign in the summer of 2014 in Cyprus in the eastern Mediterranean, 5.8 × 10⁶ molec. cm⁻³ (Mallik et al., 2018), where O₃ concentrations and J(O¹D) peak levels were similar to those observed during ChArMEx (J(O¹D) was measured during ChArMEx but not yet published). The somewhat lower ChArMEx OH noon concentrations compared to CYPHEX are consistent with higher OH reactivity observed during ChArMEx (Zannoni et al., 2017), although the direct comparison of radical chemistry at these two sites is not straightforward considering that, among other differences between these sites, biogenic VOCs at the Cyprus site, e.g. isoprene and monoterpenes, were 3–5 times lower compared to ChArMEx. About 4 times higher OH peak concentrations, 2.1 × 10⁷ molec. cm⁻³, were observed during the MINOS campaign in the summer of 2001 in Crete (central Mediterranean), with similar O₃ and J(O¹D) observed levels (Berresheim et al., 2003). This difference is difficult to explain based on the available data (Mallik et al., 2018).

The observed ChArMEx H₂SO₄ concentrations were about 2 times higher than the observed OH concentrations. For other sites the observed ratios [H₂SO₄] $/$ [OH] were in the range from 1 to 9, with only one example when this ratio was less than unity (Table S1). The ratio [H₂SO₄] $/$ [OH] depends on the SO₂ concentration and condensation sink, correlating with the aerosol particle surface area concentration. The condensation sink and [SO₂] values during ChArMEx, with median values of 6.1 × 10⁻³ s⁻¹ and 0.44 ppb, respectively, were typical of clean remote continental or coastal environments (Table S1).

The unsaturated VOCs observed during ChArMEx showed strong diel variation from about 0.4 ppb during the night to about 2 ppb at noon for the concentration of the sum of the VOCs (Figs. 1, 2 and S9 and Table S4). The major contribution during the day (from 07:00 to 20:00) was from biogenic VOCs (isoprene (22 % on average), β-pinene (14 %), α-pinene (9 %), α-terpinene (7 %), methyl vinyl ketone (MVK) (5 %) and methacrolein (MACR) (5 %)), with emission rates correlating with temperature and solar radiation (Kesselmeier and Staudt, 1999). At nighttime, the unsaturated VOCs were represented mostly by compounds of mixed biogenic and anthropogenic origin: ethene (31 % on average), acrolein (14 %) and ethyl vinyl ketone (9 %). A significant nighttime contribution was also found from isoprene (9 %) and its first-generation oxidation products MVK (6 %) and MACR (6 %).

3.2 Comparison of observed H₂SO₄ with sulfuric acid produced from OH + SO₂ (H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$)

Time series of the H₂SO₄ produced in the reaction of OH with SO₂ and H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$, calculated according to Eq. (1), and of the observed H₂SO₄ are presented in Figs. 1b and 2b showing apparently good agreement between them during the day and an underestimation of the sulfuric acid concentration by H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ during the night. The inverse variance weighted mean value of the ratio of [H₂SO₄]^OH $/$ [H₂SO₄] for the data presented in Fig. 1b is 0.86±0.04 during the day (07:00–20:00) and 0.09±0.02 during the night (20:00–07:00), respectively (Table 1). Uncertainties in the ratio [H₂SO₄]^OH $/$ [H₂SO₄] were estimated by accounting for the uncertainty in the measured ratio of [OH] $/$ [H₂SO₄] (see Sect. 2.2.1), in the SO₂ measurements (20 %) and in the CS calculations (20 %) without considering uncertainties in the reaction rate coefficient k₁ and the H₂SO₄ uptake coefficient (see Sect. 4.2 and 4.3).

Table 1 Comparison of observed [H₂SO₄] with calculations assuming H₂SO₄ formation via oxidation of SO₂ by OH and SCIs. [OH] and [H₂SO₄] are observed concentrations, and [H₂SO₄]^OH and [H₂SO₄]^SCI are calculated H₂SO₄ produced by oxidation of SO₂ by OH and SCI, respectively. Values in square brackets correspond to [H₂SO₄]^OH concentrations calculated with a rate coefficient for the reaction of OH with SO₂ from Medeiros et al. (2018) (see discussion in Sect. 4.2).

Considering the correlation of the calculated sulfuric acid concentration [H₂SO₄]^OH with the measured [H₂SO₄] shown in Fig. 3, we find that the linear regression using a bivariate fit procedure accounting for the measurement errors of both H₂SO₄ and H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ (York et al., 2004) results in slopes of 0.85 ± 0.02 and 0.97 ± 0.1 for the daytime and nighttime, respectively. The linear regression yields significant intercepts of ($-\mathrm{2.0}\pm \mathrm{0.5}$) × 10⁵ molec. cm⁻³ during the day and of ($-\mathrm{3.1}\pm \mathrm{0.3}$) × 10⁵ molec. cm⁻³ during the night. The close-to-unity slopes and the negative intercepts may be interpreted as a presence of an additional source contributing to H₂SO₄ on an average level of several of 10⁵ molec. cm⁻³. During the night this source is important compared with the observed nighttime average [H₂SO₄] of (5.8±4.8) × 10⁵ molec. cm⁻³. During the night the estimation of the contribution from missing sources derived from the linear fit is in qualitative agreement with the mean ratio of [H₂SO₄]^OH $/$ [H₂SO₄] of 0.09, indicating that the SO₂ + OH source explains only about 10 % of the H₂SO₄ formation. During the daytime, the reaction of SO₂ with the OH source explains around 90 % of the H₂SO₄ formation (Table 1).

Figure 3 Comparison of the measured H₂SO₄ and the H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$ calculated accounting only for the OH + SO₂ source during the day (red) and during the night (blue). Solid lines correspond to linear regression fitting accounting for both X and Y measurement uncertainties. Dashed lines represent 1 : 1 ratios. Inserts, log plot (upper) and linear plot (lower right) are added for clearer presentation of the nighttime data.

3.3 Comparison of observed H₂SO₄ with sulfuric acid produced from SCIs + SO₂ (H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$)

Estimated according to Eqs. (2) and (3), mean diel profiles of the sulfuric acid H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$ produced in the reactions of SO₂ with SCIs generated by the ozonolysis of the measured unsaturated VOCs, excluding α-terpinene, are presented in Fig. 4a. The calculated contribution from α-terpinene alone is up to 6 times larger than observed [H₂SO₄] (Fig. 4b). It is not clear whether the reason for this large overestimation can be related to erroneous α-terpinene measurements and/or to incorrect kinetic parameters used for the calculation of H₂SO₄ production from α-terpinene. The observed α-terpinene daytime concentrations were similar to the concentrations of α-pinene and β-pinene. Accounting for about 100 times faster α-terpinene consumption in reactions with OH and O₃ compared to other terpenes (Atkinson et al., 2006; IUPAC, 2020), that would imply about a 100 times larger α-terpinene emission rate at the measurement site, which is unlikely considering observed compositions of monoterpene emissions of biogenic origin (Geron et al., 2000). Being well outside of the uncertainty of the H₂SO₄ measurements, the contribution from α-terpinene was therefore excluded from consideration in this work.

Figure 4 Diel profiles of the mean calculated H₂SO₄ concentrations produced from ozonolysis of different VOCs: (a) filled regions correspond to [H₂SO₄]^SCI produced by ozonolysis of different VOCs; (b) profiles of ratios of [H₂SO₄]^SCI from different VOCs to the measured [H₂SO₄]. Black dotted line in (b) corresponds to [H₂SO₄]^SCI produced by the ozonolysis of α-terpinene (right axis).

The calculated concentration of the sum of H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$ reaches a maximum of about 7×10⁵ molec. cm⁻³ around midday and goes down to about 1.5×10⁵ molec. cm⁻³ during the night. The largest estimated contribution to the H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$ is from α-pinene, limonene and isoprene during the day and from MVK and EVK at nighttime (Fig. 4).

The largest contribution to the calculated sum of SCIs was from the syn form of acetaldehyde oxide, Z-CH₃CHOO (2), E-MVK-oxide (10) from isoprene, oxo-substituted E-(C(O)R)CHOO (31) (with R = H, CH₃, and C₂H₅ for the SCI from acrolein, MVK and EVK, respectively), and phenyl-substituted carbonyl oxide PhCHOO (35), from styrene and Z-pinonaldehyde-K-oxide (13) from α-pinene (the SCIs numbering given in parentheses corresponds to the SCI numbering in Tables S4 and S5.

The nighttime and daytime mean concentrations of the sums of all SCIs were about 10³ and 3×10³ molec. cm⁻³, respectively. Z-pinonaldehyde-K-oxide (13) (from α-pinene) and E-(C(O)R)CHOO (31) (from MVK, EVK and acrolein) were also the major SCI producing H₂SO₄. In addition, a comparable contribution to H₂SO₄ formation was from Z-(CHR_aR_b)(CH₃)COO (21) (from limonene ozonolysis) and E-MVK-oxide (10) (from isoprene ozonolysis). Detailed information is given in Fig. S10.

Comparing the calculated [H₂SO₄]^SCI with the missing H₂SO₄ source derived from the difference of the measured [H₂SO₄] and calculated [H₂SO₄]^OH, Fig. 5a shows that, compared to the difference of [H₂SO₄] − [H₂SO₄]^OH representing the missing H₂SO₄ source, the [H₂SO₄]^SCI is lower during the night and higher during the day, with a difference of several 10⁵ molec. cm⁻³ (Table 1). The large variance of the average [H₂SO₄] − [H₂SO₄]^OH difference presented in Table 1 is due to the large scattering of these values derived either from a small difference of large OH and H₂SO₄ signals or from the measurements of OH and H₂SO₄ concentrations close to their lower detection limits as well as due to a stochastic day-to-day natural variation.

Figure 5 Comparison of the sulfuric acid produced by oxidation of SO₂ by SCIs, H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$, and the missing source of H₂SO₄ derived from the difference of the measured [H₂SO₄] and [H₂SO₄]^OH. (a) Diel profiles of the mean [H₂SO₄]^SCI (red) and [H₂SO₄] − [H₂SO₄]^OH (black). (b) Diel profiles of the mean of the relative contributions [H₂SO₄]^SCI $/$ [H₂SO₄] (red) and 1 − [H₂SO₄]^OH $/$ [H₂SO₄] (black). Shaded areas correspond to ±1σ standard deviation.

Shown in Fig. 4b, the calculated dial profile of the relative H₂SO${}_{\mathrm{4}}^{\mathrm{SCI}}$ to H₂SO₄ contribution resembles the dial profile of a missing H₂SO₄ source derived from the relative concentration difference of H₂SO₄ and H₂SO${}_{\mathrm{4}}^{\mathrm{OH}}$, i.e. 1 − [H₂SO₄]^OH $/$ [H₂SO₄]. Both profiles exhibit a shallow well from about 08:00 to 18:00 local time (UTC+2) during the day, with a higher relative contribution during the night. According to the [H₂SO₄]^SCI calculations, the SCIs contribution is about 3 times higher during the night, constituting (38±24) % compared to (12±6) % during daytime. The calculated [H₂SO₄]^SCI contribution is significantly lower than the nighttime missing source of (91±2) % and is in good agreement with the missing (14±4) % during the day (Table 1). The large unexplained formation of H₂SO₄ during the night can be related to the large uncertainty in the calculated SCI concentrations and the rates of H₂SO₄ production from their reactions with SO₂ (Vereecken et al., 2017) as well as with an unaccounted-for contribution from the ozonolysis of some unsaturated compounds not measured during the campaign. The latter explanation is supported by significant daytime and nighttime missing OH reactivity of about 50 %, observed by Zannoni et al. (2017) during ChArMEx using the same VOC data as in the present work. The main unaccounted species were suggested to be reactive biogenic VOCs, including sesquiterpenes, oxygenated terpenes and their oxidation products. Ozonolysis of these compounds could be an additional unaccounted-for source of SCI in the present work.

4 Discussion

4.1 Validity of H₂SO₄ steady-state conditions

Estimated concentrations of H₂SO₄ produced in reactions of SO₂ with OH and with SCIs are based on the assumption of a steady state between production and loss pathways of H₂SO₄. All variations of the parameters influencing the H₂SO₄ concentration in the air masses incoming to the measurement site are assumed to occur on a timescale that is longer than the lifetime of H₂SO₄ estimated on the basis of the local aerosol measurements. These conditions are not obviously fulfilled at the Ersa site because the air masses arriving at the island may become influenced by local biogenic emissions, possibly leading to varying concentrations of these compounds along the trajectory from the coast to the measurement location (due to non-uniformly distributed emissions, development of vertical profiles of VOCs and other reasons). As the production rate of the SCIs is proportional to the corresponding concentrations of the unsaturated compounds, the variation of VOCs may induce variations in the SCI concentrations. The concentration of OH could also be affected by varying VOC concentrations considering that the lifetime of OH at the measurement site was about 0.2 s, with half of the OH reactivity explained by the local biogenic emissions (Zannoni et al., 2017).

The steady-state conditions were hardly disturbed by variations of the concentrations of SO₂ and O₃, species of non-local origin with lifetimes longer than the lifetime of H₂SO₄. Concerning the H₂SO₄ condensation sink, a variation in the aerosol particle number concentration and size distribution could be present. Recent studies evidenced that highly oxygenated molecules (HOMs) from the ozonolysis of monoterpenes may initiate new particle formation and its fast initial growth with the growth rates of tens of nanometres per hour (Stolzenburg et al., 2018; Tröstl et al., 2016). However, these variations are still slow compared to the H₂SO₄ lifetime of several minutes.

The timescales for the variations of VOCs, SCI, OH and CS may depend on the distribution of the biogenic emissions, wind speed, conditions of turbulent mixing and others. Without information about all these details, we can only estimate the maximum time for such variations, corresponding to the time of air mass presence over the land. To fulfill the steady-state conditions, this presence time has to be at least longer than the lifetime of H₂SO₄. The prevailing wind directions were from the north-east and, predominantly, from the south-west. The south-westerly direction corresponds to the shortest presence times because of the shortest distance to the coastline and the highest wind speeds corresponding to this wind direction (Figs. S11 and S12). On average, the presence time over the land, t_pr, significantly exceeded the H₂SO₄ lifetime, $t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$, with the median value of the ratio of $t_{\mathrm{pr}}/t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$ being 7.7 (4.3–17.9 interquartile range). To test the influence of the presence time on the calculated H₂SO₄ budget, the dependencies between the relative difference 1 − [H₂SO₄]^OH $/$ [H₂SO₄] and the relative contribution [H₂SO₄]^SCI $/$ [H₂SO₄] were analysed with filtered data using criteria t_pr $/$ $t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$ > 1 and t_pr $/$ $t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$ > 10. No significant difference was found compared with the unfiltered data, as is also illustrated in Fig. 6, showing no apparent correlation between the relative contribution of the OH + SO₂ source and the ratio of $t_{\mathrm{pr}}/t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$. Similarly, no apparent effect was found by filtering the data according to the wind speed and the wind direction (not presented). Finally, although relatively short timescale spatial variability of OH or SCI concentrations around the measurement site cannot be excluded, an apparent independence of the presence time or the wind speed supports the validity of the assumption used here regarding H₂SO₄ steady-state conditions.

Figure 6 Dependence of the normalized difference of the H₂SO₄ concentrations observed and produced from SO₂ + OH, 1 − [H₂SO₄]^OH $/$ [H₂SO₄], on the ratio of presence time over the land to the lifetime of H₂SO₄, $t_{\mathrm{pr}}/t_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$, coloured by the presence time over the land, t_pr. Panels (a) and (b) correspond to the daytime and nighttime data, respectively. Solid lines correspond to linear regression fits.

4.2 OH + SO₂ reaction rate constant

In this work the rate coefficient for the reaction of OH with SO₂, $k_{\mathrm{1}}=\mathrm{8.06}\times {\mathrm{10}}^{-\mathrm{13}}$ cm³ molec.⁻¹ s⁻¹ (at 760 torr and 298 K), was taken from the last published IUPAC recommendation (Atkinson et al., 2004). The two latest JPL evaluations recommend an approximately 20 % larger rate constant of $\mathrm{9.6}\times {\mathrm{10}}^{-\mathrm{13}}$ cm³ molec.⁻¹ s⁻¹ (Burkholder et al., 2015, 2019). Using the rate constant from the JPL evaluations in this work would result in about a 20 % larger H₂SO₄ production rate via OH + SO₂. This would yield a closed H₂SO₄ budget with only an OH + SO₂ source during the day and about 2 times lower contribution from a missing source during the night.

In a recent study of Blitz et al. (2017a, b), a significantly lower rate constant of $\mathrm{5.8}\times {\mathrm{10}}^{-\mathrm{13}}$ cm³ molec.⁻¹ s⁻¹ was derived from experiments with vibrationally excited OH (v=1, 2, 3) + SO₂ and using the master equation analysis of the pressure and temperature dependence of their own and some other experimental OH + SO₂ reaction rate constants. An even lower rate constant of $\mathrm{4.8}\times {\mathrm{10}}^{-\mathrm{13}}$ cm³ molec.⁻¹ s⁻¹ was derived by Medeiros et al. (2018) by applying more detailed master equation analysis of experimental data from Blitz et al. (2017a, b) and some other data. These recent results have not been confirmed by other studies. Also, they have been discussed but not recommended by the latest JPL evaluation (Burkholder et al., 2019).

Using the lower rate constant from Medeiros et al. (2018) in our study would result in about 2 times reduced H₂SO₄ production by oxidation of SO₂ by OH and would invoke either significantly larger contribution from an additional H₂SO₄ source or a lower H₂SO₄ uptake coefficient of about 0.5 instead of unity. As shown in Table 1, the reaction of OH with SO₂ would explain only about 50 % and 5 % of the observed H₂SO₄ production during the day and during the night, respectively.

In previous field studies of the H₂SO₄ budget listed in Table S1, the OH + SO₂ production rate of H₂SO₄ was calculated using a k₁ rate coefficient in the range of (8.5–12) × 10⁻¹³ cm³ molec.⁻¹ s⁻¹. Reanalysis of these data using the lower k₁ would lead to a conclusion that the H₂SO₄ budget was never observed to be closed with the uptake coefficient close to unity. On the other hand, employing the lower k₁ from Blitz et al. (2017a, b) in model studies results in a significantly larger relative contribution of SCI to the H₂SO₄ formation. For example, the SCI contribution of 7 % in a rural environment and of 70 % in tropical regions, which were estimated assuming the lower k₁ by Vereecken et al. (2017), would be reduced, respectively, to negligible and to about 30 % if the larger k₁ from IUPAC or JPL were used.

4.3 H₂SO₄ loss

The mass accommodation coefficient of unity used in this work was measured by Hanson (2005) for the H₂SO₄ uptake on 5–20 nm diameter particles composed of water and sulfuric acid. The efficient uptake of H₂SO₄ is supported by other studies where the accommodation coefficients of about 0.7 were determined for the uptake on liquid sulfuric acid (Pöschl et al., 1998) and on ammonium sulfate and sodium chloride particles (Jefferson et al., 1997). Lower mass accommodation coefficients in the range of 0.2–0.3 were determined for the uptake on hydrocarbon-coated particles (Jefferson et al., 1997), suggesting that the uptake coefficient may depend on aerosol composition. Considering the measurement uncertainty, the results obtained in this work are consistent with the accommodation coefficient in the range from about 0.8 to 1. At lower uptake values the OH + SO₂ source would significantly override the calculated H₂SO₄ loss during the day. At the same time, the apparently missing H₂SO₄ source during the night can be explained by a lower uptake coefficient, down to about 0.5.

Another possible loss mechanism of H₂SO₄ can be via collisions of sulfuric acid molecules leading to new particle formation (NPF) in the atmosphere. For some atmospheric conditions, like in the presence of high concentrations of base atmospheric components, e.g. ammonia and amines (Almeida et al., 2013), stabilizing the H₂SO₄ dimer and larger clusters, the nucleation may proceed at a collisionally limited rate corresponding to an effective bimolecular H₂SO₄ loss rate coefficient of about $\mathrm{4}\times {\mathrm{10}}^{-\mathrm{10}}$ cm³ molec.⁻¹ s⁻¹ (Kürten et al., 2014). Such conditions might have been encountered in highly polluted industrial and urban environments, regions influenced by strong agricultural emissions, and chamber experiments (Kürten et al., 2016, 2018; Yao et al., 2018). Removal of H₂SO₄ with this rate constant would significantly contribute to its loss during ChArMEx, increasing it by about a factor of 2 for the largest observed H₂SO₄ concentrations. During the ChArMEx/SAFMED experiment, the H₂SO₄ loss rate assuming sulfuric acid-initiated kinetic particle formation can be estimated from several episodes of the NPF observed during the campaign (on days from 29 July to 2 August; Berland et al., 2017). Figure S13 shows an example of NPF observed around the midday of 31 July. For this day the profiles of H₂SO₄ and N_10–15 are similar, with a time delay of about 2 h for the maximum of the size distribution of 15 nm. This allows us to assume that the observed NPF on this day could be related to the evolution of the H₂SO₄ concentration. The growth rate (GR) and 12 nm particle apparent formation rate from the SMPS measurements are 3.1 nm h⁻¹ and 8.2 × 10⁻³ cm⁻³ s⁻¹, respectively. GR was calculated using a maximum-concentration method (Kulmala et al., 2012). Using the approach of Kerminen and Kulmala (2002) and Sihto et al. (2006) to derive the rate of formation of the critical cluster of size 1 nm, J₁, we obtain around 1 cm⁻³ s⁻¹ at H₂SO₄ concentration of around 10⁷ molec. cm⁻³. Assuming a kinetically limited nucleation mechanism in which the critical cluster contains two sulfuric acid molecules, this corresponds to the bimolecular rate constant of $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{13}}$ for the removal of H₂SO₄, which would correspond to a negligible H₂SO₄ loss compared to the condensation on existing particles. Similar rates, several orders of magnitude below the collision limited rate, were found in other diverse continental and marine atmospheric environments (Kuang et al., 2008). In addition, the GR estimated from the time delay between an H₂SO₄ profile and a corresponding increase in N_10–15 particles is about 2 times faster than derived from the particle size growth rate. Using this latter GR would result in an even slower particle formation. Finally, analysis of particles' origins and their chemical composition at the measurement site made with ATOMF MS indicates that even if some traces of amines were present, they were of remote origin and not present at the measurement site (Arndt et al., 2017).

4.4 SCI interference with OH and H₂SO₄ measurements

High concentrations of SO₂ used in the chemical conversion reactor of CIMS instruments for the conversion of OH into H₂SO₄ may lead to an interference with OH and H₂SO₄ measurements due to an artificial generation of H₂SO₄ in reactions of SCIs with SO₂ inside the reactor. When the reactant used as a scavenger of OH does not react quickly with SCIs, e.g. using propane, the contribution of the artificially formed H₂SO₄ is the same for the OH measurements in the background (BG) and OH signal + background modes (OH + BG) if the SO₂ injection position rests unchanged for the measurements in both modes. In this case the OH signal derived from the difference of the OH + BG and BG signals is free from the artificial H₂SO₄ formation. However, the presence of an additional SO₂ oxidant not efficiently removed by an OH scavenger may lead to a significant increase in the BG level, as was observed in previous field measurements (Berresheim et al., 2014; Mauldin et al., 2012).

Figure 7 Interference with OH measurements from the H₂SO₄ produced in the reactor by reactions of SO₂ with SCIs: calculated contribution to measured OH (red line, left axis) and comparison of the observed background (BG) (blue line, right axis) and the BG calculated assuming its origin from the reactions of SCIs with SO₂ inside the reactor (black line, right axis).

In the instrument used in this study the OH is scavenged with NO₂. The rate constant for the reaction of NO₂ with CH₂OO, CH₃CHOO and (CH₃)₂COO stabilized CIs was found to be of about $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ (Chhantyal-Pun et al., 2017; Stone et al., 2014; Taatjes et al., 2013), which is about 10–100 times smaller than typical rate constants of the reactions of SCIs with SO₂ (Table S5). As the ratio of [NO₂] $/$ [³⁴SO₂] in the reactor was about 100, the SCIs in the reactor may react with similar rates with both SO₂ and NO₂ contributing to the BG signal. In addition, as the NO₂ and SO₂ injection positions are different for the BG and OH + BG modes (see Fig. S1 for details), the OH signal derived from the OH + BG and the BG difference may also be influenced by the artificial H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄ production in reactions of SCIs with SO₂.

As presented in Fig. 7, the BG signal observed during ChArMEx showed a diel profile similar to that of VOCs or OH (Figs. 1 and 2) with maximum at noon and minimum during the night. The peak noon and nighttime BG signals reached levels corresponding to OH concentrations of about 5×10⁶ and 1×10⁶ molec. cm⁻³, respectively. These BG levels are significantly higher than values of about (1–5) × 10⁵ molec. cm⁻³ typically observed with the present instrument during calibration with zero air or during measurements in clean air with low VOCs concentrations, e.g. in Antarctica (Kukui et al., 2014).

To examine whether the observed high BG levels can be explained by the SO₂ reaction with SCIs, the H₂SO₄ concentration produced in the reactor in reactions of the sum of SCIs with SO₂, [H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄]${}^{\mathrm{SCI}/R}$, was calculated for BG and OH+BG modes using Eq. (4), which is similar to Eq. (2) but neglects the H₂SO₄ losses in the reactor:

$$\begin{array}{}\text{(4)}& \begin{array}{rl}{\left[{\mathrm{H}}_{\mathrm{2}}{}^{\mathrm{34}}{\mathrm{SO}}_{\mathrm{4}}\right]}^{\mathrm{SCI}/R}& =\sum _{R_j}\left\{\sum _i{k}_{\mathrm{2}}^i\cdot {\left[{\mathrm{SCI}}^i\right]}^{R_j}\right\}\\ & \times {\left[{}^{\mathrm{34}}{\mathrm{SO}}_{\mathrm{2}}\right]}^{R_j}\times t_{R_j},\end{array}\end{array}$$

where the index R_j corresponds to different parts of the reactor, ${\left[{\mathrm{SCI}}^i\right]}^{R_j}$ and ${\left[{}^{\mathrm{34}}{\mathrm{SO}}_{\mathrm{2}}\right]}^{R_j}$ are the concentrations and $t_{R_j}$ is the bulk flow time in the corresponding parts of the reactor (see also Fig. S1). The concentrations of SCIs inside the reactor generated by ozonolysis of the measured unsaturated VOCs were calculated similarly to Eq. (3) but with accounting for the additional SCI loss in reactions with SO₂ and NO₂ injected into the reactor. The concentrations of VOCs, O₃ and H₂O inside the reactor were calculated using the ambient measurements with accounting for a dilution inside the reactor.

The concentration of O₃ in the IMR was corrected by accounting for ozone generated in the corona discharge ion source and added to the IMR with the flow of primary ions. Amount of O₃ generated by the ion source depends on the ion source operating configuration, i.e. flow rates of injected mixtures, composition of the mixtures and potentials of the ion source electrodes. The concentration of O₃ in the IMR was not monitored during the campaign, but according to later checks this concentration was of 2±1 ppm and this value was used for the estimation of [H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄]${}^{\mathrm{SCI}/R}$.

As shown in Fig. 7, the calculated and the observed BGs exhibit similar variability and correspond to comparable concentration levels allowing us to suggest that the observed elevated BG levels were related to the SO₂ oxidation by SCIs in the reactor. This hypothesis is supported by results of later experiments on the ozonolysis of terpenes conducted in an environmental chamber where a strong dependence of the observed BG level on the SCI production rate was confirmed, as shown in Fig. S14 for the ozonolysis of α-pinene.

Concerning a possible interference of the SO₂ + SCI reaction with the OH measurements, Fig. 7 shows that during the campaign, this interference was negligible because the difference of [H${}_{\mathrm{2}}^{\mathrm{34}}$SO₄]${}^{\mathrm{SCI}/R}$ produced in the OH + BG and the BG modes corresponded to OH concentration lower than 2 × 10⁴ molec. cm⁻³, about 10 times lower than the OH lower detection limit. Notably, this contribution is independent of the [O₃] in the IMR, influencing equally the OH + BG and BG measurements.

5 Conclusions

The formation of H₂SO₄ was observed at the Ersa station in northern Corsica, a site influenced by local emissions of biogenic VOCs. The H₂SO₄ concentration reached 10⁷ molec. cm⁻³ at midday and was around 5 × 10⁵ molec. cm⁻³ during the night. Based on the OH, H₂SO₄, SO₂ and particle number density measurements and assuming validity of a steady state between H₂SO₄ production and its loss by condensation on existing aerosol particles with a unity accommodation coefficient, we have found that the contribution of the SO₂ + OH reaction accounts for (86±4) % and only for (9±2) % of the H₂SO₄ production during the day and night, respectively. The given accuracy of these values has been estimated without accounting for the large uncertainty in the OH + SO₂ reaction rate coefficient, which results in a larger uncertainty in the contribution to H₂SO₄ formation from the OH + SO₂ source, from about a factor of 1.5 of its overestimation to about 20 % of its underestimation.

Estimating the H₂SO₄ production from the SO₂ oxidation by SCIs, we conclude that despite the low calculated SCI concentrations ((1–3) × 10³ molec. cm⁻³ for the sum of SCIs), this source may explain about 10 % of the H₂SO₄ formation during the day and represents a major source of H₂SO₄ accounting for about 40 % of its formation during the night. The sum of the H₂SO₄ production rates via SO₂ + OH and SO₂ + SCIs correspond to a closure of the H₂SO₄ budget during the day, but seem to underestimate by 50 % the H₂SO₄ production during the night, with the latter being possibly related to uncertainties in the used in this work kinetic parameters, an unaccounted contribution from the ozonolysis of some unsaturated compounds not measured during the campaign, as well as to some yet unidentified H₂SO₄ production mechanisms during nighttime.

Both the daytime and nighttime results of this study indicate that the oxidation of SO₂ by SCIs may be an important source of H₂SO₄ in VOC-rich environments, especially during nighttime.