Ozonolysis of an unsaturated hydrocarbon produces a primary ozonide that rapidly decomposes to yield pairs of Criegee intermediates (CIs) and carbonyls (Johnson and Marston, 2008). The population of CIs are formed with a broad internal energy distribution, giving both chemically activated and stabilised forms. Chemically activated CIs may undergo collisional stabilisation to an SCI, unimolecular decomposition or isomerisation. SCIs can have sufficiently long lifetimes in which to undergo bimolecular reactions (Scheme 1).

The predominant atmospheric fate for the simplest SCI, CH2OO, is reaction with water vapour, which likely occurs with the dimer ((H2O)2) (e.g. Berndt et al., 2014; Newland et al., 2015a; Chao et al., 2015; Lewis et al., 2015; Lin et al., 2016a). For larger SCI, both experimental (Taatjes et al., 2013; Sheps et al., 2014; Newland et al., 2015a; Huang et al., 2015) and theoretical (Kuwata et al., 2010; Anglada et al., 2011; Anglada and Sole, 2016; Vereecken et al., 2017) studies have shown that their kinetics, in particular reaction with water, are highly structure dependent. The significant double-bond character exhibited in the zwitterionic configurations of mono-substituted SCIs leads to two distinct chemical forms: syn-SCIs (i.e. those where an alkyl substituent group is on the same side as the terminal oxygen of the carbonyl oxide moiety) and anti-SCIs (i.e. with the terminal oxygen of the carbonyl oxide moiety on the same side as a hydrogen group). The two conformers of CH3CHOO, which are both mono-substituted, display these properties. This difference in conformer reactivities has been predicted theoretically (Ryzhkov and Ariya, 2004; Kuwata et al., 2010; Anglada et al., 2011; Lin et al., 2016a) and was subsequently confirmed experimentally (Taatjes et al., 2013; Sheps et al., 2014) for the two CH3CHOO conformers. The significantly faster reaction of anti-CH3CHOO with water is driven by the higher potential energy of this isomer, while more stable SCI, with a methyl group in syn-position, such as syn-CH3CHOO or (CH3)2COO, react orders of magnitude more slowly with water.

To date, the effects of the water dimer, (H2O)2 on SCI removal have only been determined experimentally for CH2OO (Berndt et al., 2014; Chao et al., 2015; Lewis et al., 2015; Newland et al., 2015a; Sheps et al., 2017; Liu et al., 2017) and anti-CH3CHOO (Lin et al., 2016b). Theoretical calculations (Vereecken et al., 2017) have predicted the ratio of the SCI + (H2O)2 : SCI + H2O rate constants, k5/k3, of larger and more substituted SCI to be of a similar order of magnitude as for CH2OO (i.e. 1.5–2.5 × 103).

SCIs can also undergo unimolecular isomerisation or decomposition in competition with bimolecular reactions. This is likely to be a significant atmospheric sink for syn-SCIs because of their slow reaction with water vapour (e.g. Huang et al., 2015). Unimolecular reactions of syn-CI/-SCIs are dominated by a 1,4-H shift, forming a vinyl hydroperoxide (VHP) intermediate (Niki et al., 1987; Rickard et al., 1999; Martinez and Herron, 1987; Johnson and Marston, 2008; Kidwell et al., 2016). Decomposition of the VHP formed in this process is an important non-photolytic source of OH, HO2 and RO2 in the atmosphere (Niki et al., 1987; Alam et al., 2013; Kidwell et al., 2016), which can also lead to secondary organic aerosol formation (Ehn et al., 2014). Unimolecular reactions of the anti-CI/SCIs are thought to be dominated by a 1,3-ring closure, the acid ester channel, in which the CI/SCI decomposes, through rearrangement to a dioxirane intermediate, producing a range of daughter products and contributing to the observed overall HOx radical yield (Kroll et al., 2002; Johnson and Marston, 2008; Alam et al., 2013). Alkene+O3⟶k1ϕSCI+1-ϕCI+RCHOSCI+SO2⟶k2SO3+RCHOSCI+H2O⟶k3productsSCI⟶kdproductsSCI+acid⟶k5productsSCI+(H2O)2⟶k6products Decomposition of the simplest SCI, CH2OO, is slow (< 10 s-1) and is not likely to be an important sink in the troposphere (e.g. Newland et al., 2015a; Chhantyal-Pun et al., 2015). This decomposition occurs primarily via rearrangement through a “hot” acid species, which represents the lowest accessible decomposition channel (Gutbrod et al., 1996; Alam et al., 2011; Chen et al., 2016). However, recently determined unimolecular reaction rates of larger syn-SCIs are considerably faster. Newland et al. (2015a) reported unimolecular reaction rate constants for syn-CH3CHOO of 348 (±332) s-1 and for (CH3)2COO of 819 (±190) s-1 (assuming k(syn-CH3CHOO+SO2)= 2.9 × 10-11 cm3 s-1 (Sheps et al., 2014) and k((CH3)2COO + SO2)= 1.3 × 10-10 cm3 s-1 (Huang et al., 2015), respectively). Smith et al. (2016) measured the unimolecular decomposition rate of (CH3)2COO to be 269 (±82) s-1 at 283 K, increasing to 916 (±56) s-1 at 323 K and suggesting the rate to be fast and highly temperature dependent. Novelli et al. (2014) estimated a significantly slower decomposition rate for syn-CH3CHOO of 20 (3–30) s-1 from direct observations of OH formation, while Fenske et al. (2000) estimated the decomposition rate of CH3CHOO (i.e. a mix of syn- and anti-conformers) produced from ozonolysis of trans-but-2-ene to be 76 s-1 (accurate to within a factor of 3).

Monoterpenes are volatile organic compounds (VOCs) with the general formula C10H16 and are emitted by a wide range of vegetation, but particularly from boreal forests. Total global monoterpene emissions are estimated to be 95 (±3) Tg yr-1 (Sindelarova et al., 2014) – roughly 13 % of total non-methane biogenic VOC emissions. Monoterpene emissions are dominated by α-pinene, which accounts for roughly 34 % of the total global emissions, while β-pinene and limonene account for 17 and 9 % respectively (Sindelarova et al., 2014). Monoterpenes (mainly α-pinene and limonene) are also present in indoor environments, in significant amounts where cleaning products and air fresheners are in routine use (of the order of 100 s of ppbv) (e.g. Singer et al., 2006a, b; Sarwar and Corsi, 2007), and where their ozonolysis products can affect indoor chemistry and health (e.g. Rossignol et al., 2013; Shallcross et al., 2014).

Monoterpenes are highly reactive due to the presence of (often multiple) double bonds. The oxidation of monoterpenes yields a wide range of multi-functional gas-phase and aerosol products. This process can be initiated by OH and NO3 radicals or by O3, with ozonolysis having been shown to be particularly efficient at generating low-volatility products that can form SOA, even in the absence of sulfuric acid (e.g. Ehn et al., 2014; Kirkby et al., 2016). These highly oxygenated secondary products have received considerable attention in recent years because of their role in affecting the climate through absorption and scattering of solar radiation (the direct aerosol effect). They can also increase cloud condensation nuclei concentrations, which can change cloud properties and lifetimes (the indirect aerosol effect). They have also been shown to have a wide range of deleterious effects on human health (e.g. Pöschl and Shiraiwa, 2015).

The ozonolysis reaction for monoterpenes is expected to follow a similar initial process to that of smaller alkenes, with cyclo-addition at a double bond giving a primary ozonide (POZ), followed by rapid decomposition of the POZ to yield a CI and a carbonyl (Scheme 1). Stabilisation of the large POZs formed in monoterpene ozonolysis is expected to be negligible (Nguyen et al., 2009a). However, a major difference in ozonolysis at endocyclic bonds is that, on decomposition of the POZ, the carbonyl oxide and carbonyl moieties are tethered as part of the same molecule, providing the potential for further interaction of the two. These can react together to form secondary ozonides (SOZ), which may be stable for several hours (Beck et al., 2011). However, while this has been shown to be potentially the major fate in the atmosphere for SCIs derived from sesquiterpenes (C15H24) (e.g. Nguyen et al., 2009b; Beck et al., 2011; Yao et al., 2014), formation of SOZ is predicted to be small for monoterpene-derived SCIs because of the high ring strain caused by the tight cyclisation (e.g. Nguyen et al., 2009b). Chuong et al. (2004) predicted formation of a SOZ to become the dominant atmospheric fate for SCIs formed in the ozonolysis of endocyclic alkenes with a carbon number between 8 and 15, while Vereecken and Francisco (2012) suggested that internal SOZ formation is likely to be limited to product rings containing six or more carbons due to ring strain.

No studies have yet directly determined the reaction rates of the large SCIs produced from monoterpene ozonolysis with SO2 (or any other trace gases). This is owing to the complexities of synthesising and measuring large SCI. However, Ahrens et al. (2014) concluded that the reaction of the C9-SCI formed in β-pinene ozonolysis with SO2 is as fast as that determined by Welz et al. (2012) and Taatjes et al. (2013) for CH2OO and CH3CHOO respectively (ca. 4 × 10-11 cm3 s-1) by fitting to the decay of SO2 in the presence of the ozonolysis reaction. Mauldin III et al. (2012) calculated significantly slower reaction rates for an additional oxidant (assumed to be SCI) derived from α-pinene and limonene ozonolysis, with k(SCI + SO2) determined to be 6 ×  10-13 and 8 × 10-13 cm3 s-1 for α-pinene and limonene-derived SCIs respectively. However, it seems likely that the rates calculated by Mauldin III et al. (2012) may be substantially underestimated due to the assumption of a very long SCI lifetime (0.2 s) in experiments that were performed at 50 % RH. The calculated rates scale linearly with SCI lifetime, and based on reaction rates of smaller SCIs with H2O (reported since the Mauldin III et al. work, e.g. Taatjes et al., 2013), it seems likely that the lifetime of the SCI in their experiments would have been more like 0.1–2 × 10-2 s, increasing the calculated rate constants by more than an order of magnitude and bringing them into much closer agreement with the rates reported by Ahrens et al. (2014).

Unimolecular reactions of the monoterpene SCIs are expected to proceed rapidly through the VHP route if hydrogen is available for a 1,4-H shift. Those SCIs that cannot undergo this rearrangement may undergo unimolecular reactions via the formation of the dioxirane intermediate, but this is expected to be a much slower process (Nguyen et al., 2009a). In contrast to smaller SCI, it has been observed experimentally and predicted theoretically that the VHP route will mainly lead to rearrangement into an acid (also yielding an OH radical) rather than decomposition of the molecule (e.g. Ma et al., 2008; Ma and Marston, 2008). As for the smaller alkenes, monoterpene ozonolysis has been shown to be a source of HOx (e.g. Paulson et al., 1997; Alam et al., 2013), predominantly via the VHP rearrangement. The MCMv3.3.1 (Jenkin et al., 2015) applies OH yields of 0.80, 0.35 and 0.87 for α-pinene, β-pinene and limonene respectively.

The EUPHORE facility is a 200 m3 simulation chamber used primarily for studying reaction mechanisms under atmospheric boundary layer conditions. Further details of the chamber set-up and instrumentation are available elsewhere (Becker, 1996; Alam et al., 2011), and a detailed account of the experimental procedure, summarised below, is given in Newland et al. (2015a).

Experiments comprised time-resolved measurements of the removal of SO2 in the presence of the monoterpene–ozone system as a function of humidity. SO2 and O3 abundance were measured using conventional fluorescence (reported precision ±1.0 ppbv) and UV absorption monitors (reported precision ±4.5 ppbv), respectively; alkene abundance was determined via FTIR spectroscopy. Experiments were performed in the dark (i.e. with the chamber housing closed; j(NO2)≤ 10-6 s-1), at atmospheric pressure (ca. 1000 mbar) and temperatures between 287 and 302 K. The chamber is fitted with large horizontal and vertical fans to ensure rapid mixing (ca. 2 min). Chamber dilution was monitored via the first-order decay of an aliquot of SF6, added prior to each experiment. Cyclohexane (ca. 75 ppmv) was added at the beginning of each experiment to act as an OH scavenger, such that SO2 reaction with OH was calculated to be ≤ 1 % of the total chemical SO2 removal in all experiments.

The experimental procedure, starting with the chamber filled with clean scrubbed air, comprised addition of SF6 and cyclohexane, followed by water vapour, O3 (ca. 500 ppbv) and SO2 (ca. 50 ppbv). A gap of 5 min was left prior to addition of the monoterpene to allow complete mixing. The reaction was then initiated by the addition of the monoterpene (ca. 400 ppbv for α-pinene and β-pinene, ca. 200 ppbv for limonene), and reagent concentrations followed for roughly 30–60 min; ca. 30–90 % of the monoterpene was consumed after this time, dependent on the reaction rate with ozone. Four α-pinene + O3, five β-pinene + O3 and five limonene + O3 experiments were performed in total, as a function of [H2O]. Each individual run was performed at a constant humidity, with humidity varied to cover the range of [H2O] = 0.1–19 × 1016 molecules cm-3, corresponding to an RH range of 0.1–28 % (at 298 K). Measured increases in [SO2] agreed with measured volumetric additions across the SO2 and humidity ranges used in the experiments (Newland et al., 2015a). The experimental raw data are available at 10.15124/4e9cd832-9cce-41c8-8335-c88cf32fe244 (Newland et al., 2013).

A range of different SCIs are produced from the ozonolysis of each of the three monoterpenes (see Schemes 2–4), each with their own distinct chemical behaviour (i.e. yields, reaction rates); it is therefore not feasible (from these experiments) to obtain data for each SCI independently. Consequently, for analytical purposes we necessarily treat the SCI population in a simplified (lumped) manner – see Sect. 2.2.2.

SCIs are assumed to be formed in the ozonolysis reaction with a yield φ (Reaction R1). They can then react with SO2, H2O, acids formed in the ozonolysis reaction or with other species present or they can undergo unimolecular decomposition under the experimental conditions applied (Reactions R2–R5). A fraction of the SCIs produced reacts with SO2. This fraction (f) is the loss rate of the SCIs to SO2 (k2[SO2]) compared to the sum of the total loss processes for the SCIs (Eq. 1): f=k2[SO2]k2SO2+k3H2O+kd+k5acid+L. Here, L accounts for the sum of any other chemical loss processes for SCIs in the chamber. With the exception of reaction with acids these loss processes are expected to be negligible, as discussed later. After correction for dilution and neglecting other (non-alkene) chemical sinks for O3, the following equation is derived. Corrections include reaction with HO2 (also produced directly during alkene ozonolysis; Alam et al., 2013; Malkin et al., 2010), which was indicated through model calculations to account for < 0.5 % of ozone loss under all the experimental conditions. dSO2dO3=ϕf

From Eq. (2), regression of the loss of ozone (dO3) against the loss of SO2 (dSO2) for an experiment at a given RH determines the product fφ at a given point in time. This quantity will vary through the experiment as SO2 is consumed and other potential SCIs co-reactants are produced, as predicted by Eq. (1). A smoothed fit was applied to the experimental data for the cumulative consumption of SO2 and O3, ΔSO2 and ΔO3, (as shown in Fig. 2) to determine dSO2/dO3 (and hence fφ) at the start of each experiment, for use in Eq. (2). The start of each experiment (i.e. when [SO2] ∼ 50 ppbv) was used, as this corresponds to the greatest rate of production of the SCI and hence the largest experimental signals (i.e. greatest O3 and SO2 rate of change; greatest precision), and is the point at which the SCI + SO2 reaction has the greatest magnitude compared with any other potential loss processes for either reactant species (see discussion below).

Other potential fates for SCIs include reaction with ozone (Kjaergaard et al., 2013; Vereecken et al., 2014, 2015; Wei et al., 2014; Chang et al., 2018), with other SCIs (Su et al., 2014; Vereecken et al., 2014), carbonyl products (Taatjes et al., 2012), acids (Welz et al., 2014) or with the parent alkene (Vereecken et al., 2014; Decker et al., 2017). Sensitivity analyses using the most recent theoretical predictions (Vereecken et al., 2015) indicate that the reaction with ozone is not significant under any of our experimental method, accounting for less than 1.5 % of SCI loss for anti-SCIs (based on anti-CH3CHOO) at the lowest RH (worst case) experiment. Generally, SCI loss to ozone is calculated to be < 1% for all SCI. Summed losses from reaction with SCI (self-reaction), carbonyls and alkenes are likewise calculated to account for < 1 % of the total SCI loss under the experimental conditions applied.

CH2OO and CH3CHOO have been shown to react rapidly (k= 1–5 × 10-10 cm3 s-1) with formic and acetic acid (Welz et al., 2014). In ozonolysis experiments, Sipilä et al. (2014) determined the relative reaction rate of acetic and formic acids with (CH3)2COO (i.e.k5/k2) to be roughly three. Organic acid mixing ratios in this work, as measured by FTIR, reached up to a few hundred ppbv, suggesting these will likely be a significant SCI sink in our experiments. We have therefore explicitly included reaction with organic acids in our analysis, incorporating the uncertainty arising from the (unknown) acid reaction rate constant, as described in Sect. 2.2.1.

The water dimer reactions of non-CH2OO SCIs are not considered in our analysis. The effect of the water dimer reaction with C10 and C9 SCIs (rather than the monomer) is expected to be minor at the maximum [H2O] (2 × 1017 cm-3) used in these experiments (< 30 % RH). Further, with analogy to the syn-/anti-CH3CHOO system, syn-SCI loss to the dimer (and monomer) will not become competitive at the highest [H2O] used here; for anti-SCI, the water monomer will already be removing the majority of the SCIs at the [H2O] at which the dimer would become a significant loss process. Hence the dimer reaction is deemed unimportant. For CH2OO, the reaction rates with water and the water dimer have been quantified in recent EUPHORE experimental studies, and the values from Newland et al. (2015a) are used in our analysis. Derivationofk(SCI+H2O)/k(SCI+SO2)andkd/k(SCI+SO2)

As noted above, a range of different SCIs are produced from the ozonolysis of the three monoterpenes (see Schemes 2–4), each with their own distinct chemical behaviour, which, treated individually, introduce too many unknowns (i.e. yields, reaction rates) for explicit analysis. Consequently for analytical purposes we treat the SCI population in a simplified (lumped) manner:

Firstly, we use the simplest model possible, assuming that a single SCI is formed in each ozonolysis reaction (Eq. 3). f[SO2]=SO2+k3k2H2O+kdk2+k5k2[acid]-1

In a second model, for each monoterpene, the SCIs produced are assumed to belong to one of two populations, denoted SCI-A and SCI-B. These two populations are split according to the observation that the decomposition rates and reaction rates with water for the smaller SCIs (CH3CHOO) have been predicted theoretically (Ryzhkov and Ariya, 2004; Kuwata et al., 2010; Anglada et al., 2011) and shown experimentally (Taatjes et al., 2013; Sheps et al., 2014; Newland et al., 2015a) to exhibit a strong dependence on the structure of the molecule. The syn-CH3CHOO conformer, which has the terminal oxygen of the carbonyl oxide moiety in the syn-position to the methyl group, has been shown to react very slowly with water and to readily decompose, via the hydroperoxide mechanism, whereas the anti-CH3CHOO conformer, with the terminal oxygen of the carbonyl oxide moiety in the anti-position to the methyl group, has been shown to react fast with water and is not able to decompose via the hydroperoxide mechanism. Vereecken and Francisco (2012) have shown that all SCIs studied theoretically with an alkyl group in the syn-position have reaction rates with H2O of k < 4 × 10-17 molecule cm3 s-1 (and for SCIs larger than acetone oxide, k < 8 × 10-18 molecule cm3 s-1).

We thus define two populations, assuming SCI-A (i.e. SCIs that exhibit chemical properties of the anti-type SCI) to react fast with water and not to undergo unimolecular reactions and SCI-B (i.e. SCIs that exhibit chemical properties of the syn-type SCI) to not react with water but to undergo unimolecular reactions. This simplification allows us to fit to the measurements using Eqs. (4) and (5), as shown below. The total SCI yields are determined by our experiments at high SO2, and the relative yields of SCI-A and SCI-B are determined from fitting to Eq. (5). These relative yields are then compared to those predicted from the literature.

In this model, f=γAfA+γBfB, where γ is the fraction of the total SCI yield (i.e. γA+γB= 1). fA and fB are the fractional losses of SCI-A and SCI-B to a reaction with SO2. Adapting Eq. (1) to include the two SCI species gives Eq. (4), where k5[acid] accounts for the SCI + acid reaction (see discussion of reaction rate constants below). f=γAk2A[SO2]k2ASO2+k3H2O+k5Aacid+γBk2B[SO2]k2BSO2+kd+k5Bacid

Equation (4) can be rearranged to Eq. (5) and fitted according to f / [SO2] derived from the measurements. f[SO2]=γASO2+k3k2AH2O+k5Ak2Aacid+γBSO2+kdk2B+k5Bk2Bacid

Using values for γA and γB from the literature and varying the assumed values of the reaction of SCIs with acid (k5) allows us to determine k3/k2A and kd/k2B.

The assumptions made here allow analysis of a very complex system. However, a key consequence is that the relative rate constants obtained from the analysis presented here are not representative of the elementary reactions of any single specific SCI isomer formed, but rather represent a quantitative ensemble description of the integrated system, under atmospheric boundary layer conditions, which may be appropriate for atmospheric modelling. Additionally our experimental approach cannot determine absolute rate constants (i.e. values of k2, k3, kd) in isolation and is limited to assessing their relative values, measured under atmospheric conditions, which may be placed on an absolute basis through use of an external reference value (here the SCI + SO2 rate constant).

Figure 1 shows the lower limit to the SCI yield, φmin, for the three monoterpenes, determined from fitting Eq. (5) to the experimental data. This gives values of 0.16 (±0.01) for α-pinene, 0.53 (±0.01) for β-pinene and 0.20 (±0.01) for limonene. These φmin values were then corrected as described in Sect. 2.2.2 using the k3/k2 and kd/k2 values determined from the measurements shown in Figs. 3–5 using Eq. (4). The corrected yields, φSCI, are 0.19 (±0.01) for α-pinene, 0.60 (±0.03) for β-pinene and 0.23 (±0.01) for limonene. Uncertainties are ±2σ and represent the combined systematic (estimated measurement uncertainty) and precision components. Literature yields for SCI production from monoterpene ozonolysis are summarised in Table 1.

The value derived for the total SCI yield from α-pinene in this work of 0.19 agrees within the uncertainties, with a value of 0.15 (±0.07) reported by Sipilä et al. (2014) and a value of 0.20 applied in the MCMv3.3.1.

The total SCI yield from β-pinene derived in this work, 0.60, agrees reasonably well with the recent experimental work of Ahrens et al. (2014), who derived a total SCI yield of 0.50 (0.40 for the sum of CI-1 and CI-2 and 0.10 for CH2OO, which is assumed to be formed almost completely stabilised). The MCMv3.3.1 applies a total SCI yield of 0.25, of which 0.10 is a C9-CI and 0.15 is CH2OO. Earlier studies also tended to derive lower total SCI yields ranging from 0.25 to 0.27 (Hasson et al., 2001; Hatakeyama et al., 1984).

The total SCI yield from limonene derived in this work, 0.23 (±0.01) agrees with the recently determined yield from Sipilä et al. (2014) of 0.27 (±0.12). Leungsakul et al. (2005) derived a somewhat higher yield of 0.34, while the MCMv3.3.1 applies a lower yield of 0.135.

Figure 2 shows the loss of SO2 as ozone is consumed by reaction with the monoterpene for each of the three systems. Box modelling results suggest that > 99 % of this SO2 removal is caused by reaction with SCIs produced in the alkene–ozone reaction (rather than e.g. reaction with OH, which is scavenged by cyclohexane). When the experiments are repeated at higher relative humidity, the rate of loss of SO2 decreases. This is as expected from Eq. (1) and suggests that there is competition between SO2 and H2O for reaction with the SCIs produced, in agreement with observations of smaller SCI, which demonstrate the same competition under atmospherically relevant conditions (Newland et al., 2015a, b).

However, as the relative humidity is increased further, the SO2 loss does not fall to (near) zero as would be expected from Eq. (1). This suggests that at high [H2O] the amount of SO2 loss becomes less sensitive to [H2O]. This is most likely due to there being at least two chemically distinct SCI species present. This behaviour was previously observed for CH3CHOO by Newland et al. (2015a) and fits with the current understanding that the reactivity of SCIs is structure dependent.

To recap Sect. 2.2.1, the analysis presented here considers two models to fit the observations. The first of these (Eq. 3) assumes the formation of a single SCI species, which, in addition to reacting with SO2, can react with water, undergo unimolecular reaction or react with acid. It is clearly evident from Figs. 3–5 that this model does not give a good fit to the observations for any of the monoterpene systems studied. Therefore, the results of this (single SCI) approach are not discussed explicitly hereafter. The second of the models (Eq. E5) assumes the formation of two lumped, chemically distinct populations of SCI, denoted SCI-A and SCI-B. SCI-A is assumed to react fast with H2O and to have minimal decomposition. Conversely, SCI-B is assumed to have a negligible reaction with water under the experimental conditions applied but to undergo rearrangement via a VHP. We use a least squares fit of Eq. (5) to the data to determine the values of k3/k2 and kd/k2. This approach fits the data well (Figs. 3–5) for all 3 monoterpenes and represents the overall attributes of the SCIs that formed but as noted, does not represent an explicit determination of individual conformer-dependent rate constants.

The theory-based rate coefficients show one pinonaldehyde oxide, CI-1b, with a rate of reaction with water that is significantly faster than the remaining α-pinene-derived CIs. Comparing this rate to the experimental data shows that CI-1b corresponds to SCI-A, with matching rate coefficients within an order of magnitude, i.e. within the expected uncertainty. We thus deduce that SCI-A is CI-1b. The remaining pinonaldehyde oxides, CI-1a, CI-2a and CI-2b, react predominantly through unimolecular reactions, in which theory-based rate coefficients range from 60 to 600 s-1. All are within a factor of 4 of the experimentally derived population-averaged rate of 240 ± 44 s-1, i.e. matching within the uncertainty margins. The unimolecular rate coefficients of this set of CIs are sufficiently close that it is not feasible to separate these in the experimental data, so we can only conclude that SCI-B in the α-pinene ozonolysis experiments may consist of a mixture of C-1a, CI-2a and CI-2b.

The theoretical analysis for nopinone oxides shows one isomer, SCI-4, that has a fast rate of reaction with water, but a slow unimolecular isomerisation, while the other isomer, SCI-3, shows a fast unimolecular decomposition. These can thus be unequivocally equated to the experimentally obtained SCI-A and SCI-B, respectively, inasmuch as the yield of CH2OO is minor. The predicted rate coefficients are within the expected uncertainty intervals of the theoretical data, a factor of 5 for the unimolecular rates and an order of magnitude for the reaction with H2O.

The experimental rate measurements are defined relative to the reaction rate with SO2; the value adopted for the k(SCI + SO2) reaction therefore influences the derived rate coefficient values. Ahrens et al. (2014) directly measured the SO2 rate coefficient of the longest-lived SCI (SCI-4) to be ∼ 4 × 10-11 cm3 s-1, but for SCI-3 we assume a similar rate coefficient as syn-CH3CHOO + SO2 determined by Sheps et al. (2014) of 2.9 × 10-11 cm3 s-1. Nopinone oxides are bicyclic compounds, with a bulky dimethyl-substituted 4-membered ring adjacent to the carbonyl oxide moiety. To examine the potential impact of steric hindrance on the SCI + SO2 reaction, we characterised all sulfur-substituted secondary ozonides (S-SOZ) formed in this reaction (Kuwata et al., 2015; Vereecken et al., 2012). We find that the tricyclic S-SOZ shows very little interaction between the sulfur-bearing ring and the β-pinene substituents, and little change in the ring strain. The energies of the S-SOZ adducts relative to the SCI + SO2 reactants thus remain very similar to that of CH2OO, CH3CHOO or (CH3)2COO, confirming the quality of our selection of reference rate coefficients.

Of the six non-CH2OO CIs formed in limonene ozonolysis, CI-5b was predicted to have a fast reaction rate with H2O; its oxide substitution patterns is similar to pinonaldehyde oxide CI-1b. The SAR-predicted rate coefficient of CI-5b + H2O is within a factor of 2 of the experimentally derived k3 value for SCI-A, such that we can equate SCI-A to CI-5b with confidence. The SCI-B set of Criegee intermediates then contains the summed population of the remaining five CIs, all of which react slowly with H2O. The SAR-predicted unimolecular decay rate coefficients range from 15 to 700 s-1, all within a factor of 9 of the experimentally obtained kd= 130 s-1; it should be noted that for limonene-derived CIs, no explicit theoretical calculations are available, and the SAR-predictions carry a somewhat larger uncertainty. We have performed an exhaustive characterisation of the conformers of CI-5b. The most stable conformers show an internal complex formation between the oxide moiety and the carbonyl group, similar to those characterised for the bimolecular reaction of CIs with carbonyl compounds (Jalan et al., 2013; Wei et al., 2015). The theoretical study by Jiang et al. (2013) on limonene ozonolysis appears to have omitted internal rotation and cannot be compared directly. It seems likely that the limonene-derived CIs can thus easily undergo internal SOZ formation, which is thought (Vereecken and Francisco, 2012) to be entropically unfavourable, but has a low barrier to reaction. For α-pinene, a similar internal complex formation and SOZ ring closure is not as favourable due to the geometric limitations enforced by the 4-membered ring.

A large number of transition state conformers for CI-5b + H2O were characterised, though no exhaustive search was completed. The energetically most favourable structures show interaction between the carbonyl group and the H2O co-reactant as it adds onto the carbonyl oxide moiety. Similar stabilising interactions between the carbonyl moiety and the carbonyl oxide moiety were reported recently in cyclohexene-derived CIs (Berndt et al., 2017). This interaction thus lowers the barrier to a reaction, though it is currently unclear whether it enhances the reaction rate, e.g. compared to the α-pinene-derived CI-1b, as these hydrogen-bonded structures are entropically not very favourable. The intra-molecular interactions with heterosubstituents could be investigated in future work.

A global atmospheric modelling study was performed using the GEOS-Chem chemical transport model (as described in Sect. 4) to examine the global monoterpene-derived SCI budget and the contribution of these SCIs to gas-phase SO2 oxidation. The existing chemistry scheme in the model is supplemented with monoterpene SCI chemistry based on the experimental results described in Sect. 5 and in Table 5. It should be noted here that this modelling study focuses on the chemical impacts of monoterpene SCIs formed from ozonolysis reactions only. No chemistry for other SCIs derived from isoprene and/or other (smaller) alkenes are incorporated in the adapted model chemical scheme.

The monoterpene emissions in GEOS-Chem are taken from MEGAN v2.1 (Guenther et al., 2012). The scheme emits seven monoterpenes: α-pinene, β-pinene, limonene, myrcene, ocimene, 3-carene and sabinene. The monoterpenes are oxidised within the model by OH, NO3 and O3 at rates shown in Table S1. Reaction with O3 leads to the production of monoterpene-specific SCI. Reactions with OH and NO3 do not lead to the formation of any products, with the reactions only acting as a sink for the monoterpene and the respective oxidant. The SCI yields from the ozonolysis of α-pinene, β-pinene and limonene are derived from the experimental work presented here. SCIs from each monoterpene are split into SCI-A and SCI-B as defined in previous sections. For the other four monoterpenes emitted, the SCI yields and kinetics are derived based on the similarity of the structure to one of the species studied here or previously in the literature. The main SCIs produced in the ozonolysis of myrcene and ocimene are expected to be acetone oxide ((CH3)2COO) or 4-vinyl-5-hexenal oxide (CH2CHC(CH2)CH2CH2CHOO), since ozone has been suggested to react predominantly at the internal double bond (∼ 97 % for myrcene, ∼ 90 % for ocimene Baker et al., 2004). The SCI yield is taken to be 0.30, similar to that of (CH3)2COO from 2,3-dimethyl-but-2-ene ozonolysis (Newland et al., 2015a). However, this may be an underestimation since it has been predicted that stabilisation of small CIs increase with the size of the carbonyl co-product, as this co-product can take more of the nascent energy of the primary ozonide on decomposition due to a greater number of degrees of freedom available (Nguyen et al., 2009a; Newland et al., 2015b). Sabinene is a bicyclic monoterpene with an external double bond and hence is treated like β-pinene. This assumption is backed up by recent theoretical work (Wang and Wang, 2017), who predict similar behaviour from sabinene-derived SCIs to the predicted behaviour from β-pinene SCIs by Nguyen et al. (2009a). They predict a SCI yield between 24 and 64 %. 3-carene is a bicyclic monoterpene with an internal double bond and is treated like α-pinene.

Figure 7 shows the annually averaged total SCI burden from monoterpene ozonolysis in the surface layer in the GEOS-Chem simulation. A number of interesting features are apparent from this figure and the associated information is given in Table 6:

i.

The highest annually averaged monoterpene SCI concentrations are found above tropical forests.

Annual global monoterpene emissions are dominated by the tropics (Fig. S1 in the Supplement), accounting for > 90 % during the Northern Hemisphere winter months (November–April) and 70 % even during the peak emissions from the northern boreal region during June and July (Sindelarova et al., 2014). Despite annually averaged surface ozone mixing ratios being roughly a factor of 2 higher in the northern middle to high latitudes, monoterpene SCI production is still dominated by the tropics. Annually averaged surface monoterpene SCI concentrations across the northern boreal regions are < 2 × 103 cm-3; during the summer months (JJA) this value rises to 2–5 × 103 cm-3.

More than 97 % of the total monoterpene-derived SCIs are SCI-B (Table 6). This is because typical water vapour concentrations in the tropics are > 5.0 × 1017 cm-3. This gives SCI-A removal rates (i.e. k3[H2O]) of 2 × 103–1.5 × 105 s-1, whereas removal rates of SCI-B to unimolecular reactions have been determined here to be 1–3 orders of magnitude slower, of the order of 100–250 s-1. Since the loss of SCI-B is independent of temperature in the model, the highest SCI-B concentrations would be expected to be located in the regions of highest SCI-B production. Recent experimental studies (Smith et al., 2016) have demonstrated a strong temperature dependence for the unimolecular decomposition rate of (CH3)2COO between 283 and 323 K (269–916 s-1). Therefore, it may be that in reality there would be some geographical variation in the rate of unimolecular loss.

The monoterpene SCI-A + H2O reactions are expected to lead to high yields of both large (e.g. Ma et al., 2008; Ma and Marston, 2008) and small (measured in high yield in the experiments presented here) organic acids.

Figure 8 shows the seasonal removal of SO2 by reaction with monoterpene-derived SCI, as a percentage of total gas-phase SO2 oxidation in the surface layer. Monoterpene SCIs are most important (relative to OH) for SO2 oxidation over tropical forests, where they account for up to 60 % of the local gas-phase SO2 removal during DJF and MAM in some regions. The reasons for this are two-fold: firstly, the highest modelled monoterpene SCI concentrations are found in these regions (Fig. 7); additionally, OH concentrations in the model are low over these areas (Fig. S2). Historically there have been discrepancies between modelled and observed OH concentrations over tropical forests, with models appearing to underpredict [OH] by up to a factor of 10 (e.g. Lelieveld et al., 2008). It was proposed that this was due to missing sources of OH recycling during isoprene oxidation. During recent years there have been advances in our understanding of isoprene chemistry. GEOS-Chem v-09, used here, includes an isoprene OH recycling scheme largely based on Paulot et al. (2009a, b), with updates from Peeters et al. (2009), Peeters and Müller (2010) and Crounse et al. (2011, 2012), and evaluated in Mao et al. (2013). However, more recent experimental and theoretical work is not yet included.

Annually, monoterpene SCI oxidation accounts for 1.2 % of the gas-phase SO2 oxidation in the terrestrial tropics. This accounts for the removal of 2.9 Gg of SO2. Across the northern boreal forests, monoterpene SCIs contribute 0.7 % to gas-phase SO2 removal annually, removing 0.8 Gg of SO2. Globally, throughout the whole of the atmosphere, monoterpene SCIs account for only 0.5 % of gas-phase SO2 removal, removing 8.1 Gg of SO2 annually.

It is noted that MEGAN does not contain oceanic monoterpene emissions, which may increase the global importance of SCIs for gas-phase SO2 removal. Luo and Yu (2010) determined annual global oceanic α-pinene emissions to be 29.5 TgC using a top-down approach, with only 0.013 (Luo and Yu, 2010) – 0.26 (Hackenberg et al., 2017) TgC estimated using a range of bottom-up approaches; clearly there are large uncertainties in oceanic monoterpene emissions. At the upper end of this range they could potentially provide a similar contribution to SCI production and subsequent SO2 oxidation as monoterpenes emitted from the terrestrial biosphere. SCI production could more generally be further amplified by sources such as marine-derived alkyl iodine photolysis.

Blitz et al. (2017) recently calculated a revised SO2 + OH reaction rate (k1(1 bar N2)(298 K) = 5.8 × 10-13 cm3 s-1), based on experimental work and a master equation analysis, which is ∼ 40 % lower than the rate given in the most recent JPL data evaluation (Burkholder et al., 2015) ((k1(1 bar N2)(298 K) = 9.5 × 10-13 cm3 s-1), which is used in the GEOS-Chem model simulation. Figure S3 shows the increased influence of monoterpene-derived SCIs on gas-phase SO2 oxidation if the alternative SO2 + OH rate is used. This increased the impact of monoterpene SCIs to up to 67 % of gas-phase SO2 removal in regions of the tropical forests during DJF and MAM, with the contribution of monoterpene SCIs to global gas-phase SO2 oxidation increasing to 0.7 %.