Evaluation of isoprene nitrate chemistry in detailed chemical mechanisms

Isoprene nitrates are important chemical species in the atmosphere which contribute to the chemical cycles that form ozone and secondary organic aerosol (SOA) with implications for climate and air quality. Accurate chemical mechanisms are important for the prediction of the atmospheric chemistry of species such as isoprene nitrates in chemical models. In recent years, studies into the chemistry of isoprene nitrates have resulted in the development of a range of mechanisms available for use in the simulation of atmospheric isoprene oxidation. This work uses a 0-D chemical box model to assess the ability of three chemically detailed mechanisms to predict the observed diurnal profiles of four groups of isoprene-derived nitrates in the summertime in the Chinese megacity of Beijing. An analysis of modelled C₅H₉NO₅ isomers, including isoprene hydroperoxy nitrate (IPN) species, highlights the significant contribution of non-IPN species to the C₅H₉NO₅ measurement, including the potentially large contribution of nitrooxy hydroxyepoxide (INHE). The changing isomer distribution of isoprene hydroxy nitrates (IHNs) derived from OH-initiated and NO₃-initiated chemistry is discussed, as is the importance of up-to-date alkoxy radical chemistry for the accurate prediction of isoprene carbonyl nitrate (ICN) formation. All mechanisms under-predicted C₄H₇NO₅ as predominately formed from the major isoprene oxidation products, methyl vinyl ketone (MVK) and methacrolein (MACR). This work explores the current capability of existing chemical mechanisms to accurately represent isoprene nitrate chemistry in urban areas significantly impacted by anthropogenic and biogenic chemical interactions. It suggests considerations to be taken when investigating isoprene nitrates in ambient scenarios, investigates the potential impact of varying isomer distributions on iodide chemical ionisation mass spectrometry (I⁻-CIMS) calibrations, and makes some proposals for the future development of isoprene mechanisms.

1 Introduction

Isoprene (2-methyl-1,3-butadiene) is the most emitted non-methane volatile organic compound (NMVOC) globally and accounts for around 70 % of global biogenic volatile organic compound (BVOC) emissions (Guenther et al., 1995, 2006, 2012; Sindelarova et al., 2014). Isoprene is a dialkene and so is susceptible to oxidation in the atmosphere, initiated by the breaking of one, or both, of the double bonds (Wennberg et al., 2018). Some of the products of these reactions are organonitrates which are formed either by the reaction of isoprene with hydroxyl radicals (OH) and subsequent reactions with O₂ and NO or by the addition of the nitrate radical (NO₃) to one of isoprene's double bonds. The resulting nitrates are important for their influence on the NO_x, HO_x, and O₃ budgets, as well as the potential for the formation of secondary organic aerosol (SOA) by condensation or via further reactions (Emmerson and Evans, 2009; Bates and Jacob, 2019; Schwantes et al., 2019, 2020; Vasquez et al., 2020; Palmer et al., 2022)

This work focusses on three types of primary nitrates resulting from isoprene oxidation and one group of secondary nitrates. The primary C₅ nitrates are the isoprene hydroxynitrates (IHNs, Fig. 1), isoprene carbonyl nitrates (ICNs, Fig. 2), and isoprene hydroperoxy nitrates (IPNs, Fig. 3). The molecular formulae of IHN, ICN, and IPN are C₅H₉NO₄, C₅H₇NO₄, and C₅H₉NO₅, respectively. Throughout this work an upper-case sigma is used to denote the group of nitrates as well as any other species present in a chemical mechanism with the same molecular formula. For example, ΣIHN will refer to all isoprene hydroxynitrates as well as any other C₅H₉NO₄ species present in each chemical mechanism. A glossary of the terms used to refer to different nitrated species is given in the Supplement (Table S4).

Figure 1 OH-initiated and NO₃-initiated formation of IHN. The formation of 1,4-IHN is shown here; other IHN isomers, as well as additional reaction products, will also be formed.

Figure 2 NO₃-initiated formation of ICN. The formation of 1,4-ICN is shown here; other ICN isomers, as well as additional reaction products, will also be formed.

Figure 3 NO₃-initiated formation of IPN. The formation of 1,4-IPN is shown here; other IPN isomers, as well as additional reaction products, will also be formed.

IHN may be formed by OH-initiated oxidation followed by a peroxy radical (RO₂)+ NO reaction or by NO₃-initiated oxidation followed by RO₂ cross-reactions to form the alcohol group (Fig. 1). ICN is formed by NO₃-initiated oxidation followed by RO₂ cross-reactions, hydrogen abstraction from alkoxy radicals (RO) by oxygen (RO + O₂→ ICN + HO₂), or the reaction of IPN or isoprene dinitrates (IDNs) with OH (Fig. 2). IPN is formed by NO₃-initiated oxidation followed by RO₂+ HO₂ reactions (Fig. 3) (Jenkin et al., 2015; Wennberg et al., 2018; Novelli et al., 2021; Vereecken et al., 2021)

The final group of nitrates are secondary nitrates with the formula C₄H₇NO₅, corresponding to the hydroxycarbonyl nitrate structures shown in Fig. 4, which have been shown to be a major contributor to isoprene nitrates as measured by iodide chemical ionisation mass spectrometry (I⁻-CIMS) (Tsiligiannis et al., 2022). ΣC₄H₇NO₅ refers to the isoprene-derived nitrates as well as isomeric species present in the Master Chemical Mechanism (MCM) from other volatile organic compound (VOC) sources (Jenkin et al., 2015). There are several identified formation routes of C₄H₇NO₅, including the OH-initiated oxidation of methyl vinyl ketone (MVK) and methacrolein (MACR); NO₃-initiated oxidation of MVK and MACR; OH-initiated oxidation of IHN, IPN, and ICN; the ozonolysis of IHN; and the NO₃-initiated oxidation of hydroxycarbonyls (Fig. 5) (Jenkin et al., 2015; Praske et al., 2015; Schwantes et al., 2015; Wennberg et al., 2018; Tsiligiannis et al., 2022). Analysis of these multifunctional compounds is further complicated due to its secondary nature, as well as their potentially long atmospheric lifetime (Müller et al., 2014)

Figure 4 The four C₄H₇NO₅ species resulting from isoprene oxidation present in the MCM along with the additional isomeric compounds which complete the set of ΣC₄H₇NO₅.

Figure 5 Formation of C₄H₇NO₅ compounds. Only two isomers are shown here; other formation routes for these and other isomers are also present. Additional reaction products will also be formed.

Isoprene nitrates are often identified as major products of isoprene oxidation. For example, studies performed in the Forschungszentrum Jülich SAPHIR chamber identified a large range of organonitrates resulting from the NO₃-initiated oxidation of isoprene, including the primary products mentioned here (Wu et al., 2021; Brownwood et al., 2021). Chamber experiments performed at the California Institute of Technology have also highlighted the role of nitrates in the OH-initiated oxidation of isoprene (Schwantes et al., 2019; Vasquez et al., 2020). Such nitrates have also been identified in a range of ambient environments, from rural environments such as those in the south eastern United States to polluted urban environments such as the San Francisco Bay area (Ayres et al., 2015; Zaveri et al., 2020). Previous modelling studies that investigate isoprene nitrates under ambient conditions and their impacts on atmospheric chemistry are also widespread across polluted and less polluted environments, examining both speciated nitrates and the sum of total organic nitrates (Pratt et al., 2012; Xiong et al., 2015; Romer et al., 2016; Chen et al., 2018; Zare et al., 2018; Schwantes et al., 2020).

Isoprene nitrates have also been identified as significant species during the 2017 Atmospheric Pollution and Human Health in a Chinese Megacity (APHH) summer campaign in Beijing (Hamilton et al., 2021; Newland et al., 2021). There have been two previous box-modelling investigations focussed on the data collected during the APHH-Beijing intensive field observations (Reeves et al., 2021; Whalley et al., 2021). Whalley et al. (2021) focussed on radical chemistry and ozone formation, highlighting several inconsistencies between modelled radical species and relevant measurements. Reeves et al. (2021) investigated IHN and ICN speciation and demonstrated the value of speciated measurements of isoprene nitrates by identifying several instances where the modelled IHN isomer distribution was not consistent with their measured distribution. They also discussed issues around the simplified representations of ICN isomers with regards to the initial site of attack of NO₃ and the $E/Z$ stereochemistry of 1,4-ICN and 4,1-ICN. This paper uses similar box-modelling approaches as the previously discussed studies to assess the capabilities of three detailed atmospheric oxidation mechanisms for investigating the formation and losses of isoprene-derived nitrates in this anthropogenically and biogenically impacted environment. Key statistics for each mechanism are given in Table S1.

The first mechanism used here is the Master Chemical Mechanism v3.3.1 (MCM) (Jenkin et al., 2015). The MCM is a benchmark near-explicit chemical mechanism extensively used by the atmospheric science community in a wide variety of science and policy applications where chemical detail is required. Subsets of the MCM can be directly extracted for a wide variety of VOCs (mcm.york.ac.uk). However, due to the breadth of the MCM, some simplifications have been made when constructing the mechanism. The first major simplification is the use of lumped RO₂ reactions. This means that RO₂–RO₂ cross-reactions are not treated explicitly, and it is assumed that each RO₂ will react with any other RO₂ at the same rate, which helps to greatly reduce the complexity of mechanisms (Jenkin et al., 1997). In the case of isoprene, further assumptions are made. For example, NO₃-initiated oxidation of isoprene in the MCM is represented by only one isomer (NISOPO2).

Secondly, the full v5 isoprene oxidation mechanism taken from the Wennberg et al. (2018) review of gas-phase isoprene oxidation (henceforth, the Caltech mechanism) was used (Wennberg et al., 2018). This mechanism treats isoprene RO₂ cross-reactions explicitly, unlike the lumped-RO₂ approach of the MCM. This leads to issues when integrating the Caltech mechanism with the MCM subset for additional measured VOCs, as explained further in the methodology section. The Caltech mechanism aims to provide a more-up-to-date representation of reaction rates and products. For example, the Caltech mechanism provides four different nitrated RO₂ radicals resulting from NO₃ oxidation. The Caltech mechanism also introduces some reactions that are not found in the MCM, such as intramolecular RO₂ reactions.

Finally, the mechanism developed by Vereecken et al. (2021) and further expanded in Tsiligiannis et al. (2022) was used and is referred to as the FZJ mechanism (Vereecken et al., 2021; Tsiligiannis et al., 2022). This mechanism aims to expand on the Caltech mechanism by providing more comprehensive NO₃ chemistry, including the proposed formation of epoxide species from some alkoxy radical species, and additional chemistry relevant to C₄H₇NO₅ outlined in Tsiligiannis et al. (2022).

2 Methodology

2.1 Ambient measurements

The Beijing measurements used in this work were collected at ground level at the tower section of the Institute of Atmospheric Physics (IAP) in Beijing, China, between 1 and 18 June 2017 (Shi et al., 2019). The nitrates were measured using a Filter Inlet for Gases and Aerosols (FIGAERO) coupled to a time-of-flight iodide chemical ionisation mass spectrometer (I⁻-CIMS) which allows for the measurement of particle- and gas-phase species, although only the gas-phase data are used here as the particle-phase data were unavailable (Lopez-Hilfiker et al., 2014). Each nitrate was calibrated assuming the same sensitivity as trans-beta-IEPOX, though the potential role of calibration on the measured nitrate concentrations is discussed throughout this work (Hamilton et al., 2021). Other organic compounds were measured by proton transfer mass spectrometry (PTR-MS), selected ion flow tube mass spectrometry (SIFT-MS), and dual-channel gas chromatography with flame ionisation detection (DC-GC-FID) (Hopkins et al., 2011; Huang et al., 2016; Shi et al., 2019; Reeves et al., 2021). The sum of monoterpenes measured by PTR-MS and SIFT-MS was used to constrain alpha-pinene and limonene in the models, assuming each compound comprised 50 % of the total monoterpenes. Instruments used to measure organic species are summarised in Table S2, and the details of the instruments used to measure additional compounds can be found elsewhere (Whalley et al., 2010, 2018; Zhou et al., 2018; Shi et al., 2019; Hamilton et al., 2021; Whalley et al., 2021). Where species constraints were required in the modelling and multiple measurements were taken, the mean of all of the measurements was used. The scanning mobility particle sizer (SMPS) instruments used to calculate particle surface area as outlined in Sect. 2.3.1 are described in the Supplement.

2.2 Mechanisms

This investigation involved a comparison of three different isoprene oxidation mechanisms. The MCM subset for isoprene and the additional VOCs which were measured throughout the campaign and were available in the MCM (Table S2) was extracted directly from the MCM website (mcm.york.ac.uk) (Jenkin et al., 2015). The MCM inorganic chemistry scheme was used for all three mechanisms.

The Caltech mechanism was integrated with the MCM subset for the additional VOCs by producing lumped RO₂ cross-reactions using the approach outlined in Jenkin et al. (1997). For each RO₂ species where explicit reactions are given, the geometric mean of the self-reaction rate and the CH₃O₂ self-reaction rate was used. If a self-reaction was not specified, then the CH₃O₂ self-reaction rate was used. Branching ratios were then applied to the alcohol-forming, carbonyl-forming, and alkoxy-forming reactions according to Jenkin et al. (1997).

The FZJ mechanism was produced by adding the reactions outlined in Tsiligiannis et al. (2022) to the mechanism provided in Vereecken et al. (2021) and combining it with the MCM subset for measured non-isoprene species (Vereecken et al., 2021; Tsiligiannis et al., 2022).

Each of the mechanisms used in this work has been made available online (Hamilton et al., 2022).

2.3 Modelling approach

AtChem2, an open-source zero-dimensional box-model tool, was used in this work (Sommariva et al., 2020). The AtChem2 software is open source and freely available via https://github.com/AtChem (last access: 16 May 2022). A separate model was run for each day to avoid compounding errors carrying across multiple days of the model, for example, the uncertainty that may result from imperfect accounting for physical processes. NO₂, O₃, CO, SO₂, HONO, and formaldehyde, along with 29 primary VOCs for which data were available (Table S2), were all constrained to the 30 min averaged measured values throughout the campaign. NO was left unconstrained due to the potential for local NO emissions to result in mixing ratios unrepresentative of the larger area that is important for the formation of long-lived organic products such as organonitrates. Constraining to NO would result in unrealistically low NO₃ concentrations by increasing the rate of the NO₃+ NO reaction based on elevated NO concentrations. Temperature, pressure, boundary layer height, and relative humidity were also constrained to measured values. Photolysis values in the models were constrained to measured values where available (J_O1D, J_NO2, J_HONO, J_HCHOr, J_HCHOnr, J_NO3toNO, J_NO3toNO2, J_CH3CHO, J_CH3OCH3), and remaining photolysis rates were calculated according to the parameterisation used in the MCM and scaled based on the ratio of the calculated and measured J_NO2. The models consisted of a 24 h spin-up period followed by a further 24 h period. Constraints were made by duplicating the measured values for each day to provide a 48 h constraint of two repeated 24 h periods. The model output was then considered to be the model output in the second 24 h period of the model run. The model outputs were then concatenated to produce a time series across the whole period of interest.

To account for the deposition of species to surfaces, deposition reactions were added for all species. Each species was assigned a deposition velocity based on the functionality of that compound. Deposition velocities for H₂O₂, HNO₃, and O₃ were applied directly to each compound. Separate deposition velocities for organic hydroperoxides and organic nitrates were applied to compounds containing the hydroperoxide and nitrate functional groups. Organic acid species were assigned the formic acid deposition velocity, and a general oxidised VOC deposition was assigned to carbonyl- and alcohol-containing compounds. The rate of deposition was determined by dividing the assigned deposition velocity by the measured boundary layer height. All deposition velocities were taken from Nguyen et al. (2015) and are summarised in Table S3 (Nguyen et al., 2015). For multifunctional compounds, the largest deposition velocity of each of the functional groups present in the compound was selected from Table S3.

Additionally, a loss term was included for all species to account for mixing and ventilation. A diurnally varying ventilation rate was applied, where the rate was scaled such that the modelled glyoxal concentrations matched measurements, in a similar fashion to previous work (Whalley et al., 2021; Reeves et al., 2021). The sensitivity of the model results to this term is assessed in the “Model validation” section.

Particle phase processes

In the cases of ΣIHN and ΣIPN, an analysis of the impact of the particle-phase hydrolysis of 1,2-IHN and the reactive uptake of INHE is performed. For both of these cases, the rates of loss (k_IHN and k_IHNE for IHN hydrolysis and INHE uptake respectively) are calculated using Eq. (1). S_a is the aerosol surface area, as calculated for each model time step from scanning mobility particle sizer (SMPS) measurements; r_p is the effective particle radius calculated as a weighted median of the SMPS number measurements at each model time step; D_g is the gas-phase diffusion coefficient; ν is the mean molecular speed of IHN or INHE molecules in the gas phase; and γ is the reactive uptake coefficient. ν was calculated using Eq. (2), where R is the ideal gas constant (8.314 J K⁻¹ mol⁻¹), T is the measured temperature at each time step, and M_r is the molecular mass of the compound of interest (0.147 kg mol⁻¹ for IHN and 0.163 kg mol⁻¹ for INHE). A value of 1 × 10⁻⁵ m² s⁻¹ was used for D_g, as is assumed in Gaston et al. (2014) for IEPOX (Gaston et al., 2014). This method has been extensively used to calculate the rate of reactive uptake of IEPOX (Gaston et al., 2014; Riedel et al., 2016; Budisulistiorini et al., 2017).

$$\begin{array}{}\text{(1)}& {\displaystyle }{k}_{\mathrm{IHN}}={\displaystyle \frac{S_{\mathrm{a}}}{\frac{r_{\mathrm{p}}}{D_{\mathrm{g}}}+\frac{\mathrm{4}}{\mathit{\nu }{\mathit{\gamma }}_{\mathrm{IHN}}}}}\text{(2)}& {\displaystyle }\mathit{\nu }=\sqrt{{\displaystyle \frac{\mathrm{3}RT}{M_{\mathrm{r}}}}}\end{array}$$

An estimation of γ is complicated by the dependence on particle properties. In each case, results are shown for models where a range of γ values are assumed, between the limits of 0 and 1.

3 Results and discussion

3.1 Model validation

When comparing the measured and modelled NO mixing ratios, there is good agreement during the daytime, with the models deviating from the measurement by a maximum of around 2 times (Fig. 6a). The models do not reproduce the elevated night-time NO concentrations observed in Beijing; however, this night-time NO is likely the result of local emissions and so will have little impact on the chemistry that is the focus of this study. Figure S1 in the Supplement shows the good match between modelled NO and NO measured at an altitude of 100 m showing the ability of the model to predict NO away from local sources. This is further confirmed by NO₃ predictions provided by the models being, at most, 2.5 times over-predicted (Fig. 6b). There is also a slight under-prediction of NO₃ by a factor of around 0.4 during the afternoon.

Figure 6 A selection of measured values and model predictions of inorganic species left unconstrained in the models. Each line shows the mean value for each dataset, with the shaded area indicating 1 standard deviation above and below the mean. The values of NO from each model are all overlapping in panel (a).

HO_x predictions from the models are generally good. There is close agreement to the measured OH concentrations, although the modelled concentrations are around 0.5 times the measured values during the morning period (Fig. 6c). Daytime HO₂ concentrations are around 2 times higher than the measurement during the evening in all models (Fig. 6d), which is consistent with findings from Whalley et al. (2021), where a similar box-model run using the MCM over-predicted HO₂, particularly during low-NO periods. Whalley et al. (2021) hypothesises that the HO₂ over-prediction may be caused by unaccounted for RO isomerisation reactions that result in RO₂ radical formation without concurrent HO₂ formation (Whalley et al., 2021). While the Caltech mechanism and FZJ mechanism both include additional RO isomerisation reactions for isoprene, they inherit the MCM RO chemistry for other VOCs, including longer-chain VOCs that may be more susceptible to RO isomerisations, and so this could still be a reasonable hypothesis. The major contributors to RO composition in the models are aromatic species owing to their relatively long lifetimes.

When comparing the modelled and measured MVK and MACR mixing ratios, while daytime concentrations are at-most half of the measured values, the night-time concentrations fall far below the measurements (Fig. S2). This may be the result of the long lifetime of MVK and MACR, meaning there is a high background concentration not captured by the models. Alternatively, it may be due to imperfect accounting for physical processes such as mixing and ventilation within the models or a poor understanding of MVK + MACR chemistry in this environment. There may also be some role played by the conversion of isoprene hydroxy hydroperoxides to MVK + MACR on the metal inlets of the mass spectrometers resulting in an artificially increased measurement (Rivera-Rios et al., 2014; Newland et al., 2021). It is also important to consider the effect of upwind isoprene concentrations for all of the isoprene oxidation products discussed in this work. While our modelling makes use of isoprene concentrations measured at the same site as the product measurements, the upwind isoprene concentrations would be more useful for predicting the concentrations of isoprene oxidation products.

While a ventilation term is included in the models and is scaled to glyoxal concentrations, there is uncertainty as to its true rate and diurnal variability. As a test of the models' sensitivity to the ventilation rate, the rate was halved and doubled in two separate tests (Fig. S3). The halving of the ventilation rates resulted in an average change in concentration across the models run with each mechanism of 3.1, 1.5, 1.8, and 1.8 times for ΣC₄H₇NO₅, ΣIHN, ΣICN, and ΣIPN respectively. The average changes for doubling the ventilation rate were 0.32, 0.62, 0.60, and 0.56 for ΣC₄H₇NO₅, ΣIHN, ΣICN, and ΣIPN respectively. Xiong et al. (2015) aimed to reduce the impact of ventilation by analysing nitrates as ratios with the sum of MVK and MACR (Xiong et al., 2015). However, due to the differences in MVK + MACR predicted using each mechanism, using the MVK + MACR ratio as a proxy for the absolute concentration of the nitrates complicates the comparison of different mechanisms. As such, the analysis here involves the use of mixing ratios as opposed to the ratios relative to MVK + MACR. In order to analyse the average trends over a day within the modelled period, average diurnal plots are used to examine the modelled and measured data. The mean diurnals are used here, though use of the median had little impact on the diurnal values.

Comparison of the MVK + MACR predicted using each mechanism is consistent with the work presented in Vereecken et al. (2021). Figure. S2 shows that the Caltech mechanism produces the highest night-time MVK + MACR concentrations, with the MCM and FZJ mechanism producing the lowest night-time concentrations. The MCM does not include MVK + MACR formation from isoprene + NO₃ chemistry, while the Caltech mechanism does. The FZJ mechanism does include some MVK + MACR formation from isoprene NO₃ chemistry but also reduces the yield from ozonolysis reactions resulting in similar MVK + MACR yields between the MCM and FZJ mechanism in Vereecken et al. (2021) and in the night-time period of the models presented here. During the daytime, the FZJ models produce the lowest MVK + MACR concentrations as this adjusted ozonolysis chemistry becomes more significant.

Isoprene epoxydiols (IEPOX) are a significant contributor to isoprene-derived SOA and are significant isoprene oxidation products along with the isobaric isoprene hydroxy hydroperoxides (ISOPOOH) (Paulot et al., 2009; Surratt et al., 2010; Nguyen et al., 2014). Figure S4 shows the modelled and measured ΣIEPOX + ISOPOOH. All three mechanisms resulted in a large under-prediction of ΣIEPOX + ISOPOOH. As with MVK + MACR, this under-prediction may result from ventilation from the model being too rapid. As discussed throughout the paper, there may also be an issue of calibration for the I⁻-CIMS data. Although the I⁻-CIMS data are calibrated using IEPOX, all three models predict around half of the ΣIEPOX + ISOPOOH to be comprised of ISOPOOH. Accounting for particle uptake of IEPOX would only increase this fraction of ISOPOOH. Additionally, there are multiple IEPOX isomers, whereas these data are calibrated to only one isomer. More discussion of calibration issues is given in Sect. 3.2.1.

The volatility of the nitrate species was assessed in order to determine the potential impact of condensation to the particle phase. An equilibrium partitioning approach was taken, as described in Mohr et al. (2019). This resulted in the common logarithm of saturation concentrations in units of molecules per cubic centimetre (log(C_sat)) of between 4.0 and 5.3, revealing the high volatility of these compounds. As such, the condensation of these nitrates to the particle phase is assumed to be negligible, though this approach does not account for reactive uptake to particles.

3.2 ΣIHN (C₅H₉NO₄)

Throughout the day, the three mechanisms produce similar ΣIHN mixing ratios, at approximately half of the measured value (Fig. 7). Despite the absolute differences, the profile of modelled ΣIHN matches the measurement, with decreasing mixing ratios in the afternoon reflecting the titration of NO by increasing O₃ (Newland et al., 2021). Reeves et al. (2021) shows reasonable predictions of the major IHN isomer (1,2-IHN) made by their MCM-based model, whereas the modelled 4,3-IHN showed an over-prediction of around 2 times at midday (Reeves et al., 2021). This discrepancy is likely the result of different representations of physical processes in the models. The time series for modelled and measured ΣIHN is shown in Fig. S5.

Figure 7 Measured and modelled ΣIHN. Each line shows the mean value for each dataset, with the shaded area indicating 1 standard deviation above and below the mean.

Figure 8 shows the clear split between the daytime and night-time IHN speciation in all of the models. Figure 8 also demonstrates that the contribution of non-IHN species to ΣIHN in the models is very small, meaning a measured ΣIHN (C₅H₉NO₄) signal is likely to be a reasonable measurement of IHN. OH and NO₃ addition to isoprene favours the terminal carbon atoms, so OH oxidation followed by reaction with NO results in the nitrate group being formed either on one of the central positions or the remaining terminal carbon. This means OH-initiated oxidation predominantly forms 1,2-IHN, 4,3-IHN, E/Z-1,4-IHN, and E/Z-4,1-IHN. NO₃ addition results in the nitrate group being present on the terminal carbons, at the initial site of attack (Wennberg et al., 2018). This means NO₃-initiated oxidation predominantly forms 2,1-IHN, 3,4-IHN, E/Z-1,4-IHN, and E/Z-4,1-IHN.

Figure 8 Isomer composition of the modelled ΣIHN. OH-initiated IHNs are those primarily formed by OH chemistry, the 1,2-IHN and 4,3-IHN. NO₃-initiated IHNs are those primarily formed by NO₃ chemistry, the 2,1-IHN and 3,4-IHN. Mixed-source IHN is formed in large amounts by both routes, the E/Z-1,4-IHN and E/Z-4,1-IHN.

The night-time shows an enhancement in IHN species produced by NO₃ chemistry. This is most obvious in the MCM model, where all isoprene + NO₃ chemistry is channelled through just one isomer, ISOPCNO3. As such, ISOPCNO3 makes up very little of the daytime IHN but up to 80 % of night-time IHN just before sunrise. Similarly, the ΣIHN modelled using the Caltech mechanism and FZJ mechanism is almost exclusively comprised of ISOP1OH2N and ISOP3N4OH during the day, but there is a more even distribution at night, with major contributions from ISOP1N2OH, ISOP1N4OHt, and ISOP1N4OHc. The FZJ mechanism contains a reduced rate of ISOP1N2OH formation from ISOP1N2OO cross-reactions compared to the Caltech mechanism, hence the lower contribution of “NO₃-initiated IHN” to ΣIHN in the FZJ mechanism model.

Previous work has shown that the hydrolysis of 1,2-IHN occurs rapidly in the atmosphere (Vasquez et al., 2020; Liu et al., 2012). To test the sensitivity of our results to 1,2-IHN hydrolysis, loss reactions of 1,2-IHN were added to each of the mechanisms with a rate calculated as described in Sect. 2.3.1. Figure S6 shows the modelled ΣIHN using each of the mechanisms with 1,2-hydrolysis reactions included. Since the majority of daytime ΣIHN is comprised of 1,2-IHN, removal of this compound can have a large effect on the modelled ΣIHN. A γ_IHN value of 1 removes most, but not all, of the 1,2-IHN, and a value of 0.1 brings modelled ΣIHN concentrations close to when the value is 1. Conversely, γ_IHN values below 0.01 only result in small changes to modelled ΣIHN compared to the base model where no IHN hydrolysis is included.

ΣIHN calibration

As previously noted, the I⁻-CIMS data presented here are calibrated relative to IEPOX, which results in two potential issues. Firstly, the sensitivity of I⁻-CIMS to the compounds of interest may be significantly different from the sensitivity to IEPOX, leading to a bias in the measurement. Secondly, if I⁻-CIMS has different sensitivities to the different isomers of a particular formula, the changing isomer distribution over time will result in a varying sensitivity to the entire $m/z$ signal as each isomer contributes more or less. For example, it has been previously shown that I⁻-CIMS is more sensitive to IHN isomers in which the NO₃ group is located close to the OH group, such as 4,3-IHN and Z-1,4-IHN. Isomers where the NO₃ and OH groups are not in close proximity, such as E-1,4-IHN, show much lower responses to iodide-adduct ionisation. (Lee et al., 2014). The “Mixed-source IHN” in Fig. 8 includes both E and Z isomers of 1,4-IHN and 4,1-IHN. Since there is a higher proportion of mixed-source IHN during the night in all models, the sensitivity of ΣIHN can be expected to be lower at night than during the day due to a higher proportion of E-1,4-IHN and E-4,1-IHN.

Lee et al. (2014) report sensitivity values for IEPOX alongside the sensitivity values for three IHN isomers (4,3-IHN, Z-1,4-IHN, and E-1,4-IHN) (Lee et al., 2014). Dividing the sensitivities of each of these isomers by the IEPOX sensitivity allows a relative sensitivity to be obtained for each. These relative sensitivities are 15.64, 14.62, and 0.9487 for 4,3-IHN, Z-1,4-IHN, and E-1,4-IHN respectively. Relative sensitivities for the remaining IHN isomers can be assigned based on the orientation of the OH and NO₃ groups (Xiong et al., 2015). A total ΣIHN sensitivity can then be estimated using the modelled isomer distribution from each set of models. Figure 9a shows the diurnally varying relative sensitivity for each of the models. The largest discrepancy between the models can be seen at night, resulting from the differing NO₃ chemistry in each mechanism. Taken together, the models indicate that I⁻-CIMS may be between 2.5 and 1.4 times less sensitive to ΣIHN during the night than during the day.

Figure 9 (a) Diurnal variation in the sensitivity of I⁻-CIMS to ΣIHN relative to IEPOX according to the isomer distribution predicted by each model. (b) The measured ΣIHN data adjusted using the relative sensitivity values from each mechanism.

Applying this relative ΣIHN sensitivity to the IEPOX calibrated data dramatically reduces the measured concentrations of ΣIHN, due to the high sensitivities of the majority of IHN isomers (Fig. 9b). It is interesting to note differing ΣIHN concentrations predicted using the isomer distribution from each mechanism. At midnight, the FZJ-adjusted ΣIHN data are around twice that of the Caltech-adjusted data. According to these adjusted ΣIHN data, all of the models would be over-predicting ΣIHN by around an order of magnitude. Even when comparing to the most extreme 1,2-IHN hydrolysis case previously presented, ΣIHN concentrations are over-predicted by 1.5 to 3 times compared to the adjusted I⁻-CIMS data. Additionally, the adjusted calibration factors change the shape of the ΣIHN diurnal, resulting in a second peak in mixing ratios at around 20:00 (all references to time are in local time). Using the isomer distribution predicted by the FZJ mechanism suggests that this second night-time peak could be as large as the midday peak.

The use of relative responses here aims to eliminate some issues associated with the direct comparison of data from different instruments but may not eliminate all of the unknown differences. Nevertheless, adjusting the measured ΣIHN in this way suggests that the perceived under-prediction in ΣIHN by all of the models may instead be a closer representation to the true ΣIHN concentrations, if not an over-prediction. IHN is the most widely studied of the nitrates presented here, and so the calibration correction can be applied quantitatively; however, the impact of calibration on the measured organonitrate concentrations must be considered throughout this work.

3.3 ΣIPN (C₅H₉NO₅)

The measured ΣIPN shows little diurnal variation (Fig. 10). Contrary to observations, all models produced strong diurnal profiles of ΣIPN. This is because the majority of IPN is formed through NO₃ oxidation of isoprene at night when there are few losses. The only losses of IPN in all mechanisms, besides the added deposition reactions, are photolysis reactions and the reaction with OH. The strong diurnal profile results in night-time mixing ratios being over-predicted by around 1.5 times and daytime mixing ratios being close to 0. Both the MCM and FZJ mechanism result in ΣIPN reaching a minimum at sunrise, slightly increasing throughout the day, before a rapid night-time increase. The daytime under-prediction of ΣIPN may be indicative of mixing in the models being overestimated. The time series for modelled and measured ΣIPN is shown in Fig. S7. The data presented in Fig. S7 show that there is substantial noise in the ΣIPN data, which may also mask diurnal trends and indicate that the ΣIPN concentrations are close to the instrument's detection limit for these compounds.

Figure 10 Measured and modelled ΣIPN (a). Each line shows the mean value for each dataset, with the shaded area indicating 1 standard deviation above and below the mean.

While none of the mechanisms include NO₃ or O₃ oxidation of IPN, the Wennberg et al. (2018) review of isoprene chemistry does list estimated reaction rates of IPN, ICN, and IHN with NO₃, O₃, and OH (Wennberg et al., 2018). Figure S8 shows the average proportional night-time chemical loss for IHN, IPN, and ICN calculated using the rates given in Wennberg et al. (2018) and the measured OH, O₃, and NO₃ concentrations between 20:00 and 05:00. For the IPN isomers, OH oxidation accounts for the majority of the chemical loss of IPN at night, with around 10 %–15 % being lost to reaction with NO₃. Reaction with O₃ also makes up a substantial fraction of the chemical loss in the 1,4-IPN and 4,1-IPN isomers, though OH is still the major sink. Since OH oxidation is included in the mechanisms, then the majority of the chemical losses should be captured by the models. Physical processes also dominate the losses of ΣIPN at night, so the addition of more chemical losses would not have a large impact on ΣIPN concentrations.

To understand the trends in ΣIPN, it is important to consider the multiple isomeric (non-IPN) species present in each of the mechanisms which can make up a large proportion of the modelled ΣIPN (i.e. species with the formula C₅H₉NO₅). The most significant isomers of IPN are C51NO3, originally from the MCM and present in all mechanisms; C524NO3, originally from the MCM and also present in the FZJ mechanism; ISOP1N23O4OH, present in the Caltech mechanism and FZJ mechanism; and ISOP1N253OH4OH, present in the Caltech mechanism (Fig. S9).

C51NO3 is a nitrated hydroxy carbonyl compound in the MCM with formation routes from isoprene, as well as from hydrocarbons such as pentane. C524NO3 is an isoprene OH oxidation product from the MCM. In the MCM and FZJ mechanism models, C51NO3 and C524NO3 make up the majority of modelled ΣIPN composition during the daytime (Fig. S10). These are the species responsible for the slight increase in ΣIPN throughout the day in the MCM and FZJ mechanism models. C51NO3 and C524NO3 production from isoprene is not included in the Caltech mechanism, and the only formation routes to C51NO3 are from non-isoprene species. As such, C51NO3 and C524NO3 only make a small contribution to total ΣIPN in the Caltech mechanism model, and the daytime increase is not present.

ISOP1N253OH4OH is only present in the Caltech mechanism and is initially formed from an intramolecular H shift of the 1,4 isoprene alkoxy nitrate (INO), ISOP1N4O. The Caltech mechanism does not contain any loss reactions for this species, which may account for its moderate contribution to modelled night-time ΣIPN (Fig. S10). This INO H-shift pathway is not included in the FZJ mechanism, and so ISOP1N253OH4OH is not present.

ISOP1N23O4OH is a nitrated hydroxyepoxide that was proposed, alongside other positional isomers which are produced by the models in lower amounts, as a product of IPN OH oxidation by Schwantes et al. (2015), where it is termed isoprene nitrooxy hydroxyepoxide (INHE) (Schwantes et al., 2015). While the formation of INHE from IPN is present in the Caltech mechanism, epoxidation reactions from alkoxy radicals that are predicted in Vereecken et al. (2021) result in much more INHE production in the FZJ mechanism model. The FZJ mechanism model results predict that at midnight, around half of the total ΣIPN is composed of INHE (Fig. 11). If such large concentrations of these epoxides are produced, then this could have a significant impact on SOA formation via reactive uptake in a similar fashion to IEPOX (Paulot et al., 2009; Surratt et al., 2010; Schwantes et al., 2015; Hamilton et al., 2021).

Figure 11 Isomer composition of the modelled ΣIPN as a percentage of total ΣIPN. “Other” is comprised of ISOP1N253OH4OH, C530NO3, PPEN, C524NO3, C51NO3, and C5PAN4.

In order to assess the potential for reactive uptake of INHE on the modelled ΣIPN, loss reactions for each of the four INHE isomers in the FZJ mechanism were added to the mechanism and the models rerun. The rate coefficient for the reactive uptake of INHE (k_INHE) was calculated as described in Sect. 2.3.1. Figure S11 shows the modelled ΣIPN produced by a set of models for which a range of γ_INHE was assumed, between the limits of 0 and 1. When γ_INHE=1 and γ_INHE=0.1, almost all of the INHE is removed from the gas phase at any time, which brings the modelled night-time concentrations of ΣIPN to around two-thirds of the measured value. When γ_INHE=0.01, the modelled night-time ΣIPN is reasonably in line with the measurements between 20:00 and 00:00, after which the modelled concentrations fall with the diurnal profile explained previously. γ_INHE=0.001 results in modelled concentrations close to the values without any particle uptake. Previous estimations of the reactive uptake coefficient of IEPOX (γ_IEPOX) usually range between 7 × 10⁻² and 2 × 10⁻⁴, though measurements have been made as low as 9 × 10⁻⁷ (Gaston et al., 2014; Riedel et al., 2015; Budisulistiorini et al., 2017).

As with all of the nitrates investigated here, the role of the I⁻-CIMS calibration on the data presented must be considered. As shown previously, all models predict a diurnally varying isomer distribution with night-time ΣIPN being largely comprised of IPN and/or INHE and daytime ΣIPN being comprised of smaller concentrations of other species. If the daytime isomers were much more sensitively detected than the night-time isomers, then this could offset the diurnal concentration profile modelled to produce a constant measured signal throughout the day, as is observed. The daytime ΣIPN concentrations predicted by the MCM and FZJ models is around 0.06 times the measured values, meaning that the daytime isomers would need to be around 17 times more sensitively detected than IEPOX to reproduce the flat diurnal signal observed, assuming the night-time isomers had the same sensitivity as IEPOX. There has been very little research to quantify the sensitivity of I⁻-CIMS to hydroperoxides, but Lee et al. (2014) reported the sensitivity of peroxyacetic acid to be 0.04 times that of acetic acid, suggesting that the non-hydroperoxide daytime nitrates may be more sensitively detected than the night-time IPN (Lee et al., 2014).

3.4 ΣICN (C₅H₇NO₄)

ΣICN shows the largest difference between mechanisms. In line with the measurements, all models show low concentrations of ΣICN during the day (Fig. 12). ΣICN then increases at sunset, due to NO₃-initiated formation from isoprene, and then reduces in concentration into the early morning as production ceases. There is a large over-prediction of a factor of around 25 times in the night-time mixing ratio modelled using the MCM, which is consistent with findings from Reeves et al. (2021), who also found ICN to be over-predicted in their models using the MCM; however, the lack of NO constraint in our models results in slightly higher modelled ICN concentrations due to elevated NO₃ concentrations; hence, the discrepancy between the model and measurement is slightly larger in this work (Reeves et al., 2021). This over-prediction decreases to around 7 times when using the Caltech mechanism and decreases further to around 3 times when using the FZJ mechanism. A plot of ΣICN concentrations normalised to the concentration at midnight is shown in Fig. S12. The time series for measured and modelled ΣICN is given in Fig. S13.

Figure 12 Measured and modelled ΣICN. Each line shows the mean value for each dataset, with the shaded area indicating 1 standard deviation above and below the mean.

The large over-prediction made by the MCM is the result of large production terms from the decomposition of all INO radicals (represented by NISOPO in the MCM) into ICN. In contrast, the Caltech mechanism provides alternative INO decomposition routes including fragmentation and H-shift autoxidation reactions (Fig. S14). The FZJ mechanism includes much of this updated chemistry, as well as proposing the previously discussed epoxide formation reactions from some alkoxy radicals, which further reduces the ICN production route (Fig. S14). The improvement in predictions of ΣICN indicates that the assumption made by the MCM of 100 % of INO decomposing to form ICN is unlikely to be valid. The loss of ΣICN is dominated by physical processes in all of the models, particularly at night when ΣICN concentrations are the highest. Additional ICN losses being added to the MCM may improve ΣICN predictions; for example, Hamilton et al. (2021) proposed ICN as a precursor to particle-phase species observed in Beijing via an isoprene nitrooxy hydroxy-α-lactone (INHL) species (Hamilton et al., 2021). However, the MCM already includes reactions with O₃ and NO₃ that are not included in the Caltech or FZJ mechanisms, suggesting that the issue lies in the MCM's faster formation processes. Further discussion of the uncertainties in ICN losses is given by Reeves et al. (2021)

While this account of increasingly complex alkoxy radical chemistry gives good reason to question the high ICN formation rates from the MCM, it is also important to consider that previous work has found the lower sensitivity to aldehyde and ketone groups by I⁻-CIMS compared to alcohols, and as such it should be expected that the measured ΣICN is most likely to be under-quantified by use of the IEPOX calibrant compared to species such as IHN (Lopez-Hilfiker et al., 2014; Iyer et al., 2016; Lee et al., 2014). For example, Lee et al. (2014) show that the sensitivity to hydroxyacetone is around 20 times lower than the similarly structured 1,2-butanediol and the sensitivity to 2,5-hexanedione is around 70 times lower than that of 5-hydroxy-2-pentanone. Assuming the relative sensitivity of ICN to IEPOX is lower than that of IHN, i.e. the sensitivity relative to IEPOX is lower than 15.64 (Sect. 3.2.1), would mean that the over-prediction made by the MCM could not be solely accounted for by the calibration. However, it is more difficult to comment on the accuracy of the FZJ mechanism compared to the Caltech mechanism in this respect as a reasonable calibration correction could bring the measurement in line with either model.

3.5 ΣC₄H₇NO₅

ΣC₄H₇NO₅ mixing ratios are under-predicted by around an order of magnitude in all models (Fig. 13). The modelled ΣC₄H₇NO₅ diurnals only slightly vary between each model, despite the additional dark formation rates added to the FZJ mechanism, with the Caltech mechanism actually producing the highest concentrations. This is because the formation of ΣC₄H₇NO₅ is dominated by the OH oxidation of MVK and MACR. The time series for measured and modelled ΣC₄H₇NO₅ is given in Fig. 15.

Figure 13 Measured and modelled ΣC₄H₇NO₅. Each line shows the mean value for each dataset, with the shaded area indicating 1 standard deviation above and below the mean.

The under-prediction in MVK + MACR and the potentially high ventilation (see Sect. 3.1) may account for some of this under-prediction, particularly in light of the potentially long lifetime of C₄H₇NO₅; however, the under-prediction is much stronger than is observed for the MVK + MACR precursors (Müller et al., 2014). Without previous work investigating the sensitivity of I⁻-CIMS to C₄H₇NO₅, it is difficult to assess the impact of calibration on this measurement. Assuming a similar sensitivity as the most sensitively detected IHN isomer, where the OH and NO₃ groups are in close proximity like in the C₄H₇NO₅ isomers, would bring the measurement in line with the models.

4 Conclusions

Model results making use of three different detailed chemical mechanisms, comparing their predictions of several isoprene organonitrates, have been presented. While the gas-phase box-modelling approach used here allows for the use of such complex mechanisms, the simplified representation may not fully represent physical processes such as boundary layer mixing in the morning and evening. Additionally, hydrolysis and aerosol uptake processes are not included in the mechanisms, meaning there may be unaccounted losses for species such as INHE. While the impact of I⁻-CIMS sensitivity on measurements of these nitrates has been considered throughout this work, the availability of authentic standards would greatly improve the ability to quantify such organonitrates.

When considering ΣIPN, the model results presented here indicate that large proportions of the measured ΣIPN can be composed of non-IPN species. This is especially true during the daytime, when ΣIPN concentrations are lowest. However, the epoxide-forming reactions proposed by Vereecken et al. (2021) suggest that around half of the measured night-time ΣIPN could be comprised of INHE (Vereecken et al., 2021). Assuming reactive uptake coefficients similar to those previously measured for IEPOX results in small reductions in predicted ΣIPN, meaning that the FZJ mechanism predicts ΣIPN to be comprised of mostly non-IPN species for the majority of the day. Further studies of isoprene nitrate chemistry should investigate these species with techniques able to distinguish between the isomeric ΣIPN compounds and their reaction products, such as chromatographic techniques, in order to determine the role of INHE in isoprene oxidation. Such large INHE production terms would have implications for the formation and growth of secondary organic aerosol (SOA) by reactive uptake to acidified particles (Hamilton et al., 2021). Generally, the large contribution of non-IPN species to the modelled ΣIPN highlights the caution that should be applied in interpreting measurements of ΣIPN solely as a measurement of IPN.

The changing distribution of ΣIHN isomers over the course of 24 h has implications for the calibration of ΣIHN measurements. For example, I⁻-CIMS could be 2.5 to 1.4 times less sensitive to ΣIHN overnight where NO₃ chemistry is dominant, due to the increased contribution of E-1,4-IHN and E-4,1-IHN to ΣIHN. This means that the use of a constant calibration factor is likely to under-quantify night-time IHN, even if the calibration factor was accurate during the day. Furthermore, while comparison of the models to IEPOX-calibrated data suggests an under-prediction by the models, adjusting this calibration to account for the sensitivity of IHN isomers suggests a potentially very large over-prediction by the models.

The much improved ΣICN predictions when using the Caltech and FZJ mechanisms compared to the MCM indicate that the assumptions around alkoxy radical decomposition made by the MCM are likely to be inaccurate, even when calibration uncertainties are accounted for. Future studies focussed on isoprene nitrates should not overlook the inclusion of more complex INO decomposition routes, beyond the direct decomposition route to ICN present in the MCM.

While the results presented here surrounding C₄H₇NO₅ are not conclusive, there is potential for all of the mechanisms to under-predict C₄H₇NO₅. Additional C₄H₇NO₅ from NO₃ chemistry, as is included in the FZJ mechanism model, does not improve predictions as the majority of the modelled C₄H₇NO₅ resulted from OH chemistry. Assuming an I⁻-CIMS sensitivity of C₄H₇NO₅ similar to that of the more sensitively detected IHN isomers would mean that the modelled C₄H₇NO₅ is approximately correct.

While physical processes dominated the loss of the organonitrates in all of the models presented here, the chemical losses of these species are not well understood. Estimated rate constants for the reaction of IHN, IPN, and ICN from Wennberg et al. (2018) indicate that the OH reactions which are included in all of the mechanisms may be the major chemical loss pathways, with NO₃ oxidation comprising a larger loss than reaction with O₃. This has implications for NO_x recycling, indicating that most of the NO_x consumed to form the organonitrates is subsequently lost from the gas phase or transported away from the site of formation (Bates and Jacob, 2019).

Generally, the mechanisms presented here do a reasonable job at reproducing isoprene nitrate chemistry in Beijing, particularly with the inclusion of improved alkoxy radical chemistry, though it is clear that better constraints on the sensitivity of I⁻-CIMS to nitrated compounds would aid in the analysis of these compounds.