To simulate the autoxidation reactions formed from ozonolysis five new peroxy radical species were added to the base mechanism. The peroxy radicals formed from ozonolysis of α-pinene and subsequent autoxidation steps are collectively termed O3RO2. In the base mechanism, α-pinene reacts with ozone to produce the single lumped peroxy radical RN18AO2 and acetone. This single mechanistic step represents multiple chemical steps, with RN18AO2 representing a six or seven carbon species. In addition, TNCARB26 (closed-shell carbonyl species) and RCOOH25 (pinonic acid) arise from the reaction of Criegee intermediates with water. The yields of these species, 17.5 % and 2.5 % respectively, remain unchanged from the CRI v2.2 mechanism and are well supported in the literature (IUPAC, 2020; Atkinson and Arey, 2003; Johnson and Marston, 2008). RN18AO2 goes on to react with standard peroxy radical reaction partners; HO2-forming hydroperoxides; NO- and NO3-forming alkoxy radicals; and the peroxy-radical-pool-forming alkoxy radicals, carbonyls and alcohols, as described in Jenkin et al. (2019b).

In our new mechanism, RN18AO2 is replaced with the tracers RN26BO2 and RTN24O2. RN26BO2 represents the 10-carbon peroxy radicals formed directly from the cleavage of the ozonide and subsequent addition of atmospheric oxygen, which can then undergo autoxidation. RTN24O2, a species already in the CRI mechanism, represents the 9-carbon peroxy radical species (MCM species C96O2) which is also formed from ozonolysis but does not undergo autoxidation in this mechanism. RN26BO2 is termed “first generation” as it has undergone one oxidation step and it can undergo autoxidation to form the second-, third- and fourth-generation and lumped higher-generation species, termed RN25BO2O2, RN24BO4O2, RN23BO4O2 and RNxBOyO2 species respectively (RNxBOyO2 does not undergo further autoxidation but does undergo all the other reactions). In the base mechanism, the first number featured in a species' name is an index which refers to the number of NO-to-NO2 conversions possible, which depends on the number of C–C and C–H bonds. During the H-shift step of autoxidation, a C–H bond is usually broken to produce the alkyl radical which then forms the peroxy radical from atmospheric oxygen, and so each autoxidation step reduces the index by 1 while the number of oxygens is increased by 2. For example, the autoxidation of the second-generation O3RO2 to the third generation is expressed by Eq. (5). 5RN25BO2O2→RN24BO4O2 Each generation of peroxy radicals also undergoes bimolecular reactions. Reaction with HO2 produces a hydroperoxide species; for the second and later generations, the product is classified as a HOM (C10z) as it fulfils the criteria discussed by Bianchi et al. (2019), while for the first-generation species the resulting hydroperoxide is RTN26OOH, a species already present in the CRI (Eq. 6). 6RNaBObO2+HO2→RTN26OOH or C10z Reaction with NO and NO3 yields nitrates or alkoxy radicals, and accurately representing the behaviour of these products is crucial to reproducing the effect of NOx on HOM formation. Alkoxy radicals are not represented explicitly due to their rapid reactions which, typically for alkoxy radicals formed from larger peroxy radicals, are decomposition or isomerisation. Decomposition produces two smaller species, one is closed shell and one is a peroxy radical, while isomerisation produces a more functionalised peroxy radical via an alkyl radical intermediate with one fewer oxygen than would have been added via autoxidation. Faced with very limited data and the fact that the precise fate of an alkoxy radical will depend considerably on molecular structure and neighbouring groups, a branching ratio of 50:50 for decomposition and isomerisation was adopted. Sensitivity tests perturbing the branching ratio between 75:25 and 25:75 were performed to probe the consequences of this uncertainty. These tests suggested the precise value of this branching ratio within this range did not affect the fitting of rate coefficients for autoxidation and accretion product formation (Sect. 3.1). However, these branching-ratio perturbations did lead to changes in HOM yield (Fig. S4b in the Supplement) and are discussed in more detail in Sect. 3.2. The decomposition products are existing CRI species CARB16 and RN10O2 or RN9O2, and the isomerisation product is the next-generation peroxy radical as shown in the example reaction (Eq. 7). 7RN25BO2O2+NO→0.5RN24BO4O2+0.5CARB16+0.5RN9O2 A schematic of the additions made to the CRI for the ozonolysis scheme is shown in Fig. 1.

Autoxidation through the OH initiated oxidation pathway resulted in the addition of six new species, including five new peroxy radicals. The peroxy radicals formed from OH oxidation of α-pinene and subsequent autoxidation steps are termed OHRO2. The single peroxy radical RTN28O2 in the base mechanism is replaced by RTN28AO2, representing the two species which do not undergo autoxidation (APINAO2 and APINBO2 in the MCM), and RTN28BO2 (MCM APINCO2) which can undergo autoxidation to form higher-generation peroxy radicals (Xu et al., 2019). The second- and third-generation OHRO2 are represented explicitly (RTN27BO2O2 and RTN26BO4O2), and all fourth-generation and higher species are lumped together as RTNxBOyO2 for mechanistic simplicity. The chemical treatment of RTN28AO2 is the same as for the original CRI species RTN28O2, while all other OHRO2 species (except RTNxBOyO2) can undergo autoxidation (Eq. 8). 8RTNaBObO2→RTN1-aBOb+2O2 Reaction of the first- and second-generation OHRO2 (RTN28BO2 and RTN27BO2O2) with HO2 yields the hydroperoxide RTN28OOH which is not classified as a HOM due to insufficient oxygens. The HOM produced by all later-generation OHRO2 species is termed C10x (Eq. 9). 9RTNaBObO2+HO2→RTN28OOH or C10x Reaction with NO and NO3 is treated in the same manner as O3RO2 except for RTN28BO2 which follows the reaction of the analogous species APINCO2 in the MCM. A schematic of the additions made to the base mechanism for the OH oxidation scheme is shown in Fig. 2.

The pathway initiated by reaction of α-pinene with NO3 was not considered in this work but is identified as an area for future work. A summary of the peroxy radical species in the two pathways is given in Table 1, and a full mechanistic description is provided in the Supplement.

Reactions between peroxy radicals can result in the formation of two alkoxy radicals (Eq. 10), a carbonyl and an alcohol (Eq. 11) or accretion product (Eq. 12; Jenkin et al., 2019b). 10RO2+R′O2→RO+R′O+O211RO2+R′O2→R-HO+R′OH+O2or R-H′O+ROH+O212RO2+R′O2→ROOR′+O2 Rather than represent every possible RO2–RO2 reaction combination, the base mechanism uses a peroxy radical pool. Each peroxy radical undergoes a unimolecular reaction with a first-order rate coefficient determined by the total peroxy radical concentration and the geometric mean of the self-reaction rates of the methyl peroxy radical and radical of interest (Jenkin et al., 2019b).

While computationally efficient, such a mechanism fails to represent the effect of peroxy radical size on the distribution of products. While negligible for small peroxy radicals, accretion product formation is more favourable when larger, more functionalised peroxy radicals react (Berndt et al., 2018a; Schervish and Donahue, 2020). To describe the reactions between the differently sized peroxy radicals, we have split the single peroxy radical pool into three pools for small (less than four carbons), medium (four to seven carbons) and big (more than seven carbons) peroxy radicals. Each big radical reacts separately with each peroxy radical pool, while, to minimise the total number of reactions, all small peroxy radicals react with the total pool as accretion product formation is much less favourable (Jenkin et al., 2019b). Medium peroxy radicals are discussed below. The use of large and medium peroxy radical pools allows for improved representation of the competition between peroxy radicals with different reactivity in our new mechanism and is a substantial improvement over the base mechanism.

Table 2 summarises the products for a specific peroxy radical reacting with the different peroxy radical pools. As discussed previously, alkoxy radials were not simulated explicitly; rather they decomposed into closed-shell products and peroxy radicals. A full list of the contents of each peroxy radical pool is given in the Supplement.

In practice, the alkoxy radicals formed from the reaction of isoprene-derived peroxy radicals (which are likely to dominate the medium size pool) with other peroxy radicals decompose rapidly into the major products: closed-shell carbonyls methyl vinyl ketone and methacrolein (UCARB10) and the minor product hydroxy vinyl carbonyl (UCARB12; Jenkin et al., 2015). The accretion of isoprene-derived peroxy radicals has been measured to be over an order of magnitude slower than the accretion of peroxy radicals derived from α-pinene (Berndt et al., 2018a), supporting the theory that accretion product formation becomes more favourable with increasing peroxy radical size. Therefore, to limit complexity, all medium peroxy radicals in the mechanism simply reacted with the overall peroxy radical pool and their accretion product formation was ignored.

The number of different molecules falling under the C10x, C10z, C15d and C20d umbrellas is huge, making the treatment of loss processes complex. Losses will occur via chemical or photolytic degradation as well as to condensation to aerosols, to the nucleation sink, and dry and wet deposition. Physical loss is believed to be the major sink for HOMs (Dal Maso et al., 2002; Petäjä et al., 2009; Tan et al., 2018; Wu et al., 2007; Bianchi et al., 2019). For simplicity, in the simulations below, we ignore wet and dry deposition but do include loss to the condensation sink for modelling simulations C and D (Table 3).

Chemical losses of HOMs are highly uncertain. It is suggested that HOMs will react with OH (Bianchi et al., 2019). In this model, OH reacts with C10x, C10z, C15d and C20d with the rate coefficient of the large hydroperoxide, RTN28OOH, to produce the smaller closed-shell CRI species CARB10 and CARB15 as well as UCARB10 (lumped methacrolein and methyl vinyl ketone) for 15-carbon dimers. This rate coefficient was 2.38×10-11 cm3 molec.-1 s-1, and, in light of the suggestion that the rate coefficient of OH with HOMs could be higher (Bianchi et al., 2019), sensitivity tests increasing the rate coefficient to 1×10-10 cm3 molec.-1 s-1 were performed, but no material effect was observed. Photolysis of peroxide and carbonyl linkages produce alkoxy radicals which behave as previously described. Photolysis frequencies are taken from the MCM (Jenkin et al., 1997; Saunders et al., 2003). Given the small concentrations of HOMs we predict that uncertainty in these gas-phase loss processes is likely to have small impacts on the general features of tropospheric chemistry (i.e. OH reactivity or ozone production).

Physical loss is believed to be the major sink for HOMs (Dal Maso et al., 2002; Petäjä et al., 2009; Tan et al., 2018; Wu et al., 2007; Bianchi et al., 2019). Loss to the condensation sink presents a complex challenge. The saturation vapour pressure will vary considerably (Kurtén et al., 2016) for HOMs, even within the C10 umbrella, affecting the fraction which partitions into the aerosol phase. Furthermore, some HOMs are likely to have aldehyde and alcohol moieties which will enhance their removal via reactive uptake into the aerosol phase, particularly if it is aqueous. When using our new mechanism in different simulations (Table 3), condensation sinks have been set to fixed values or values taken from the literature.

Having described the additions and changes made to the base mechanism to develop our new mechanism, we now discuss the optimisation and validation of the mechanism.

There exist a limited number of experimental data which provide an insight into the behaviour of the multiple generations of peroxy radicals produced from ozonolysis and OH oxidation of α-pinene (Berndt et al., 2018a). Using a flow cell, Berndt et al. (2018a) measured the concentration of α-pinene-derived peroxy radicals produced by ozonolysis (O3RO2) and OH oxidation (OHRO2) and 20-carbon (C20d) and 15-carbon (C15d) accretion products at the end of the flow tube using a chemical ionisation–atmospheric pressure interface time-of-flight (CI-APi-TOF) mass spectrometer and a chemical ionisation time-of-flight (CI3-TOF) mass spectrometer. The observed peroxy radicals spanned several generations of autoxidation, namely the first to fourth generation for O3RO2 species and first to third generation for OHRO2. Berndt et al. (2018a) also calculated rate coefficients for accretion product formation using the observation that accretion product concentration increased linearly with time with an assumed uncertainty no greater than a factor of 3. Reagent ions used in the CI-APi-TOF were C3H7NH3+, CH3COO- and NO3-, and in the CI3-TOF the reagent ion was NH4+. The flow tube experiments lasted for 7.9 s, at which point the flow was sampled by the mass spectrometers. Reactions proceeded under dark conditions at 1 atm and 297 K under low [NOx] (<108 cm-3). The low concentrations of bimolecular reaction partners HO2 and NO meant that multiple autoxidation steps could occur in the reaction time.

Flow tubes operating under laminar flow are easily modelled using box models as there are very few complications to consider in terms of mixing and wall loss, and no new particle formation was observed. A box model version of the mechanism was compiled in the BOXMOX framework (Knote et al., 2015). The experimental data allowed for the autoxidation coefficients of the peroxy radical species and the rate coefficients of accretion product formation to be constrained. The concentrations of peroxy radicals and accretion products in the box model were evaluated at the end of the 7.9 s reaction period and compared with experiments. A process of iterative adjustment to autoxidation and accretion product formation rate coefficients in the mechanism was performed to produce the best reproduction of the experimental data by the mechanism.

Two experiments from Berndt et al. (2018a) were considered. In the first experiment, flow tube runs were performed with varying initial concentrations of α-pinene (3–50 ppb) with initial O3 at 26 ppb (Simulation A). In the second experiment, runs were performed with fixed initial α-pinene (15.6 ppb) and O3 (80 ppb) but with initial isoprene concentrations varying from 0 to 60 ppb (Simulation B). Comparison with these experimental data facilitated examination of the model's ability to reproduce the concentration of HOM precursors and accretion products with and without isoprene as well as at moderate and high O3 mixing ratios.

An important parameter in the mechanism was the yield of RN26BO2 from α-pinene ozonolysis. This yield is uncertain, and it was found to affect the autoxidation coefficients required to reproduce the experimental data for the O3RO2 species. To constrain it, a first-order autoxidation rate coefficient of 0.206 s-1 for RN26BO2 was imposed, based on theoretical analysis of the α-pinene ozonolysis system (Kurtén et al., 2015), and the yield was adjusted until the mechanism was able to achieve the best possible fit to the data. This resulted in a yield of 50 % for RN26BO2 and 30 % for RTN24O2. However, this remains a source of uncertainty and warrants further investigation. The low-NOx conditions meant that the autoxidation coefficients dominated the concentration of later-generation O3RO2 and OHRO2, and, from this starting point, the autoxidation rate coefficients for later generations were fitted against experimental data over multiple rounds of optimisation (Table 4). The autoxidation coefficient for the first-generation OHRO2, RTN28BO2, was taken as 2.1 s-1 based on Xu et al. (2019). An estimation of the uncertainty in the autoxidation is also provided in Table 4. These values were calculated by adjusting the autoxidation rate coefficients one at a time to determine the maximum and minimum values of an autoxidation rate coefficient for which the corresponding peroxy radical would fall within the experimental uncertainty region. This approach neglects any cross-sensitivities through the joint uncertainty in several rate coefficients. A full Monte Carlo uncertainty analysis addressing this issue is beyond the scope of this paper but would make a valuable follow up for future work in this field. Therefore, the autoxidation rate coefficient uncertainties are large as the experimental error uncertainties are large.

The autoxidation coefficients in Table 4 are higher than those considered in the theoretical study of Schervish and Donahue (2020) but closer to the values measured by Zhao et al. (2018) and the values suggested by Roldin et al. (2019). The mechanism used the autoxidation coefficients from Table 4 and predicted the lumped higher-generation species (fifth generation for O3RO2, fourth generation for OHRO2) at concentrations higher than those observed in the work by Berndt et al. (2018a). This suggests there may be additional, as yet unknown, loss processes for the more highly oxidised peroxy radical species which are not incorporated into this work. Additional loss processes would likely reduce the fitted autoxidation coefficients because they would provide an additional sink for the RO2 species which does not lead to the production of the next-generation RO2. Therefore, the autoxidation coefficients determined in this work are likely to be upper limits, but further insight into this is not possible with the data currently available. This is a key area for further study.

Unfortunately, the flow tube studies of Berndt et al. (2018a) lack observations to constrain the full chemical space simulated by the box model. In particular there were no measurements of OH, HO2 or NO. The effect of the uncertainty in the initial experimental concentrations of NO, HO2 and OH on the modelled concentrations of O3RO2, OHRO2 and accretion products which thus fitted the autoxidation coefficients and accretion production formation rate coefficients was investigated with a series of sensitivity tests. Initial conditions of 106 cm-3 for OH and 4 ppt for HO2 were used. NO and NO2 were initialised at 4 ppt, based on the purity of the flow gas (personal communication with Torsten Berndt). For HO2, NO and NO2, sensitivity simulations indicated that increases of 10 ppt (250 % increase) and decreases of 3 ppt (75 % decrease) did not lead to deviations in the concentrations of RO2 or accretion products sufficient to warrant a change in the rate coefficients for autoxidation or accretion product formation. Initial OH concentration had a negligible effect (<5 % change) on O3RO2, OHRO2 and C20d when varied over 105–2×106 cm-3 (90 % decrease, 100 % increase).

Autoxidation reactions have significant positive temperature dependencies (Praske et al., 2018; Bianchi et al., 2019; Jenkin et al., 2019b). Accordingly, HOM yields are expected to be highly temperature sensitive. Quéléver et al. (2019) recorded a 50-fold increase in HOM yield at 293 K relative to 273 K. This temperature variation cannot be attributed to the temperature dependence of the initial oxidation of α-pinene as the rate coefficient of ozonolysis increases only 17 % between 273 and 293 K while the reactions with OH and NO3 exhibit negative temperature dependencies. Frege et al. (2018) measured a decrease in O:C ratio values in HOMs with reducing temperatures, attributing this to a reduction in autoxidation.

Variation in peroxy radical structure and functionality will result in different-generation peroxy radicals having different barriers to autoxidation (Bianchi et al., 2019). A few modelling studies have considered the temperature dependencies of the autoxidation rate coefficient in peroxy radicals from α-pinene derivatives. Schervish and Donahue (2020) considered a simple approach where all generations of peroxy radicals from α-pinene ozonolysis had a fixed activation energy of 62.4 or 66.5 KJmol-1 (θ=7500–8000 K, where the rate coefficient is expressed as k=Ae-θ/T), while noting that a reduction in barriers to autoxidation with increasing functionality is plausible but so far unproven. By contrast, Roldin et al. (2019) considered a higher activation energy of 100.4 KJmol-1 (θ=12077 K) based on the theoretical work of Kurtén et al. (2015) which identified activation energies of 90–120 KJmol-1 for α-pinene.

Given the lack of additional literature in this area, three versions of the new mechanism were created to probe the effects of temperature and activation energy on HOM yield and subsequent evolution. In each mechanism all autoxidation reactions (for O3RO2 and OHRO2) had the same activation energy while all other rate coefficients were the same across mechanisms (Table S2 in the Supplement). Activation barriers of θ=6000 K, θ=9000 K and θ=12077 K were chosen as they included the range suggested by Roldin et al. (2019) and Schervish and Donahue (2020), and the mechanism versions were termed HOM6000, HOM9000 and HOM12077 respectively. For the temperature-dependent versions, the pre-exponential factor of the autoxidation coefficient (Table S5) was adjusted so that the autoxidation coefficients were the same at 297 K as those derived from the comparison to experimental data from Berndt et al. (2018a). It is recognised that the autoxidation steps are likely to have different activation energies, but this analysis provides a first approximation of the influence of activation energy on HOM formation.

In a simulation modelling an instantaneous injection of α-pinene (Simulation C), the HOM yield for the 10-carbon species, individually and in total (defined in the Supplement), was calculated with the three different temperature dependencies (HOM6000, HOM9000 and HOM12077) at temperatures of 270, 290 and 310 K for initials conditions of α-pinene at 15 ppb, O3 at 40 ppb, OH at 106 cm-3 and a temperature-independent condensation sink of 2×10-3 s-1.

Figure 6a shows the results from the simulations performed with initial concentrations of NO and NO2 of 0.01–10 ppb. These simulations showed that the 10-carbon HOM yield tends to increase slightly from very low (0.02 ppb) to moderate (2 ppb) NOx, before starting to decrease with increasing NOx thereafter. This behaviour is likely to be due to the inclusion in the mechanism of the isomerisation pathway via reaction with NO which yields the next-generation peroxy radical. This pathway has been suggested as an important route for forming more highly oxidised derivatives of α-pinene due to the potential rapid ring-opening mechanism involving alkoxy radicals and the cyclobutyl ring found in α-pinene ozonolysis products (Rissanen et al., 2015). Figure 6a indicates that the absolute yield is also sensitive to temperature, with the highest yields simulated at the highest temperatures. At low temperatures (blue data), the uncertainty in autoxidation temperature dependence has the greatest effect, while at high temperatures this feature is muted. The increase in yield with temperature is in qualitative agreement with observation (Quéléver et al., 2019; Simon et al., 2020).

The model predicted total HOM yields at 290 K of 1.9±0.2 % (0.01 ppb NO) to 3.9±0.5 % (1 ppb NO), with the quoted range resulting from the range of temperature dependencies considered. This is within the ranges previously suggested by Jokinen et al. (2015; 1.7 %–6.8 %) and close to the values from Ehn et al. (2014; 3.5 %–10.5 %) and Sarnela et al. (2018; 3.5 %–6.5 %), while lower than Roldin et al. (2019; ∼7 %). In addition, the HOM yield at 270 K of ∼0.6 %–1.9 % compared favourably with the yield of ∼2 % determined by Roldin et al. (2019). This suggests that the mechanism is doing a good job of simulating HOM yield. The slight low bias may be in part due to the values of k14 and k15 which were shown to influence the HOM yield relatively strongly. Sensitivity tests involving doubling and halving of the rate coefficients produced HOM yield changes of around +65 % and -40 % respectively while preserving the general dependencies on NOx and temperature (Fig. S4a; Table S6). This area of uncertainty will be the focus of future work.

The HOM yield showed negligible sensitivity to the alkoxy radical decomposition–isomerisation branching ratio below 200 ppt of NOx and around ±0.7 percentage points (∼20 %) at 2 ppb NOx. However, this range was encompassed by the range arising from autoxidation temperature dependence uncertainty. Above 2 ppb NOx, this ratio had greater influence as NO reactions with RO2 started to compete more efficiently with autoxidation, but this coincided with the sharp drop in HOM yield (Fig. S4b). Therefore, while further work is needed to develop the isomerisation–decomposition branching ratio description, it is unlikely to have a significant influence in the low-NOx conditions where HOMs are predicted to be most prevalent, and in these conditions the uncertainty in temperature dependence of autoxidation is predicted to have a larger effect.

The ability of the new mechanism to reproduce the concentrations of key atmospheric species from CRI v2.2 under different emissions of NOx and α-pinene was assessed using an 8 d box-modelling run (Simulation D). Over the majority of emissions space, O3 differed by less than 0.05 ppb (0.1 %), OH by less than 0.4 % and NO by less than 2.5 ppt (0.4 %; Figs. S6–S8) with similar (or better) agreement for other important species (Figs. S9–S17). Acetone was routinely underpredicted (Fig. S18) by between a factor of ∼14 at 50 ppt NOx and ∼20 % at 2–10 ppb of NOx, but this did not result in significant deviation between the base mechanism and new mechanism for O3 or OH. This indicates that the basic features of atmospheric chemistry, such as HOx recycling processes added in CRI v2.2, which have been shown to have important consequences for atmospheric composition (Jenkin et al., 2019a), are preserved in the new mechanism.

Given the important role Gordon et al. (2016) identified for HOMs in NPF, we extend our 1D calculations to investigate the implications of the predicted HOM profiles on nucleation rates using monthly mean climate model data from the PD and PI period. Nucleation rates from two different nucleation mechanisms were studied: (i) neutral and ion-induced pure biogenic nucleation (PBN; Kirkby et al., 2016) and (ii) activation of sulfuric acid (SAact; Kulmala et al., 2006; Sihto et al., 2006) suitable for the boundary layer. All HOMs were treated as being equally proficient at nucleating new particles, in agreement with the approach and nucleation rates used by Kirkby et al. (2016) and Gordon et al. (2017). Recent work by Heinritzi et al. (2020) suggests that 20-carbon accretion products may be better at nucleating new particles, and therefore the results presented are likely to be an upper bound although nevertheless informative. Representing the different nucleation efficiencies of different HOM species will be investigated in future work. The results of the calculations of nucleation rates using these schemes are summarised in Fig. 8. (The nucleation rate expressions are given in the Supplement.)

There exist few observational data on nucleation solely from PBN mechanisms, making model validation hard. Modelled surface sulfuric acid concentrations at Hyytiälä (2–3×106 cm-3) fall within the range of observations (3×105–2×107 cm-3; Boy et al., 2005; Petäjä et al., 2009). Modelled concentrations in the Amazon (3×104 cm-3) were lower than observations (105–106 cm-3; Wimmer et al., 2018) although the observations were taken in a pasture site downwind of Manaus surrounded by the rainforest and not in the rainforest itself and are therefore likely to be higher than in situ rainforest values. Thus, the nucleation rates we have calculated for SAact are likely to be a reasonable estimate in Hyytiälä and low biased in the Amazon.

Figure 8 shows predicted nucleation rates in the PI period and PD in the Amazon and Hyytiälä derived from our simulated [HOMs] vertical profile in the boundary layer and low free troposphere using June monthly mean data from a United Kingdom Earth System Model (UKESM) historical run taken from the PI period (June average 1851–1856) and PD (June average 2009–2014). In all cases, the PBN rates decline rapidly with height above the boundary layer. In the boreal forest, the nucleation rate from PBN at very low altitudes is calculated to be around 20 %–25 % of that from SAact in the PD. However, in the PI period it is comparable to the SAact rate, contributing 40 %–80 % of the total nucleation rate in the lowest 500 m (Fig. S23). The greater relative importance of PBN in the PI period, despite lower predicted [HOMs], was attributed to two factors. Firstly, predicted steady-state ion concentrations were higher in the PI period in Finland than in the PD due to the PI period's lower ion CS. This increased the rate of the ion-induced PBN pathway. Secondly, the considerably lower modelled concentrations of sulfuric acid in the PI period (around 10× lower than in the PD) reduced the importance of SAact. By contrast, the lower concentrations of predicted [HOMs] in the Amazon led to PBN having a much smaller contribution to the total nucleation rate (<5 % in the PD and a negligible impact in the PI period). This is in agreement with multiple sources (Andreae et al., 2015; Wimmer et al., 2018; Varanda Rizzo et al., 2018). The importance of PBN in the PI atmosphere in certain locations, qualitatively in agreement with Gordon et al. (2016), illustrates the potential importance including PBN in climate models could have on aerosol burden and the associated radiative effects.