The first approach (called hereafter KIN) is based on the hypothesis that oligomer formation may be represented through a kinetic process (Morris et al., 2006; Carlton et al., 2010). This hypothesis is supported by a series of smog chamber experiments conducted by Kalberer et al. (2004), where an important fraction of organic aerosol mass was shown to be composed of oligomers. The authors reported that, after 20 h of processing, 50 % of the total organic aerosol mass was transformed into oligomers. From this result, Morris et al. (2006) proposed the use of a first-order rate constant k1=9.6×10-6 s-1 to account for the oligomerization formation process, corresponding to a half-life of 20 h for organic species in the particulate phase. In this approach, biogenic and anthropogenic species are all potential oligomer precursors. However, due to low amounts of anthropogenic semivolatile organic compounds (SVOC) from the oxidation of classic precursors (Toluene, Xylene, Trimethylbenzene, etc.) over Europe, the production of anthropogenic oligomer could be negligible (Aksoyoglu et al., 2011).

To transcribe this approach in the model, we have allocated a first-order oligomer production kinetics to all the hydrophobic and hydrophilic surrogate species (AnA0-1-2D and BiA0-1-2D, AnBlP, AnBmP, BiBmP, ISOPA1 and ISOPA2) of the CHIMERE aerosol module. Preliminary simulations with CHIMERE confirmed the precedent findings, i.e., a very low budget of oligomers of anthropogenic origin (concentrations reach 10-3 ng m-3 at the maximum over the domain) compared with biogenic oligomers (which concentrations reach a few µg m-3 for oligomers over many continental areas).

Thus, for simplification, only the six biogenic surrogate species (BiA0D, BiA1D, BiA2D, BiBmP, ISOPA1 and ISOPA2) were considered here (Gas-phase chemical scheme for SOA formation is available in Table 6 of Menut et al., 2013). Furthermore, as will be discussed below, our study will focus on monoterpenes, a common species of both modeling approaches. To that end, a new species family called BiOLG, representing the total sum of oligomerized pBiA∗D compounds, was introduced in CHIMERE. It accounts for oligomer formation from the oxidation of monoterpenes only and will be the basis for the intercomparison of the two approaches.

In this empirical parameterization, oligomerization is considered as an irreversible process. This approach has the advantage of simplicity, as it proposes a similar chemical reactivity for all organic oligomer precursors in the particulate phase (hydrophilic and hydrophobic species), one single chemical pathway for oligomer formation, and only one type of oligomer product. However, the drawback of this method is that it does not account for the details of the gas-phase SVOC speciation, for the variability of the aerosol nature (deliquescent aerosol or not), nor for ambient parameters such as pH. Thus, it may lead to biases in the quantitative estimation of oligomer and OA production. Moreover, owing to the choice of a kinetic approach with a half life of 20 h, oligomer production is expected to be dominant away from source areas (except in the presence of severe anticyclonic conditions), enhancing the role of pollutant transport.

The second approach (called here KPH) combines the laboratory works of Jang et al. (2005) – who showed that the polymerization of aldehydes may happen through a variety of acid-catalyzed reactions – and the observations of Gao et al. (2004) – who indicated that at least 10 % of the total organic aerosol mass is converted into oligomers due to the formation of organic acids in the aerosol. From these results, Pun and Seigneur (2007) developed an equation for the calculation of the gas-to-particle partitioning constant of semi-volatile aldehydes. It represents their increased partitioning toward the aqueous phase due to acidity: Kp,eff,i=Kp,i1+K0,eff,i,ref×CH+CH+,ref1.91, where Kp,eff,i is the effective partitioning coefficient of the ith compound between the gas phase and the aerosol aqueous phase; Kp,i is its standard partitioning coefficient – calculated for non-acidic conditions – and CH+ represent the aqueous concentration of hydronium ions. In this approach, CH+,ref is set to 10-6 mol L-1 and K0,eff,i,ref stands for the value of 0.1 found by Gao et al. (2004) under the CH+,ref conditions. According to the results of Jang et al. (2005), aldehydes appear to be more reactive than ketones by 2 orders of magnitude. To simplify the parameterization, Pun and Seigneur (2007) considered as a first approximation that only aqueous aldehydes undergo oligomerization. In our model, it is equivalent to assuming that only BiA0D surrogates can lead to oligomer formation. Such a consideration derives from the fact that isoprene oxidation products in CHIMERE are not associated with a given molecular structure. Thus, oligomerization processes could not be attributed to isoprene surrogates without more chemical details here, using the KPH approach. Our study then focuses on what can be learned from oligomerization modeling approaches on the basis of monoterpene surrogate reactivity.

The KPH approach only artificially reproduces oligomer production. Indeed, the reactivity in the particulate phase that leads to the consumption of dissolved organic species it restituted by an increase in the value of their effective partitioning coefficient, according to Eq. (1). As a consequence, oligomerization is treated here as a fully reversible process. Furthermore, this approach does not require any new model species to represent the aqueous oligomers. This is why it is necessary to perform two types of simulations to estimate the effect of the oligomerization process: a reference case – called hereafter REF – and a scenario case (KPH). The differences in the pBiA0D concentration fields between the two simulations represent aqueous oligomerization in the KPH approach: [Oligomers]=[pBiA0D]KPH-[pBiA0D]REF. To implement this approach in the model and ensure the robustness of the modified partitioning constant value, it was necessary to adequately account for the acidity of the deliquescent particles. The particle pH is calculated in CHIMERE by an online coupling with the ISORROPIA model that solves the transition between solid and aqueous phases through the estimation of the deliquescent relative humidity. However, it is also possible to run ISORROPIA in a metastable configuration, which considers that aerosols remain in a liquid state under conditions of low relative humidity, thus avoiding the transfer of dissolved BiA0D back to the gas phase and favoring oligomer persistence as well as its atmospheric transport. This alternative is taken into account for the evaluation of the KPH approach.

ISORROPIA model also provides – for each cell and at every time step of the model calculation – particle water content and ion species equilibrium concentrations. At the end of the ISORROPIA computation, we constrained the particle pH to a range of values between 2 and 6. The upper value limit of 6 allows us to be consistent with the parameterization and to avoid partitioning constant values lower than that of the reference (see Eq. 1). The lower limit was set for numerical reasons, as the transfer of the concerned organic species to the aqueous phase becomes total under a pH of 2.

In order to examine the gas-particle partition of the model surrogates, we report in Fig. 2 the average concentration fields of the hydrophilic and hydrophobic surrogates simulated by CHIMERE in the reference case for the period 20 July–3 August 2006. This figure indicates that BiA1D is the highest hydrophilic contributor to the organic aerosol mass concentration, while BiA0D remains quasi-exclusively in the gas phase. However, among the monoterpene surrogates, the hydrophobic species BiBmP is the largest contributor to the organic aerosol mass concentration. On average, hydrophilic and hydrophobic species account for 25 and 75 % of this organic aerosol mass concentration, respectively.

As the impact of the KH partitioning constant value is likely to be important for the formation of oligomers, we focused on gaseous hydrophilic species and on the processes governing their transfer toward the particulate phase. To that end, we analyzed two different situations. In the first one, the aerosol is treated as a deliquescent aerosol where the distribution of the hydrophilic species between the gas and the condensed phases is driven by Henry's law. In the second one, we consider a dry aerosol where the partition of hydrophilic species is driven by Raoult's law.

For the deliquescent aerosol situation, we calculated the partitioning coefficient as described by Mouchel-Vallon et al. (2013), where the fraction of the surrogate species in the aqueous phase is obtained as follows: ξi=CaiCai+Cgi=1+1HiRTL-1.

In this equation, Cai and Cgi represent (in µg m-3) the concentration of species i in the particulate and gas phases, respectively; Hi is the Henry's law constant (in Matm-1); R is the ideal gas law constant; T is the temperature; and L is the liquid water content (LWC) of the aerosol (in cm3 liquid water per cm3 air). We set the liquid water content value within the 10-11–10-12 range of values proposed by Engelhart et al. (2011) for a deliquescent aerosol.

For a dry aerosol we used an equation similar to Eq. (3), which has been shown to apply equally to the organic compounds that condense into an organic phase (Eq. 4) (e.g., Donahue et al., 2009; Valorso et al., 2011). There, Mw stands for the mean organic aerosol molar mass (set to 250 g mol-1 based on Robinson et al., 2007), COA represents the total organic aerosol mass concentration (µg m-3) and Pvap is the saturation vapor pressure (atm) and considering an ideal mixture. ξi=CaiCai+Cgi=1+MWPvapCOART106-1 Figure 3 illustrates the gas-particle partition of the three semi-volatile compounds considered in our work for the two distinct situations. The fraction of the compound present in the particulate phase (represented by ξi values) is plotted as a function of KH for a deliquescent aerosol under typical atmospheric liquid water content situations (upper graph), and as a function of Pvap in the case of a dry organic aerosol with COA ranging from low (0.1 µg m-3) to high (10 µg m-3) atmospheric concentrations (lower graph). This figure shows how the magnitude of the condensation process increases with the KH value (Fig. 3a) and decreases with the saturation vapor pressure (Fig. 3b). To analyze these results, each graph can be split into three parts.

For deliquescent aerosols:

When the Henry's law constant value is lower than 107 Matm-1 (part I) or greater than 1013 Matm-1 (part III), considering the selected range of LWC values, the equilibrium is either in favor of the gas phase (part I, not significantly present in the aqueous phase) or in favor of the particulate phase (part III, highly soluble compounds), respectively.

It is thus important to determine how uncertainties in the KH value influence the results and efficiency of the two oligomer production approaches. For this purpose, we conducted sensitivity tests to the refinement of the most uncertain KH values, taking into account the structure of the model species and of its components.

CHIMERE simulations were launched in the reference, KIN, and KPH configurations (both modes) for the two periods of interest defined above. The quantitative differences in the concentrations of the simulated biogenic oligomers, as well as their spatial and temporal features, were investigated. As mentioned previously, we focused on the comparison between the BiOLG (KIN approach) and the pBiA0DKPH – REFERENCE (KPH approaches) concentration fields.

Figure 4 presents the oligomer daily concentration maxima simulated by CHIMERE from the oxidation of monoterpenes for both parameterizations and for 1 representative day of the simulated period. It highlights large differences in the oligomer concentration fields produced in each approach, both in terms of intensity and spatial distribution. Indeed we can see that, using the KIN approach, the highest oligomer concentrations reach about 0.80 µg m-3 over southeastern Europe (Fig. 4a) while in both KPH configurations the peak values are highly localized (not necessary in the same areas according to the mode used) and may exceed 1 µg m-3 (Fig. 4b and c), with local peaks around 1.50 µg m-3 (not visible on the color scale). The same divergences between the KIN and the KPH model configurations are observed for every day of the summer period, with daily concentration maxima spanning the 0.30–1 µg m-3 and the 0.80–2.50 µg m-3 ranges, respectively. In terms of hourly peaks, we can learn from the KPH results that there are areas of high gaseous precursor concentrations where BiA0D solubility is (at least transiently) strongly enhanced by local reductions in pH. According to Fig. 3 the decline in pH has to be greater than 3 or 4 units, with regard to the reference value of 6, so as to increase the BiA0D partitioning constant by several orders of magnitude and allow the massive transfer of the species to the particulate phase. Such conditions appear to be met off the eastern Italian and notably over well-delimited forested continental areas of northern Spain. From the elevated peak values, it seems likely that the formation of oligomers proceeds by rapid changes in the BiA0D partitioning. In return, the inhomogeneity of oligomer concentration fields suggests a recurring evaporation of the particulate aerosol component in the deliquescent mode and/or the instability of low pH values. As for the KIN approach, we can see that the time required for the kinetic process, as well as the irreversible nature of the coded process, allows for the presence of large regional oligomer plumes with smooth concentration gradients, as well as the presence of significant numbers of this species over the entire domain.

When averaging our results over the whole summer period, we observe no significant change in the location of high oligomer concentrations, though concentration values are logically lower than hourly peaks, and concentration fields show smoother gradients (Fig. 5). However what is interesting is that the quantitative trends differ from those predicted previously. Indeed, the KIN parameterization produces the highest average oligomer concentrations that range from 0.1 to 0.4 µg m-3 over most of the simulation domain. This approach forms well-mixed secondary plumes similar to those of other long-lived atmospheric oxidants such as ozone, with maxima over central Europe and Mediterranean areas. On the contrary, KPH oligomers only slightly exceed 0.1 µg m-3 (in both deliquescent and metastable modes), except over small regions of the Adriatic Sea and over northern Spain areas where they reach a value 0.3 µg m-3 in the deliquescent mode. It is noticeable that, due to the persistence of an aqueous phase, the metastable mode produces higher oligomer concentrations over the entire domain. However, the difference remains moderate in terms of absolute mass concentration. This feature confirms the lack of oligomer mass accumulation in the KPH approach that was observed in the spatial analysis of hourly maps. It indicates that, beyond the question of relative humidity, favorable conditions for oligomers production in the KPH approach are not often met along time. The conditions of the process reversibility thus have to be more precisely identified and understood, for both modes of this approach.

We explored these differences in order to identify the parameters driving production, transport and decomposition of oligomers over continental areas for both approaches. First, the parameters describing the aerosol properties together with the BiA0D partition were plotted over the domain and analyzed for a given time step of the simulation. Then we investigated the temporal evolution of the BiA0D partition and oligomer formation at one grid point of the domain in the three CHIMERE configurations.

Figure 6 presents the nature (humid or dry) and the pH of the aerosol simulated over Europe for 24 July 2006 at 05:00 UTC, in relation to BiA0D concentration fields. The similarity of the aerosol type (dry or humid, Fig. 6a) determined by ISORROPIA and of the oligomer concentration fields (Fig. 6d) indicates that the existence of a deliquescent aerosol is not ensured in all grid cells and proves to be a discriminatory parameter for oligomer production in the simulations. Figure 6 also emphasizes the role of pH in this process. In northern Spain, significant oligomer formation is observed in the presence of both a wet aerosol and a very acidic aqueous phase (pH around 2.5), although this is not a region where the concentrations of BiA0D are high. On the contrary, over Great Britain, where there is no significant oligomer formation, CHIMERE predicts the presence of a deliquescent aerosol, low gaseous BiA0D concentrations and a pH value around 4. These results place the pH threshold for a significant oligomer production from BiA0D at a value comprised between 3 and 4. Our previous calculations indicate that the fraction of BiA0D in the aerosol phase remains lower than 1 % for a pH of 4, but reaches up to 6–39 % for a pH of 3, considering a LWC in the 10-11 to 10-12 range (cm3 water cm-3). This exponential relationship supports the local formation of high oligomers concentration peaks in Fig. 6d, with regards to the conditions shown in Fig. 6a and b. Clearly, although the presence of the precursor is the first requirement for oligomer production, it is not a determining parameter of the structure of oligomer concentration fields. As the modeled pH strongly impacts the rate and the intensity of oligomer formation, its robustness was questioned. Although no direct measurements of the pH of the aerosol have been realized yet, our calculations are consistent with previous experimental studies reporting strongly acidic fine particles (Ludwig and Klemm, 1990; Herrmann, 2003; Keene et al., 2004). Our results are also consistent with the work of Xue et al. (2011), which is based on chemical composition and meteorological data collected at a suburban site in Hong Kong and which estimated the aerosol pH to range between -1.87 and 3.12. Despite the uncertainty that cannot be fully removed on the modeled pH value, we did not consider necessary to run other assessment methods, on the basis of the recent works of Henningan et al. (2015), who affirm that thermodynamic models like ISORROPIA are more adapted to estimate the aerosol pH than proxy methods such as the ones using ion balance and ratios.

In order to address the temporal variation of the aerosol properties related to oligomer formation, concentration time series for BiA0D (reference simulation – blue line) and for oligomers (KIN approach – red line, KPH approach – green line for the deliquescent mode, black line for the metastable mode) have been plotted in Fig. 7 for a given grid cell in northern Spain for the period from 20 to 24 July.

In the KIN approach, BiOLG progressively accumulates in the air mass and shows a smoothed concentration curve along time. Furthermore, oligomer concentrations are not strongly correlated with the presence of gaseous precursors due to the time required for the kinetic formation process. In the KPH approach, oligomer concentrations are highly variable, showing intense peaks that alternate with periods of near-zero content in the particle phase. It is noted that the black curve (KPH, metastable mode) presents high values on 22 and 23 July that are not observed for the results of the deliquescent mode. These events are neither correlated with a specific origin of the air mass (analysis not shown here) nor with a given BiA0D concentration threshold, but both take place during shaded periods and can therefore be attributed to the limiting effect of a dry aerosol in the deliquescent mode. However, from the co-variability of pBiA0D concentrations in shaded and non-shaded areas, it appears that the existence of a deliquescent aerosol is not the only driving parameter of this formation/evaporation cycle. Indeed, sharp decreases in the particulate fraction of BiA0D are simultaneously observed whatever the aerosol physic state (see 21–22 and 24 July for instance), which implies that pH variability also plays a decisive role in the calculations, during a large part of the day. During these periods, the pH value was indeed comprised between 4 and 6, thus being the principal limitation for BiA0D storage in the particulate phase. Thereby, whatever the selected mode (deliquescent or metastable), there is no continental transport of oligomers due to fast and quantitative release processes. It results in the simulation of short duration peaks, accounting for local production from emissions.

Finally, Fig. 7 reveals the recurrent loss of particulate BiA0D in northern Spain during the period of study, mostly during daytime periods. It shows an average duration of 2 to 6 h for the oligomer peak events, which is quite short in view of the time required for pollutant mixing and transport in the troposphere. Therefore, these local phenomena cannot affect PM mixing ratios over large areas and for extended time periods. As the transfer of BiA0D to the gas phase from the aerosol is frequent and total in the KPH approach, its consistency has to be considered. This process appears to be highly dependent both on the pH variability – which has been poorly measured up to now – and on the KH change (from Eq. 1) required to significantly alter the partition of BiA0D between the two phases. That is, the choice of the reference KH value may be of primary importance. Such findings question the relevance of simulating a low-constrained reversibility for the formation of oligomers in 3-D models.

From these results, three key points can be inferred. First, the structure of oligomer concentration fields is driven both by the kinetic constant rate and by average pBiA∗D concentrations in the KIN approach, while it mainly depends on the physical and chemical aerosol properties in the KPH approach. In that latter approach, the formation of large quantities of oligomers appears to be conditional on the presence of a deliquescent aerosol and of strong acidity, sufficient initial particulate material, and possibly high radical levels for the oxidation of biogenic VOCs. However, most of the differences between this equilibrium approach and the kinetic one may be reduced by considering a greater stability (better constrained reversibility) in the pH-dependent oligomerization process. The relevance of taking this into consideration in 3-D models will be discussed in the last part of this article. Second, the total mass of simulated oligomers, as well as their participation in the organic fraction of the aerosol, is clearly specific to the adopted approach. This is quantitatively described in Sect. 3.1.4. Finally, we have shown that the default solubility to BiA0D is a determining element of the model results in the KPH approach. As it affects the default quantities of BiA0D (and other oligomer precursors) in the aerosol, it may also play a major role in the results of the KIN approach. As the allocation of this parameter is quite uncertain, the sensitivity of the model results to KH will be investigated in Sect. 3.2.

In a second step, we estimated the contribution of the modeled oligomers to the biogenic secondary organic aerosol (BSOA) budget. For this analysis, we first considered the ratio of oligomers arising from monoterpenes only to the so-called BSOAterp (fraction of SOA induced by both hydrophilic and hydrophobic species from monoterpenes, Fig. 8) and then, using the KIN approach only, all biogenic (isoprene included) oligomers (Fig. 9) and total BSOA.

When considering monoterpenes as the only oligomer precursors, the implementation of a kinetic approach (Fig. 8a and b) results in a significant increase (+1–2 µg m-3) of the average OA mass concentration inside the plume. Although the general structure of the plumes is not changed, the kinetic production of oligomers leads to the presence of significant BSOAterp values over an area that is much broader than in the reference case. On the opposite, the KPH approach in deliquescent mode (Fig. 8c) does not modify the average mass concentration and spatial distribution of BSOAterp. The same conclusion can be drawn from the metastable version of KPH (not shown here). In terms of ratios, the OA fraction that remains under the form of oligomers (Fig. 8d and e, representing pOLG to BSOAterp ratio) represents 20 to 50 % of the organic aerosol mass originating in monoterpenes over all the continental areas in the KIN approach. It is due to the stabilization of a very large proportion of biogenic organic species in the condensed phase under the form of oligomers. However, extreme values of this ratio are simulated over marine areas (see the purple color, meaning that approximately 80 % of BSOAterp is under the form of oligomers). This phenomenon can be explained by a combination of two factors. First, irreversible and continuous oligomer formation is the only possible chemical evolution pathway for condensed biogenic species in this version of the model. Second, in our model, marine areas are very little influenced by fresh organic emissions, which tend to favor the omnipresence of an aged OA over the sea. This is probably wrong, as high contributions of primary organic matter to the marine aerosol were predicted. However, they are not taken into account in our simulations (Ovadnevaite et al., 2011). Furthermore, such a high degree of OA conversion to oligomers has never been reported in the literature. Although it is limited on that point, it may be partly unrealistic to simulate a single fate for all biogenic organics present in the particulate phase. Despite this statement, the absolute OA concentration simulated over the sea remains low (< 0.2 µg m-3), thereby limiting the impact of this potential bias in the model. With regard to KPH simulations, the model indicates (as expected) a very low average contribution of oligomers to the mass of BSOAterp over continental areas, except in the north of Spain – where the contribution of oligomers represents 10 to 20 % of the SOA mass concentration – and over marine areas where it sometimes exceeds 40 %. Over continental areas, the oligomer fraction is shown to be insignificant because of the frequent reversal of the formation process due to wide pH variations (see above).

Isoprene oxidation products are a major contributor (around 50 % in our simulations) to the total SOA mass. Therefore, when their potential for oligomerization is considered in KIN, they significantly contribute to this aged organic fraction. Indeed, as can be seen in Fig. 9, when isoprene surrogates are included in the OA aging process, the average BSOA mass fraction increases by 2 to 4 µg m-3 over the entire eastern and southern areas of our domain. In these areas, its total concentrations reach 3 to 6 µg m-3. The largest increases are obtained over Italy, as well as over the Mediterranean and Adriatic seas, where the recirculation of continental air masses possibly favors air mass aging under low dispersion conditions.

These results highlight the importance of closer identifying the oxidation products of the main atmospheric biogenic volatile organic compounds (BVOCs), as well as their structure and reactivity. In particular, questions still arise about the way the evolution of condensed isoprene derivatives should be represented. Indeed, the assumption of Carlton et al. (2010), which states that the formation of oligomers is driven by a same first-order rate constant whatever the oxidation products, is questionable. First, because this parameterization derives from the evolution of cyclic compounds in chamber experiments, which is the case for α- and β-pinene, the two most common monoterpenes, but not for isoprene and its derivatives. The oxidation of isoprene by hydroxyl radicals leads to the formation of methyl vinyl ketone and methacrolein (Pandis et al., 1991, Paulot et al., 2009), which in turn produces tetrols and methylglyceric acid (Claeys et al., 2004; Surratt et al., 2006; Kleindienst et al., 2009) that are aliphatic compounds. Although oligomer formation from the oxidation of isoprene has been shown to occur in smog chambers (e.g., Sato et al., 2011; Nguyen et al., 2011a, b; Liu et al., 2012a; Tan et al., 2012; Lin et al., 2014), the oligomer formation process is likely to differ significantly from that from aromatics as measured by Kalberer et al. (2004). Second, since this kinetic constant only stands for an average reactivity, Kalberer et al. (2004), during their experiments, could only observe the fact that 50 % of the total organic mass was conversed to oligomer-like species. Such results cannot establish whether all aromatic compounds have undergone oligomerization following the same pathway or if its evolution was only attributable to a specific set of compounds. Applying this parameterization to a large set of biogenic species may cause an incorrect assessment of the contribution of oligomers to the total SOA budget.

As mentioned above, no direct measurement of the oligomer fraction of SOA is available at ground-based measurement stations. However, we can assess the role of oligomer formation processes in improving model–measurement comparisons, knowing that the organic fraction of atmospheric aerosols is usually underestimated by models (Heald et al., 2011). In this section, we present the comparison of CHIMERE organic carbon (OC) mass concentration in the PM10 fraction of aerosols, obtained with four different model configurations (REF, KIN and KPH in both modes) with measurements obtained at two EMEP background sites: the rural stations of Harwell in the United Kingdom (100 km west of London) and Melpitz in eastern Germany (150 km south of Berlin). Figure 10 presents these comparisons for the period 20 July–3 August 2006, the statistical data (mean bias, MB, normalized mean bias, NMB, root mean square error, RMSE, normalized root mean square error, NRMSE, and correlation coefficient, R) being given in Table 2.

Globally, whatever the configuration, the modeled OC is severely underestimated at both stations. Nevertheless, the KIN approach provides an increase in the OC mass concentration of about 1 µg m-3, which reduces significantly the gap between model and measurements, both at Harwell and Melpitz sites. According to Table 2, the mean bias is reduced from -1.10 to -0.82 µg m-3 (Harwell) and from -2.71 to -1.82 µg m-3 (Melpitz) compared with the reference simulation, but the correlation coefficient remains the same (around 0.5 and 0.7, respectively). This is due to the fact that the impact of the kinetic-dependent production of oligomers is quite little time-dependent and thus does not allow for the restitution of the peaks observed along the period and missed by CHIMERE in its reference configuration. Thus, this approach rather provides an increase in the OC background level and does not position oligomers as likely to account for the short-time variability of OC in summer. This result highlights the importance of ensuring the consistency of the process kinetics, and intensity (which is KH-dependant).

The pH-dependent approaches have shown to cause a fast and intense production of oligomers that may induce such a short-time variability in the SOA fraction of the aerosol. Here, though, there is no quantitative impact of this process on the OC mass concentration level all along the period, whatever the site. Such results could be expected in the deliquescent configuration, since we concluded that the simulated relative humidity was too low to permit the transport of oligomers over long distances. But it appears that the metastable mode, which promotes oligomer persistence and its transport in the atmosphere, also does not significantly impact the organic carbon concentration at those sites. One possible explanation for the lack of effects is the non-inclusion of isoprene as an oligomer precursor in the KPH simulations, especially because the analysis of the model output reveals that 60 to 70 % of KIN oligomers derived from isoprene at both stations. However, the conditions in which the KPH simulation was launched, and mainly the KH value used for the BiA0D species in conjunction with the variability of the aerosol pH, could also account for the low production of oligomers in remote continental areas of Europe.

The sensitivity of oligomer parameterizations to the KH input parameters is investigated in the next paragraph.

In view of surrogate properties presented in Fig. 3a, our sensitivity study focused on the transition area, that is the 4×108–4×109 Matm-1 range of KH, which allows for accounting for the solubility of all the potential oxidation products mentioned before, while providing estimates of the impact of correcting the global BiA0D KH value. In this range, we considered three specific KH values for BiA0D (4.97×104, 4×108 and 4×109 Matm-1). Before conducting the sensitivity tests in CHIMERE, we evaluated the influence of KH on the partitioning coefficient of BiA0D, using the same graphs as in Sect. 2, over the whole range of possible pH values and with a liquid water content of 10-11 cm3 water cm-3. The results are presented in Fig. 11. The reference value (KH=4.97×104 Matm-1, black curve of Fig. 11) corresponds to the left part of Fig. 3a, that is a quite null value of the partitioning coefficient. Here, we can see that only an acidic aqueous phase (pH < 4) allows for the quantitative formation of oligomers. When increasing KH to a value in the 4×108 to 4×109 Matm-1 range, we enter the second area of Fig. 3a, where the particulate fraction of BiA0D becomes significant for a LWC of 10-11 cm3 water cm-3. There, a significant formation of SOA takes place from neutral conditions with 10 to 52 % of BiA0D being in the condensed phase, depending on the KH value. For a pH of 5, particulate fraction reaches 48 and 90 % in favor of the aerosol phase, for KH=4×108 and 4×109 Matm-1, respectively. However, in this transition area, the partition of the surrogate species remains strongly influenced by the liquid water content. Such results underline the threshold condensation phenomenon for this range of KH values. Also, such a sensitivity of BiA0D solubility to the KH value may have important consequences for the results of the KPH approach (whatever the mode considered). Indeed, considering the highest KH value instead of the standard one, at pH = 6, in the reference simulations, causes the reference particulate fraction of BiA0D to increase from 0 to 52 % (with LWC =10-11 cm3 water cm-3). The impact of implementing a pH-dependent approach will thus be lower and the resulting speciation of the OA material will show a much lesser proportion of oligomers.

The sensitivity tests were launched with CHIMERE in the reference, KIN and KPH configurations (in both deliquescent and metastable modes) using each time a different KH value, as mentioned in the previous section. The average simulated oligomer concentrations fields are shown in Fig. 12 for the KIN (left), KPH deliquescent (center) and KPH metastable (right) approaches.

In the KIN approach, we observe that an increase in the value of the Henry's law constant value (from top to bottom, left column) induces an increase in average simulated oligomer concentrations, due to the low solubility of the BiA0D species in the standard configuration, which was identified as a limiting parameter for the kinetic production of oligomer in the condensed phase. However, this dependency is nonlinear. The increase of KH by almost 4 orders of magnitude (from 4.97×104 to 4×108 Matm-1) induces approximately the same response as a further increase by 1 order of magnitude (from 4×108 to 4×109 Matm-1), i.e., +0.1 to +0.2 µg m-3 over Italy and the Adriatic Sea in each case. Clearly, there is a low effect of KH variability under a threshold located around 108–109 Matm-1 in the simulated atmospheric conditions

The interpretation of the model behavior is more complex in the KPH configuration. As stated above, the KPH parameterization affects the partition between the gas and particulate phases, and oligomer concentrations are accounted for by an increment in the quantities of the condensed surrogate BiA0D. For the deliquescent mode, when KH is set to 4×108 Matm-1 (Fig. 12e), oligomer concentrations increase over continental areas by 0.1 to 0.2 µg m-3 on the average, compared with the simulation using the standard KH value (Fig. 12b). Indeed, as the solubility of Bia0D becomes higher, the decrease in pH required to form particulate material is reduced. Thus, even for pH values around 4–5, the partitioning of BiA0D towards the aerosol phase is favored. In this configuration, the oligomer maxima are located over the continent and not over the Adriatic, which means that the spatial and temporal evolution of SOA is substantially modified by the choice of the default KH value. When shifting again the KH value by 1 order of magnitude (4×109 Matm-1; Fig. 12h), we observe a decrease in the oligomer concentrations compared with Fig. 12e. This result illustrates the fact that, in this configuration, the default BiA0D partition is much in favor of the particulate phase, and that there is no significant effect of further increasing the KH value through Eq. (1). However, in these three simulations, the total SOA mass from hydrophilic biogenic species (not shown, corresponding to pBiA0D dissolved by default + the incremental fraction due to the effect of Eq. 1 on KH) increases from the low to the high KH value scenario. With regard to the metastable mode, the absolute increase in the oligomer concentration due to acidity is significantly higher than in the deliquescent mode (see the concentration scale) due to the fact that, in this configuration, there is no parameter (such as relative humidity, RH) able to set the quantity of oligomer present in the condensed phase back to zero. There, as for the deliquescent mode, the spatial and temporal features of oligomer production are profoundly altered by the assignation of the BiA0D KH value. Knowing the complex composition of this surrogate species, it is a major difficulty in the implementation of the KPH approach.

Finally, whatever the choice of BiA0D solubility, the location and the spatial extent of oligomer formation remain different in the three configurations of CHIMERE. While the kinetic production of oligomer species leads to a diffuse plume with maximum values in the Mediterranean and over southern Europe, while the highest concentrations are observed over forested areas of central Europe – thus closer to biogenic sources – in the KPH approaches where instantaneous oligomer production is simulated. This result draws our attention to the impact of the oligomer formation rate on the distribution of SOA in continental plumes, especially considering the diversity of relevant SOA precursors in the BiA0D species. Finally, it is worth noting, however, that the high KH scenario of the metastable KPH mode makes little sense, as the KPH approach is based on the possibility for OA formation to depend on the specificities of the aerosol aqueous phase, which is no longer the case in Fig. 12e and h.