The box model is constructed in order to represent the South Coast Air Basin during CalNex in spring–summer 2010. The measurements of aerosols used in this study were conducted in Pasadena, California (34.1406∘ N, 118.1224∘ W), located to the northeast of downtown Los Angeles (Hayes et al., 2015). An overview of CalNex has been published previously (Ryerson et al., 2013). The location and the meteorology of the ground site at Pasadena are described in further detail in Hayes et al. (2013). Pasadena is a receptor site for pollution due to winds that transport emissions from the ports of Los Angeles and Long Beach and downtown Los Angeles. Airborne measurements of aerosols were also carried out in the South Coast Air Basin as part of the CalNex project. A detailed description of the airborne measurements is given in Bahreini et al. (2012). Furthermore, measurements of POA composition and volatility taken at the Caldecott Tunnel in the San Francisco Bay area reported in previous work (Worton et al., 2014) are also used to constrain the model as described below. The tunnel air samples were collected during July 2010.

Two additional data sets are used to evaluate the model. In addition to sampling ambient air, an aerosol mass spectrometer (AMS) sampled air that had been photochemically aged using an OFR (Ortega et al., 2016). The OFR exposed ambient air to varying concentrations of OH radicals in order to obtain photochemical ages much higher than the ambient levels observed at the Pasadena site, and the amount of SOA produced was quantified as a function of OH exposure. Moreover, radiocarbon (14C) analysis has been performed on filter samples and results were combined with positive matrix factorization (PMF) data to determine fossil and non-fossil fractions of the SOA components as reported in Zotter et al. (2014). The 14C results are used for subsequent comparison against the box model from which fossil and non-fossil SOA mass can be estimated.

The SOA model is set up to include three types of precursors: VOCs, P-IVOCs, and P-SVOCs. The parameters used in the box model to simulate the formation of SOA from these precursors are listed in Tables S1 to S3 of the Supplement. The box model dynamically calculates the evolution of organic species in an air parcel as it undergoes photochemical aging, hence producing SOA. The total SOA also includes background SOA (BG-SOA) at a constant concentration of 2.1 µgm-3, as determined in our previous work (Hayes et al., 2015). The model accounts for P-SVOC emissions from vehicular exhaust and cooking and treats POA as semi-volatile (Robinson et al., 2007). It should be noted that the model uses CO and NOx as inputs to constrain the model, and the SOA yields for high-NOX conditions are used, based on our previous work (Hayes et al., 2013, 2015). Therefore, to verify model performance, both predictions of VOC and POA concentrations have been compared against field measurements and the model performance appears to be satisfactory (Hayes et al., 2015).

A schematic of the model is shown in Fig. 1. All the model cases are listed in Table 1, and all the parameterizations are shown schematically in Fig. 2. The first model case (ROB+TSI) incorporates the Robinson et al. (2007) parameterization for SOA formation that models P-IVOCs and P-SVOCs (i.e., P-S/IVOCs) using a single volatility distribution and oxidation rate constant. The ROB+TSI case also uses the Tsimpidi et al. (2010) parameterization for SOA formation from VOCs. A detailed description of the parameters used in ROB+TSI can be found in Hayes et al. (2015), and the ROB+TSI model case used here is identical to the case of the same name used in that paper. Briefly, as displayed in Fig. 2a, the Tsimpidi et al. (2010) parameterization proposes that the VOCs undergo an initial oxidation step that will form four lumped products with different volatilities (c*=1, 101, 102, 103 µgm-3, where c* is the effective saturation concentration). The first-generation oxidation products can be further oxidized, decreasing their volatility by 1 order of magnitude (i.e., aging). This “bin-hopping” mechanism repeats until the lowest-volatility product is reached (c*=10-1 µgm-3 in this study and 1 µgm-3 in other studies such as Tsimpidi et al. (2010) and Hayes et al. (2015). The Robinson et al. (2007) parameterization proposes that the P-S/IVOCs are initially distributed in logarithmically spaced volatility bins ranging from c*=10-2 to 106 µgm-3. Thereafter, the oxidation of P-S/IVOCs decreases their volatility by 1 order of magnitude until the lowest-volatility product is reached (c*=10-2 µgm-3). The lowest-volatility product possible is not the same for the oxidation of VOCs vs. the oxidation of the P-S/IVOCs (10-1 vs. 10-2 µgm-3, respectively). However, whether the mass is distributed into either bin has a negligible effect on the SOA mass simulated in the box model because of the relatively high SOA concentrations during the case study.

In this work, five model parameterizations are tested that incorporate new measurements of IVOCs and P-SVOC volatility as well as updated VOC yields that account for wall losses of vapors (Zhang et al., 2014; Krechmer et al., 2016). For the first new case (ROB+ZHAO+TSI), we incorporate IVOC data measured in Pasadena during the CalNex campaign as reported from Zhao et al. (2014). In particular, the measured concentrations of speciated and unspeciated IVOCs and their estimated volatility are used to constrain the initial concentration of these species (as discussed in Sect. 2.2.2 below) as well as to estimate their yields (Zhao et al., 2014). Therefore, we replace the inferred concentrations of IVOCs that were used in our previous work and were based on the volatility distribution of Robinson et al. (2007) with concentrations that are directly constrained by measurements. In the ROB+ZHAO+TSI case, the SOA formation parameters used (e.g., yields, oxidation rate constants) are taken from Zhao et al. (2014) for the IVOCs and from Hayes et al. (2015) for the VOCs and SVOCs. Hodzic et al. (2016) have also estimated the IVOC yields while accounting for wall losses using recent laboratory studies. However, the yields reported in that study are for a single lumped species, whereas in our work we estimate the yields using 40 IVOC categories, each representing a single compound or a group of compounds of similar structure and volatility. This method allows a more precise representation of IVOC yields and rate constants in the SOA model.

For the second new case (WOR+ZHAO+TSI), the volatility distribution of P-SVOCs is updated using measurements of POA performed at the Caldecott Tunnel in the California Bay Area (Worton et al., 2014). In the previous two cases described above, the relative volatility distribution of P-SVOCs was taken from the work of Robinson et al. (2007). In this distribution, the relative concentration of SVOCs increases monotonically between the c*=10-2 and 102 µgm-3 bins. The P-SVOC volatility distribution in the WOR+ZHAO+TSI case increases monotonically as well, but the relative concentrations in each bin are different and notably there is a much higher relative concentration of SVOCs in the c*=102 µgm-3 bin (see Fig. 2 and Table S3). In this model case, the updated P-SVOC volatility distribution is only applied to vehicular P-S/IVOCs, whereas the volatility distribution proposed by Robinson et al. (2007) is still used for cooking emissions.

Several recently published papers have found that chamber experiments may underestimate SOA yields due to the loss of semi-volatile vapors to chamber walls (Matsunaga and Ziemann, 2010; Zhang et al., 2014; Krechmer et al., 2016). A sensitivity study has been performed to explore this uncertainty by running the three model cases described above (ROB+TSI, ROB+ZHAO+TSI, and WOR+ZHAO+TSI) with a revised version of the SOA yields for VOCs that account for these wall losses. This revised set of parameters is denoted as MA, whereas the original parameterization for VOC oxidation has been denoted as TSI. A detailed description of how these updated yields were estimated is provided in the Supplement and the values can be found in Table S4. Briefly, equilibrium partitioning is assumed to hold for the organic mass found in the gas phase, particle phase, or chamber walls. The SOA yields are then obtained by refitting SOA chamber yield curves using a model that accounts for partitioning between the three compartments (particle, gas, and wall) and incorporates the equivalent wall mass concentrations published in Krechmer et al. (2016), which are volatility dependent. The SOA chamber yield curves that were refitted were first calculated using the parameters published in Tsimpidi et al. (2010). There are limits to the assumption that partitioning between the three phases occurs on short enough timescales for all four VOC product volatilities to reach equilibrium during a SOA chamber study. Specifically, at lower volatilities (c*≤1 µgm-3), the partitioning kinetics of the organic mass from the particles to the chamber walls have an effective timescale of more than an hour, which is similar to or longer than typical chamber experiments (Ye et al., 2016). The limiting step in the partitioning kinetics is evaporation of SVOCs from the particles to the gas phase, and therefore the exact rate of evaporation depends on the OA concentration in the chamber.

Furthermore, as described in the Supplement, the updated SOA yields for VOC oxidation result in distribution of SVOC mass into lower-volatility bins compared to the original parameterization, although the sum for the SVOC yields (αi) remains similar. In the absence of aging, the SOA yields, Y, resulting from the wall-loss correction should be considered upper limits (MA parameterization), whereas the original yields serve as lower limits due to the considerations discussed above (TSI parameterization without aging). As shown in the Supplement (Figs. S1–S7) when aging (TSI parameterization with aging) is included, the SOA yields increase beyond those observed when applying the wall loss correction for most of the VOC classes at longer photochemical ages. It should be noted that SOA masses in Figs. S1–S7 were calculated using the same background as for the other model cases, 2.1 µgm-3. This feature of the aging parameterization is likely to blame for SOA overpredictions observed at long aging times when comparing with ambient data (e.g., Dzepina et al., 2009; Hayes et al., 2015).

According to Krechmer et al. (2016) and other chamber experiments (Matsunaga and Ziemann, 2010), the gas–wall equilibrium timescale does not vary strongly with the chamber size. The timescale for gas–wall equilibrium reported in these previous studies was 7–13 min. Similar timescales have been calculated for a variety of environmental chambers, including chambers that were used to determine many of the yields used in this paper. In addition, Matsunaga and Ziemann (2010) found that partitioning was nearly independent of chamber treatment, reversible, and it obeyed Henry's law. Thus, the effective wall concentrations determined from the chamber experiments reported in Krechmer et al. (2016) are likely applicable to other chambers with different sizes.

The three model cases accounting for wall losses of organic vapors are named ROB+MA, ROB+ZHAO+MA, and WOR+ZHAO+MA. For these cases, the aging of the secondary SVOCs formed from the oxidation of VOCs was not included since multi-generation oxidation is not well-constrained using data from chamber studies that are run over relatively short timescales (i.e., hours). In addition, aging and correcting for wall losses of organic vapors have been separately proposed to close the gap between observed and predicted SOA concentration from pre-2007 models and are thought to represent the same missing SOA mass. Therefore, we run the model with one of these options at a time, as they are conceptually different representations of the same phenomenology. The aging of secondary SVOCs formed from the oxidation of P-IVOCs (and P-SVOCs) has been kept for all of the MA cases, however. To our knowledge, P-IVOC and P-SVOC mechanisms proposed in the literature have always included aging. A similar approach for correcting the yields as described above cannot be applied to P-IVOCs because organics with low volatilities (c*<10 µgm-3) will partition to chamber walls very slowly, and SVOCs from P-IVOC oxidation tend to have lower volatilities than the SVOCs formed from VOC oxidation (Tables S1 and S2). Indeed, when trying to refit the VOC and IVOC yield curves, the model assuming equilibrium partitioning between particles, the gas phase, and the walls was able to reproduce the yield curves for VOCs, but not for IVOCs. This difference in the results is consistent with equilibrium not having been reached during the chamber studies on the IVOCs, which produce a greater amount of lower-volatility SVOCs when compared to VOCs during oxidation. These lower-volatility SVOCs have relatively slow evaporation rates from the particles, which prevents the chamber system from reaching equilibrium (Ye et al., 2016).

Simulations of O : C have been previously evaluated in Hayes et al. (2015) using laboratory and field data from CalNex to constrain the predicted O : C. It was concluded in that work that it was not possible to identify one parameterization that performed better than the other parameterizations evaluated because of the lack of constraints on the different parameters used (e.g., oxidation rate constant, oxygen mass in the initial generation of products and that added in later oxidation generations, SOA yields, and emissions). Therefore, incorporating O : C predictions into the current box model and using those results in the evaluation discussed here would not provide useful additional constraints.

The VOC yields are taken from Tsimpidi et al. (2010) or determined in this work as described below. The estimation of the IVOC yields (based on values taken from Presto et al., 2010) and of the OH reaction rate constants for IVOCs follows the same approach used by Zhao et al. (2014). However, instead of using the total SOA yield, Y, for a fixed OA concentration as reported in Zhao et al. (2014), we use the SVOC yield, α, of each c* bin. It is important to note here that the SOA yields taken from Tsimpidi et al. (2010) and Presto et al. (2010) use a four-product basis set with c*=100, 101, 102, 103 µgm-3 and c*=10-1, 100, 101, 102 µgm-3, respectively. For this box model, it is more appropriate to have a uniform VBS in terms of the bin range utilized; thus, a bin with a lower volatility (c*=10-1 µgm-3) has been added to the VBS distribution of Tsimpidi et al. (2010). The yield for bin c*=10-1 µgm-3 is 0 for VOC oxidation, but when aging occurs mass can be transferred into this bin. However, the change in the total V-SOA mass is negligible because for both bins c*=10-1 and 100 µgm-3 the secondary products almost completely partition to the particle phase.

The OH reaction rate constants are taken from the literature (Atkinson and Arey, 2003; Carter, 2010) as described previously in Hayes et al. (2015). During aging, the oxidation products undergo subsequent reactions with OH radicals with a reaction rate constant of 1×10-11 and 4×10-11 cm3molec-1s-1 for the products of VOC oxidation and P-S/IVOC oxidation, respectively (Hayes et al., 2015). For each oxidation step during aging, there is a mass increase of 7.5 % due to added oxygen.

The partitioning between gas and particle phases is calculated in each bin by using the reformulation of Pankow theory by Donahue et al. (2006). xp,i=1+CiCOA-1;COA=∑iSVOCixp,i, in which χp,i is the particle-phase fraction of lumped species i (expressed as a mass fraction), Ci is the effective saturation concentration, and COA is the total mass of organic aerosol available for partitioning (in micrograms per cubic meter). Only species in the gas phase are allowed to react with OH radicals in the model, since particle-phase species react at much lower rates (Donahue et al., 2013).

The simulated SOA mass from the model is compared to field measurements of aerosol composition, including results from PMF analysis of aerosol mass spectrometry data (Hayes et al., 2013, 2015). Specifically, the model predictions of urban SOA (i.e., SOA formed within the South Coast Air Basin) are compared to the semi-volatile oxygenated organic aerosol (SV-OOA) concentration from the PMF analysis. The other OA component also attributed to SOA, low-volatility oxygenated organic aerosol (LV-OOA), is primarily from precursors emitted outside the South Coast Air Basin and is used to estimate the background secondary organic aerosol (BG-SOA) as discussed previously (Hayes et al., 2015).

As described in Hayes et al. (2015), during the transport of the pollutants to Pasadena, the planetary boundary layer (PBL) heights increase during the day. Using CO as a conservative tracer of emissions does not account for how the shallow boundary layer over Los Angeles in the morning influences gas-particle partitioning due to lower vertical mixing and higher absolute POA and SOA concentrations at that time. Thus, as shown in the gas-particle partitioning equation above, there will be a higher partitioning of the species to the particle phase and less gas-phase oxidation of primary and secondary SVOCs. Later in the morning and into the afternoon the PBL height increases (Hayes et al., 2013), diluting the POA and urban SOA mass as photochemical ages increase. However, this is a relatively small effect as the partitioning calculation in the SOA model is relatively insensitive to this effect and the absolute OA concentrations (Dzepina et al., 2009; Hayes et al., 2015). Our previous work (Hayes et al., 2015) found in a sensitivity study a +4/-12 % variation in predicted urban SOA when various limiting cases were explored for simulation of the PBL (e.g., immediate dilution to the maximum PBL height measured in Pasadena vs. a gradual increase during the morning).

To account for the effect of absolute OA mass on the partitioning calculation, the absolute partitioning mass is corrected using the following method. A PBL height of 345 m is used for a photochemical age of 0 h and it reaches a height 855 m at a photochemical age of 9.2 h, which is the maximum age for the ambient field data. Between the two points, the PBL is assumed to increase linearly. The boundary layer heights are determined using ceilometer measurements from Pasadena at 06:00–09:00 and 12:00–15:00 LT, respectively (Hayes et al., 2013). The second period is chosen because it corresponds to when the maximum photochemical age is observed at the site. The first period is chosen based on transport times calculated for the plume from downtown Los Angeles (Washenfelder et al., 2011) that arrives in Pasadena during the afternoon. There are certain limitations to this correction for the partitioning calculation. First, the correction is based on a conceptual framework in which a plume is emitted and then transported to Pasadena without further addition of POA or SOA precursors. A second limitation is that we do not account for further dilution that may occur as the plume is advected downwind of Pasadena. However, such dilution is not pertinent to the OFR measurements, and thus for photochemical ages beyond ambient levels observed at Pasadena, we focus our analysis on the comparison with the OFR measurements.

We follow an approach similar to Hayes et al. (2015) in order to analyze the model results. The model SOA concentration is normalized to the background-subtracted CO concentration to account for dilution, and the ratio is then plotted against photochemical age rather than time to remove variations due to diurnal cycles of precursor and oxidant concentrations. The photochemical age is calculated at a reference OH radical concentration of 1.5×106 moleccm-3 (DeCarlo et al., 2010). Figure 3 shows this analysis for each model case for up to 3 days of photochemical aging. Since fragmentation and dry deposition are not included in the model, it has only been run to 3 days in order to minimize the importance of these processes with respect to SOA concentrations (Ortega et al., 2016). Nevertheless, it is very likely that gas-phase fragmentation of SVOCs (e.g., branching between functionalization and fragmentation) occurs during oxidative aging over these photochemical ages as is discussed in further detail below.

In each panel of Fig. 3, field measurements are included for comparison. The ambient urban SOA mass at the Pasadena ground site is generally measured under conditions corresponding to photochemical ages of 0.5 days or less (Hayes et al., 2013). The airborne observations of SOA in the Los Angeles basin outflow are also shown as the average of all data between 1 and 2 days of photochemical aging (Bahreini et al., 2012). The gray region on the right serves as an estimate for very aged urban SOA based on data reported by de Gouw and Jimenez (2009). The data from the OFR and a fit of the ambient and reactor data (dotted black line) are also displayed in Fig. 3 (Ortega et al., 2016). In addition, Fig. 4 shows the ratio of modeled-to-measured SOA mass on a logarithmic axis to facilitate evaluation of model performance.

As displayed in the graphs for Fig. 3, it should be noted that the measurements from the OFR (Ortega et al., 2016) and from the NOAA P3 research aircraft (Bahreini et al., 2012) give quite similar results for SOA/ΔCO. The OFR measurements are not affected by particle deposition that would occur in the atmosphere on long timescales or at long photochemical ages. Only a few percent of the particles are lost to the walls of the reactor, and this process has been corrected for already in the results of Ortega et al. (2016). The similarity in the two types of observations suggests that ambient particle deposition and plume dispersion do not significantly change the SOA/ΔCO ratio over the photochemical ages analyzed here.

In ROB+TSI, as described in previous work (Hayes et al., 2015), there is a large overprediction of SOA mass at longer photochemical ages. As displayed in Fig. 3, the amount of SOA produced in the model is higher than all of the field measurements taken at a photochemical age longer than 0.5 days. Moreover, the ratios of model to measurement are higher than the upper limit of the gray bar representing the ratios within the measurement uncertainties. There is an agreement with the measurements at moderate photochemical ages (between 0.25 and 0.50 days), but the SOA mass simulated by the model is slightly lower than the measurements at the shortest photochemical ages (less than 0.25 days) even when accounting for measurement uncertainties. In this parameterization, most of the SOA produced comes from the P-S/IVOCs, and uncertainties in the model with respect to these compounds likely explain the overestimation observed at longer photochemical ages. As discussed in the introduction, a major goal in this work is to better constrain the amount of SOA formed from the oxidation of P-S/IVOCs, and the following two model cases (ROB+ZHAO+TSI and WOR+ZHAO+TSI) seek to incorporate new measurements to better constrain the box model with respect to the P-S/IVOCs.

When the yield, rate constants, and initial concentrations of P-IVOCs are constrained using the field measurements reported in Zhao et al. (2014) (ROB+ZHAO+TSI), the SOA mass simulated by the model shows much better agreement with the measurements at longer photochemical ages (Figs. 3 and 4). There is a slight overprediction at 2 days of photochemical aging, but the model is still within the range of measurements of very aged urban SOA reported by De Gouw and Jimenez (2009). The parameterization reported in Robinson et al. (2007) for P-S/IVOCs is based on one study of the photooxidation of diesel emissions from a generator (Robinson et al., 2007). The results obtained here for the better-constrained ROB+ZHAO+TSI case indicate that the initial concentrations of P-IVOCs as well as the P-IVOC yields within ROB + TSI are too high, which leads to overprediction of SOA concentration at longer photochemical ages. Conversely, the SOA mass simulated in ROB+ZHAO+TSI is biased low at shorter photochemical ages (less than 1 day). Similar to other recent studies (Gentner et al., 2012; Hayes et al., 2015; Ortega et al., 2016), there may be unexplained SOA precursors, which rapidly form SOA, not included in the model or yields for fast-reacting species including certain VOCs may be biased low. Both of these possibilities are explored in the other model cases discussed below.

The WOR+ZHAO+TSI case simulates higher SOA concentrations at shorter photochemical ages compared to the previous case (ROB+ZHAO+TSI), but it is still biased low at shorter photochemical ages. The more rapid SOA formation is due to the updated SVOC volatility distribution in this model case compared to the cases that use the Robinson et al. (2007) distribution. Specifically, as shown in Fig. 2f, there is a higher relative concentration of gas-phase SVOCs in the c*=102 bin and thus a higher ratio of P-SVOC to POA. Given that in the box model (and in most air quality models) the P-SVOC emissions are determined by scaling the POA emissions according to their volatility distribution, a higher P-SVOC-to-POA ratio will then result in a higher initial P-SVOC concentration. Furthermore, SOA formation from P-SVOCs is relatively fast. Together these changes lead to increases in SOA formation during the first hours of photochemical aging when using the Worton et al. (2014) volatility distribution. This case suggests that P-SVOCs in their highest volatility bin (c*=102 µgm-3 bin) that are emitted by motor vehicles may be responsible for some of the observed rapid SOA formation within the South Coast Air Basin. When observing the SOA mass simulated at photochemical ages higher than 1 day, the simulation is similar to ROB+ZHAO+TSI. There is better model–measurement agreement than for the ROB+TSI case, but a small overprediction is observed in the comparison to the reactor data at 2 days of photochemical aging.

Also shown in the right-hand panels of Figs. 3 and 4 are the results with the updated yields for the VOCs that account for gas-phase chamber wall losses. For these last three cases (ROB+MA, ROB+ZHAO+MA, and WOR+ZHAO+MA), the rate of SOA formation at short photochemical ages is faster because the secondary SVOC mass from the oxidation of the VOC precursors is distributed into lower-volatility bins compared to the Tsimpidi et al. (2010) parameterization. In the ROB+MA case (Figs. 3d and 4d), similar to ROB+TSI, an overprediction is obtained at longer photochemical ages. There is an improvement in the model at the shortest photochemical ages, but the simulated mass is still lower than the measurements even when considering the measurement uncertainty. Both of these cases perform less well for SOA formation within the South Coast Air Basin, and therefore the remainder of this study is focused on the other four model cases. Overall, the model cases using the updated yields for V-SOA show improvement for the shorter photochemical ages, and the evolution of SOA concentration as a function of photochemical age better corresponds to the various measurements taken at Pasadena and from the OFR.

Specifically, the ROB+ZHAO+MA and the WOR+ZHAO+MA cases both better represent SOA formation and exhibit better model–measurement agreement among the different cases used in this work. They are both consistent with the OFR reactor data at longer photochemical ages as shown in Figs. 3 and 4 compared with the other cases. At a qualitative level, the MA parameterization simulations are more consistent with the fit of the OFR measurements in which the SOA mass remains nearly constant at longer photochemical ages. In contrast, the cases with the TSI parameterization do not follow this trend as the SOA mass keeps increasing between 2 and 3 days age, which is not observed in the measurements. As already mentioned, the model used for this work does not include fragmentation reactions, and including these reactions, in particular branching between functionalization and fragmentation during gas-phase SVOC oxidation, may improve the cases in which this potential update of the TSI parameterization is implemented as discussed below. Figure 4f indicates that including additional P-SVOC mass in the model and accounting for gas-phase wall losses in chamber studies improves SOA mass concentration simulations with respect to the measurements. However, in the WOR+ZHAO+MA case there is still a slight under-prediction of SOA formed at shorter photochemical ages (between 0.05 and 0.5 days), and this discrepancy is observed in all the other model cases. Given the uncertainties in the model setup discussed in the experimental section, it is not possible to conclude if one of the four cases (i.e., ROB+ZHAO+TSI, WOR+ZHAO+TSI, ROB+ZHAO+MA, WOR+ZHAO+MA) more accurately represents SOA formation in the atmosphere.

According to the OFR data from Ortega et al. (2016), the mass of OA starts to decay due to fragmentation after heterogeneous oxidation at approximately 10 days of photochemical aging. The results are consistent with other OFR field measurements (George and Abbatt, 2010; Hu et al., 2016; Palm et al., 2016). In this work, the model is run only up to 3 days, which is much shorter than the age when heterogeneous oxidation appears to become important. In fact, when including a fragmentation pathway for each of the model cases, a reduction of OA of only 6 % is observed compared to the cases without fragmentation at 3 days of photochemical aging. In this sensitivity study, the fragmentation is parameterized as an exponential decrease in OA concentration that has a lifetime of 50 days following Ortega et al. (2016). Given the results, the inclusion of fragmentation due to heterogeneous oxidation in the model does not significantly change the model results or the conclusions made in this work.

More generally, there are at least three different fragmentation mechanisms that could be responsible for the decrease in SOA formation at very high photochemical ages. The first mechanism is the reaction of oxidants (e.g., OH) with the surface of an aerosol particle and decomposition to form products with higher volatility, i.e., due to the heterogeneous oxidation just described. The second type of fragmentation that may be important for very high photochemical ages in the OFR is due to the high concentration of OH (Palm et al., 2016). Most of the molecules in the gas phase will react multiple times with the available oxidants before having a chance to condense, which will lead to the formation of smaller products too volatile to form SOA. However, this is only important at very high photochemical ages in the OFR, which are not used in this work. A third type of fragmentation can occur during the aging of gas-phase SVOCs (Shrivastava et al., 2013, 2015). The TSI parameterization used in the model from this work and from previous modeling works (Robinson et al., 2007; Hodzic et al., 2010; Shrivastava et al., 2011) only includes the functionalization of the SVOCs and neglects fragmentation reactions. More recently, Shrivastava et al. (2013) modified the VBS approach in a box model by incorporating both pathways and performed several sensitivity studies. The results, when including fragmentation, generally exhibit better agreement with field observations, but as noted in that work the agreement may be fortuitous given that both the emissions as well as the parameters representing oxidation in the model are uncertain. This third type of fragmentation is not simulated in our sensitivity study using the approach above, and it remains poorly characterized due to the complexity of the chemical pathways and the number of compounds contributing to SOA formation as described in Shrivastava et al. (2013).

Despite having higher SOA yields initially, over regional scales (i.e., photochemical ages at and above approximately 2 days) the parameterizations with updated V-SOA yields and without aging produce less SOA because the organic mass in higher volatility bins (c*=100 and 1000 µgm-3) is not further oxidized by aging reactions to produce organics with sufficiently low volatilities to form SOA (Figs. S1–S7). Furthermore, large SOA overpredictions have been shown to occur in gridded 3-D models when using parameterizations with aging that do not include fragmentation reactions (Shrivastava et al., 2015). Fragmentation with aging reactions may still play a role in determining SOA concentrations on such regional scales. However, for the photochemical ages studied here, our results as well as the recent findings regarding gas-phase wall losses in chamber studies suggest the inclusion of updated V-SOA yields as well as accurate parameterizations for I-SOA and S-SOA and for the emissions of precursors is more important for accurately predicting urban SOA concentrations.

Finally, Woody et al. (2016) recently proposed a meat-cooking volatility distribution and therefore we perform a sensitivity study by using this distribution in our model for P-SVOCs from cooking sources. The results are displayed in the Supplement (Fig. S8), in which this alternate approach has been implemented for the WOR+ZHAO+TSI and WOR+ZHAO+MA cases. By comparing the results obtained from this sensitivity study with Fig. 3, the two cases in the sensitivity study display a slight decrease in SOA/ΔCO values over 3 days of photochemical aging with a difference of approximately 9 % at 3 days. Thus, the model–measurement comparison does not change significantly relative to the base case. Given the similarities between the sensitivity study and Fig. 3, as well as the possibility of cooking SOA sources other than meat cooking (i.e., heated cooking oils; Liu et al., 2017), the remainder of our work uses the Robinson et al. (2007) volatility distribution for P-SVOCs from cooking sources.

Recent results from Ortega et al. (2016) point to the importance of fast-reacting precursors for urban SOA during CalNex, and we can use their results to further evaluate our box model. The fraction of SOA formed from each precursor class as a function of the precursor rate constant is displayed in Fig. 6. The right axis of Fig. 6 shows the correlation (R2) of different VOCs with the maximum concentration of SOA formed using the OFR as a function of their oxidation rate constants as reported in Ortega et al. (2016). This analysis of the OFR data allows us to constrain the rate constants of the most important SOA precursors. A detailed description of how the R2 values were obtained can be found in Ortega et al. (2016). According to the R2 data, the VOC compounds that correlate best with maximum SOA formation potential are those that have log⁡kOH rate constants ranging from -10.5 to -10.0. When comparing the percentage of SOA mass simulated by the model with the observed R2 values, all of the four cases are not entirely consistent with the R2 data. According to the model, more SOA mass is formed from precursors in the bin ranging from -11.0 to -10.5 (the majority of mass formed comes from P-IVOCs) rather than the bin ranging from -10.5 to -10.0. In contrast, the R2 value is higher for the more reactive bin. If either fast-reacting precursors were missing in the model or if the rate constants of the currently implemented precursors were too small, then correcting either error would shift the relative distribution shown in Fig. 6 towards faster-reacting SOA precursors. In turn, the trend in the percentage of modeled SOA mass may more closely follow the trend in R2 values.

Based on the evaluations carried out up to this point on the six model cases, the WOR+ZHAO+MA case seems to most closely reproduce the observations. Thus, the entire volatility distribution of the OA, precursors, and secondary gas-phase organics is analyzed for this model case. Figure 7 shows this distribution for three selected photochemical ages: 0, 5, and 36 h. The figure allows us to track the evolution of SOA and secondary gas-phase organics from each precursor class in terms of their concentration and volatility and also to evaluate the reduction of precursor concentrations. For the results, the volatility distribution of all organics resolved by precursor class, except for the VOCs and P-IVOCs, can be taken directly from the model. To determine the volatility distribution of the VOCs and P-IVOCs, the SIMPOL.1 method (Pankow and Asher, 2008) is used to estimate the effective saturation concentration of each compound or lumped species in the model. Also included in Fig. 7, in the bottom-right panel, is the observed volatility distribution for the Pasadena ground site, which is an average of measurements collected during 12:00–15:00 LT and corresponds to 5 h of photochemical aging. For the measurements, the volatility distribution of VOCs was determined using gas chromatography mass spectrometry (GC-MS) data (Borbon et al., 2013), whereas the IVOC distribution is taken from Zhao et al. (2014). The volatility distribution of SVOCs was determined using combined thermal denuder AMS measurements (see the Supplement for further details).

For the volatility distribution of the model at time 0, the concentrations of P-SVOCs and P-IVOCs monotonically increase with the value of c*. However, a discontinuity in the mass concentration exists between the c*=102 and 103 µgm-3 bins. This discontinuity can be explained by several factors. First, the measured IVOC mass concentration in the c*=103 µgm-3 bin is very low, and since the initial concentrations of IVOCs in the model are constrained by the field measurements, the model will also have very low concentrations. Zhao et al. (2014) already noted that the concentration of P-IVOCs in this bin is relatively low when compared to the volatility distribution from Robinson et al. (2007). Another possible explanation is the presence of cooking sources, which in the model are responsible for substantial P-SVOC mass (∼50 %) but may have a smaller contribution to the P-IVOC mass.

During oxidation the volatility distribution evolves and the concentration of secondary organics increases in the bins between c*=10-1 and 103 µgm-3 (inclusive), and the largest portion of SOA is found in the c*=1 µgm-3 bin. This result is due to the partitioning of the organic mass to the particle phase and the lack of particle-phase reactions in the model, which leads to very slow oxidation rates for species found in the lower-volatility bins. After 36 h, a large portion of the precursors have been reacted, although some primary and secondary material remains in the gas phase, giving rise to more gradual SOA formation.

In Fig. 7, it is possible to compare the measured volatility distribution with the model simulation at 5 h of photochemical aging. It should be noted that the relatively high concentrations of VOCs in the model compared to the measurements are due to the model containing VOCs for which measurements were not obtained in Pasadena. There are 47 VOCs used in the model and only 19 VOCs were measured. However, the remaining VOCs have been measured in other urban locations (Warneke et al., 2007; Borbon et al., 2013) and thus it is assumed they are also present in the South Coast Air Basin. For this work, we include these 28 remaining VOCs by assuming that they are also emitted in the South Coast Air Basin with identical emission ratios (ΔVOC/ΔCO). When comparing only measured and modeled VOCs (shown in hollow black bars), the results are consistent (3.1, 3.6, and 2.2 µgm-3 from c*=107 to 109 µgm-3 bins vs. 3.8, 3.7, and 2.2 µgm-3 for the measurements). Conversely, the model appears to have a low bias for the concentrations of P-IVOCs (0.16, 0.63, 0.89, and 2.3 µgm-3 from c*=103 to 106 µgm-3 bins vs. 0.21, 1.39, 2.65, and 3.82 µgm-3 for the measurements). This low bias is seen for each volatility bin and could possibly be explained by either oxidation rate constants that are too high or ΔIVOC/ΔCO ratios that are too low. The latter explanation seems more likely given that the rate constants estimated using surrogate compounds and structure–activity relationships for the unspeciated P-IVOCs are generally lower limits (Zhao et al., 2014), which would result in a high bias rather than a low bias. The ΔIVOC/ΔCO ratios may be low because the photochemical age between 00:00 and 6:00 LT is not strictly zero, and some oxidation may have occurred during the period used to determine the ratio values. Emission ratios such as ΔIVOC/ΔCO facilitate incorporating P-IVOC emissions into 3-D models that already use CO emissions inventories, and the ΔIVOC/ΔCO ratios reported here could be used for this purpose. However, the resulting I-SOA concentrations should be considered lower limits given that the emission ratios, and also the rate constants, are likely themselves lower limits.

To further explore the impact of potential errors in the initial IVOC concentrations, a sensitivity study has been carried out using initial concentrations calculated based on the observed photochemical age and measured IVOC concentrations at Pasadena as well as the estimated IVOC oxidation rate constants (Zhao et al., 2014). This alternate approach is implemented for the ROB+ZHAO+MA and WOR + ZHAO + MA cases and does not use nighttime IVOC-to-CO ratios. The results when using this alternative approach are shown in the Supplement (Fig. S10). When comparing Fig. S10 with Fig. 3, differences are minor. The model–measurement agreement improves slightly at shorter photochemical ages (less than 1 day). At the same time a slightly larger overprediction is observed at longer photochemical ages. However, the formation of SOA modeled in this sensitivity test is similar to the original cases from Fig. 3 with an average difference of only 21 %, which represents a relatively small error compared to other uncertainties in SOA modeling. The IVOC initial concentrations used in this sensitivity test are slightly higher than those calculated using the IVOC-to-CO ratio, which explains the small increase in modeled SOA/ΔCO. Ultimately, the different approaches for determining the initial IVOC concentration in the model are reasonably consistent, and both approaches perform similarly given the model and measurement uncertainties.

For the measurements of SVOCs, all the mass in bins lower than 10-2 µgm-3 are lumped into this bin for Fig. 7 since the model does not contain lower-volatility bins. In addition, the 101 and 102 µgm-3 bins are not well-resolved because the thermal denuder did not consistently reach temperatures low enough (less than 37 ∘C) to resolve SVOCs in this range of volatilities. Thus, the 101 µgm-3 bin may contain some higher-volatility particulate mass although this contribution is expected to be small due to the low particle-phase fraction of compounds in the 102 µgm-3 bin. With these considerations in mind, the volatility distribution of the SVOCs is somewhat different in the model compared to the measurements. Most notably, the model does not form a significant amount of lower-volatility SOA in the 10-2 µgm-3 bin, whereas the measurements have much higher concentrations in this bin. A factor that may explain this difference between the volatility distributions is the lack of particle-phase reactions that continue to transform SOA into lower-volatility products, a process which is not considered in the model. One example of a particle-phase reaction is the formation of SOA within deliquesced particles, including the partitioning of glyoxal to the aqueous phase to produce oligomers as discussed in Ervens and Volkamer (2010), although that specific mechanism was of little significance during CalNex (Washenfelder et al., 2011; Knote et al., 2014). Alternatively, the use of an aging parameterization in which the volatility may decrease by more than 1 order of magnitude per oxidation reaction would also distribute some SOA mass into lower c* bins. Hayes et al. (2015) previously evaluated different parameters for aging. However, the results from this previous study showed that substantial overprediction of SOA was observed when using the Grieshop et al. (2009) parameterization in which each oxidation reaction reduced volatility by 2 orders of magnitude. New parameterizations may be necessary to produce the observed SOA volatility and concentration simultaneously (Cappa and Wilson, 2012). However, we note that the additional low-volatility organic mass will not significantly change SOA predictions in urban regions where OA concentrations are relatively high. When comparing the total amount of particle-phase SVOCs, it seems that the model reproduces the measurements reasonably well (6.2 vs. 9.0 µgm-3) as expected based on the comparisons of the total SOA concentration discussed above. In addition, the total concentration of SVOCs (particle and gas phase) is similar (11.2 vs. 11.8 µgm-3), although it is difficult to determine the gas-phase concentration of SVOCs in the 102 µgm-3 bin from measurements due to the lack of particle mass in this bin under ambient concentrations as well as the limited temperature range of the thermal denuder system.

Recently, Woody et al. (2016) published a paper that modeled SOA over California using the Environmental Protection Agency's Community Multiscale Air Quality Model that had been updated to include a VBS treatment of SOA (CMAQ-VBS). As discussed in that paper, the modeled P-S/IVOC emission inventories remain an important source of uncertainty in 3-D grid-based models. In that previous study several different ratios of P-S/IVOC-to-POA emissions were evaluated against measurements, and it was found that a ratio of 7.5 gave the best agreement between the CMAQ-VBS model and observations. From the results shown in Fig. 7 at a photochemical age of 0 h, a P-S/IVOC-to-POA ratio of 5.2 is calculated. This ratio is different from that determined by Woody et al. (2016), and may be biased low due to possibly low ΔIVOC/ΔCO emission ratios as discussed earlier in this section, but it both serves as a useful lower bound and has the advantage of being determined from empirical measurements of aerosols rather than by tuning a model to match measured SOA concentrations. As stated in Woody et al. (2016), the higher ratio may compensate for other missing (or underrepresented) formation pathways in SOA models or excessive dispersion of SOA in their model.