The structure of the UNIPAR SOA model has been described previously (Cao and Jang, 2010; Im et al., 2014; Beardsley and Jang, 2016; Zhou et al., 2019; Yu et al., 2021c, 2022; Choi and Jang, 2022; Madhu et al., 2022; Han and Jang, 2023). The CAMx–UNIPAR of this study simulates SOA formation via multiphase reactions of 10 aromatics, 3 biogenics (isoprene, terpene, and sesquiterpene), and 3 alkane groups as summarized in Table 1. The lumping species, which are generated by using semi-explicitly predicted products of the oxidation of HCs, are involved in multiphase partitioning and aerosol-phase reactions to form SOA mass.

The prediction of stoichiometric coefficients associated with the lumping species from the oxidation of 10 aromatics (MCM v3.3.1; Jenkin, 2004) potentially increases the accuracy of the prediction of aromatic SOA formation under varying emissions. For biogenic HCs, recently identified biogenic oxidation mechanisms that yielded low-volatility products have been applied to the prediction of lumping species. For example, the peroxy radical autoxidation mechanism (Roldin et al., 2019) is known to form highly oxygenated organic molecules (HOMs) (Molteni et al., 2019). Additionally, HOMs form via the accretion reaction to form ROOR from RO2 species (Bates et al., 2022; Zhao et al., 2021). These HOMs are included in biogenic lumping species in the current CAMx–UNIPAR. In order to represent day and night chemistry, CAMx–UNIPAR is equipped with the oxidation-path-dependent stoichiometric coefficients from individually processed reactions of biogenic HCs with three major oxidants (OH radicals, ozone, and nitrate radicals) (Han and Jang, 2023). Thus, nighttime SOA formation, which is dominated by oxidation via ozone and nitrate radicals, can be simulated in CAMx–UNIPAR. By using the recent chamber study by Madhu et al. (2022), the lumping species generated from the oxidation of long-chain alkanes ranging from C9 to C24 have been newly integrated with CAMx–UNIPAR, which increases the predictability of SOA formation from intermediate volatility organic compounds (IVOCs). Alkane gas mechanisms include autoxidation of alkoxy radicals to form HOMs (Madhu et al., 2022; Crounse et al., 2013; Bianchi et al., 2019; Roldin et al., 2019). Importantly, the estimation of activity coefficients of lumping species in both the organic phase and the inorganic aqueous-phase enables the simulation of multiphase partitioning of lumping species and their aerosol phase reactions. Aqueous reactions in CAMx–UNIPAR facilitate the evaluation of the impact of humidity, aerosol acidity, and aerosol-phase state on SOA formation in regional scales. Briefly, the key components of the UNIPAR model are described as follows:

The SOA mass forms via multiphase partitioning, organic-phase oligomerization, and aqueous reactions in a wet inorganic salted solution. For the multiphase SOA formation, a fundamental assumption is that organic constituents are internally mixed with inorganic constituents under the liquid–liquid phase separation between organic phase and salted aqueous phase.

Figure 1 shows the overall structure of the CAMx–UNIPAR model. The Weather Research and Forecast model (WRF v4.1) generated meteorological input data to drive the CAMx v7.1 using the North American Mesoscale (NAM) data of the National Centers for Environmental Prediction (NCEP). The WRF modeling domains comprised three nested grids with horizontal resolutions of 36, 12, and 4 km. The outer domain, with a 36 km horizontal resolution, covered the entire western USA. The second domain, with a 12 km horizontal resolution, covered California and portions of Nevada. The third domain, with a 4 km horizontal resolution, covered central California. The air quality simulation for gas and particle pollutants in central California was performed for the third domain (Fig. 2a) with 185×185 grids and 22 vertical layers. The detailed configurations of the WRF and CAMx modeling system are described in Table S6. Emission inputs are based on California Air Resources Board regional inventories and provided by the Bay Area Air Quality Management District (BAAQMD, 2023).

The UNIPAR SOA model was incorporated with the CAMx model as a sub-model to predict SOA formation in California. Precursor HC consumption and other gas species were estimated using the SAPRC07TC gas mechanism (Hutzell et al., 2012) in the CAMx model. The inorganic thermodynamic model (ISORROPIA) provides the inorganic aerosol composition at equilibrium for inorganic aerosol species. The current CAMx–UNIPAR model includes 251 lumping species, of which 50 originate from 10 aromatics; 50 originate from three alkane groups; 50 originate from terpene; 50 originate from sesquiterpene; and 51 originate from isoprene (Table 1).

The emissions of 10 aromatic HCs were sourced from benzene, toluene, three xylenes, and 1,2,4-trimethylbenzene. Toluene was used to estimate the emissions of ethylbenzene and propylbenzene using factor of 0.082, and 1,2,4-trimethylbenzene was used to estimate the emissions of 1,2,3-trimethylbenzene and 1,3,5-trimethylbenzene using a factor of 0.3. Long-chain alkanes are important IVOCs, which are emitted from automobile exhaust (Pye and Pouliot, 2012; Ensberg et al., 2014) and plants (Simoneit, 2002; Yao et al., 2009; Li et al., 2022). Laboratory studies showed that SOA yields from alkanes changed with carbon length (Lim and Ziemann, 2009; Tkacik et al., 2012; Presto et al., 2010; Srivastava et al., 2022). In the model, alkanes in different carbon-chain lengths are split into three groups due to their different SOA formation potential: C9–C14, C15–C19, and C20–C24 (Table 1). Speciation factor of 0.52 was used to estimate the emission of alkanes from SAPRC07 ALK5 species, which contains other non-aromatic compounds (i.e., alcohols, ethers, esters, and carboxylic acids) in addition to alkanes (Carter, 2015). The emission factor of alkanes that were not fully covered by ALK5 (i.e., alkanes longer than C19; Carter, 2015) was estimated using the HC emission recently reported by the US Environmental Protection Agency (US EPA) (Pye et al., 2023) and the study by Mcdonald et al. (2018). In this study, all types of alkanes including linear, branched, and cyclic alkanes were surrogated with linear alkanes based on a carbon number.

The SOA mass in the CAMx–UNIPAR model is attributed to the OMH and OMP for each precursor (Table 1). The total SOA is the sum of OMH_AR, OMH_AK, OMH_TE, OMH_SP, OMH_IS, OMP_AR, OMP_AK, OMP_TE, OMP_SP, and OMP_IS. Total OM is the sum of total SOA and single primary organic aerosol (POA) species. POA is a single non-volatile species that does not chemically evolve (Environ, 2020). The simulation period was the winter (January–February) in 2018, excluding the wildfire season in California. Here, we focused on the simulation results that showed considerable OM levels between 23 January and 24 February 2018.

The US EPA has operated the national Chemical Speciation Monitoring Network (CSN) since 2000 to obtain information on the spatial and temporal chemical composition of ambient fine particles (Solomon et al., 2014). CSN measures the major components of fine particles that are 2.5 µm or less in diameter (PM2.5) including sulfate, nitrate, ammonium, organic carbon (OC), and elemental carbon (EC) and operates on a 1-in-3-day sample collection schedule. Figure 2a shows four CSN sites in California – San Jose, Sacramento, Fresno, and Bakersfield selected in this study. Table 2 summarizes information on the observation sites. The San Jose site is within the boundaries of the San Francisco Bay Area Air Basin (SFBAAB or Bay Area). The Sacramento, Fresno, and Bakersfield sites are located on flat land in the Central Valley. The Central Valley is bounded by mountain ranges and coastal areas. This bowl-shaped geography of the Central Valley creates conditions conducive to holding pollutants in place and the accumulation of secondary photochemical compounds.

The Great Basin High occurs in California during the cold season (Herner et al., 2005). When the Great Basin High develops, the pressure gradients between the coast and the Central Valley decline, and the planetary boundary layer (PBL) height becomes low. This condition holds pollutants close to the ground, allowing them to accumulate over several days, as fine particles and their precursors continue to be emitted. Due to a combination of unfavorable geographical and meteorological factors for ventilation, many cities in the bowl-shaped region, including San Jose, Sacramento, Fresno, and Bakersfield, undergo persistent air quality issues (Lurmann et al., 2006; Young et al., 2016; Prabhakar et al., 2017; Chen et al., 2020; Sun et al., 2022).

The measured mass concentrations of EC at the San Jose, Sacramento, Fresno, and Bakersfield sites during the simulation period were used to separate the concentration of the measured total OC (OCtot) into primary OC (POC) and secondary OC (SOC) (Turpin and Huntzicker, 1995). Because EC and POC often have the same sources, there is a representative ratio of POC/EC for a given area (Strader et al., 1999). The POC is calculated based on Eq. (1) and the SOC is estimated by subtracting the resulting POC from the OCtot as shown in Eq. (2) (Turpin and Huntzicker, 1995). 1POC=EC×POCEC2SOC=OCtot-POC EC and OCtot were measured from the same CSN system. In this study, the POC/EC ratio reported by Strader et al. (1999) by using field data obtained in California during the winter of 1995–1996 has been applied to estimate POC and SOC. The averaged POC/EC ratio was set to 2.4 with an upper limit of 2.75 and a lower limit of 2.05. OCtot data, the estimated POC, and the estimated SOC were converted to total OM, POA, and SOA, respectively, using a conversion factor of 1.7 (Mcdonald et al., 2015).

To show the overall tendency, emissions of HCs and POA were averaged between January and February in 2018 as shown in Fig. 2. HC emissions are speciated according to SAPRC07 gas mechanisms. The amounts of major SOA precursors – aromatics (ARO), alkane (ALK5), terpene (TERP), sesquiterpene (SESQ), and isoprene (ISOP) emissions for each site and the total of the domain – are shown in Fig. 2b. The spatial distributions of POA and major SOA precursors emissions for California are shown in Fig. 2c–h. Aromatic emission is the sum of benzene, toluene, o-xylene, p-xylene, m-xylene, and 1,2,4-trimethylbenzene. The alkane corresponds to ALK5 in SAPRC07 emission data.

On average, terpene, isoprene, alkane, aromatics, and sesquiterpene emissions in California accounted for 44 %, 31 %, 18 %, 7 %, and 1 %, respectively, indicating the dominance of biogenic emissions, particularly terpene emissions, in California. For the selected sites, alkane emissions accounted for more than 60 %, followed by aromatic emissions at approximately 32 %. Terpene and isoprene emissions accounted for less than 5 %, and sesquiterpene emission was negligible, indicating the dominance of alkane emission in urban areas. Figure 2c–h depict a distinct difference in the spatial distribution of biogenic (terpene, sesquiterpene, and isoprene) and anthropogenic (POA, aromatics, and alkane) emissions. The spatial patterns of biogenic emissions followed the distribution of mountain ranges surrounding the Central Valley, whereas the spatial patterns of POA, aromatics, and alkane emissions were concentrated in the source area such as industrial, transportation, and buildings in the Central Valley and Bay Area. In addition, long-chain alkanes can also be attributed to biogenic sources. For example, alkanes are emitted from terrestrial higher plants, cuticle wax, suspended spores, and aquatic plants, and they can be emitted to atmosphere during wildfires (Simoneit, 2002; Yao et al., 2009; Li et al., 2022).

The time series and scatter plots of the surface temperature, relative humidity, and wind speed simulated by the WRF model against observations at the four sites are shown in Figs. S1–S3, respectively, and their statistical summaries of correlation coefficient (R), index of agreement (IOA), and mean bias (MB) are described in Table S7. Detailed descriptions of these statistical parameters are presented in Table S8. Overall, the surface temperature, relative humidity, and wind speed were well predicted with high R and IOA values, reducing uncertainties caused by the meteorological input data in the air quality simulation. Figure S4 shows the wind rose plots for the four sites. Northwesterly winds prevailed at all sites, leading to the convergence of the pollutants in the southern area. Figure S5 shows the time series of the hourly simulated PBL height at the four sites. The relatively low PBL height and weak wind speed appeared together in some periods (i.e., 26 January 2018–13 February 2018), creating conditions conducive to the accumulation of pollutants.

In the CAMx–UNIPAR model, the phase state of inorganic aerosol is determined by using the calculated ERH based on a pre-trained neural network mathematical equation (Yu et al., 2021b) and inorganic compositions (sulfate, nitrate, and ammonium) predicted from an inorganic thermodynamic model, ISORROPIA (Fountoukis and Nenes, 2007). The ERH and DRH of the salted aerosol and its phase state (wet or dry) are illustrated in Fig. S6. During the simulation period, the inorganic aerosol phase was mostly wet, except for a few dry periods.

Figure 3 shows the time series of the simulation of the total OM (Fig. 3a–d), POA (Fig. 3e–h), and SOA (Fig. 3i–l) with the CAMx–UNIPAR model against the observations at the four sites with statistical parameters (R, IOA, MB, root mean square error (RMSE), and normalized MB (NMB) as described in Table S8). Overall, the simulated mass concentrations of total OM, consisting of POA and SOA, at four ground sites (San Jose, Sacramento, Fresno, and Bakersfield) showed a good agreement with the observations. The high R (0.77–0.89) and IOA values (0.82–0.87) in Fig. 3 indicate a good agreement between the predicted total OM and observed total OM concentrations. The marginally negative values for MB and NMB indicate that the model underestimated the total OM to some extent.

The simulation of the POA and SOA could capture observations, but it shows a marginal decrease in their R and IOA values compared with the total OM. The simulated POA was slightly overpredicted, and the simulated SOA was somewhat underestimated at the four urban sites. Both MB and NMB values of POA were positive, while those of SOA were negative. The negative bias of the predicted SOA is generally greater than the positive bias of the POA, which affects the negative bias of the total OM from the observations.

The underestimation of SOA mass can be attributed to missing precursor HCs and unidentified chemistry in the gas and aerosol phases. The precursor HCs such as phenols (Bruns et al., 2016; Majdi et al., 2019; Choi and Jang, 2022), branched and cyclic alkanes (Chan et al., 2013; Gentner et al., 2017; Madhu et al., 2023), and polycyclic aromatic HCs (PAHs) (i.e., naphthalene) (Riva et al., 2015; Wang et al., 2021) are currently missing in the UNIPAR model. For example, all alkanes in this study are treated as linear alkanes, increasing some uncertainties. Branched alkane SOA can be slightly overestimated by substituting it with linear alkanes at the same carbon length, but cyclic alkane SOA can be underestimated by using linear alkanes (Madhu et al., 2022, 2023). Zhang and Ying (2012) reported that PAHs including naphthalene, methylnaphthalene and dimethylnaphthalene can contribute to 4 % of the anthropogenic SOA mass. Pye et al. (2023) reported in their regional simulation using the Community Regional Atmospheric Chemistry Multiphase Mechanism (CRACMM) that a significant amount of phenolic compounds is missing in the current models. They estimated that most phenol mass (69 %) is directly emitted with the balance from benzene oxidation, and cresols are mainly chemically produced (80 %). The missing emissions of phenol and cresol can account for 30% of the total aromatic SOA mass (Pye et al., 2023). The SOA formation from low-volatility aromatic HCs (aromatics substituted with long-chain alkyl groups) is also missing in the SOA simulation of this study.

Additionally, the statistical analysis may vary, owing to the lack of observational data for the simulation periods. For example, the OC and EC observation data were only available for daily averaged data every three days (Sect. 2.3), and this low-time-resolution observational data limited the verifications of the simulated OM mass, especially SOA formation during daytime and nighttime from the CAMx–UNIPAR simulations. In addition, the observed POA estimated using the POC/EC ratio (Sect. 2.4) also has uncertainties because the POC/EC ratio is inconsistent from source to source but varies between sources (Strader et al., 1999). The simulated POA can also be inaccurate due to the uncertainty in primary OC emission data.

The SOA/total OM mass ratios estimated from the observation data ranged from 0.50 to 0.73 indicating a significant contribution of SOA mass to total OM. The simulated SOA/total OM ratios (0.25–0.52) were relatively lower than those in the observed ratios, which are calculated using decoupled SOA and POA with a POC/EC ratio (Sect. 2.4), suggesting that POA is overpredicted and SOA is underpredicted in the CAMx–UNIPAR simulations. For both observations and simulations, SOA/total OM mass ratios in southern areas, such as Fresno and Bakersfield, were higher than those in northern areas, such as San Jose and Sacramento. The northern area, including the Bay Area, is located on the upwind side of the southern area. A strong wind appeared in the northern area during the simulation period (Table S7 and Fig. S4), decreasing the residence time of pollutants, which reduced secondary products of pollutants in this region. The concentration of total OM, POA, and SOA increased from 23 January 2018 and maintained the high OM mass by early February. During this period, the wind speed was relatively weak (Fig. S3) and the PBL height was suppressed (Fig. S5), which is favorable for the accumulation of pollutants in urban areas.

Figure 4a–d show the time series of the simulated POA and total SOA with the predicted aerosol phase state (wet and dry) at the four sites. Both POA and SOA mass were noticeably high between 23 January and 13 February 2018. Figure 4e–h show the time series of the simulated SOA species and pie charts to represent the averaged fraction of each SOA species during the period in Fig. 4. The predicted total SOA mass was predominated by alkane SOA (33 %–76 %) and terpene SOA (18 %–60 %) across all four sites. The contribution of alkane SOA and terpene SOA to the local SOA mass burden varied according to the location of the sites. For example, the fraction of alkane SOA was higher than that of terpene SOA in all sites except Sacramento. The terpene concentrations can be high at the Sacramento site due to the proximity to the northern and eastern mountain ranges. Overall, the contributions of the isoprene SOA and aromatic SOA to the total SOA mass were small (∼5 %) and that of sesquiterpene SOA was nearly negligible.

A high fraction of OMP mass attributed to the total SOA ranging from 0.59 to 0.77 as shown in Fig. 4e–h. In particular, the alkane OMP fraction of total SOA ranged from 0.2 to 0.41, and the terpene OMP fraction of total SOA ranged from 0.15 to 0.53. In the current UNIPAR model, the low-volatility products produced from the oxidation of long-chain alkanes can significantly increase SOA growth via their gas–particle partitioning to the pre-existing OM. Additionally, the model includes the low-volatility products originating from autoxidation of α-pinene ozonolysis products (Roldin et al., 2019; Crounse et al., 2013; Bianchi et al., 2019). The importance of autoxidation mechanisms on terpene SOA formation was demonstrated in a recent study by Yu et al. (2021c) for daytime chemistry. In their study, the peroxy radical autoxidation mechanism (PRAM) developed by Roldin et al. (2019) was included in UNIPAR to evaluate the impact of HOMs on terpene SOA formation. In the sensitivity test of SOA prediction associated with PRAM, α-pinene SOA mass increased by 15 %–35 % in the presence of PRAM, suggesting that substantial impact of PRAM on the total SOA mass (Yu et al., 2021c).

In addition, the chamber study and the UNIPAR simulation by Han and Jang (2023) showed a significant potential for nighttime biogenic SOA formation. In their study, α-pinene and isoprene SOA growth during nighttime is even more significant than their daytime growth due to the considerable contribution of both ozonolysis of biogenic HCs and the reaction with nitrate radicals, which yield low-volatility products. Ozone is produced via the atmospheric oxidation of HCs integrated with a photochemical cycle of NOx that extends through nighttime and promotes the formation of a nitrate radical in the presence of NO2. This nitrate radical can attack an alkene in terpenes to form an alkylperoxy radical, leading to the formation of low-volatility peroxide accretion products (ROOR) (Hasan et al., 2021; Bates et al., 2022; Han and Jang, 2023).

The fractions of OMH in anthropogenic SOA (aromatic and alkane SOA) ranged from 0.41 to 0.47, and those of biogenic SOA ranged from 0.13 to 0.18. The anthropogenic OMH fractions are consistent with reported values predicted by Pye and Pouliot (2012) in regional scales in the US domain. For example, they reported that the oligomeric SOA simulated mainly from alkanes and partly from PAHs accounted for about half of the anthropogenic SOA in the US domain. In the regional simulation by Yu et al. (2022), the SOA mass was simulated with both the two-product SOA (SOAP) model and the UNIPAR SOA model during the KORUS-AQ campaign. The fraction of OMH to the total SOA is on average 0.31 and 0.40 with the SOAP SOA model and the UNIPAR SOA model, respectively, (Yu et al., 2022). The alkane OMH fractions of the total SOA ranged from 0.13 to 0.35, which indicates that alkane OMH is significant, although less than alkane OMP (Fig. 4e–h). In the UNIPAR model, this alkane OMH is mainly associated with non-volatile products originating from the autoxidation of long-chain alkanes. Unlike alkanes, other precursor HCs yield OMH via oligomerization of reactive semi-volatile organic species. Under California's 2018 winter simulation, the alkane OMH was larger than that sourced from non-alkane OMH. The attribution of autoxidation-driven low-volatility products (alkane and terpene) to the total SOA mass can also promote gas–particle partitioning of other products (non-autoxidation products), by increasing the preexisting OM. Furthermore, OMP is dependent on temperature with a negative relation with temperature (Odum et al., 1996). The contribution of OMH to the total SOA can also be impacted by HC species.

Figure 5 shows the diurnal variation of SOA species averaged between 23 January and 24 February 2018. The alkane SOA increased during the daytime because alkanes are mainly oxidized by reactions with an OH radical. As discussed above, terpene can be oxidized with an OH radical, a dominant oxidant in daytime, and furthermore terpene reacts with ozone and nitrate radicals during nighttime to form low-volatility products, which can be a significant source of OMP. The time series of the simulated concentrations of NO2, ozone, and nitrate radicals are shown in Fig. S7. The time series of simulated SOA precursor HC concentrations (i.e., aromatic HCs, alkane, terpene, sesquiterpene, and isoprene) are shown in Fig. S8. Figures S9 and S10 show the time series of emissions of precursor HCs and SOA species, respectively. The terpene SOA mass at Fresno and Bakersfield noticeably increased (Fig. S10) between 29 January and 11 February 2018 when the concentrations of ozone and nitrate radicals were high (Fig. S7). During the simulation period, no specific fluctuations appeared in both terpene concentrations (Fig. S8) and terpene emissions (Fig. S9), suggesting that terpene SOA formation is positively influenced by the concentrations of ozone and nitrate radicals.

The surface-level spatial distributions of the total SOA, POA, and individual SOA species, averaged between 23 January and 24 February 2018, are displayed in Fig. 6. The spatial distribution of individual SOA species can be influenced by the emission of each HC, available atmospheric oxidants, the reactivity of each HC with atmospheric oxidants, and winds (speed and direction). Figure 2c–h illustrate the spatial distributions of the emission of POA and each HC, and Fig. S11a–c show those of NO2 and atmospheric oxidants (ozone and nitrate radicals), respectively. The spatial distribution of the concentrations of each HC is shown in Fig. S11d–h.

Biogenic HCs are rapidly consumed day and night, due to their fast rate constants with OH radicals, ozone, and nitrate radicals, and quickly form SOA. Hence, the spatial distributions of biogenic SOA were substantially influenced by the distribution of precursor HC emission sources. As shown in Fig. 6e, the terpene SOA mass was evenly distributed along the Central Valley, which was influenced by the high terpene emission from the surrounding mountains including the Cascade Range to the north, the Sierra Nevada to the east, and the Tehachapi Mountains to the south. On the other hand, high NO2 concentrations appeared in urban areas of the Central Valley as shown in Fig. S11a. Both ozone and nitrate radicals react with biogenic HCs to effectively form SOA via the production of low-volatility products as discussed in Sect. 3.2 (Li et al., 2011; Jenkin, 2004; Han and Jang, 2023). The formation of nitrate radicals is favorable in urban areas because of the high concentrations of NO2. Owing to the reaction of terpene with this nitrate radicals, the concentration of nitrate radicals was, however, low in the Central Valley. The maximum terpene SOA concentration appeared between the terpene ridge (Fig. S11f) and the NO2 ridge (Fig. S11a) where the reaction rate between terpene and nitrate radicals was high. The sesquiterpene SOA distribution (Fig. 6f) was slightly southward compared with the terpene SOA distribution. In addition to emissions from mountain ranges, sesquiterpene can be sourced from various areas as shown in Fig. 2g. California's isoprene emissions (Fig. 2h) are expected to originate from oak trees and from eucalyptus trees and are distributed in the central California foothills and South Coast Ranges. Thus, the isoprene SOA distribution (Fig. 6g) was oriented more southward than that of the terpene SOA. Both sesquiterpene SOA and isoprene SOA concentrations were extremely small as discussed in Sect. 3.2.

The spatial distributions of anthropogenic SOA were noticeably impacted by the southward wind direction. For example, the spatial distributions of both aromatic SOA (Fig. 6c) and alkane SOA (Fig. 6d) were extremely southward, although their emissions were relatively even along with the Central Valley (Fig. 2d and e). Unlike biogenic HCs, both aromatic and alkane HCs have a relatively long lifetime for their atmospheric oxidation. Additionally, their major oxidation path with OH radicals occurs in daytime. Thus, anthropogenic HCs can be transported along with the southward wind during the simulation period, which can increase the formation of anthropogenic SOA in the southern area. A PM2.5 particle has an average lifetime of approximately eight days (Hodan and Barnard, 2004; Chowdhury et al., 2022). Noticeably, the POA also drifted to the south due to the transportation by the southward wind (Fig. 2c vs. Fig. 6b) and the high POA concentration augmented anthropogenic SOA growth in the southern area.

Numerous studies (Lim et al., 2010; Liu et al., 2012; Mcneill, 2015; Srivastava et al., 2022) have revealed that aqueous reactions of hydrophilic, reactive organic species in electrolytic inorganic aerosol produce non-volatile oligomeric matter and increase SOA mass. These heterogeneous reactions are known to be accelerated by acid catalyst species (Jang et al., 2002; Hallquist et al., 2009). In order to simulate the SOA formation potential by aerosol acidity at the four sites, the time series of hourly simulated concentrations of ionic species (sulfate, nitrate, and ammonium in Fig. S12) were applied to estimate the aerosol acidity by the charge balance of the inorganic electrolytes. In Fig. S13, the charge balance estimated using the simulated and observed ionic concentrations suggested that the aerosol acidity was nearly neutral. The one-to-one line shown in Fig. S13 shows the fully titrated inorganic composition. Thus, SOA growth by the acid-catalyzed heterogeneous reactions of reactive lumping species might not have been effective during the simulation period of this study. Overall, nitrate concentrations in aerosol were high in the urban areas of California during the winter of 2018. The aerosols, which are enriched with ammonium nitrate salt, can be hygroscopic and lower the aerosol ERH and DRH (Fig. S6). As described in Sect. 2.6, the inorganic aerosol phase was mostly wet due to the low ERH and DRH with the abundant nitrate ammonium salt.

The sensitivities of different SOA species to aerosol hygroscopicity are dissimilar. For example, aromatic and isoprene oxidation products are reactive for heterogeneous reactions and hydrophilic. Thus, they can effectively yield SOA in inorganic salted aqueous phase (Yu et al., 2021b). In contrast, both alkane and terpene oxidation products are relatively hydrophobic. Thus, their solubility in the aqueous phase is low due to their large activity coefficients. Evidently, α-pinene SOA and alkane SOA have a low O:C ratio (∼0.55) (Zhang et al., 2015; Galeazzo et al., 2021; Madhu et al., 2022) compared with isoprene SOA (∼1.1) (Song et al., 2015). In order to evaluate the sensitivity of different SOA species to aerosol hygroscopicity, the isoprene to alkane SOA mass ratios were calculated during the wet and dry periods as shown in Fig. 7. The SOA mass ratios of isoprene to alkane during the wet period were higher than those during the dry periods for all sites: San Jose, Sacramento, Fresno, and Bakersfield by factors of 3.0, 1.9, 2.8, and 2.0, respectively. Such high SOA mass ratios of isoprene to alkane during the wet period indicate the importance of the role of aerosol hygroscopicity on the SOA formation in an environment with a high emission of isoprene or aromatic HCs. The impact of aerosol hygroscopicity on SOA mass was minimal under California's atmospheric environment during the simulation period because of the dominance of alkane and terpene SOA. In contrast, the SOA mass simulated during the KORUS-AQ campaign was dominated by aromatic HCs, which produced reactive and hydrophilic products (Yu et al., 2022). In their study, the CAMx–UNIPAR model well captured a significant contribution of aromatic SOA to the total OM during the low-level transport/haze period (Crawford et al., 2021) where the aerosol water content was high.

To understand the impact of NO2 on SOA formation, the correlation coefficients (R) between NO2, nitrate aerosol, and SOA mass associated with each HC were estimated as shown in Table 3. The analysis of R between NO2, nitrate, and SOA was performed during high PBL height periods (11–24 February 2018). The formaldehyde-to-NO2 ratio (FNR) is typically used to indicate NOx levels. When FNR is less than 1, it represents VOC-limited condition (Duncan et al., 2010; Hoque et al., 2022). Based on the spatial distribution of FNR in Fig. S14, the four urban sites of this study were VOC-limited (high NOx levels) conditions. Under this environment, a typical SOA production in daytime is negatively correlated with NO2 concentrations (Presto et al., 2005; Yang et al., 2020; Madhu et al., 2022). However, all correlation coefficients between NO2 and SOA mass shown in Table 3 were positive. Biogenic SOA was more strongly correlated with NO2 (larger positive R) than anthropogenic SOA.

As discussed in Sect. 3.2 and 3.3, biogenic HCs, particularly terpene, react with a nitrate radical to form low-volatile products and effectively increase SOA mass. NO2 is linked to the formation of nitrate radicals at nighttime, and it can be positively related to biogenic SOA mass. Increased nighttime biogenic SOA mass (Fig. 5) can also influence OMP of anthropogenic SOA, weakening the negative correlation between NO2 and anthropogenic SOA formation. For example, the last column in Fig. 5, which displays the diurnal variation of the SOA concentrations, evinces the influence of terpene SOA on anthropogenic SOA mass. Anthropogenic SOA mass still gradually increased after sunset (17:00 local standard time (LST)) when the production of OH radical was nearly inactive, and it continued until midnight (i.e., 00:00 LST at Fresno). As shown in Fig. S15, a rapid change in the PBL height appeared between 15:00 and 17:00 LST, and no change appeared in the PBL height after 19:00 LST. Thus, the influence of PBL height changes on anthropogenic SOA mass after 19:00 LST can be trivial.

Under the Central Valley's environments in this study, ammonia was rich, temperature was relatively low, and humidity was high. The high concentration of NO2 in this region is favorable to form inorganic nitrate aerosol, which can promote aqueous phase reactions of organic species. Evidently, a strong positive correlation appeared between inorganic nitrate concentrations and SOA mass (R: 0.41–0.86 in Table 3) declining a conventional negative correlation between NOx concentration and anthropogenic SOA formation at high NOx levels.