A specific version of the WRF-Chem model (Grell et al., 2005) developed by Li et al. (2010, 2011a, b, 2012) at the Molina Center for Energy and the Environment is used in the present study. A detailed model description can be found in previous studies (Li et al., 2018; Wu et al., 2017; Feng et al., 2016; Xing et al., 2019). Briefly, the model includes a new flexible gas-phase chemical module and the Community Multi-scale Air Quality (CMAQ) aerosol module developed by the US EPA (Binkowski and Roselle, 2003). The wet deposition uses the method in the CMAQ module, and the dry deposition of chemical species is parameterized following Wesely (1989). The photolysis rates are calculated using the Fast Tropospheric Ultraviolet and Visible Radiation Model (FTUV; Li et al., 2005; Tie et al., 2003), with the aerosol and cloud effects on the photochemistry (Li et al., 2011a). The ISORROPIA version 1.7 is applied to calculate the inorganic components (Nenes et al., 1998). The secondary organic aerosol (SOA) is simulated using a nontraditional module, including the volatility basis set (VBS) modeling approach and SOA contributions from glyoxal and methylglyoxal. The anthropogenic emission inventory with a horizontal resolution of 6 km is developed by Zhang et al. (2009), with the base year of 2013, including industry, transportation, power plant, residential, and agriculture sources. The Model of Emissions of Gases and Aerosols from Nature (MEGAN) is used to calculate the biogenic emissions online (Guenther et al., 2006).

Traditionally, the brute force method (BFM) is generally used to quantify the formation pathway of particulate matter and chemical compounds in modeling studies (Dunker et al., 1996). The BFM evaluates the importance of a certain formation pathway by including and excluding the pathway in simulations, but it lacks a consideration of interactions of the complicated physical and chemical processes in the atmosphere (Zhang and Ying, 2011). The source-oriented method introduces additional chemical species to represent formations from different pathways, providing a direct and quantitative determination of the contributions of different pathways (Ying and Krishnan, 2010). Coupled source-oriented air quality models have been widely used to study the source apportionment of particulate matter and chemical compounds. A detailed description of the method can be found in previous studies (Ying and Kleeman, 2006; Ying and Krishnan, 2010; Zhang and Ying, 2011). In the present study, four reactive tagged species are introduced to track sulfate formation pathways.

A persistent air pollution episode with high levels of O3 and PM2.5 from 4 to 15 July 2015 in BTH is simulated in association with the observation of air pollutants and secondary aerosols. Detailed information about the episode can be found in Wu et al. (2017). Figure 1 shows the WRF-Chem model simulation domain, and Table 1 presents the model configuration.

Four sulfate formation pathways are considered in the WRF-Chem model, including (1) the heterogeneous reaction of SO2 involving aerosol water (hereafter referred to as HR_SO2), (2) SO2 oxidation by OH (hereafter referred to as OH_SO2), (3) primary emissions, and (4) SO2 oxidation by sCIs (hereafter referred to as sCI_SO2). The sulfate formed in the four pathways is tagged and traced in the model to study their contributions to sulfate formation. It is worth noting that the WRF-Chem model cannot resolve clouds formed in the planetary boundary layer (PBL) well, so aqueous SO2 oxidation in cloud or fog droplets is not considered in the study, which might cause sulfate underestimation; on the other hand, it might overestimate the contributions of the four pathways to the sulfate concentration. The HR_SO2 is parameterized as a 1st-order irreversible uptake of SO2 by aerosol water, with a reactive uptake coefficient of 0.5×10-4, assuming that alkalinity is sufficient to maintain the high iron-catalyzed reaction rate in BTH (Li et al., 2017). Aerosol hygroscopic growth is directly predicted by ISORROPIA in the model, and the aerosol water surface area is scaled from the calculated wet aerosol surface area using the third moment of aerosol species.

The effects of sCI chemistry on sulfate formation depend on κsCI+SO2 and κsCI+H2O, as well as the sCI precursor concentration. In the study, sCIs are assumed to result from the ozonolysis reaction of five alkenes based on the SAPRC99 mechanism, including ethene (ETHE), terminal olefin (OLE1), internal olefin (OLE2), isoprene (ISOP), and monoterpenes (TERPs). Detailed information about the sCI chemistry associated with sulfate formation can be found in Table 2.

CH2OO (sCI1) is used to represent sCIs produced from the ozonolysis reaction of ETHE and OLE1, and the sCI yield of the two reactions is described in Sarwar et al. (2013). CH3CHOO (sCI2) is formed from the ozonolysis reaction of OLE2 and proposed to have two isomers: syn-CH3CHOO and ant-CH3CHOO (Anglada et al., 2011). The reported reaction rate constants of syn-CH3CHOO and ant-CH3CHOO with H2O are 3.23×10-18 and 3.23×10-13 cm3 s-1, respectively. We use syn-CH3CHOO (sCI2) to represent sCIs from the ozonolysis reaction of OLE2 to minimize the removal of sCIs by water vapor and maximize sulfate production following Ying et al. (2014). sCI3 is used to represent sCIs from the ozonolysis reaction of isoprene and monoterpenes, and the detailed chemistry of sCI3 (syn-CH3-anti-(cis-CH=CH2)CHOO) is described in Sarwar et al. (2013, 2014).

In the base case (hereafter referred to as the B case) simulation used to compare with observations in BTH, we use a single κsCI+SO2 reported by Welz et al. (2012) for reactions of SO2 with sCI1,2,3. For the removal of sCI1,2,3 by water vapor, we employ the κsCI+H2O suggested by Ying et al. (2014). While not important, the reaction of sCI1,2,3 with NO2 is also implemented in the model, and the rate constant is taken from Welz et al. (2012).

Simulations are compared to available meteorological and air pollutant observations to validate the model performance. The meteorological parameters, including surface temperature (TSFC), relative humidity (RH), and wind speed and direction with a 3 h interval, are obtained from the website http://www.meteomanz.com (last access: 28 October 2019). The hourly measurements of PM2.5, O3, SO2, and NO2 used in this study are downloaded from the website http://www.aqistudy.cn (last access: 28 October 2019). Submicron sulfate, nitrate, ammonium, and organic particulate matter are observed by the Aerodyne Aerosol Chemical Speciation Monitor (ACSM) at the National Center for Nanoscience and Technology (NCNST), Chinese Academy of Sciences, Beijing (116.39∘ E, 39.99∘ N). A detailed description of the methods to obtain the primary organic aerosol (POA) and secondary organic aerosol (SOA) mass concentration from the results of ACSM are given in Wu et al. (2017). Figure 1 shows the locations of the ambient air quality monitoring sites and the NCNST observation site.

In this study, the mean bias (MB), root mean square error (RMSE), and index of agreement (IOA) are used to evaluate the model performance. 1MB=1N∑i=1NPi-Oi2RMSE=1N∑i=1NPi-Oi2123IOA=1-∑i=1NPi-Oi2∑i=1NPi-O‾+Oi-O‾2 Pi and Oi are the simulated and observed variables, respectively. N is the total number of simulations for comparison, and O‾ denotes the average of the observation. The IOA ranges from 0 to 1, with 1 showing a perfect agreement of the simulation with the observation.

Figure 6a provides the diurnal profile of simulated and observed submicron sulfate concentrations at the NCNST site in Beijing from 4 to 15 July 2015. The model tracks temporal variations of the observed sulfate concentration reasonably well, with an MB and IOA of -0.9 µg m-3 and 0.71, respectively. During 11 to 12 July 2015, the model noticeably underestimates the high sulfate concentrations against the measurements. As mentioned in Sect. 2, the aqueous oxidation of SO2 in cloud or fog droplets is not considered in the simulation, which might be one of the reasons for the underestimation.

Figure 6b–e present the contributions of the four pathways to sulfate formation during the episode at the NCNST site in Beijing. On average, HR_SO2 plays the most important role in sulfate formation, with a contribution of about 32.1 % (Fig. 6b). Li et al. (2017) have also shown that HR_SO2 is the dominant sulfate source, contributing around 58.4 % to sulfate concentrations in Beijing during wintertime due to the very humid conditions and inefficient sulfate formation from gas-phase SO2 oxidation due to the low AOC. In this study, the average simulated RH is not high in Beijing, less than 50 % during the episode, and high O3 concentrations enhance the AOC to facilitate gas-phase SO2 oxidation, causing the decreased sulfate contribution of HR_SO2. It is worth noting that HR_SO2 relies on the assumption that alkalinity is sufficient to maintain the high iron-catalyzed reaction rate (Li et al., 2017). Figure 7 presents the temporal variation of the average simulated aqueous pH in Beijing during the episode. The simulated pH generally fluctuates between 5 and 7, with an average of 6.2, demonstrating an efficient iron-catalyzed reaction involving aerosol water. High O3 concentrations substantially increase sulfate formation efficiency through SO2 oxidation by OH and sCIs. OH_SO2 play a considerable role in sulfate formation, with a contribution of 30.8 % (Fig. 6c). It is worth noting that the primary emission pathway contributes 24.0 % of the sulfate concentration at the NCNST site.

The sCI_SO2 accounts for about 13.1 % of sulfate concentrations at the NCNST site, which is less than the contribution of the other three pathways. The effects of sCI_SO2 on sulfate formation depend on the κsCI+SO2. The reported κsCI+SO2 from previous studies spans orders of magnitude (Welz et al., 2012; Maudlin et al., 2012; Jenkin et al., 1997). In the present study, an upper limit of κsCI+SO2 (3.9×10-11 cm3 s-1) is used in the B case, which is reported by Welz et al. (2012). Furthermore, the reaction of sCIs with H2O is the main loss pathway for sCIs in the atmosphere, and the κsCI+H2O used in this study represents a lower limit (1.97×10-18 cm3 s-1) (Ying et al., 2014). Therefore, the contribution of sCI_SO2 to sulfate formation might be overestimated in the present study.

Figure 8b–e present the simulated temporal variations of the four pathways to the sulfate concentration averaged over the whole BTH from 4 to 15 July 2015. On average, HR_SO2 is still the dominant sulfate source, with a contribution of 35.3 % (Fig. 8b). OH_SO2 plays an important role in sulfate formation, accounting for 33.1 % of sulfate mass (Fig. 8c). The primary emission pathway and sCI_SO2 contribute 22.5 % and 9.1 % of the sulfate concentration, respectively (Fig. 8d and e).

Figure 9 presents the spatial distribution of the contributions of the four pathways to sulfate formation averaged during the episode. The contribution of HR_SO2 to sulfate formation is substantial in BTH, particularly in the plain area, with the sulfate contribution exceeding 4.0 and being up to 7.0 µg m-3 (Fig. 9a). Under conditions of high O3 concentrations, OH_SO2 oxidation also becomes an important sulfate source, with a sulfate contribution of more than 3.0 µg m-3 in the plain area of BTH, which is comparable to the heterogeneous pathway (Fig. 9b). Similar to the spatial distribution of SO2 concentrations, the sulfate contribution of primary emissions is mainly concentrated in cities and their downwind areas (Fig. 4c). In the plain area of BTH, the sulfate contribution of primary emissions is more than 2.0 µg m-3 on average and exceeds 7 µg m-3 in highly industrialized cities, such as Shijiazhuang, Tangshan, and Xingtai. The sulfate contribution of sCI_SO2 is not as important as the other three sources; it is more than 0.8 µg m-3 in the plain area of BTH and the most striking in Beijing, with a contribution exceeding 1.2 µg m-3 (Fig. 9d).

Figure 10 shows the diurnal profiles of sCI1, sCI2, and sCI3 concentrations in BTH from 4 to 15 July 2015. The average concentration of sCI1, sCI2, and sCI3 is 1.8, 2.0, and 1.9×104 molecules cm-3, respectively. Novelli et al. (2017) estimated the concentration of sCIs in the lower troposphere based on observations in a boreal forest in Finland and in rural southern Germany. The results show that the average concentration of sCIs is about 5.0×104 molecules cm-3 with an order of magnitude uncertainty, generally consistent with our study. Dominant sCI peaks frequently occur during nighttime, mainly caused by the low PBL facilitating the accumulation of alkenes and sCIs as well as low reaction rates of sCIs with other species (Smith et al., 2015; Stone et al., 2014; Taatjes, 2017). It is worth noting that sCIs are predominantly quenched by reactions with water vapor in the atmosphere.

Considering the large variation of the reported κsCI+SO2 and the importance of water vapor in sCI removal, sensitivity studies are further conducted to evaluate the sulfate contribution of the sCI_SO2 in BTH when the different κsCI+SO2 and κsCI+H2O are used in simulations. In the B-case simulation, an upper limit of κsCI+SO2 and a lower limit of κsCI+H2O are used. The simulated average sulfate concentration is 10.8 µg m-3 in BTH, constituting a major component of PM2.5. HR_SO2 and OH_SO2 constitute the two most important sulfate sources, with a sulfate contribution of 35 % and 33 %, respectively. Primary emissions make up about 23 % of the sulfate in BTH, caused by high SO2 emissions. The sulfate contribution of sCI_SO2 is about 1.0 µg m-3 or 9.1 %, which is less than that in Beijing with a higher O3 concentration. Pierce et al. (2013) used the same κsCI+SO2 in the GEOS-Chem model as the B case in this study, revealing that the H2SO4 concentration is increased by 4 % due to sCI_SO2 on global average. The H2SO4 enhancement is 10 %–25 % over forested regions in the Northern Hemisphere (up to 100 % in July), but it is generally negligible elsewhere. The sulfate contribution of sCI_SO2 in BTH is close to that over forested regions in Pierce et al. (2013), which is primarily caused by the increasing trend of O3 and the high precursor emissions of sCIs such as ethene, isoprene, and monoterpenes during summertime in the region. Additionally, Boy et al. (2013) employed the κsCI+SO2 reported by Mauldin et al. (2012) and Welz et al. (2012) to verify the sulfate contribution of sCI_SO2 in Europe, showing an H2SO4 contribution of as much as 33 %–46 % at the ground level. These different sulfate contributions of sCI_SO2 are mainly caused by the variation of the reaction constant of sCIs with SO2, NO2, and H2O, as well as the sCI precursor concentration and the atmospheric conditions in the simulations (Taatjes, 2017).

Although sCI_SO2 is not an important sulfate source, its contribution might be overestimated. The κsCI+SO2 used in the B case is only measured for the smallest sCI, H2COO, but the larger sCIs (such as those produced from typical larger alkenes in the atmosphere) might have a lower reaction rate with SO2 and produce stable low-volatility species such as sulfur-bearing secondary ozonides (Spracklen et al., 2011; Vereecken et al., 2012). Additionally, Welz et al. (2012) measured κsCI+SO2 at low pressure (4 Torr), making it unclear if those rates are appropriate for atmospheric conditions.

In the S1 case, the reported κsCI+SO2 (6.0×10-13 cm3 s-1) by Mauldin et al. (2012) is used, which is deduced from the ozonolysis of α-pinene under boundary layer atmospheric conditions, and the κsCI+H2O and κsCI+NO2 are the same as those in the B case. The sulfate contribution of sCI_SO2 becomes insignificant; it is around 0.3 µg m-3 or less than 3 % of the total simulated sulfate concentration on average during the episode in BTH (Fig. 11). Compared to the B case, the sulfate contribution of sCI_SO2 is decreased by more than 70 % in the S1 case. The substantial reduction reveals that further studies are needed to precisely determine κsCI+SO2.

One of the largest uncertainties concerning the lifetime of sCIs is related to κsCI+H2O, but few studies have been conducted to directly measure κsCI+H2O. The reported κsCI+H2O varies widely, ranging from 2×10-19 to 1×10-15 cm3 s-1 (Hatakeyama and Akimoto, 1994), and several studies show that κsCI+H2O needs to be adjusted when κsCI+SO2 is adjusted (Li et al., 2013; Calvert et al., 1978; Suto et al., 1985). In order to evaluate the effect of water vapor on sCI_SO2, in the S2 case, κsCI+H2O is increased to 2.4×10-15 cm3 s-1 based on the reported ratio of κsCI+H2O to κsCI+SO2 (6.1×10-5) (Calvert et al., 1978), and the κsCI+SO2 and κsCI+NO2 are the same as those in the B case. The average sulfate contribution of sCI_SO2 in BTH is decreased to 0.2 µg m-3 or less than 2 % of the total simulated sulfate concentration due to the competition of water vapor with SO2 for sCIs (Fig. 11). Additionally, if a low κsCI+SO2 is used in the S2 case, the effect of water vapor on sCI removal becomes more substantial. In the S1 case and S2 case, there is a dominant peak of sulfate concentrations on 10 July, which might be caused by the reaction rate constants used in the two cases. We have performed an additional sensitivity study (S3 case), in which the reported κsCI+SO2 (3.42×10-11 cm3 s-1) and κsCI+H2O (7.4×10-12 cm3 s-1) suggested by Stone et al. (2014) and Smith et al. (2015) are used. The results show that the average sulfate contribution of sCI_SO2 becomes more insignificant; it is about 0.06 µg m-3 or less than 0.6 %. However, there is no obvious peak around 10 July (Fig. 11), indicating that the large uncertainty in contributions of sCI_SO2 to sulfate mass is due to the different value of κsCI+SO2 and κsCI+H2O used in the sensitivity studies.

It is worth noting that the uncertainty in HR_SO2, as the most important sulfate source, also influences the sulfate contribution of sCI_SO2. Several factors influence the heterogeneous reactions of SO2 on aerosol surfaces, including aerosol water surface area, aerosol acidity, and organic coating. In the B case, the predicted average aerosol liquid water and wet surface areas are 18.8 µg m-3 and 2.4×10-4 m2 m-3 in the BTH during the episode, and the uptake coefficient of SO2 by aerosols (γ) is assumed as 0.5×10-4. To investigate the sensitivity of sCI_SO2 sulfate contributions to uncertainties in HR_SO2, we perform sensitivity simulations with γ of 0.25×10-4 and 1.0×10-4. The sulfate concentration of HR_SO2 is considerably affected by the variation of γ, with an average change of -18.3 % and 25.6 % in BTH during the episode when the γ is assumed as 0.25×10-4 and 1.0×10-4, respectively. However, the effects of the γ change on the sulfate contributions of sCI_SO2 are not significant, with a change of -4.4 % and 3.9 % when the γ is assumed as 0.25×10-4 and 1.0×10-4, respectively.