A Comprehensive Observational Based Multiphase Chemical Model Analysis of the Sulfur Dioxide Oxidations in both Summer and Winter

Sulfate is one of the main components of the haze particles and the formation mechanism remains controversial. 10 Lacking of detailed and comprehensive field data hindes the accurate evaluation of relative roles of prevailing sulphate formation pathways. Here, we analyzed the sulfate production rates using a state-of-art multiphase model constrained to the observed concentrations of transition metal ions (TMI), nitrogen dioxide, ozone, hydrogen peroxide, and other important parameters in winter and summer in the North China Plain. Our results showed that aqueous TMI-catalyzed oxidation was the most important pathway followed by the surface oxidation of Mn in both winter and summer, while the hydroxyl and 15 criegee radicals oxidations contribute significantly in summer. In addition, we also modeled the published cases for the fog and cloud conditions. It is found that nitrogen dioxide oxidation is the dominant pathway for the fog in a higher pH range while hydroperoxide and ozone oxidations dominated for the cloud.


Introduction 20
Secondary sulfate aerosol is an important component of fine particles in severe haze periods Huang et al., 2014b;Guo et al., 2014), which adversely affect the environmental quality and human health. Traditional atmospheric models evaluate secondary sulfate formation via the gas-phase oxidation of sulfur dioxide (SO2) and a series of multiphase oxidation of dissolved SO2 in cloud water. During haze events, multiphase oxidation of dissolved SO2 is more important than SO2 directly oxidized by gas-phase radicals (Atkinson et al., 2004;Barth et al., 2002) because of the significantly reduced 25 ultraviolet (UV) radiation intensity due to the aerosol dimming effect. Gas-phase reactions, especially those favouring multiphase chemistry, cannot capture the high concentrations of sulfate aerosols during haze events. Moreover, rapid sulfate production is observed during cloud-free conditions indicating that aerosol multiphase oxidation may be important during https://doi.org/10.5194/acp-2021-377 Preprint. Discussion started: 31 May 2021 c Author(s) 2021. CC BY 4.0 License. haze periods (Moch et al., 2018). These effects cause a major gap between the measured sulfate concentrations under weak UV radiation and the concentrations calculated using traditional atmospheric models. 30 Assessing the mechanism of multiphase secondary sulfate formation during haze periods helps evaluate the effect of multiphase oxidation. While the gas-phase oxidation rate of SO2 and OH is well constrained, there are many uncertainties in the quantification of the relative contribution of each multiphase SO2 oxidation pathway during haze periods. Multiphase oxidation pathways of dissolved SO2 (Seinfeld and Pandis, 2016;Liu et al., 2020a;Seigneur and Saxena, 1988; include oxidation by (1) hydrogen peroxide (H2O2); (2) ozone (O3); (3) transition metal ions [TMI,i.e.,35 Fe (III) and Mn (II)] catalyzed oxidation pathway (aqTMI)]; and (4) Mn-catalyzed oxidation of SO2 on aerosol surfaces pathway (Mn-surface) (Wang et al., 2021). Some studies Xue et al., 2016; also suggested that nitrogen oxides may play a crucial role in the explosive growth of sulfate formation during severe haze days in Beijing because of the high pH near a neutral system, by facilitating the catalysis of mineral dust  or the photolysis of nitrous acid . However, the average pH during Beijing haze 40 periods is approximately 4.2 , and a high level of NH3 does not increase the aerosol pH sufficiently to yield NO2-dominated sulfate formation (Guo et al., 2017). Other studies (Ye et al., 2018;Liu et al., 2020b) emphasized the importance of H2O2 oxidation to sulfate formation due to the underestimation of H2O2 concentrations during haze episodes in previous studies or the influence of high ionic strength (Is) of aerosol solutions on the H2O2 oxidation rate, which implies that oxidant concentrations for SO2 oxidation constrained to the observed values from field measurements are required. Previous 45 study  showed that photosensitization is a new pathway for atmospheric sulfate formation and requires further verification. According to previous studies of the GEOS-Chem model and including the measurements of oxygen isotopes (Δ 17 O (SO4 2− )) Shao et al., 2019;Yue et al., 2020), several studies showed that aqTMI was important during some haze periods. Overall, the formation mechanisms of the missing sulfate sources remain unclear and controversial. 50 Sulfate formation is a complex multiphase physicochemical reaction process, in which parameters have multiple interrelationships. The previous studies have mostly selected typical conditions with fixed parameters for numerical calculations, ignoring the fact that sulfate formation is a complex dynamic process. A comprehensive and explicit evaluation of the sulfate generation process requires real-time feedback and explicit constraints of observational data. Therefore, it is crucial to apply constrained parameters from field campaigns in the calculations. Moreover, as proposed in previous studies 55 Cheng et al., 2016), due to the lower water content in aerosol particles than in cloud water, the non-ideality effects of aerosol solutions should be carefully considered.
In this study, we modeled the concentrations of the main reagents of sulfate formation reactions using a state-of-art Peking-University-Multiple-phAse Reaction Kinetic Model (PKU-MARK) based on the data measured in two field campaigns conducted in the winter and summer in the North China Plain (NCP) where several particle pollutions happened. The non-60 ideality of aerosol solutions was considered in the calculation of both gas solubility and aqueous-phase reaction rates.
Chemical regimes in the aerosol particle bulk phase were analyzed to understand the role of gas-phase radical precursors, https://doi.org/10.5194/acp-2021-377 Preprint. Discussion started: 31 May 2021 c Author(s) 2021. CC BY 4.0 License.
particle TMIs, aerosol surface concentrations and the aerosol liquid water content (ALWC) on the aqueous reactant levels and the sulfate formation rate.
The overall goal of this work is to evaluate the contribution of different secondary sulfate formation pathways under actual 65 field measurement conditions in the NCP. Effects of non-ideality of condensed particle phase and the solubility of gas-phase reactants on the reactions enable the comparisons with parameters previously obtained in model calculations. In addition, episodes at different pollution levels in the winter and summer campaigns were selected to evaluate the contribution of prevailing sulfate formation pathways proposed in previous studies. As a study evaluating the contribution of different sulfate formation pathways during field campaign observations, this work provides an improved understanding of 70 atmospheric sulfate formation at different pollution levels in the NCP. Table 1 shows the key meteorological parameters, trace gases concentrations, calculated ALWC, ionic strength, pH and sulfate formation rates under different pollution conditions in PKU-17 and WD-14 comprehensive field campaigns. 75

Overview of the field observations
Sampling location and experimental methods used in these two campaigns are summarized in the Method part. The pollution degree is classified according to the mass concentration of PM2.5. The clean condition means PM2.5 smaller than 35 μg/m 3 , the slightly polluted condition is 35-75 μg/m 3 , the polluted condition is 75-150 μg/m 3 and highly polluted is larger than 150 μg/m 3 . Sulfate formation rates were modeled by the Multiple-phAse Reaction Kinetic Model (PKU-MARK) (mentioned in Method) with constrained parameters. The effects of aerosol non-ideality were considered in the size-segregated model. Data 80 points with relatively humidity (RH) smaller than 20% and AWLC smaller than 1 μg/m 3 were abandoned to improve the accuracy of the results.
Transition metals concentrations including Fe and Mn increased with PM mass. Photochemical oxidants including H2O2 and O3 exhibited a decreasing trend with the increase of PM mass because of the significantly reduced solar ultraviolet (UV) radiation intensity due to the aerosol dimming effect. Some studies reported high H2O2 concentrations during haze 85 episodes (Ye et al., 2018), whereas in PKU-17 field campaign, the average concentration of H2O2 was only 20.9±22.8 pptV in highly polluted conditions. Higher sulfate concentration was observed in the high range of RH and ALWC indicating their enhancement effects on the sulfate formation. We also picked four haze periods in PKU-17 observation, the time series of these key parameters are provided in Supplementary Information (SI) Fig. S4.
Aerosol pH values were calculated using the ISORROPIA-II model. The calculated particle pH values as shown in the Table  90 1 are in good agreement with the values reported in other studies (Guo et al., 2017;. The lower pH in the range of 4.0-5.5 is beneficial to sulfate formation via aqTMI. Aerosol liquid water is another key component, higher loading of aerosol liquid water is more conducive to the occurrence of multiphase reactions. The ALWC in the PKU-17 and WD-14 campaigns was calculated via the ISORROPIA II model with input concentrations of aerosol inorganic components (see https://doi.org/10.5194/acp-2021-377 Preprint. Discussion started: 31 May 2021 c Author(s) 2021. CC BY 4.0 License.

Method M.3).
Aerosol liquid water did not freeze at winter temperatures below 273 K in the PKU field campaign because of 95 the salt induced freezing point depression (Koop et al., 2000). Wind speeds during these haze events were persistently low (0.3-1.5 m/s), indicating the minor contribution of regional transport to sulfate production.
Aqueous TMI concentration level is crucial in the evaluation of secondary sulfate formation in real atmospheric conditions. Atmospheric anthropogenic sources of transition metals such as iron (Fe), copper (Cu), and manganese (Mn) are mainly from combustion. Concentrations of transition metals are highly variable, ranging from <0.1 ng m -3 to >1000 ng m -3 globally 100 (Alexander et al., 2009). Fe solubility in atmospheric aerosols has been reported to range from 0.1% to 80% (Ito et al., 2019;Hsu et al., 2010;Heal et al., 2005;Shi et al., 2012;Mahowald et al., 2005), and elevated levels of Fe solubility have been observed in aerosols dominated by combustion sources. The average fractional Fe solubility in areas away from dust source regions is typically between 5 and 25% (Baker and Jickells, 2006;Baker et al., 2006;Hsu et al., 2010). A recent study reported the average Fe solubility as 2.7-5.0% in Chinese cities, and more than 65% of nano-sized Fe-containing particles 105 were internally mixed with sulfates and nitrates . The solubility of Mn tends to be higher than that of Fe (Baker et al., 2006), which is 22-57% in urban aerosol particles (Huang et al., 2014c). In this study, we chose the solubility of total Fe as 5% and total Mn solubility as 50% assuming that aerosol particles are internally mixed. In Beijing, high concentrations of Fe, Cu, and Mn were observed ( Table S9). Concentrations of transition metals are strongly correlated during these haze periods; thus, we propose a fixed ratio of Fe/Mn to account for the lack of Mn data in PKU-17 and WD-14 110 field campaigns (SI Text S2).
Aerosol trace metal speciation and water solubility are affected by factors such as photochemistry, aerosol pH, and aerosol particle size (Baker and Jickells, 2006;Oakes et al., 2010). Soluble iron in aerosol water exists as Fe (II) and Fe (III), with a series of redox recycling between the two species and other ions. Partitioning between Fe (II) and Fe (III) varies diurnally with the highest fraction of Fe (II) found during the day because of the photochemical reactions reducing Fe (III) to Fe (II). 115 Photolysis reactions of iron hydroxides and organic complexes were documented as the most important source of Fe (II) in cloud and fog water. Oxalic acid and its deprotonated form, oxalate, have strong coordination ability with Fe and form Feoxalate complexes, which have higher photochemical activity than Fe hydroxide. All these mechanisms are included in the PKU-MARK model. Diurnal trends of sulfate formation were observed during haze periods indicating the diurnal distribution of different states of iron. Redox cycling of other TMIs such as Cu and Mn are also considered in the PKU-120 MARK model. Averaged percentage of soluble Fe (III) and Mn (II) was 0.79% and 19.83% in winter polluted conditions and 2.57% and 52.15% in summer polluted conditions. The main reason for the difference between winter and summer metal solubility is that summer aerosols have higher water content and lower ionic strength, which is conducive to the dissolution of Fe and Mn. The solubility range is in good agreement with the values reported in previous observations (Ito et al., 2019;Hsu et al., 2010). 125 The influence of aerosol ionic strength on aqTMI reaction rates was considered carefully in the study. Higher ALWC is typically accompanied by lower ionic strength, which increases the activity of TMI. The relationship  between the rate coefficients of the TMI pathway and ionic strength is displayed in Fig. S1. The sulfate formation rate  Contributions of the gas-phase radical oxidants were much higher during summer time. To fully explain the relative 135 contributions to sulfate formation from different pathways, the stabilized criegee intermediates (SCIs) oxidant was also considered in the calculations. Based on the previous report (Sarwar, 2013), the inclusion of the SCIs oxidation pathway further enhances sulfate production. We modified the Regional Atmospheric Chemistry Mechanism (RACM2) Table S2  . αFe (III) is defined as the product of the Fe (III) activity coefficient, concentration, molecular weight (56) and aerosol liquid water content. Compared to the total Fe concentration, it 145 is more effective to evaluate the impact of αFe (III) on sulfate formation. The relationship between αFe (III) and SOR in PKU-17 winter field campaign was shown in SI Figure S5. Because of the inhibition of the effects of high ionic strength on the rate constant of aqTMI, a high volume of aerosol water during the haze event increased the TMI activity coefficient benefiting sulfate formation. Obvious correlations between αFe (III) and sulfate concentration shown in Fig. 1

(c) and (d)
were observed in the haze periods both in summer and winter verified the important contributions from aqTMI pathway to 150 the sulfate formation. Affected by the higher boundary layer height and higher gas phase radical concentration in summer, the correlation between sulfate oxidant ratio SOR (≡n(SO2)/n(SO2+SO4 2-)) and PM mass in summer is not as significant as that in winter. In summer, as illustrated in Fig. S6, there was still an obvious positive dependence between SOR and RH and Fig. 1 (e) and (f), the sulfate formation through gaseous reaction was more important in summer than in winter, mainly provided by 155 gas phase radicals (OH and SCIs). In WD-14 field campaign, heterogeneous aqTMI pathways were still dominant in the secondary sulfate formation.

Dependence of the Secondary sulfate formation rates on aerosol pH and water content
Aerosol pH and ALWC were calculated using the ISORROPIA-II model (Method M3). Because of the high sensitivity of sulfate formation to pH, the lower range of aerosol pH during these two campaigns made the aqTMI the most important one.
The effects of high aerosol ionic strength on the dissolution equilibrium and reaction rates were considered in calculations ) (SI Table S2 to S4). Due to the low H2O2 concentration (~0.023 ppbV) and low ALWC observed in the PKU-17 field campaign, the average contribution of H2O2 in haze periods (PM2.5 > 75 μg/m 3 ) was about 0.11±0.15 μg/m 3 /h.
Higher gas-phase H2O2 concentration may further increase the contribution of this pathway to sulfate formation. Based on a recent report (Ye et al., 2018), higher gas-phase H2O2 concentrations were observed in the NCP during different haze events, 165 including severe haze episodes in suburban areas. At 0.1 ppbV H2O2 (about five times higher than the observed H2O2 concentration), the calculated sulfate formation rate was 0.52±0.76 μg/m 3 /h in haze periods with great uncertainty and still lower than the contribution of the TMI pathway (1.17±1.48 μg/m 3 /h).
Due to the potential interaction between various factors in the atmosphere, fixing certain parameters and changing only the pH to obtain the sulfate production rate may cause errors. With the development of haze, concentrations of O3 and OH 170 radicals decrease due to reduced UV radiation caused by the aerosol dimming effect. Despite its minor contribution to sulfate production in winter, the increase in the ozone oxidation rate with pH was slower under actual conditions. Contributions of gas-phase radicals also showed a weak downward trend in the summer campaign ( Fig. 2 (c)). The bias between calculated and observed values indicated a dynamic balance of atmospheric oxidation in the gas phase and aerosol phase. If we arbitrarily use the average values during haze periods and only changed the pH of the aerosols as in previous studies, the 175 obtained sulfate production rate will deviate from the observed values. Actual ambient sulfate formation rates calculated using the measured values in polluted periods in two field campaigns are illustrated in Fig. 2 (a) and (c). Average values except for pH during the haze periods were used to calculate the sulfate formation rates as shown in Fig. 2 (b) and (d). The peak of the H2O2 line in the figure is caused by the change in the water content and ionic strength. In the pH range of 4.0-6.0, the calculated ALWC was in the highest range, increasing the contribution of H2O2 proportionally as calculated using 180

equation (1).
Aerosol water content is another key factor that influences the contribution of different pathway to sulfate formation. The sulfate formation rate can be calculated via the following equation with the modeled ( ) ( −1 ): where ALWC is in units of μg m -3 and is the water density in kg L -1 . At high ionic strength, this expression is more 185 accurate than the equivalent expression with the unit of M s -1 . ALWC directly influences the contribution via external oxidizing substances such as H2O2, O3, and NO2 but not aqTMI pathway. Most H2O2, O3, and NO2 come from gas phase through dissolution equilibrium, while TMI is formed in particles. The reaction kinetics and rate constants summarized in Table S2 suggest that there is a proportional relationship between ALWC and sulfate formation pathways except aqTMI.
One reason for the lower sulfate formation rate observed in the PKU-17 (1-3 μg m -3 h -1 ) is that the ALWC values were lower 190 than those assumed in previous studies (ALWC = 300 μg m -3 ). This deviation from the ALWC significantly reduces the contribution of several other pathways, but not the contribution of transition metals to sulfate formation. Due to the obvious heterogeneous reactions contribution to sulfate formation in winter, we evaluated the influence of ALWC on sulfate formation pathways in winter. TMI relevant pathways including aqTMI and Mn-surface pathway were dominate in all range of ALWC as illustrated in Fig.3. In PKU-17 field campaign, with the increasing of ALWC from 1 to 195 150 μg/m 3 , the ratio of aqTMI to Mn-surface continuously decreased mainly because of the decreasing particle specific surface areas. The reduction effect of ionic strength on aqTMI rate reached a "platform" when ALWC exceeding 150 μg/m 3 in winter, which means that higher ALWC will not increase the rate of aqTMI. Mn-surface contributed most in lower ALWC range where particle specific surface area was high and provide more reaction positions. Transition metal mass will not increase with the aerosol hygroscopic growth. With the aerosol hygroscopic growth, the increasing of transition metal 200 mass is slower than water mass in PKU-17 as shown in Due to the slight increase of aerosol pH and the dilution effect of aerosol hygroscopic growth on TMI when ALWC exceeding 150 μg/m 3 , the importance of aqTMI and Mn-surface contributions were lowered. At this time, the contributions of external oxidizing substances pathways such as H2O2, NO2 or O3 may rise in the proper pH range as illustrated in Fig.4. In 205 winter fog or cloud conditions with higher water content, the contribution from TMI may decrease a lot for their low solubility and concentrations.
The same analysis also used in the summer WD-14 field campaign (as shown in SI Fig.S8). "The dilution effect" occurred more dramatically in summer compared to that in winter because of a higher RH and higher percentage of water in the aerosol. In this situation, the contribution of aqTMI or Mn-surface was inhibited due to the low soluble TMI concentrations. 210 Considering the positive relationships of SOR and RH in summer WD-14 field campaign, aqueous and surface sulfate formation contributions mentioned in the study could not explain the missing source of secondary sulfate. Because of the low pH range observed in WD-14 field campaign, the contributions from H2O2, NO2, O3 or NO3photolysis were negligible.
The missing contribution may mainly come from other pathways such as photosensitizing molucules  under stronger UV in summer or contributions from hydroxymethane sulfonate (Moch et al., 2018; which 215 need further studies.

Discussion and Conclusion
We evaluated the contribution of different pathways to secondary sulfate formation using a state-of-art size-segregated multiphase model constrained to the observed parameters from two field campaigns in the North China Plain. In addition, the effects of aerosol solution non-ideality on aqueous-phase reaction rates as well as dissolution equilibriums were considered 220 in the calculations. The results indicated that the aqueous TMI-catalyzed oxidation pathway (aqTMI) was a major contributor to sulfate formation during haze episodes, which is consistent with the results of the isotope and WRF-CHEM studies Shao et al., 2019;Yue et al., 2020;Tao et al., 2020). External oxidizing substances such as NO2 and O3 had little contribution to sulfate formation during these haze periods because of the high aerosol acidity. High pH (near 7) values were observed in these field campaigns when the contribution of 235 the NO2 pathway was dominant at some point but not during the entire pollution process; its proportion was much lower than that of aqTMI. Although the enhancement factor of H2O2 oxidation was considered based on the measurement of previous study , the contribution of H2O2 oxidation was still below 0.5 μg S(VI)/m 3 /h because ALWC was about 10 times lower than 300 μg m -3 , which was used in previous studies Liu et al., 2020b).
The sulfate formation rate is limited by the ALWC according to equation (1). Aerosol particles have lower water content 240 than cloud droplets, which provides larger space for aqueous phase reactions. Therefore, at the gas-phase SO2 concentrations of 5-50 ppb, 10-100 times higher water content in fog and cloud droplets can cause higher sulfate formation rates up to 100 μg m -3 h -1 assuming 0.1 g m -3 water in clouds (Fig. 4). A high H2O2 concentration (1 ppb), which was 50 times higher than that in the PKU field campaign, was used in the calculation in the Cloud_5.0 regime(Seinfeld and Pandis, 2016). No obvious contribution from the NO2 oxidation pathway was observed in the PKU-17 and WD-14 field campaigns because of the lower 245 pH range. As proposed in a previous study, the particulate nitrate photolysis can explain the missing source of sulfate in Beijing haze (Zheng et al., 2020). However, according to the recent laboratory report (Shi et al., 2021), the nitrate photolysis enhancement factor is no larger than 2 at all RH ranges. We also included the calculation of nitrate photolysis in this study due to the high loading of particle nitrate and found that the contribution was rather small (~0.008 μg m -3 h -1 in winter haze periods); thus, we did not include this pathway in the figures. 250 According to our modeled results and the newest study (Wang et al., 2021), Mn surface reactions contributed a lot to sulfate formation. Except for possible Mn(OH)x (3-x) reacting with SO2, Zhang et al. (2006) proposed that other metal oxides such as Fe2O3 and Al2O3 can also react with SO2 on the surface of particles. While as mentioned above, the ratio of contributions from Mn-surface and aqTMI to produce sulfate will decrease with aerosol hygroscopic growth owning higher ALWC.
What's more, the organic coating of aerosol particles can largely reduce the reactivity of surface reactions. The results in this paper indicate that sulfate formation has different chemical behaviors in different conditions. Aqueous TMI-catalyzed oxidation was the most important pathway followed by the surface oxidation of Mn in both winter and 270 summer, while the hydroxyl and criegee radicals oxidations contribute significantly in summer. Due to the differences in the physical and chemical properties between aerosol water, fog water and cloud, nitrogen dioxide oxidation is the dominant pathway in higher pH range and hydroperoxide and ozone oxidations dominated for the cloud. In model studies, the averaged and fixed values should be used dialectically and carefully in the calculation of sulfate formation rate because of the mutual restriction between factors such as pH, effective ion activity and concentration, and aerosol water content. Model 275 evaluation or numerical calculations of secondary pollutants should focus on the application of actual atmospheric conditions observed in field campaigns with the application of closure study. Our results highlight the important role of aerosol aqTMI in sulfate formation during haze periods and the monitoring network of aerosol metal is necessary for the studies of secondary sulfate formation. The aqTMI independent of solar radiation also explains the explosive growth of sulfate production at night-time, which is frequently observed during haze episodes in the NCP. 280 Compared to the gas-phase oxidants, the control of anthropogenic emissions of aerosol TMI is conducive to the reduction of secondary sulfates. The promotion of clean energy strategies aiming at reducing coal burning to improve air quality in North China has reduced not only the primary emissions of SO2 but also the anthropogenic emissions of aerosol TMIs  and thus the production of secondary sulfate. Our findings showed that urban aerosol TMIs contribute to sulfate formation during haze episodes and play a key role in developing mitigation strategies and public health measures in 285 megacities worldwide, but the physicochemical processes of transition metals in particles require further research. Influences of organic matter and photosensitizing molecules on the solubility of transition metal and the mechanism of sulfate formation need further research to understand this complex and dynamic multiphase process from a broader perspective.

Sampling location and experimental methods 290
The data from the 2014 Wangdu (WD) and 2017 Peking University (PKU) field campaigns, both conducted in summer, were used in our analysis. The WD field campaign was carried out from June to July 2014 at a rural site in Hebei (38.70° N,115.15° E) characterized by severe photochemical smog pollution (Tan et al., 2017;. The 2017 PKU campaign was performed from November to December 2017 at the campus of Peking University (39.99° N, 116.31° E), which is in the city centre of Beijing and characterized by strong local anthropogenic emissions from two major roads (Ma et 295 al., 2019).
Observations from both field campaigns include gas-phase measurements of SO2 and O3 from commercial Thermo Scientific monitors and NO2 detected after conversion through a custom-built photolytic converter with UV-LED at 395 nm; aerosol mass concentration from a set of commercial particle instruments containing Nano scanning mobility particle sizer (SMPS) and aerodynamic particle sizer (APS) to cover the size range of 3 nm to 10 μm. The In-situ Gas and Aerosol Compositions 300 monitor (IGAC) (Young et al., 2016), which can collect gases and particles simultaneously, was used to measure watersoluble ions online with 1-h time resolution. Both gas and aerosol samples were injected into 10 mL glass syringes, which were connected to an ion chromatograph (IC) for analysis (30-min time resolution for each sample). The concentrations of eight water soluble inorganic ions ( NH4 + , Na + , K + , Ca 2+ , Mg 2+ , SO4 2− , NO3 − , and Cl − ) in fine particles were measured.
Transition metal (Fe and Cu) concentrations in PM2.5 were measured using the Xact 625 Ambient Metal Monitor. With Xact, 305 ambient air was introduced through a PM2.5 cyclone inlet at a constant flow rate of 16.7 L min -1 and collected on the reel-toreel poly tetrafluoroethylene filter. Then trace elements in ambient fine particles on the filter were automatically detected using the United States Environmental Protection Agency (USEPA) standard method via x-ray fluorescence (XRF) analysis . Ambient temperature and pressure data were measured using commercial meteorological sensors; selected volatile organic compounds (VOCs) were measured via off-line gas chromatography-mass 310 spectrometry (GC-MS) in tower measurements using sampling canisters and via online GC−MS in the surface campaign.
The OH and HO2 concentrations were measured via laser-induced fluorescence (LIF) with the time resolution of 30 s as described in previous study . The concentrations of gas-phase peroxides were measured using highperformance liquid chromatography (HPLC, Agilent 1200, USA) with a time resolution of 21 min.

Brief overview of the PKU-MARK model 315
The Multiple-phAse Reaction Kinetic Model (PKU-MARK) was first developed to calculate the heterogeneous reaction rate of reactive gas molecules . The units of aqueous reagents are converted to molecules· cm −3 in the model by a factor kmt, which combines both gas-phase molecular diffusion and liquid-phase interface mass transport processes (Schwartz, 1984;Schwartz, 1986) and used in the calculation for gas-liquid multiphase reactions in many modelling studies (Lelieveld and Crutzen, 1991;Chameides and Stelson, 1992a;Sander, 1999;Hanson et al., 1994;. In this study, the PKU-MARK model was further developed with the correction of ionic strength for all ions and reactants and applied to a size-segregated system to investigate the influence of aerosol particle size distribution and ALWC distribution. Eleven bins of aerosol particle diameters and corresponding ALWC values were applied in the model. With the input of onehour averaged parameters observed in the field campaign, the PKU-MARK model produced the state-state concentrations of aqueous reactants including reactive oxygen species (H2O2, O3, OH, HO2, O2 -), Fe (III), Mn (II), SO2(aq), and NO2(aq). 325 Considering the mutual influence of various factors in the reaction system can effectively prevent bias caused by arbitrarily fixing a certain value as was often done in previous studies.

Calculation of aerosol pH, aerosol liquid water, and ionic strength
ALWC and aerosol pH were calculated using the ISORROPIA-II model and measured concentrations of inorganic ions in particles. ISORROPIA-II is a thermodynamic equilibrium model that predicts the physical state and composition of 330 atmospheric inorganic aerosols. Its ability to predict pH has been demonstrated in detail in previous studies . Ionic strength was calculated via equation (2) (Ross and Noone, 1991): where is the molality of an ion (mol L -1 ), and is the corresponding charge. In the PKU-MARK model, reaction rates were replaced by the activity coefficient. The ionic strength was estimated using the ISORROPIA-II model assuming that the 335 condensed phase is in the meta-stable state and complete external mixing state.
In order to consider the influence of particle diameter on aqueous SO2 concentrations, which is key to calculate sulfate formation, we used a 11-bin actual particle diameter distribution rather than one even distribution used in previous studies . The distribution of particle number concentration and water content is illustrated in Fig. S2. We also considered the distribution of ALWC in different particle diameter bins based on the κ-Köhler theory (Petters and 340 Kreidenweis, 2007) using observed kappa values from High Humidity Tandem Differential Mobility Analyser (HH-TDMA) and the Twin Differential Mobility Particle Sizer (TDMPS)/APS (Bian et al., 2014). Calculated ALWC values were strongly correlated with the ISORROPIA-II results (Fig. S3).
To combine both gas-phase molecular diffusion and liquid-phase interface mass transport processes, the approach adopted in this study uses one variable called (Schwartz, 1984;Schwartz, 1986), which is used in multiphase reactions in many 345 modelling studies (Lelieveld and Crutzen, 1991;Chameides and Stelson, 1992b;Sander, 1999;Hanson et al., 1994). The definition of is given in equation (3): The rate of gas-phase reactions (X) diffusing and dissolving to the condensed phase can be calculated in the framework of aqueous-phase reactions as _ × where X is the reactant molecule (please see Table S8 for more details). 350 Moreover, the conversion rate of aqueous-phase reactions to gas-phase reactions can be calculated as is s -1 , as contains the conversion from mair -3 of the gas-phase molecule concentrations to maq -3 of the aqueous-phase molecule concentrations. Particle diameter can influence the mass transport rate of SO2 and its aqueous concentration. Based on the model results of (Xue et al., 2016), diameter had an impact on sulfate formation rates: for larger particles (radius >1 µm), is determined by gas-phase diffusion; for smaller particles (radius <1 µm), is determined by the 355 accommodation process. The PKU-MARK model can simultaneously simulate two-phase (gas and liquid) reaction systems in the same framework.

Model Evalution
Concentrations of sulfate were calculated by integrating an extension of the Eulerian box model described in previous study (Seinfeld and Pandis, 2016). Sulfate concentrations are related to dry deposition, transport, dilution as the boundary 360 layer height (BLH) expands, emissions, and net production. Due to the higher and more dramatically diurnal changing BLH in summer (Lou et al., 2019), and the lack of relevant data in WD-14 field campaign, we could not get the modelled results of sulfate concentrations in summer haze periods. Direct emissions and transport of sulfate were not considered in the calculation because secondary sulfate is the predominant source in winter haze periods. Dilution was not considered either because the atmosphere is relatively homogeneous during winter haze episodes. Since haze events are normally accompanied 365 by a low boundary layer height (Ht), Ht was set at 300 m at night-time and 450 m at noon (Xue et al., 2016). At other times, Ht was estimated using a polynomial (n = 2) regression as recommended in previous study (Xue et al., 2016). The diurnal trends of sulfate concentrations of the winter haze period using the deposition velocity of 1.5 cm/s are shown in Fig. 1 (c).
Model results had the same trend with the observed values and could explain the missing source of sulfate aerosol to some extent. 370  The contributions to sulfate formation from each multiphase oxidant pathways including Mn-surface oxidant (green), gas phase OH radical and Stabilized Criegee Intermediates (SCIs) oxidant (pink), aqueous phase NO2 (grey), O3 (yellow), H2O2 (orange) and aqTMI (blue) were colored in the figure. Obvious particle growth and removal was observed in winter (26 th to 385 31 st , December, 2017) and diurnal variation patterns of sulfate concentration were observed in summer (23 th to 28 th , June, 2014). Diurnal trends of modeled winter period's sulfate concentration (grey dash line) using deposition velocity as 1.5 cm/s are illustrated in panel (c). The dotted lines in the (e), winter and (f), summer indicate the SOR with pollution level in the whole campaigns and the capitalized letters "C", "S", "P", "H" are the abbreviations for "Clean", "Slightly polluted", "Polluted" and "highly polluted", respectively.  Given the actual measured concentration, the steady-state concentration of each reactant was calculated using the MARK 395 model accounting for the impact of ionic strength on the Henry's law coefficient of the gas-phase reactants. Panels (a) and (c) show the cluster averaged results with a pH span of 0.5. Panels (b) and (d) show the sulfate formation rate obtained by fixing the average precursors levels during the haze periods and by changing the aerosol pH, which is consistent with the calculation method of previous studies . Grey-shaded areas indicate the ISORROPIA-II(Fountoukis and Nenes, 2007) model calculated pH ranges during the haze periods of two field campaigns. The coloured solid lines represent 400 sulfate production rates calculated for different multiphase reaction pathways with oxidants: enhanced H2O2, O3, TMIs, NO2, surface Mn and gas-phase radicals (OH+SCIs). The solid orange line represents the calculated sulfate formation rate via H2O2 with a factor of 100 in winter and summer according to the latest research results . Reactant concentrations, aqueous reaction rate expressions, and rate coefficients are summarized in the SI.

Data Availability
Data supporting this publication are available upon request for the corresponding author (k.lu@pku.edu.cn).

Conflict of interests 430
The authors declare that they have no conflict of interest.

Supplementary information includes:
Supplementary Information Text Text S1. Activity coefficients of main reactants in the MARK model 445 Text S2. The concentration of aerosol particle transition metals in urban areas Supplementary Information Figures Fig.S1-S9   Fig. S1. Ionic strength of aerosol particle solution influence on the aqTMI rate constant.    Supplementary Information Tables S1-S9. Table S1. Reaction rate expression and constant for SO2 oxidation by OH in the gas-phase. Table S2. Aqueous-phase reaction rate expressions, rate constants (k) and influence of ionic strength (Is) on k for sulfate production in aerosol particle condensed phase. Table S3. Calculations of Henry' law coefficients and influence of ionic strength. 465 Table S4. Typical activity coefficient values and expressions used in the MARK model. Table S5. Kinetic data for the simulation of reactions in the aerosol particle condensed phase.