Relative humidity and O3 concentration as two prerequisites for sulfate formation

Sulfate formation mechanisms have been discussed extensively but are still disputed. In this work, a yearlong particulate matter (PM2.5) sampling campaign was conducted together with measurements of gaseous pollutant concentrations and meteorological parameters in Beijing, China, 5 from March 2012 to February 2013. The sulfur oxidation ratio (SOR), an indicator of secondary sulfate formation, displayed a clear summer peak and winter valley, even though no obvious seasonal variations in sulfate mass concentration were observed. A rapid rise in the SOR was found at 10 a relative humidity (RH) threshold of ∼ 45 % or an O3 concentration threshold of ∼ 35 ppb, allowing us to first introduce the idea that RH and O3 concentrations are two prerequisites for rapid sulfate formation via multiphase reactions. In the case of the RH threshold, this is consistent with 15 current understanding of the multiphase formation of sulfate, since it relates to the semisolid-to-liquid phase transition of atmospheric aerosols. Correlation analysis between SOR and aerosol water content (AWC) further backed this up. In the case of the O3 concentration threshold, this is con20 sistent with the consumption of liquid oxidants in multiphase sulfate formation. The thresholds introduced here lead us to a better understanding of the sulfate formation mechanisms and sulfate formation variations. H2O2 might be the major oxidant of sulfate formation, since another liquid-phase oxi25 dant, O3, has previously been shown to be unimportant. The seasonal variations in sulfate formation could be accounted for by variations in the RH and O3 prerequisites. For example, over the year-long study, the fastest SO2-to-sulfate conversion occurred in summer, which was associated with 30 the highest values of O3 (and also H2O2) concentration and RH. The SOR also displayed variations with pollution levels; i.e. the SOR increased with PM2.5 in all seasons. Such variations were primarily associated with a transition from the slow gas-phase formation of sulfate to rapid multiphase re35 actions, since RH increased higher than its prerequisite value of around 45 % as pollution evolved. In addition, the selfcatalytic nature of sulfate formation (i.e. the formation of hydrophilic sulfate aerosols under high RH conditions results in an increase in aerosol water content, which results in greater 40 particle volume for further multiphase sulfate formation) also contributed to variations among the pollution scenarios.

from March 2012 to February 2013. The sulfur oxidation ratio (SOR), an indicator of secondary sulfate formation, displayed a clear summer peak and winter valley, even though no obvious seasonal variations in sulfate mass concentration were observed. A rapid rise in the SOR was found at a relative humidity (RH) threshold of ∼ 45 % or an O 3 concentration threshold of ∼ 35 ppb, allowing us to first introduce the idea that RH and O 3 concentrations are two prerequisites for rapid sulfate formation via multiphase reactions. In the case of the RH threshold, this is consistent with 15 current understanding of the multiphase formation of sulfate, since it relates to the semisolid-to-liquid phase transition of atmospheric aerosols. Correlation analysis between SOR and aerosol water content (AWC) further backed this up. In the case of the O 3 concentration threshold, this is con-20 sistent with the consumption of liquid oxidants in multiphase sulfate formation. The thresholds introduced here lead us to a better understanding of the sulfate formation mechanisms and sulfate formation variations. H 2 O 2 might be the major oxidant of sulfate formation, since another liquid-phase oxi-25 dant, O 3 , has previously been shown to be unimportant. The seasonal variations in sulfate formation could be accounted for by variations in the RH and O 3 prerequisites. For example, over the year-long study, the fastest SO 2 -to-sulfate conversion occurred in summer, which was associated with 30 the highest values of O 3 (and also H 2 O 2 ) concentration and RH. The SOR also displayed variations with pollution levels; i.e. the SOR increased with PM 2.5 in all seasons. Such variations were primarily associated with a transition from the slow gas-phase formation of sulfate to rapid multiphase re- 35 actions, since RH increased higher than its prerequisite value of around 45 % as pollution evolved. In addition, the selfcatalytic nature of sulfate formation (i.e. the formation of hydrophilic sulfate aerosols under high RH conditions results in an increase in aerosol water content, which results in greater 40 particle volume for further multiphase sulfate formation) also contributed to variations among the pollution scenarios.

Introduction
Beijing, the capital of China, suffers from serious air pollution due to its rapid economic growth and urbanisation (Hu 45 et al., 2015). The chemical composition and sources of fine particulate matter (PM 2.5 ) in Beijing have been studied extensively (Han et al., 2015;Lv et al., 2016;Zhang et al., 2013;Zheng et al., 2005). Secondary components, especially sulfate, nitrate, and ammonium (SNA), are the main contrib-50 utors to PM 2.5 (Huang et al., 2014). On the most severely polluted days, SNA accounts for more than half of total PM 2.5 mass concentrations and plays a more important role than on clean days (Quan et al., 2014;Y. S. Wang et al., 2014; G. J. Zheng et al., 2015). 55 The kinetics and mechanisms of the formation of sulfate, a major component of SNA, are complex and remain unclear (Ervens, 2015;Harris et al., 2013;Warneck, 2018 (oxidants, catalysts, meteorological conditions, etc.) influence sulfate formation, and (2) how multiple formation routes compete and contribute together to sulfate formation under ambient conditions. In general, sulfate is produced from SO 2 via gasphase oxidation reactions involving the hydroxide radical (OH) and Criegee intermediates (Gleason et al., 1987;Sarwar et al., 2014;Vereecken et al., 2012), heterogeneous reactions (mainly on dust aerosols), and multiphase transformations with O 3 , H 2 O 2 , or O 2 (catalysed by transition metal 10 ions (TMIs) (i.e. TMIs + O 2 ) and NO 2 (NO 2 +O 2 )) as liquidphase oxidants, which occur mainly in clouds but also in aerosol droplets near the ground (Zhu et al., 2011).
Due to the major role of multiphase transformations, sulfate production is presumed to be self-catalysed; i.e. the formation of hydrophilic sulfate aerosols under high relative humidity (RH) conditions results in an increase in aerosol water content (AWC), which results in greater particle volume for further multiphase sulfate formation (Cheng et al., 2016;Pan et al., 2009;Xu et al., 2017). Analyses of the correlation of 20 sulfate formation with RH and AWC have been conducted to test this hypothesis, using the concept of the sulfur oxidation ratio (SOR), defined as the molar ratio of sulfate to total sulfur (the combination of sulfate and SO 2 ). It is used to indicate the magnitude of the secondary formation of sulfate 25 and expressed as (Wang et al., 2005) where n SO 2− 4 and n SO 2 represent the molar concentrations of sulfate and SO 2 , respectively. Even though regional transport or intrusion of SO 2 or sulfate (or local sulfate emissions) 30 would modify the SOR, it has still often been a relatively good proxy of secondary sulfate formation (i.e. local SO 2to-sulfate conversion). For example, Sun et al. (2014Sun et al. ( , 2013 found positive correlations between the SOR and RH, and observed rapid increases in SORs at elevated RH levels. Xu 35 et al. (2017) found positive correlations of the SOR with both RH and AWC. Multiphase transformation routes, including O 3 oxidation, TMIs + O 2 , and NO 2 + O 2 , are pH sensitive and suppressed at low pH (Seinfeld and Pandis, 2006). Sulfate production raises the acidity of aerosols, and therefore 40 the multiphase transformations of sulfate are presumed to be self-constrained (Cheng et al., 2016). For example, a significant contribution from the O 3 oxidation route can only be expected under alkaline conditions (e.g. sea salt); otherwise, O 3 oxidation is a minor pathway for sulfate formation 45 (Alexander et al., 2005;Sievering et al., 2004). How the selfconstraining nature of sulfate formation influences the relative significance of the TMIs + O 2 and NO 2 + O 2 routes is still under debate. Cheng et al. (2016) proposed that the NO 2 + O 2 route is important during severe haze events under 50 neutral pH conditions Wang et al., 2016). Guo et al. (2017) suggested that aerosols are acidic in Bei-jing (except for during the limited cases of dust or sea-salt events), casting doubt on the importance of the NO 2 + O 2 route in sulfate formation (M. Liu et al., 2017). According 55 to laboratory-based Raman spectroscopy studies, sulfate can be produced via the aqueous oxidation of SO 2 by NO 2 + O 2 , with an SO 2 reactive uptake coefficient of 10 −5 , which represents an atmospherically relevant value (Yu et al., 2018), whereas others have suggested that this route is of minor im-60 portance in the atmosphere (Li et al., 2018;Zhao et al., 2018). In addition, Xie et al. (2015) proposed that NO 2 could enhance the formation of sulfate in certain cases, for example, in biomass burning plumes or dust storms . Evaluation of the contribution of TMIs + O 2 reactions ap-65 pears to be more complex since it depends on aerosol acidity, solubility, oxidation state, and the synergistic effects of different TMIs (Deguillaume et al., 2005;Warneck, 2018).
The compensating effects among AWC, aerosol acidity, and the concentrations of precursors and catalysts show that 70 the kinetics and mechanisms of sulfate formation are highly complex. It can be inferred that there is competition between the various routes, with dependence on atmospheric conditions (e.g. seasonal and pollution-level variations) likely, but this has not received much research attention previously. 75 Here, daily PM 2.5 samples were collected in Beijing from March 2012 to February 2013 and their chemical composition was analysed. The main parameters that influenced sulfate formation (i.e. RH, O 3 concentration, TMIs, etc.) were determined. This valuable dataset enabled us to explore 80 (1) the specific role of each influencing factor in sulfate formation, and (2) how multiple sulfate formation routes compete in different seasons and under various pollution scenarios.

Filter sampling and analysis
Each PM 2.5 sample set consisted of one quartz filter (47 mm; 5 Whatman QM/A, Maidstone, England) and three Teflon filters (47 mm; pore size 2 µm; Whatman PTFE). The quartz filters were baked for 5.5 h at 550 • C before use. The Teflon filters were weighed in a weighing room before and after sampling using a delta range balance (0.01 mg/0.1 mg pre-10 cision; AX105; Mettler Toledo, Switzerland). To minimise contamination, all Teflon filters were placed in a super-clean room (temperature of 22±1 • C; RH of 40±2 %) for 24 h before being weighed. After sampling, all filters were stored at −20 • C prior to analysis.

Estimation of the mass concentrations of PM 2.5 components
The chemical components of PM 2.5 were divided into eight 30 categories: sulfate, nitrate, ammonium, organic matter (OM), EC, minerals, trace element oxides (TEOs), and others. The mass concentrations of OM, minerals, and TEOs were calculated from OC, Al, and trace element concentrations, respectively. The details of this method are provided in the Supple-35 ment. For minerals, validation of the method using only Al to represent all minerals is shown in Fig. S1 in the Supplement. TEOs mostly originated from anthropogenic sources (Fig. S2).

Quality assurance and quality control 40
The PM 2.5 sampling instruments were cleaned and calibrated every 2-3 months. Before the daily filter replacement, filter plates were scrubbed with degreasing cotton that had been immersed in dichloromethane. For water-soluble ions, OC/EC, and trace element measurements, standard solutions 45 were analysed before each series of measurements. The R 2 values of the calibration curves were all > 0.999. For watersoluble ion measurements, beakers, tweezers, and vials were cleaned with deionised water (18.2 M ; Milli-Q, USA) three times before use. Certified reference standards (National In-50 stitute of Metrology, China) were used for calibration. For OC/EC measurements, tweezers and scissors were scrubbed with degreasing cotton immersed in dichloromethane for every filter. Total organic carbon (TOC) was calculated based on calibration with external standard solutions. For trace el-55 ement measurements, containers and tweezers were cleaned three times with nitric acid before use, and the analysis of a certified reference standard (NIST SRM-2783) was used to verify accuracy. The recovery of all measured trace elements fell within ±20 % of their certified values. For gaseous pol-60 lutants and meteorological parameters, all instruments were maintained and calibrated weekly based on manufacturers' protocols.
3 Results and discussion 3.1 General description 65 The annual and seasonal mean (± 1 standard deviation; SD) concentrations of PM 2.5 and its seven major known components are summarised in Table 1. The annual mean PM 2.5 concentration was 84.1 (±63.1) µg m −3 , which is more than 2 times greater than the Chinese National Ambient Air Stan-70 dard annual mean concentration of 35 µg m −3 . On 145 of the 318 (46 %) measurement days, daily mean PM 2.5 concentrations were above the Chinese National Ambient Air Standard 24 h mean concentration of 75 µg m −3 . Time series of PM 2.5 concentrations and its seven major known components 75 are shown in Fig. 2. Seasonal variations in PM 2.5 loading are obvious, with spring and winter peaks and summer and autumn valleys. OM and EC concentrations displayed common seasonal variations, with a plateau from mid-October to mid-February and a valley in summer (Fig. 2), which resembles the variations in PM 2.5 , K + , Cl − , and F − (Figs. 2 and 5 3). The seasonal variations in minerals also indicate an important contribution of dust events to PM 2.5 loading during spring, which is a well-known phenomenon (Zhang et al., 2003;Zhuang et al., 2001). TEOs displayed no obvious seasonal variations (Fig. 2). SNA accounted for more than one-10 third of PM 2.5 annually and showed similar seasonal variations to that of PM 2.5 (Fig. 2), with the notable exception that sulfate became the highest contributor to PM 2.5 (∼ 25 %) in summer (Fig. 4). The summer peak in sulfate could be accounted for by fast secondary formation, as will be discussed 15 later.
On an annual basis, the seven major known components accounted for over 80 % of PM 2.5 (Fig. 4). The diversity of the seasonal variations in PM 2.5 and its major components found in our study imply that there were seasonal varia-20 tions in both the primary sources and secondary formation of PM 2.5 .

Influence of various parameters on sulfate formation
To further explore the parameters that influenced sulfate for-25 mation, SORs were plotted against RH and the concentrations of O 3 , NO 2 , and Fe (total Fe, including both watersoluble and water-insoluble Fe), which is a major tracer of transition metals (Figs. 5 and 6). As shown in Fig. 5a, an RH threshold of ∼ 45 % was 30 critical for efficient SO 2 oxidation (i.e. a high SOR). Such a threshold effect was thought to be reasonable given that AWC increases sharply when RH was above a threshold of 45 %, at which the aerosol undergoes a phase transition from a (semi-)solid particle to a droplet (Pan et al., 2009;Russell 35 and Ming, 2002). Further correlation analysis between SOR and AWC further supports that the multiphase reactions are responsible for sulfate formation (  Zheng et al., 2015) but is slightly lower than the in situ phase transition threshold RH of 50 %-60 % previously observed in Beijing (Y. C. Liu et al., 2017). Correlation analysis of SOR and RH (or AWC) has often been conducted in previous studies. For 45 example, Wang et al. (2005) found a weak positive correlation of SORs with RH (R = 0.38), while Sun et al. (2006) found a strong positive correlation (R = 0.96). However, the analysis in the present work and those of a few previous studies revealed that the relationship between the SOR and RH is 50 nonlinear (Sun et al., 2013(Sun et al., , 2014; G. J. Zheng et al., 2015). In fact, the RH threshold suggests that high RH (or AWC) is a prerequisite for fast sulfate formation via multiphase reac-tions, which are known to account for the majority of sulfate accumulation. 55 From the large scattering of data points around the fit line in Fig. 5a, it might be inferred that RH was not the only prerequisite for fast SO 2 -to-sulfate conversion. As shown in Fig. 5b, a significant increase in the SOR was also observed at an O 3 concentration threshold of ∼ 35 ppb. High 60 O 3 concentrations (i.e. > 35 ppb) were accompanied by high SOR values of ∼ 0.4 (right-hand side of Fig. 5b). Correlation analyses of SORs with O 3 have been conducted but inconsistent results were reported. Wang et al. (2005) found a weak positive correlation between SORs and O 3 (R = 0.47) 65 for continuous observations in Beijing during 2001-2003. However, Liu et al. (2015 found a weak negative correlation between SORs and O 3 (R = −0.53, p = 0.01) during a haze episode in September 2011. Zhang et al. (2018) found no correlation between SORs and O 3 during winter 70 haze days in 2015. Quan et al. (2015) found that the SOR decreased with O 3 when O 3 concentrations were lower than 15 ppb but increased with O 3 when O 3 concentrations were higher than 15 ppb, for observations made during autumn and winter 2012. In the present study, our observations revealed 75 that the relationship between the SOR and O 3 concentration, like RH, was nonlinear and that a high O 3 concentration was another prerequisite for fast sulfate formation. Such a conclusion was a surprise first, since O 3 oxidation was not thought to be a major route for SO 2 -to-sulfate conversion (He 80 et al., 2018;Sievering et al., 2004). However, as a primary precursor to OH radicals and H 2 O 2 (via HO 2 ) (Lelieveld et al., 2016;Lu et al., 2017), high O 3 concentrations (e.g. > 35 ppb) correspond to a high concentration of oxidants, which favours multiphase sulfate formation and thus a high 85 SOR, whereas low O 3 concentrations suggest a lack of available oxidants for multiphase SO 2 -to-sulfate conversion and thus a low SOR. In addition, the simultaneous occurrence of low SORs and low O 3 concentrations had a secondary cause. Low O 3 concentrations in the Beijing urban area were often 90 due to the titration of O 3 by NO (Li et al., 2016), which accumulated together with SO 2 (Fig. S4). The accumulation of SO 2 , which "diluted" the SOR (Eq. 1), was thus naturally accompanied by the titration of O 3 . The L-shaped dependence of the SOR on several other primary pollutants, such as EC, 95 NO, and Se (Fig. S5), further confirmed this secondary cause. Therefore, the accumulation of primary pollutants might also help to explain the low SOR values of ∼ 0.1 on the left-hand side of Fig. 5b, in addition to the lack of available oxidants for multiphase SO 2 -to-sulfate conversion.

100
The large scattering of data points around the fit line in Fig. 5b suggests that O 3 concentration, like RH, was not the only prerequisite for fast SO 2 -to-sulfate conversion. The dependence of the SOR on RH was separated into low (< 35 ppb) and high (> 35 ppb) O 3 groups (solid black circles 105 and solid blue circles, respectively, in Fig. 5a). SOR values above the fit line are found mostly for the high O 3 group. After the dependence of the SOR on O 3 concentration was separated into low (< 45 %) and high (> 45 %) RH groups (solid black circles and solid blue circles, respectively, in Fig. 5b), a similar pattern was found for the high RH group. In other words, fast multiphase SO 2 -to-sulfate conversion could only occur when both O 3 and RH exceeded their re-5 spective thresholds simultaneously. The seasonal variations of such thresholds of RH and O 3 were further discussed. As show in Fig. 6, the RH threshold was roughly around 45 % during all four seasons in Beijing, while the threshold of O 3 varied among seasons (Fig. 7). 10 A turning point of 25-40 ppb was observed for fast SOR increase in spring, summer, and autumn, while the turning point is not clear due to lack of high O 3 data in winter. The variation of O 3 threshold value might be due to the shift of O 3 -H 2 O 2 relationship which might be modified by temper-15 ature, etc. in different seasons. Despite of the variation of thresholds of RH and O 3 in different seasons or even in different sampling locations (not discussed here), the thresholds of RH and O 3 for fast sulfate formation further found in our study have its implications on the sulfate formation mecha-20 nism (see below).
The SOR was further plotted against Fe and NO 2 . No clear dependence of the SOR on concentrations of Fe or NO 2 was found ( Fig. 8a and b). Possible reasons and implications of this result will be discussed in the following section.

Implications for sulfate formation mechanisms
Our observations of the factors that influence sulfate formation have implications for sulfate formation routes and its variations among seasons and pollution conditions.
In retrospect, thresholds in RH and O 3 concentrations were found to be critical to the SOR, suggesting that AWC and liquid-phase oxidant were two prerequisites for fast multiphase SO 2 -to-sulfate conversion. H 2 O 2 and O 3 are the two liquid-phase oxidants which are responsible for sulfate formation. The O 3 oxidation route was proposed to not be im-10 portant in high aerosol acidity areas, such as Beijing (Guo et al., 2017;Sievering et al., 2004 positive correlation was found between them (Fig. S7). In addition, coincident increases in the concentration of H 2 O 2 and PM 2.5 in winter of Beijing also led to an important role of the H 2 O 2 oxidation route in sulfate formation (Ye et al., 2018).
Based on the above discussions, we propose that H 2 O 2 might 30 be the major oxidant for sulfate formation in Beijing. The plot of SORs against Fe, the dominant transition metal species, shows no clear dependence (Figs. 8a and S8). Similarly, the plot of SORs against NO 2 shows no clear dependence either (Fig. 8b). If Fe acted as a catalyst, its concentra-35 tion might not be directly proportional to SORs. Therefore, such a pattern does not safely exclude TMIs + O 2 as a major route for sulfate formation. Several laboratory studies excluded NO 2 as a direct oxidant in SO 2 -to-sulfate conversion. For example, Zhao et al. (2018) tested the oxidation of SO 2 40 by NO 2 in an N 2 atmosphere and concluded that NO 2 is not an important oxidant, since NO 2 was more likely to undergo disproportionation (Li et al., 2018). However, Yu et al. (2018) further explored this reaction, and found that the reaction rate was 2-3 orders of magnitude greater in an O 2 + N 2 atmo-45 sphere, indicating potentially important roles of NO 2 + O 2 oxidation in sulfate formation Ma et al., 2018). As with Fe, if NO 2 acted as a catalyst, its concentration might not be directly proportional to that of sulfate. Therefore, such a pattern does not safely exclude NO 2 + O 2 50 as a major route for sulfate formation either. Although direct aerosol pH measurement is not available here, previous studies have reported a mean aerosol pH value of 4.2 with a low limit of 3.0 in Beijing (Ding et al., 2019;M. Liu et al., 2017), which suggests that several routes of sulfate for-55 mation, including NO 2 + O 2 , TMIs + O 2 , O 3 oxidation, etc., are suppressed. Hence, we carefully propose here that neither TMIs + O 2 nor NO 2 + O 2 seem to be a major route for sulfate formation.
On one hand, a direct measurement of aerosol pH is also 60 urgently needed in the future to examine our proposal here; on the other hand, our proposal here has further implication on the understanding of sulfate formation. Previously, aerosol surface area and concentrations of Fe, Mn, and NO 2 were used in model evaluations of catalytic sulfate forma-65 tion in the boundary layer (Y. Wang et al., 2014;B. Zheng et al., 2015). However, our proposals here suggest that a careful reassessment of such calculations is required. In addition, model calculations have often suggested important contributions of in-cloud processes to sulfate accumulation near the 70 ground (Barth et al., 2000), although few observational constraints are available for confirmation of these model results (Harris et al., 2014;Shen et al., 2012). The O 3 concentration and RH prerequisites found in the present work might indicate a major role of in situ sulfate formation in the boundary 75 layer, via multiphase reactions with H 2 O 2 as the main oxidant, rather than in-cloud processes and intrusion from the free troposphere.
As the two prerequisites showed strong seasonal and pollution-level variations over the measurement year, the 80 SOR exhibited corresponding variations. As shown in Fig. 9, SORs displayed clear seasonal variations, with the highest value (±1 SD) of 0.46 (±0.22) in summer, followed by spring (0.23 ± 0.14), autumn (0.18 ± 0.15), and winter The boxes represent, from top to bottom, the 75th, 50th, and 25th percentiles in each bin ( RH = 5 %; O 3 = 5 ppb). The whiskers, solid red squares, and open red circles represent 1.5 times the IQR, mean values, and outlier data points, respectively. The red lines are best fits to mean values based on a sigmoid function. Data for days with rain or snow were excluded from these plots.
(0.09 ± 0.05). The highest SOR (i.e. fastest SO 2 -to-sulfate conversion rate) was found in summer, which is not surprising because the ambient conditions in summer were conducive SO 2 -to-sulfate conversion (Wang et al., 2005). RH and O 3 concentrations in summer were not only the high-5 est in the year but on average were also both higher than their thresholds of 45 % and 35 ppb, respectively, which was unique among the four seasons. In summer, the median and mean (±1 SD) RH levels were 57.4 % and 57.6 (±13.6) %, respectively, and the median and mean O 3 concentrations 10 were 46.9 ppb and 46.0 (±18.3) ppb. It should be noted that the median and mean SO 2 concentrations were 2.6 and 4.0 (±3.7) ppb, respectively, which were the lowest in the year. Despite the low concentrations of SO 2 , there were considerable sulfate concentrations (Figs. 2 and 9), which can be 15 accounted for by fast SO 2 -to-sulfate conversion. Although the rapid accumulation of secondary sulfate during winter haze days in Beijing has been widely reported (Y. S. Wang et al., 2014;G. J. Zheng et al., 2015), the lowest SOR was observed during winter in the present study (Fig. 9a), which 20 is consistent with previous observations (Wang et al., 2005). On winter haze days, RH values of up to 73.6 % and PM 2.5 mass loadings of up to 375.3 µg m −3 were observed. Therefore, AWC was not the limiting factor in SO 2 -to-sulfate conversion ( Fig. 9b and e). The SO 2 -to-sulfate conversion rate in 25 winter could have been limited by the reduced concentration of oxidants (Fig. 9c) as a result of both high emissions of the primary pollutant NO (Fig. S9) and low solar radiation levels (Fig. 9f). Sulfate concentrations in winter were comparable to those in summer, which might have been driven by high 30 SO 2 concentrations in winter (Fig. 9d), despite slow SO 2 -tosulfate conversion. The lower boundary layer height in winter relative to other seasons would also have encouraged the accumulation of both PM 2.5 and its components, including sulfate Zhang et al., 2015). The SORs in spring and autumn were comparable and moderate, possibly representing a transition in conditions between summer and winter.

5
For each season, four pollution scenarios were classified according to PM 2.5 level. The lowest 25 %, 25 %-50 %, 50 %-75 %, and highest 25 % of pollution levels were defined as "clean", "moderate pollution", "heavy pollution", and "severe pollution", respectively. The relative contribu-10 tions of the seven major known components of PM 2.5 among the four pollution scenarios are shown in Fig. 10. In all four seasons, the relative contribution of SNA increased with PM 2.5 loading. This phenomenon has been reported in previous studies, but data availability was limited in autumn (Xu 15 et al., 2017) and winter (G. J. Zheng et al., 2015). The SOR increased consistently in all four seasons as pollution accumulated, where both the highest value and strongest variability were observed in summer (Fig. 11a). Although SO 2 should have reduced the SOR (Eq. 1), concurrent increases 20 in primary SO 2 and SORs were observed ( Fig. 11a and b), indicating a significant increase in the SO 2 -to-sulfate conversion rate with PM 2.5 loading, which offset the "dilution" effect (Eq. 1). Such variations in sulfate formation with pollution levels can be accounted for by the corresponding vari-25 ations in both O 3 concentrations and RH ( Fig. 11c and d).  In all four seasons, RH increased consistently as pollution accumulated (Fig. 11d). O 3 concentrations decreased consistently as pollution evolved in all of the seasons except for summer (Fig. 11c). The distinct variations in O 3 during 30  summer, imply strong photochemistry and high concentrations of OH, which might result in a non-negligible contribution of gas-phase reactions to the formation of sulfate. However, gas-phase reactions alone could not account for the rate of sulfate formation either in Beijing or globally 5 (Finlayson-Pitts and Pitts Jr., 2000; He et al., 2018), due to the relatively slow reaction of SO 2 with OH. For example, the lifetime of SO 2 with respect to OH oxidation is about 3-4 d, assuming a 24 h average OH concentration of 1 × 10 6 molecules cm −3 and a pseudo-secondary-order rate con-stant of 10 −12 cm 3 molecule −1 s −1 (Brothers et al., 2010). However, the overall oxidation lifetime of SO 2 is on the order of hours (Berglen et al., 2004;He et al., 2018). Overall, the increase in SO 2 -to-sulfate conversion with PM 2.5 loading can be attributed to the self-catalytic nature of the multi-15 phase formation of sulfate; i.e. both RH and PM 2.5 increased continuously with the accumulation of PM 2.5 , resulting in a rapid rise in AWC and providing greater reaction volume for further sulfate formation. Therefore, the increases in RH and PM 2.5 could have compensated for the low concentra-20 tion of oxidants, resulting in fast sulfate formation as pollution evolved. Particularly in summer, not only did both RH and O 3 concentrations increase as pollution evolved, but both RH and O 3 concentrations were generally above their respective thresholds at all pollution levels (dashed lines in Fig. 11c   5 and d). This explains our observations of both the highest values and strongest dependence on pollution level for SORs in summer.

Conclusions
In this study, the annual mean concentration of PM 2.5 in 10 Beijing during 2012-2013 was 84.1 (±63.1) µg m −3 , with clear seasonal and pollution-level variations in its chemical components, highlighting the contribution of SNA formation to the accumulation of PM 2.5 in all seasons. RH and O 3 concentrations were identified as two prerequisites for fast 15 SO 2 -to-sulfate conversion. RH above a threshold of ∼ 45 % greatly accelerated the conversion rate. A similar effect was also found for O 3 at a concentration threshold of ∼ 35 ppb. Such dependence has interesting implications. First, they indicate a major role of the H 2 O 2 route in sulfate formation, 20 which might further indicate a major role of in situ sulfate production in the boundary layer, rather than in-cloud processes and intrusion from the free troposphere. Second, the observed dependence was also able to account for the seasonal and pollution-level variations in SO 2 -to-sulfate conver-25 sion rates. Both the highest value and strongest variability of SOR were observed in summer, which might be attributed to the highest values of O 3 concentrations and RH in summer. SO 2 -to-sulfate conversion accelerated as pollution accumulated, which was primarily attributed to a shift from gas-30 phase oxidation to the multiphase oxidation route, which is self-catalytic in nature. The increase in RH was able to offset the low concentration of oxidants under heavily polluted conditions and resulted in increasingly fast SO 2 -to-sulfate conversion as pollution accumulated. While our simultaneous 35 observations of the SOR and concentrations of Fe and NO 2 could not exclude TMIs + O 2 and NO 2 -based reactions, a reassessment of the relationships between sulfate formation, aerosol surface area, and the concentrations of Fe and NO 2 is necessary. Future quantitative studies of the relative con-40 tributions of different sulfate formation routes should include additional measurements, namely NH 3 for the proxy calculation of pH values, and H 2 O 2 to confirm its contribution under different conditions. Data availability. The data of stationary measurements are avail-45 able upon request. Radiation data can be applied through the National Meteorological Information Center (http://data.cma.cn/ TS3 ).
Author contributions. TZ designed the study. YF, CY, and TZ pre-50 pared the manuscript with input from all co-authors. YF and JW collected and weighed the PM 2.5 filter samples and carried out the analysis of the components of PM 2.5 . FX carried out the measurement of water-soluble Fe. YW and MH provided the data for gaseous pollutants, temperature, and RH. WL provided the solar ra-55 diation data.
Competing interests. The authors declare that they have no conflict of interest.
Special issue statement. This article is part of the special issue "Regional transport and transformation of air pollution in eastern 60 China". It is not associated with a conference.
Review statement. This paper was edited by Jianmin Chen and reviewed by three anonymous referees.

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