The BEST-ONE campaign took place at the suburban site Huairou (40.41∘ N, 116.68∘ E), 60 km northeast from the center of Beijing. Instruments were set up on the campus of the University of the Chinese Academy of Sciences (UCAS) as shown in Fig. 1. Beijing is located on the northwest edge of the NCP and is confined by the Yan Mountains from the northeast to the west. The topography of Beijing facilitates the accumulation of pollutants if southern winds carry emissions from the NCP region. The measurement site was located in a valley of the Yan Mountains, acting as an intermediary of air mass transportation from downtown Beijing. As shown in Fig. S1 in the Supplement, the concentrations of CO, NO2, SO2, and PM2.5 observed at the site showed good correlations with the measurements conducted in the city center (12 EPA stations). This demonstrates that the measurement site is a representative for conditions in the city of Beijing. In contrast, a previous field campaign that included OH–HO2–RO2 radical measurements was performed at a rural site in Wangdu in summer 2014 (Tan et al., 2017). The Wangdu site was located in the middle of the North China Plain, about 200 km southwest of Beijing. The site was mainly influenced by regional transportation of air pollutants from anthropogenic emissions (Fuchs et al., 2017b). A road with moderate traffic and a small village were located east of the university campus. Thus, local anthropogenic activities might have influenced the measurement site, especially during traffic rush hours and cooking hours.

Most instruments were placed on the top floor of a 20 m high building with their inlet lines going through the ceiling. All inlet lines were set at the same height as close as possible to each other to guarantee to sample of the same air masses. The sampling height for all inlet lines was 1.7 m above the surface of the building.

A box model based on the Regional Atmospheric Chemical Mechanism version 2 (RACM2) updated with the newly proposed isoprene mechanism (Goliff et al., 2013; Peeters et al., 2014) was used to simulate the concentrations of the short-lived OH, HO2, and RO2 radicals. Measurements of photolysis frequencies, long-lived trace gases (NO, NO2, O3, HONO, CO, CH4, C2–C12 VOCs), and meteorological parameters were used to constrain the model by observations. The model was operated in a time-dependence mode with 5 min time resolution for which measurements used as constraints updated the model values. The 2-day spin-up time was used to initiate the model. Secondary species were not constrained but generated numerically by the model. A constant artificial loss rate that corresponds to an atmospheric lifetime of 24 h was used for all unconstrained species to represent the effect of unspecified physical losses such as deposition, convection, and horizontal transportation. Sensitivity tests showed that the response of the calculated ROx concentrations to changes of this artificial loss rate by a factor of 2 was less than 5 %. The validity of the approach was tested by comparing the model results to parameters which were measured during the campaign but was not used as a model constraint. The comparison for oxygenated VOCs (e.g., acetaldehyde) and PAN (Peroxyacetyl Nitrate) showed agreement within 20 % and 24 %, respectively. Furthermore, kOH and formaldehyde gave agreement within 10 %, indicating that the model approach was able to describe the long-lived oxidation products reasonably well. The uncertainty of the model calculations is derived from the uncertainties in the measurements used as model constraints and the reaction rate constants. Taking into account the 1σ uncertainties of both measurements and kinetic rate constants, a series of tests based on Monte Carlo simulations shows that the uncertainty of the model calculations is approximately 40 % (Tan et al., 2017).

The observed trace gas concentrations were highly variable depending on the particular meteorological conditions. In Fig. 1, the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) back-trajectory analysis (Stein et al., 2015) shows two typical air mass transportation pathways. The dominating wind direction in Beijing during wintertime is northwest from the Siberian tundra or from the Mongolian desert. The back-trajectory analysis shows that the air parcels arriving in the city of Beijing either came directly from these remote regions, bringing clean air to the UCAS site, or first reached the Beijing downtown region and then turned to the UCAS site, loaded with pollutants from the Beijing city region. As presented in Fig. 3, the CO concentration, a proxy for anthropogenic pollution, shows a distinct variation from day to day. The chemical conditions could be classified into three groups, namely background, clean, and polluted, respectively, based on observed kOH, CO, and PM2.5. The measured OH reactivity was used to separate polluted from clean periods by a threshold value of kOH=15s-1 (daily average). This corresponds also to CO mixing ratios higher than 1 ppmv and PM2.5 higher than 50 µg m-3 since these parameters were highly correlated. The difference between the background and clean episodes is whether there is a diurnal variation in the CO and kOH, and PM2.5. Only 3 days (22 and 23 January and 23 February) were classified as background conditions, during which strong northern winds (wind speed up to 10 m s-1) were observed. The strong wind enhanced the dilution of pollutants coming from the Beijing region and prevented the buildup of a stable nocturnal surface layer. As shown in Fig. 4, the mean diurnal profiles of CO, NO2, HONO, and O3 were flat over most of the day. For the majority of the campaign, the wind velocity was relatively small, as reflected by the local wind speed measurements (less than 2 m s-1). Hence, although the air masses originated over the Mongolian desert or the Siberian tundra, the observations at the UCAS site were slightly influenced by local emission from the nearby village and from close-by car traffic. The time periods for these relatively clean episodes are listed in Table 2.

The pollution episodes happened on 15, 16, 20, 21, 27, 28, 29 January, 21 February, and 1 to 4 March. The back-trajectory analysis shows that for those days the air masses were at least partly influenced by the Beijing city area which is located south of the UCAS site. In addition, the relative humidity increased from 28 % for the clean episodes to 44 % for the pollution episodes for daytime averaged conditions, suggesting that the site was influenced by humidified air from the south. The concentrations of trace gases and particle matter increased noticeably during the pollution episodes (Table 2).

The dissimilarities between different episodes can be easily illustrated using the mean diurnal profiles (Fig. 4). Solar radiation, indicated by the measured photolysis frequencies, e.g., j(O1D), was comparable during the background and the clean episodes but reduced by about 20%-30% during the pollution episodes (Table 2). NO concentrations were below 1 ppbv during the background episodes. The diurnal peak of NO (4 ppbv) appeared at 09:00 CNST during the clean episodes. During the polluted episodes, NO concentrations increased significantly to reach a maximum of 15 ppbv around sunrise. O3 remained nearly constant at 38 ppbv at all times during daytime of the background episodes, which can be regarded as a continental wintertime O3 background concentration. During clean episodes, the wind velocity was reduced, so that local NO emissions could accumulate and titrate away the ozone, especially during nighttime when vertical mixing was reduced. NO2 showed an anti-correlation with O3 because of this interconversion. Besides the titration effect, there were deposition processes and non-photochemical reactions which additionally diminished the concentration of ozone (and of NO2) in the shallow surface layer during night hours. However, the maximum O3 concentrations during afternoon hours, when vertical mixing inhibited the accumulation of the local NO emissions, were comparable to those observed during the background episodes (Fig. 4). These processes led to a slow reduction of the near-surface ozone concentration starting at sunset, to a minimum just at sunrise, and to a fast recovery within the next 2–3 h. This increase of O3 in the morning hours during the clean episodes was at least partly a result of entrainment of background O3 from the residual layer.

During the pollution episodes, the ozone concentrations showed a distinct diurnal variation due to a strong titration by NO. The concentration of NO2 was high at night but decreased after sunrise, which could be due to the poor dilution conditions at night and fast photolysis after sunrise. Ox is the sum of NO2 and O3, which is considered as a more conservative metric than O3 because it is not affected by the interruption of fresh NO emission, especially in urban environments (Kley et al., 1994; Kleinman et al., 2002). Ox increased from 30 ppbv at 07:00 CNST to 50 ppbv at 16:00 CNST during the pollution episodes. After sunset, Ox started to decrease due to physical losses, like deposition and transportation of O3 and NO2, or chemical conversion to N2O5. The fast increase in Ox concentrations during daytime was a specific feature for the pollution episodes, which indicated the strong photochemistry happening during the haze events.

SO2 is a tracer for regional air pollution originating from coal combustion, e.g., power plants and residential heating. For background and clean episodes, SO2 exhibited low concentrations around 1 ppbv. It increased from 5 ppbv at sunrise to 10 ppbv at 16:00 CNST during the pollution episodes. The large increase of SO2 concentrations during pollution episodes which showed a distinct diel increase could be related to the pollutants' accumulation process.

Typically, HONO accumulated during the night (most probably from heterogeneous reactions of NO2 on humid surfaces) and started to decrease after sunrise due to fast photolysis. This was observed during clean or polluted episodes when the measured HONO showed a distinct diurnal minimum during the afternoon and started to increase between sunset and sunrise up to values around 1 ppbv during the night. In contrast, the averaged HONO concentrations were about 0.05 ppbv without obvious diurnal variation for background conditions (Table 2).

Figure 5 shows the measured and modeled OH, HO2, and RO2 radical concentrations and OH reactivity. The largest OH concentration appeared around noontime with large day-to-day variability. The daily maximum varied in the range 1×106 to 1×107cm-3. The highest OH concentrations were observed during the second half of the campaign (27 and 28 February) when the temperature was above the freezing point and the photolysis frequencies for the short wavelength region, e.g., j(O1D), were higher than in January (Fig. 3).

In general, the model could reproduce the observed OH concentrations within 30 %. It is important to notice that the good agreement between measured and modeled OH concentrations was mainly due to the availability of observed HONO concentrations. A sensitivity test showed that the calculated OH radical concentrations were reduced by 43 % if the model was not constrained to the HONO measurements. This underlines that the currently known gas-phase formation of HONO from the reaction of OH with NO is not sufficient to sustain the high HONO concentrations observed during this winter campaign. The result agrees with numerous field and laboratory studies which have reported additional daytime sources of HONO (e.g., Kleffmann et al., 2005), for example, from the heterogeneous conversion of nitrogen species (nitrates, nitric acid, NOx) at surfaces and soil emissions (see overview in Meusel et al., 2018, and references therein). The present study demonstrates that at least some of the additional HONO sources are also effective at cold conditions and play an important role for the wintertime oxidation of pollutants in urban atmospheres. It also confirms the need for in situ HONO measurements during field studies focusing on the investigation of atmospheric radical chemistry (Alicke et al., 2003; Su et al., 2011; Lu et al., 2012; Kim et al., 2014).

The overall correlation between observed OH concentrations and photolysis frequencies is shown in Fig. 6. Both observed and modeled OH concentrations show a good correlation with j(O1D) and with j(NO2) with the coefficient of determination R2 being larger than 0.7, which can be expected in summer when the radical chemistry is initiated mainly by photolysis processes including ozone photolysis. However, j(O1D) increased by a factor of 2 from the start to the end of the campaign while j(NO2) remained nearly constant (Fig. 3). The correlation between calculated OH and j(NO2) is more compact and linear than that between OH and j(O1D), reflected in a slightly higher correlation coefficient (Fig. 6). In the model, the OH concentrations tend to depend strongly on j(NO2). This can be explained by HONO photolysis being the dominant primary source of OH radicals (see Sect. 4.1) and the well-known linear correlation between j(NO2) and j(HONO) (Kraus and Hofzumahaus, 1998). The OH observations do not show such a difference; j(O1D) and j(NO2) both exhibit the same good correlation coefficient.

Despite the general agreement, the model systematically underestimates OH concentrations for 2 days (27 and 28 February) by a factor of 2 (Fig. 5). The OH reactivity was relatively small on these days (<10 s-1). A model sensitivity run with an additional primary OH source of 0.25 ppbv h-1 shows that the modeled OH concentrations would increase by 50 %, which would be enough to close the gap between measured and modeled OH for these 2 days. However, the possibility of an instrument failure of the PKU-LIF during these 2 days cannot be excluded. An indication may be that the data points on these 2 days do not follow the generally very good OH–j(O1D) correlation (Fig. 6). Therefore, we excluded these 2 days from the analysis.

The daytime averaged peroxy radical concentrations are smaller by a factor of 5 compared to summertime at the rural site of Wangdu in the North China Plain (Tan et al., 2017). The strong reduction in radical concentrations is due to the attenuated solar radiation and thus smaller primary radical sources. In addition, NOx concentrations during the BEST-ONE campaign were larger, resulting in a faster peroxy radical loss and thus shorter lifetimes.

For the background episodes, the calculated RO2 data are not shown in Fig. 7 because the observed NO concentrations were close to the limit of detection of the NO instrument (60 pptv), and thus the model was highly sensitive to the fluctuations of the NO measurements around zero (Fig. 5). The observed RO2 radical concentrations do not show a significant difference between background, clean, and pollution episodes, while a large difference can be observed for the calculated RO2 concentrations (Fig. 7). In fact, the observed radical concentrations are rather comparable in all episodes, while the model predicts a suppression of radical concentrations in the polluted episodes. This is most obviously seen for HO2 and RO2. The comparisons between observed and modeled OH, HO2, and RO2 concentrations for clean and polluted episodes are shown in Fig. S3. Both the calculated OH and HO2 radical concentrations were lower than observed during polluted days. Overall, during clean days, the model can reproduce the observed OH, HO2, and RO2 radical concentrations with an observed-to-modeled ratio of 1.31, 1.03, and 0.98 for daytime conditions, respectively (Fig. S3). The nighttime RO2 radicals are often overestimated by the model calculations by up to a factor of 10, which could be the result of a NO measurement below the detection limit. The observed NO concentrations were often below the limit of detection of the NOx instrument (60 pptv), which did not allow precise measurements due to the fluctuation of the background signal. In addition, it also led to large variability in the modeled NO3 and resulted in overprediction in the nighttime RO2 (Tan et al., 2017). On the other hand, a small bias in the NO measurement could lead to an unrealistically long lifetime of RO2 radicals in the model. A model sensitivity run showed that RO2 concentrations could be significantly reduced if the constrained NO concentrations in the model were increased by 20 pptv, which is within the precision of the instrument. A loss of NO inside the inlet line of the instrument would already be enough to explain this effect that was within the limit of detection.

The model underestimates the observed OH concentrations by a factor of 1.8 during polluted days, and the peroxy radical concentrations are significantly underestimated by up to a factor of 5 (Fig. 7). A detailed analysis of these days is given in Sect. 4.2. A chemical model based on the Master Chemical Mechanism (MCM) 3.3.1 also predicts similar results as RACM2, suggesting that such underestimation is not a result of the “family approach” for organic molecules used in RACM2.

The model was able to reproduce the directly observed OH reactivity within 10 % during all episodes (Fig. 7). This calculation includes the reactivity from observed VOCs (about 73–83 % of the observed kOH) and the estimated contributions from OVOCs calculated by the model (17–27 %). The speciation of the total OH reactivity showed that the major OH reactants were NOx and CO. On average, CO and NOx contributed 23 % and 37 % to the total OH reactivity, respectively. A total of 18 % of the observed reactivity can be attributed to measured VOC species. In comparison, the model-generated species contributed 22 % to the total reactivity. For the polluted episodes, the average OH reactivity increased from 10 to 26 s-1 with a significant increase in the relative contributions from the inorganic compounds (from 52 % to 63 %).

As shown in Fig. 8, the radical chain reactions were mainly initiated by photolysis processes. HONO photolysis was the most important radical primary source. It contributed up to 46 % (averaged rate 0.26 ppbv h-1) of the total primary production rate of radicals for daytime conditions. During the BEST-ONE campaign, the production rates of radicals varied slightly between different episodes (Fig. 9). The production rates were highest during the polluted episodes compared to the background and clean episodes. The major difference was due to the contribution from HONO photolysis, which accounted for the major source in all cases contributing 25 % (0.10 ppbv h-1), 40 % (0.21 ppbv h-1), and 55 % (0.37 ppbv h-1) of diurnally averaged rates of 0.10, 0.21, and 0.37 ppb h-1 for background, clean, and polluted episodes, respectively. Alkene ozonolysis was the major radical source of nighttime and the second largest primary radical source during the day (28 %, 0.16 ppbv h-1). The relative importance of the ozonolysis of alkenes was slightly larger during the background (39 %) and clean (33 %) episodes. The ozone photolysis was almost negligible for our wintertime BEST-ONE campaign. At high solar zenith angles, short wavelength radiation (<320nm) is suppressed due to the strong attenuation by the longer pathway through the ozone layer in the stratosphere. In addition, the water vapor mixing ratio at the low winter temperatures decreases to below 0.3 %, 1 order of magnitude lower than during summertime. Formaldehyde photolysis contributed on average 17 % to the total ROx primary production. The photolysis of carbonyl compounds calculated by the model also made a noticeable portion of the total primary production of radicals, about 7 % (Fig. 8).

The importance of HONO photolysis is reported in previous studies for other locations, both urban and suburban (Alicke et al., 2003; Dusanter et al., 2009; Mao et al., 2010; Ren et al., 2013). For winter campaigns, HONO photolysis was found to be the dominant (>50%) daytime ROx radical source in New York City (NYC) (Ren et al., 2006), Tokyo (Kanaya et al., 2007), and Boulder, Colorado (Kim et al., 2014). During the PUMA campaign in Birmingham, HONO photolysis contributed only 36 % to the total OH radical primary sources (Emmerson et al., 2005b). Meanwhile, the reported value of 36 % is a lower limit, since HONO was not measured. Instead, it was calculated from the equilibrium between HONO and OH+NO. As OH and NO can recombine to nitrous acid, the net effect of HONO photolysis to radical production might be partly compensated. Kanaya et al. (2007) found that the OH+NO (+M) reaction was balanced by the HONO photolysis during the morning hours. In our study, the gas-phase HONO formation only compensated 10 % of the observed HONO photolysis. Therefore, the net effect of HONO photolysis remains the dominant radical source in wintertime during the BEST-ONE campaign. In Fig. 9, the radical production for the Wangdu summer campaign is shown in comparison to the current campaign. The total daytime radical production rate was reduced in winter by a factor of 6 compared to summertime. The contribution of HONO photolysis also changed, contributing 39 % to the total radical production for the Wangdu summer campaign.

The importance of alkene ozonolysis to the primary ROx radical production was also found in the IMPACT winter campaign in Tokyo, where it contributed 49 % of the ROx production on a 24 h basis (Kanaya et al., 2007). In other campaigns, alkene ozonolysis was comparable to HONO photolysis even during daytime, which contributed 42 % in NYC (Ren et al., 2006) and 63 % in Birmingham (Emmerson et al., 2005b), respectively. During the summertime in Wangdu, the contribution from alkene ozonolysis was only 15 % (Fig. 9). However, the absolute rate was 0.47 ppbv h-1, larger than what was observed at Huairou/Beijing in wintertime (0.16 ppbv h-1).

Different from our study, the photolysis of ozone was found to be relatively important in a rural site of Colorado, contributing 15 % to the OH primary production for noontime conditions. The absolute radical production rate is comparable in these two campaigns (Table 3); the higher contribution of ozone photolysis is due to the fact that the Colorado campaign took place at a slightly later time (February and March) of the year (Kim et al., 2014).

The photolysis of carbonyl compounds can be an important radical source for urban and suburban areas (Emmerson et al., 2005b). HCHO photolysis contributed up to 6 % of the total HOx (=OH+HO2) production in NYC (Ren et al., 2006) and 10 % in Tokyo (Kanaya et al., 2007) for wintertime conditions, comparable to their contributions in summertime, for example, 8 % for NYC (Ren et al., 2006) and 18 % for Tokyo (Kanaya et al., 2007).

The termination of ROx radicals is achieved either by the reaction with NOx or by the peroxy radical self-reactions. The NOx termination reactions can be further subdivided into OH+NO, OH+NO2, RO2+NO, and RO2+NO2. As shown in Fig. 8, the reaction between OH and NO2 dominated the total radical termination process during the BEST-ONE campaign, which contributed 49 % of the total ROx loss for daytime average. The equilibrium between peroxy radicals and PAN-type compounds was a sink for ROx radicals due to the low ambient temperature during the winter campaign. The net PAN-type compounds species formation had a noticeable impact on the radical budget (25 % daytime averaged). Since the observed and modeled PAN concentrations agree within 24 %, it gave confidence to the net PAN formation rate. In London, the net PAN formation was also found to be a major radical sink, contributing 35 % to the total radical destruction rate (Whalley et al., 2018). The ROx self-reactions were nearly negligible (<3%) as the peroxy radical concentrations were small (<1×108cm-3). For comparison, this is 1 order of magnitude smaller than in the summertime Wangdu campaign, where the radical termination process was mainly dominated by the hydroperoxide formation path (Fig. 9).

The relative importance of various loss pathways was compared between the different episodes (Fig. 9). The reaction between OH and NO2 contributed 40 % and 61 % to the total ROx loss during clean and polluted episodes. The net loss of PAN-type compounds became of relative importance during background episodes, contributing 50 % to the total radical termination because of the lower temperatures (Table 2).

As shown in Fig. 10, the observed RO2 concentrations were relatively constant over the whole NO regime. However, the model predicted a strong decreasing trend with higher NO concentrations. This is further illustrated by the observed-to-modeled ratio, which increased from a value of 1 at 1 ppbv of NO to 9 at 6 ppbv of NO (Fig. 11). As shown in Fig. 11, the underestimation of both HO2 and RO2 radical concentrations became larger with higher NOx. In contrast, the observed-to-modeled ratio of OH concentrations was almost constant with a value of 1.5 over the full NOx regime, which is within the combined uncertainties of measurement and model calculations. An underestimation of HO2 radical concentrations by the model at high NOx values was also observed in previous studies (Shirley et al., 2006; Ren et al., 2006, 2013; Emmerson et al., 2007; Kanaya et al., 2007; Griffith et al., 2016). HO2 measurements in previous field campaigns could have suffered from interferences from specific RO2 species, so that the reported observed-to-modeled ratios could have been even larger in these campaigns. It was suggested that one reason for this discrepancy might be due to the poor mixing and segregation between NO and peroxy radicals (Dusanter et al., 2009). Alternatively, it can also imply missing peroxy radical sources in the current chemical mechanisms relevant in particular for the high NOx regime. In addition, the underestimation of the measured RO2 radicals by the model could explain partly the discrepancy observed for HO2 radicals due to insufficient recycling from the OH oxidation chain.

In the present study, the radical cycling between OH and the peroxy radicals is relatively well constrained due to the availability of measured kOH and NO. Since the model reproduces kOH within 10 %, unmeasured VOCs cannot be responsible for a possible underestimation of the peroxy radical production resulting from the reaction of VOCs with OH. As the NO concentration in the model was constrained to measurements, also the main loss processes of peroxy radicals in the high NOx regime, the reactions with NO, are well determined. In addition, a possible segregation effect by the fast variability of radical precursors in combination with non-synchronous observations was minimized by the experimental setup. The inlets of the LIF instrument and of other instruments were very close to each other (within 2 m). The sampling height was about 20 m above ground, 50 m away from the next street. Therefore, segregation is expected to play only a minor role. This is supported by the observed O3, NO, and NO2 concentrations, which were close (within 10 %) to a steady state. All these arguments indicate that the significant peroxy radical underestimation is probably caused by missing primary sources in the model.

Based on the discussion above, we can assume that the peroxy radicals were in the steady state so that their production and destruction rates were balanced at all times. The production of peroxy radicals P(HO2+RO2) can be calculated as follows: P(HO2+RO2)=kVOC×[OH]+P(HO2)primary+P(RO2)primary.

Here, kVOC denotes the part of OH reactivity which is caused by CO, CH4, VOC, and OVOC reactions. This value is equal to the difference between observed total OH reactivity and NOx reactivity. The known HO2 and RO2 primary sources contribute less than 5 % compared to the radical recycling rate at high NOx conditions.

The loss rate of HO2 and RO2 can be expressed as L(HO2+RO2)=kHO2+NO×[HO2]×[NO]+L(HO2)termination+L(RO2)termination.

For high NOx conditions, the termination rates for HO2+HO2, HO2+RO2, and RO2+RO2 are less than 1 % compared to the reaction rates between HO2 and NO. We also tested the equilibrium between HO2 and HNO4 as well as between RO2 and PAN-type compounds. They had only a minor impact on the ROx budget calculation (<4%). The reaction of RO2 and NO is not in Eq. (4), because this reaction converts to HO2 and thus is not an effective loss of peroxy radicals.

Because the production and destruction rates of peroxy radicals must be balanced, the missing peroxy radical source P′(ROx) can be determined by the difference between known radical loss rate and production rate. It is worth noting that all primary sources and termination processes of HO2 and RO2 are negligible compared to the radical propagation. P′(ROx)=kHO2+NO×[HO2]×[NO]-P(HO2)primary-P(RO2)primary-kVOC×[OH]+L(HO2)termination+L(RO2)termination

As shown in Fig. 12, P′(ROx) is essentially zero in background air. In the clean and polluted cases, however, a significant missing radical source is found during daytime. On polluted days, P′(ROx) is very large and shows a broad maximum with a peak value of about 5 ppbv h-1 at 10:00 CNST. The production rate is 2.5 ppbv h-1 on average, nearly a factor of 5 larger than the known primary source of ROx during the polluted days (0.62 ppbv h-1). The error of the P′(ROx) determination is estimated to be ±1.7 ppbv by considering the uncertainty from measurement and kinetic reaction rates. On the clean days (Fig. 12), the missing radical source is significant only during morning hours, peaking at 3 ppbv h-1 at 10:00 CNST.

A missing primary radical source was already proposed to explain a morning RO2 underestimation by the model during the summer campaign in Wangdu (Tan et al., 2017). The proposed source originated from photolysis of ClNO2 generating chlorine radicals, which can oxidize VOC to RO2. However, the observed ClNO2 (0.5 ppbv, maximum of diurnal average; Tham et al., 2016) and Cl2 (Liu et al., 2017) concentrations could only explain 10 % and 30 % of the missing primary ROx source for the summer Wangdu campaign (Tan et al., 2017). During the winter campaign in Beijing, the missing primary ROx source was 2 to 3 times larger than what was found during the Wangdu summer campaign. The underestimation of RO2 concentrations in the model occurred mainly during the pollution episodes, when the measurement site was influenced by air masses transported from the Beijing central area or by local emissions. Since ClNO2 and molecular chlorine were not measured in this campaign, their possible role in the production of ROx is difficult to quantify. High N2O5 concentrations were observed in this campaign with values up to 10 ppbv during the pollution episodes (Wang et al., 2017a) and also aerosol chlorine was abundant (up to 7 µg m-3) to facilitate the production of ClNO2. Therefore, the ClNO2 has the potential to explain at least part of the missing RO2 source. However, the production rate of ClNO2 depends on the N2O5 aerosol uptake coefficient and the ClNO2 yield, both of which can be highly variable (Tham et al., 2018). Therefore, measurements of chlorine-chemistry-related species would be essential to evaluate its effect on the OH–HO2–RO2 radical system, but they are not available here. Implementing a generic primary RO2 radical source in the model allows increasing the modeled HO2 and RO2 concentrations. However, matching the modeled RO2 concentrations to the observations leads to an overprediction of OH by more than a factor of 5. To maintain a relatively good agreement between observed and modeled OH, an additional OH sink would be needed, but this is difficult to reconcile with the good agreement between the measured and modeled kOH.

From the time series (Fig. 3) and the mean diurnal profiles (Fig. 4) of Ox, it is possible to deduce that excess Ox higher than the typical Ox value of 40 ppbv during afternoon only appeared during the pollution days. This indicates that the Ox was produced by local photochemical reactions and/or was transported from the upwind areas. The change of the Ox concentration is caused by both chemical production/destruction and physical processes (advection, vertical mixing, deposition, and so on). Therefore, it is important to note that the large local production rate is not necessarily observed in the measured local Ox concentration. In this study, we compared the chemical production rate and the Ox concentration change to illustrate whether chemical production can support the Ox concentration increase. The maximum instantaneous ozone production rate (not including any Ox potential loss process) can be approximated by the oxidation rate of NO by HO2 and RO2: P(O3)=kHO2+NO[HO2][NO]+∑kRO2,i+NO[RO2]i[NO].

The base model underpredicts the observed HO2 and RO2 concentrations significantly, leading to the strong underestimation of this local ozone production rate (Fig. 12). As discussed above, an additional primary radical source is required to close the ROx budget, which would be the dominant contributor to the fast ozone production rate during pollution episodes. Similarly, ozone production rates that were directly measured in cities in the US were significantly higher than model calculations for high NOx regimes (Baier et al., 2017; Brune et al., 2016; Cazorla et al., 2012).

The observed OH concentrations presented in this study are nearly 1 order of magnitude larger than what global models predict for northern China in winter (Lelieveld et al., 2016; Huang et al., 2014). The higher-than-expected OH concentrations indicate that the oxidation capacity of the atmosphere was high in Beijing and in the North China Plain in wintertime. As shown in Table 3, the averaged OH concentrations in Beijing for January were also higher than at other midlatitude field studies in which OH concentrations were measured in winter. In this study, the observed OH radical concentrations at noontime ranged from 2.4×106cm-3 in severely polluted air (kOH∼27s-1) to 3.6×106cm-3 in relatively clean air (kOH∼5s-1). The reported OH maximum concentrations for urban and suburban locations in the northern hemispheric winter were 1.4×106cm-3 in NYC (Ren et al., 2006), 1.7×106cm-3 in Birmingham (Heard et al., 2004), and 1.5×106cm-3 in Tokyo (Kanaya et al., 2007), respectively (Table 3). Comparably high OH concentrations of up to 2.7×106cm-3 were observed at a rural site in Colorado in late February (Kim et al., 2014). In our study, the OH maximum reached 5×106cm-3 from 20 to 28 February with similar j(O1D) values (maximum 1×10-5s-1 on average) to those observed at the Colorado site. On the other hand, the OH reactivity was on average less than 5 s-1, which resulted in much slower OH turnover rates at that rural site in the US with an estimated maximum of 1.6 ppbv h-1 (Kim et al., 2014). The combination of high OH concentration and moderate OH reactivity at Huairou/Beijing resulted in a fast oxidation rate by OH up to 3.6 ppbv h-1 for the campaign average conditions.

The primary radical production rate at Huairou/Beijing was in the lower range among all other winter HOx campaigns (Table 3). However, the high observed OH concentrations and moderate OH reactivities led to a fast OH turnover rate, which had to be sustained by a large radical chain length. The radical chain length is used to describe the efficiency of radical propagation. It can be calculated as follows: ChL=[OH]⋅kVOC/P(ROx).

The radical chain length was up to five at Huairou/Beijing but was observed to be in the range from two to three in other winter campaigns (Table 3). This indicates radical propagation is very efficient during the BEST-ONE campaign. However, if radical primary production is missing in the calculation, the calculated radical chain length would be too large. Therefore, for this study, the chain length should be regarded as an upper limit. For example, in the NACHTT campaign, only the OH production rate was taken into account by Kim et al. (2014), which leads to an overestimation of the radical chain length.

Secondary products are believed to be major contributors to aerosol particles in haze events (Guo et al., 2014; Cheng et al., 2016; Wang et al., 2016, 2017b). An important question is what is the contribution of gas-phase reactions to haze formation. Previous studies attempted to quantify the contributions of gas-phase and aerosol-phase reactions to oxidation processes during wintertime by chemical models (Huang et al., 2014; Guo et al., 2014; Nan et al., 2017). In this study, the in situ observations of the OH radical provide an experimental constraint to quantify the sulfate and nitrate production by OH oxidation. As discussed above, the high OH concentrations indicate a fast gas-phase oxidation during wintertime in Beijing. As a consequence, the nitrate acid production rate P(HNO3) during wintertime at Huairou/Beijing was 0.28 ppbv h-1 for daytime averaged, only 3 times slower compared to the campaign in Wangdu during summertime (0.81 ppbv h-1). In comparison, the SO2 oxidation rate was 0.02 ppbv h-1. One should keep in mind that the formation of gas-phase sulfate and nitrate via OH oxidation does not necessarily lead to particle formation, due to the dependence on the gas–aerosol partitioning. The relatively fast oxidation rate presented here only shows the particle growth potential from gas-phase reactions. Nevertheless, the in situ measurements presented in this study provide experimental evidence for a strong gas-phase production potential of aerosol precursors, which underlines the importance of taking OH chemistry into account for the understanding of the wintertime haze formation.