Production of N₂O₅ and ClNO₂ in summer in urban Beijing, China

The heterogeneous hydrolysis of dinitrogen pentoxide (N₂O₅) has a significant impact on both nocturnal particulate nitrate formation and photochemistry on the following day through the photolysis of nitryl chloride (ClNO₂), yet these processes in highly polluted urban areas remain poorly understood. Here we present measurements of gas-phase N₂O₅ and ClNO₂ by high-resolution time-of-flight chemical ionization mass spectrometer (ToF-CIMS) during summer in urban Beijing, China as part of the Air Pollution and Human Health (APHH) campaign. N₂O₅ and ClNO₂ show large day-to-day variations with average (±1σ) mixing ratios of 79.2±157.1 and 174.3±262.0 pptv, respectively. High reactivity of N₂O₅, with τ (N₂O₅)⁻¹ ranging from 0.20 × 10⁻² to 1.46 × 10⁻² s⁻¹, suggests active nocturnal chemistry and a large nocturnal nitrate formation potential via N₂O₅ heterogeneous uptake. The lifetime of N₂O₅, τ (N₂O₅), decreases rapidly with the increase in aerosol surface area, yet it varies differently as a function of relative humidity with the highest value peaking at ∼ 40 %. The N₂O₅ uptake coefficients estimated from the product formation rates of ClNO₂ and particulate nitrate are in the range of 0.017–0.19, corresponding to direct N₂O₅ loss rates of 0.00044–0.0034 s⁻¹. Further analysis indicates that the fast N₂O₅ loss in the nocturnal boundary layer in urban Beijing is mainly attributed to its indirect loss via NO₃, for example through the reactions with volatile organic compounds and NO, while the contribution of the heterogeneous uptake of N₂O₅ is comparably small (7–33 %). High ClNO₂ yields ranging from 0.10 to 0.35 were also observed, which might have important implications for air quality by affecting nitrate and ozone formation.

1 Introduction

Dinitrogen pentoxide (N₂O₅) is an efficient nocturnal sink for nitrogen oxides (NO_x; Dentener and Crutzen, 1993; Brown et al., 2006). N₂O₅ exists in a rapid temperature-dependent thermal equilibrium with the nitrate radical (NO₃) – one of the most important oxidants at nighttime (Wayne et al., 1991). Although NO₃ and N₂O₅ levels can be suppressed by the rapid titration of NO₃ against NO and volatile organic compounds (VOCs) in urban areas (Brown et al., 2003b), heterogeneous uptake by aerosol particles, fog, and cloud droplets is often found to be the major pathway for direct N₂O₅ removal (Bertram and Thornton, 2009; Wagner et al., 2013; Brown et al., 2006; Chang et al., 2011; Thornton et al., 2003). N₂O₅ can produce nitryl chloride (ClNO₂) on chloride-containing aerosols, which serves as an important reservoir of NO_x (Finlayson-Pitts et al., 1989; Thornton et al., 2010; Phillips et al., 2012). It has been found that levels of particulate nitrate formed through the hydrolysis of N₂O₅ at nighttime were comparable to those produced from the reaction of NO₂ with the OH radical during daytime (Geyer et al., 2001). Furthermore, ClNO₂ can be photolyzed into NO₂ and atomic chlorine (Cl) after sunrise, resulting in significant impacts on daytime photochemistry, for example trace gas degradation and ozone formation (Osthoff et al., 2008; Sarwar et al., 2014; Riedel et al., 2012; Mielke et al., 2013). Thus, it is of great importance to understand N₂O₅ and ClNO₂ chemistry in the nocturnal boundary layer of various environments.

The heterogeneous reaction of N₂O₅ and activation of ClNO₂ are parameterized by the N₂O₅ uptake coefficient (${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}})$ and ClNO₂ product yield (ø), which are defined as the reaction probability of N₂O₅ upon its collision on an aerosol surface and the number of ClNO₂ molecules formed per lost N₂O₅ molecule upon uptake, respectively (Wagner et al., 2013; Brown, 2006; Roberts et al., 2009). Previous laboratory studies have shown a large variability of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (0.0002–0.3) depending on the physical characteristics of the substrates (e.g., aerosol surfaces, water droplets, and ice and crystal surfaces), environmental conditions (e.g., acidity, relative humidity, and temperature), and chemical composition of aerosol particles (e.g., nitrate, sulfate, black carbon, and organic coating; Sander et al., 2006; Chang et al., 2011; Anttila et al., 2006; Cosman et al., 2008; Thornton and Abbatt, 2005; McNeill et al., 2006). To reveal the effects of each factor on N₂O₅∕ClNO₂ chemistry, several parameterizations of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø have been proposed during the last decade (Riemer et al., 2003; Evans and Jacob, 2005; Anttila et al., 2006; Davis et al., 2008; Riemer et al., 2009; Griffiths et al., 2009). For example, Bertram and Thornton (2009) constructed a parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ as a function of aerosol liquid water, nitrate, and chloride content based on the measurements of laboratory-generated internally mixed chloride–nitrate particles. Similarly, ø was parameterized as a function of aerosol liquid water content and aerosol chloride (Roberts et al., 2009). These results have great implications for regional and global chemical transport models that aim to improve the simulations of nitrate and ozone (Evans and Jacob, 2005; Sarwar et al., 2014). However, the field-derived values of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø often exhibit large inconsistencies with laboratory results, suggesting a more complex nature of heterogeneous N₂O₅ uptake in the ambient atmosphere (Brown et al., 2006; Chang et al., 2011).

N₂O₅ and NO₃ can be measured by various different techniques, which have been summarized in Chang et al. (2011). For example, N₂O₅ can be derived from thermal equilibrium with NO₂ and NO₃ that are simultaneously measured by differential optical absorption spectroscopy (DOAS; Platt and Stutz, 2008; Stutz et al., 2004). Another indirect measurement of N₂O₅ is subtracting ambient NO₃ from the total measured NO₃ after converting N₂O₅ to NO₃ in a heated inlet and then detected by cavity ring-down spectroscopy (CRDS), cavity-enhanced absorption spectroscopy (CEAS), or laser-induced fluorescence (LIF; O'Keefe and Deacon, 1988; Brown et al., 2001; Smith et al., 1995; Wood et al., 2003; Stutz et al., 2010). Simultaneous indirect measurements of N₂O₅ and NO₃ can be implemented using thermal dissociation–chemical ionization mass spectrometer (TD–CIMS) with high sensitivity and time resolution (Stutz et al., 2004), although the interference of m∕z 62 (NO₃) from the thermal decomposition of peroxy acetyl nitrate (PAN) and other related species needs to be considered (Wang et al., 2014). Recently, the CIMS using iodide reagent ions (I-CIMS) with an unheated inlet configuration allowed for direct measurements of N₂O₅ (Kercher et al., 2009; Tham et al., 2014, 2016; Wang et al., 2016). The I-CIMS is also widely used to measure ClNO₂ in both laboratory and field studies (Thornton and Abbatt, 2005; McNeill et al., 2006; Osthoff et al., 2008; Tham et al., 2014, 2016; Wang et al., 2016). A large amount of ClNO₂ was first observed in polluted coastal regions owing to the abundant chloride from sea salt aerosol, for example in the Gulf of Mexico and the Los Angeles basin (Osthoff et al., 2008; Riedel et al., 2012; Kercher et al., 2009). High levels of ClNO₂ from anthropogenic chloride sources were also reported in some inland areas (Thornton et al., 2010; Mielke et al., 2011; Phillips et al., 2012, 2016; Bannan et al., 2015). More recently some studies in Hong Kong (Tham et al., 2014; Brown et al., 2016a; Wang et al., 2016) and in the North China Plain (NCP; Tham et al., 2016; X. Wang et al., 2017; Z. Wang et al., 2017; Wang et al., 2018) observed consistently high mixing ratios of N₂O₅ and ClNO₂. In particular, ClNO₂ can be rapidly formed in the plumes of coal-fired power plants in the NCP, which serves as an important source of chloride in non-ocean regions. Besides these measurement efforts, recently, some modeling studies have also evaluated the impacts of N₂O₅ and ClNO₂ chemistry on the ozone formation and regional air quality in China (Xue et al., 2015; Wang et al., 2016; Li et al., 2016). Despite this, our understanding of N₂O₅ and ClNO₂ chemistry in highly polluted urban regions with high levels of NO_x, O₃, and high particulate matter is far from complete.

Beijing has been suffering from severe haze pollution during the last 2 decades (Chan and Yao, 2008). As a result, extensive studies have been conducted to characterize the sources and formation mechanisms of haze episodes (Huang et al., 2014; Guo et al., 2014; Li et al., 2017). The results show that nitrate and its precursors have been playing increasingly important roles in pollution events since 2006 mainly due to the continuous decrease in SO₂ (van der A et al., 2017). While the formation mechanisms of nitrate are relatively well known, the relative contributions of different mechanisms can have large variability and uncertainties. Pathak et al. (2009) found that the heterogeneous hydrolysis of N₂O₅ contributed 50 %–100 % of the nighttime enhancement of nitrate concentration in Beijing. WRF-Chem model simulations showed only 21 % enhancement of nitrate during highly polluted days (Su et al., 2016). A recent study also observed a large nocturnal nitrate formation potential from N₂O₅ heterogeneous uptake, which is comparable to and even higher than that from the partitioning of HNO₃ in rural Beijing in autumn (H. Wang et al., 2017). A large contribution of the heterogeneous hydrolysis of N₂O₅ to the high PM_2.5 nitrate, even in the daytime due to persistently high NO₂, was also reported in Hong Kong (Xue et al., 2014a). All these results highlight the fact that N₂O₅ heterogeneous uptake might be an important pathway of nitrate formation in Beijing. A recent modeling study has evaluated the impacts of heterogeneous ClNO₂ formation on next-day ozone formation in Beijing (Xue et al., 2014b). However, the roles of N₂O₅ in nitrate formation and of N₂O₅ and ClNO₂ in nighttime and daytime chemistry in summer in urban Beijing during field campaigns are not characterized yet, except for one measurement in suburban Beijing in the summer of 2016 (Wang et al., 2018).

In this work, two high-resolution time-of-flight CIMSs using the same iodide ionization system operated by the Institute of Atmospheric Physics (IAP-CIMS) and University of Manchester (UoM-CIMS), respectively, were deployed in urban Beijing for real-time measurements of gas-phase N₂O₅ and ClNO₂. A broadband cavity-enhanced absorption spectrometer (BBCEAS) operated by the University of Cambridge was also deployed synchronously for the intercomparison of N₂O₅. The temporal variations of N₂O₅ and ClNO₂ in summer and their relationships are characterized. The heterogeneous N₂O₅ uptake coefficients and ClNO₂ production yields are estimated, and their implications in nitrate formation are elucidated.

2 Experimental methods

2.1 Field campaign site and meteorology

The measurements were conducted during the Air Pollution and Human Health (APHH) summer campaign from 11 to 16 June 2017 at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (39^∘58^′28${}^{\prime \prime }$ N, 116^∘22^′16${}^{\prime \prime }$ E, 49 m a.s.l.), which is an urban site located between the north 3rd and 4th ring roads in Beijing. The meteorological variables including wind direction (WD), wind speed (WS), relative humidity (RH), and temperature (T) at 15 and 100 m were obtained from the Beijing 325 m meteorological tower (BMT) at the sampling site. The hourly average RH ranged from 12.9 % to 82.8 %, with an average value of 36.8±15.9 %, and the hourly average temperature ranged from 17.9 to 38.7 ^∘C averaged at 26.7±4.9 ^∘C. All IAP instruments were deployed on the roof of a two-story building (∼ 10 m), while UoM-CIMS and BBCEAS were housed in two containers at ground level (∼ 4 m) approximately 20 m away. More details about the sampling site can be found in previous studies (Sun et al., 2012). All data in this study are reported in Beijing local time.

2.2 Instruments

2.2.1 IAP-CIMS

Ambient air was drawn into the sampling room through ∼ 2 m Teflon perfluoroalkoxy tubing (PFA; 1/4 inch inner diameters) at a flow rate of 10 standard liters per minute (SLM), from which ∼ 2 SLM was subsampled into the CIMS. Methyl iodide gas (CH₃I) from a heated CH₃I permeation tube cylinder (VICI, 170-015-4600-U50) was ionized by flowing through a soft X-ray ionization source (Tofwerk AG, type P) under an ultrahigh-purity nitrogen (N₂, 99.999 %) flow (2.5 SLM). This flow enters an ion molecule reaction (IMR) chamber, which was maintained at a pressure of 200 mbar using an SH-112 pump fitted with a Tofwerk blue pressure control box to account for changes in ambient pressure. A short segmented quadrupole (SSQ) positioned behind the IMR was held at a pressure of 2 mbar using a Tri scroll 600 pump. Note that the voltage settings used for the guidance of ions were carefully tuned to avoid declustering as much as possible (Lopez-Hilfiker et al., 2016). The gas-phase background was determined once during the campaign by passing dry N₂ into the inlet for 5 min.

2.2.2 UoM-CIMS

The UoM-CIMS setup has been described elsewhere (Priestley et al., 2018); a Filter Inlet for Gases and AEROsols (FIGAERO; Lopez-Hilfiker et al., 2014) was additionally used in this study. The gas-phase inlet of UoM-CIMS consisted of 5 m 1/4${}^{\prime \prime }$ ID PFA tubing connected to a fast inlet pump with a total flow rate of 13 SLM from which the ToF-CIMS subsampled 2 SLM. CH₃I gas mixtures in N₂ were made in the field using a custom-made manifold (Bannan et al., 2014). A total of 20 standard cubic centimeters per minute (SCCM) of the CH₃I mixture was diluted in 4 SLM N₂ and ionized by flowing through a Tofwerk X-ray ionization source. This flow enters into the IMR, which was maintained at a pressure of 400 mbar using an SSH-112 pump also fitted with a Tofwerk blue pressure control box, while the subsequent SSQ was held at a pressure of 2 mbar using a Tri scroll 600 pump. During the campaign, gas-phase backgrounds were established through regularly overflowing the inlet with dry N₂ for 5 min continuously every 45 min as has been performed previously.

The ambient target molecules were first ionized by reagent ions in the IMR and then detected as adduction products with iodide, for instance ClNO₂ as $\mathrm{I}\cdot {\mathrm{ClNO}}_{\mathrm{2}}^{-}$ at m∕z 208 and 210 ($\mathrm{I}{\cdot }^{\mathrm{37}}{\mathrm{ClNO}}_{\mathrm{2}}^{-}$), and N₂O₅ as $\mathrm{I}\cdot {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}^{-}$ at m∕z 235 (Slusher et al., 2004; Kercher et al., 2009) at a time resolution of 1 s. Data analysis is performed using the “Tofware” package (version 2.5.11) running in the IGOR Pro (WaveMetrics, OR, USA) environment. The mass axis of UoM-CIMS was calibrated using I⁻, I${}_{\mathrm{2}}^{-}$, and I${}_{\mathrm{3}}^{-}$, while that of IAP-CIMS was calibrated using ${\mathrm{NO}}_{\mathrm{3}}^{-}$, I⁻, $\mathrm{I}\cdot {\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}^{-}$, $\mathrm{I}\cdot {\mathrm{CH}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}^{-}$, $\mathrm{I}\cdot {\mathrm{HNO}}_{\mathrm{3}}^{-}$, and I${}_{\mathrm{3}}^{-}$ covering a wide range from m∕z 62 to 381. Examples of high-resolution peak fittings of m∕z 208, 210, and 235 for IAP-CIMS are presented in Fig. S1 in the Supplement.

2.2.3 Broadband cavity-enhanced absorption spectrometer (BBCEAS)

A detailed description of BBCEAS has been given in Kennedy et al. (2011). Briefly, ambient air is first heated to 140 ^∘C to thermally dissociate N₂O₅ into NO₃ and then enters the observational cavity that consists of two high-reflectivity mirrors. The sum of N₂O₅ and NO₃ is determined using the measured optical absorption of NO₃ in the wavelength of 640–680 nm. The temperature of the cavity is kept at 85±1 ^∘C to prohibit the recombination of NO₃ and NO₂ and to maintain the stability of the optical transmission signal. A very fast flow rate of 20 L min⁻¹ is adopted to minimize the residence time of gases through PFA tubes. The loss of NO₃ through the system was estimated to be approximately 10 %.

Considering that the relatively high aerosol loadings in Beijing can attenuate the intracavity light intensity and thus deteriorate instrument sensitivity, a poly tetrafluoroethylene (PTFE) filter of pore size 1 µm was used to remove aerosol particles from the airstream. This filter also acts a point loss (∼ 10 %) for NO₃ but has a negligible impact on N₂O₅ (Dube et al., 2006). Because the mixing ratio of N₂O₅ is higher than NO₃ by a factor of >10 during the APHH summer campaign, the influence of filter loss on the measurements of N₂O₅ + NO₃ is expected to be small. Aging of aerosol particles on the filter may potentially introduce uncertainties for the transmission efficiencies of NO₃ and N₂O₅, but was found to be insignificant in this study.

2.3 Calibrations and intercomparisons

During the campaign, field calibrations for UoM-CIMS were regularly carried out using known concentration formic acid gas mixtures made in the custom-made manifold. A range of other species were calibrated after the campaign, and relative calibration factors were derived using the measured formic acid sensitivity during these calibrations as has been performed previously (Le Breton et al., 2014, 2017; Bannan et al., 2014, 2015).

The UoM-CIMS was calibrated post-campaign for both N₂O₅ and ClNO₂ relative to formic acid that was calibrated and measured throughout the campaign. This is completed assuming that the ratio between formic acid and ClNO₂ sensitivity remains constant. ClNO₂ was calibrated using the method described in Kercher et al. (2009). Briefly, a stable source of N₂O₅ is generated and passed over a salt slurry in which excess chloride reacts to produce gaseous ClNO₂. The N₂O₅ for this process was synthesized based on the methodology described by Le Breton et al. (2014). Excess O₃ is generated through flowing 200 SCCM O₂ (BOC) through an ozone generator (BMT, 802N) into a 5 L glass volume containing NO₂ (Sigma-Aldrich, >99.5 %). The outflow from this reaction vessel is cooled in a cold trap held at −78 ^∘C (195 K) by a dry ice–glycerol mixture in which N₂O₅ is condensed and frozen. The trap is allowed to reach room temperature and the flow is reversed whereby it is then condensed in a second trap held at 220 K. This process is repeated several times to purify the mixture. The system is first purged by flowing O₃ for 10 min before usage. To ascertain the N₂O₅ concentration in the line, the flow is diverted through a heated line to decompose the N₂O₅ and into to a Thermo Scientific 42i NO_x analyzer in which it is detected as NO₂. According to the intercomparisons with the BBCEAS, including this study and others (e.g., Le Breton et al., 2014; Bannan et al., 2017), the possible interference of NO_y on the NO_x analyzer is not deemed important in terms of our reported N₂O₅ concentrations.

ClNO₂ was produced by flowing a known concentration of N₂O₅ in dry N₂ through a wetted NaCl scrubber. Conversion of N₂O₅ to ClNO₂ can be as efficient as 100 % on sea salt, but it can also be lower, for example if ClNO₂ is converted to Cl₂ (Roberts et al., 2008). In this calibration we have followed the accepted methods of Osthoff et al. (2008) and Kercher et al. (2009) that show a conversion yield of 100 % and have assumed this yield in the calibrations of this study.

The second method used to verify our ClNO₂ calibration is cross-calibration with a turbulent flow tube chemical ionization mass spectrometer (TF-CIMS; Leather et al., 2012). A known concentration of 0–20 SCCM Cl₂ (99.5 % purity Cl₂ cylinder, Aldrich) from a diluted (in N₂) gas mix is flowed into an excess constant flow of 20 SCCM NO₂ (99.5 % purity NO₂ cylinder, Aldrich) from a diluted (in N₂) gas mix, to which the TF-CIMS has been calibrated. This flow is carried in 52 SLM N₂ that is purified by flowing through two heated molecular sieve traps. This flow is subsampled by the ToF-CIMS in which the $\mathrm{I}\cdot {\mathrm{ClNO}}_{\mathrm{2}}^{-}$ adduct is observed. The TF-CIMS is able to quantify the concentration of ClNO₂ generated in the flow tube as the equivalent drop in NO${}_{\mathrm{2}}^{-}$ signal. This indirect measurement of ClNO₂ is similar in its methodology to ClNO₂ calibration by quantifying the loss of N₂O₅ reacted with Cl⁻ (e.g., Kercher et al., 2009). The TF-CIMS method gives a calibration factor 58 % greater than that of the N₂O₅ synthesis method; therefore this is taken as our measurement uncertainty. This calibration was scaled to those in the field using formic acid calibrations carried out in the laboratory by overflowing the inlet with various known concentrations of gas mixtures (Bannan et al., 2014).

Figure 1 Time series of (a–b) meteorological parameters (WS, WD, RH, T) and surface area density (S_a), (c) trace gases (O₃, NO, NO₂), and (d–e) IAP-CIMS species (N₂O₅, ClNO₂). The UoM-CIMS and BBCEAS measurements are also shown for intercomparison. The four nights (i.e., P1, P2, P3, and P4) are marked for further discussions.

The IAP-CIMS calibration for N₂O₅ was performed by comparing with the measurements from the BBCEAS. As shown in Fig. S2, the raw signals of N₂O₅ from the IAP-CIMS measurements were highly correlated with those from BBCEAS (R²=0.84). Given that the intercomparison between the two instruments was relatively constant throughout the study, the average regression slope of 0.54 was then applied to determine the mixing ratio of N₂O₅ for the IAP-CIMS. The estimated N₂O₅ mixing ratios were then compared with those measured by UoM-CIMS. As shown in Fig. 1, the two N₂O₅ measurements tracked well with each other (R²=0.84, slope = 1.42) although some differences at midnight on 13 June were observed. The raw signals of ClNO₂ given by the IAP-CIMS were first converted to mixing ratios by assuming the same sensitivity between ClNO₂ and N₂O₅ (i.e., 0.54 cps pptv⁻¹). The results show that the estimated ClNO₂ for the IAP-CIMS agrees well with that measured by UoM-CIMS and calibrated post-campaign (R²=0.93, slope = 0.905, Fig. 1). Overall, the uncertainty is 17 % and 58 %, and the detection limit is 1.7 and 0.7 pptv for N₂O₅ and ClNO₂ of IAP-CIMS, respectively. All the discussions below are based on IAP-CIMS measurements unless otherwise stated.

2.4 Collocated measurements

An Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-AMS hereafter) and an Aethalometer (AE33, Magee Scientific Corp.) were deployed on the roof of the two-story building to measure size-resolved non-refractory submicron aerosol (NR-PM₁) species with a time resolution of 5 min, including organics (Org), sulfate (SO${}_{\mathrm{4}}^{\mathrm{2}-})$, nitrate (NO${}_{\mathrm{3}}^{-})$, ammonium (NH${}_{\mathrm{4}}^{+})$, chloride (Cl⁻) (DeCarlo et al., 2006; Canagaratna et al., 2007), and black carbon (BC). A more detailed description of the operations and calibrations of this HR-AMS can be found in Xu et al. (2015) and Sun et al. (2016). Other collocated measurements in two containers at ground level included gaseous species of O₃ (TEI 49C UV absorption analyzer), NO (TEI 42i TL NO analyzer), and NO₂ (CAPS NO₂ monitor, Aerodyne Research Inc.) and size-resolved particle number concentrations (11–550 nm) by a scanning mobility particle sizer (SMPS) equipped with a long differential mobility analyzer (DMA, TSI, 3081A) and a condensation particle counter (CPC, TSI, 3772).

2.5 Data analysis

2.5.1 Estimation of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$

NO₃ is formed from the reaction of NO₂ with O₃ (Reaction R1) with a temperature-dependent reaction rate constant k₁. NO₃ rapidly photolyzes during daytime, but at night it reacts with NO₂ to produce N₂O₅ (Reaction R2). N₂O₅ can thermally decompose back to NO₃ and NO₂, and the equilibrium rate coefficient K_eq is a function of ambient temperature. In this study, values of k₁ and K_eq recommended by Atkinson et al. (2004) and Brown and Stutz (2012) were used. The indirect loss of N₂O₅ is mainly through reactions of NO₃ with either NO or VOCs (Reaction R3), while direct N₂O₅ loss is predominantly from the heterogeneous hydrolysis on the surface of aerosol particles that contain water (Reaction R4) or chloride (Reaction R5). Note that “het” is an abbreviation of heterogeneous in the equations. The net reaction of Reactions (R4) and (R5) can be described as Reaction (R6) where $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ is the heterogeneous uptake rate of N₂O₅, and ø is the ClNO₂ yield.

$$\begin{array}{ll}\text{(R1)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}},k_{\mathrm{1}}\text{(R2)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+M\leftrightarrow {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M,K_{\text{eq}}\text{(R3)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\left(\text{NO or VOCs}\right)\to \text{products},k_{{\mathrm{NO}}_{\mathrm{3}}}\text{(R4)}& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\text{het}\right)\to \mathrm{2}{\mathrm{HNO}}_{\mathrm{3}}\left(\text{aq}\right)\text{(R5)}& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}\left(\text{het}\right)\to {\mathrm{NO}}_{\mathrm{3}}^{-}\left(\text{aq}\right)+{\mathrm{ClNO}}_{\mathrm{2}}\text{(R6)}& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\text{or}{\mathrm{Cl}}^{-}\right)\left(\text{het}\right)\to (\mathrm{2}-\mathit{ø}){\mathrm{NO}}_{\mathrm{3}}^{-}\left(\text{aq}\right){\displaystyle }& {\displaystyle }+\mathit{ø}{\mathrm{ClNO}}_{\mathrm{2}},k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\end{array}$$

When the uptake reaction was not limited by gas-phase diffusion, $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ can be simplified as Eq. (1) (Riemer et al., 2003; Dentener and Crutzen, 1993):

$$\begin{array}{}\text{(1)}& k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\times c\times S_{\text{a}}\times {\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}},\end{array}$$

where c is the mean molecular speed of N₂O₅ (unit, m s⁻¹), and S_a is the aerosol surface area density calculated from the size-resolved particle number concentrations assuming spherical particles (unit, µm cm⁻³). Note that S_a determined under dry conditions was converted to that under ambient RH levels by using the hygroscopic growth factor in Liu et al. (2013).

The nocturnal mixing ratio of NO₃ can be derived from simultaneous measurements of NO₂ and N₂O₅ (Reaction R2) assuming that the equilibrium between NO₃ and N₂O₅ is rapidly established after sunset (Brown et al., 2003a).

$$\begin{array}{}\text{(2)}& \left[{\mathrm{NO}}_{\mathrm{3}}\right(\text{cal}\left)\right]={\displaystyle \frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{K_{\text{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}\end{array}$$

The nitrate radical production rate p(NO₃) can be calculated from Reaction (R1) assuming that the nitrate radical is solely from Reaction (R1).

$$\begin{array}{}\text{(3)}& p\left({\mathrm{NO}}_{\mathrm{3}}\right)=k_{\mathrm{1}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\end{array}$$

With a steady-state assumption for NO₃ and N₂O₅, the inverse N₂O₅ steady-state lifetime, τ(N₂O₅)⁻¹, which is defined as the ratio of p(NO₃) to the N₂O₅ mixing ratios, can be expanded to Eq. (4) after the substitution of Eqs. (2) and (3) into the approximate time change rate for N₂O₅ (Brown et al., 2003a).

$$\begin{array}{}\text{(4)}& \mathit{\tau }({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}{)}^{-\mathrm{1}}={\displaystyle \frac{p\left({\mathrm{NO}}_{\mathrm{3}}\right)}{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}}\approx {\displaystyle \frac{k_{{\mathrm{NO}}_{\mathrm{3}}}}{K_{\text{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}+k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\end{array}$$

$\frac{k_{{\mathrm{NO}}_{\mathrm{3}}}}{K_{\text{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}$ represents the contribution to τ(N₂O₅)⁻¹ from the indirect N₂O₅ loss pathway, i.e., through NO₃ reactions with VOCs and NO, while $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ indicates the direct loss of N₂O₅ through heterogeneous uptake.

Considering that the production of ClNO₂ is predominantly from heterogeneous N₂O₅ uptake within stable air masses and precursors, the production rate of ClNO₂ (pClNO₂) can be related to the heterogeneous loss rate of N₂O₅ by

$$\begin{array}{}\text{(5)}& p{\mathrm{ClNO}}_{\mathrm{2}}={\displaystyle \frac{\mathrm{d}{\mathrm{ClNO}}_{\mathrm{2}}}{\mathrm{d}t}}=\mathit{ø}\times \left({\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\times c\times S_{\text{a}}\times {\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\right).\end{array}$$

The production rate of particulate nitrate (pNO${}_{\mathrm{3}}^{-})$ was obtained from HR-AMS measurements assuming that the measured p${\mathrm{NO}}_{\mathrm{3}}^{-}$ was totally from the production of nitrate by Reaction (R4) (Phillips et al., 2016). Note that the formation of particulate nitrate from regional transport or via the net uptake of HNO₃ to aerosol is not taken into consideration.

$$\begin{array}{}\text{(6)}& p{\mathrm{NO}}_{\mathrm{3}}^{-}={\displaystyle \frac{\mathrm{d}{\mathrm{NO}}_{\mathrm{3}}^{-}}{\mathrm{d}t}}=(\mathrm{2}-\mathit{ø})\times \left({\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\times c\times S_{\text{a}}\times {\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\right)\end{array}$$

Only periods with concurrent nighttime formation of ClNO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ meet the requirement that both are produced only from heterogeneous N₂O₅ uptake. By combining Eq. (5) with Eq. (6), ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø can be represented as follows.

$$\begin{array}{}\text{(7)}& {\displaystyle }& {\displaystyle }{\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}={\displaystyle \frac{\mathrm{2}(p{\mathrm{ClNO}}_{\mathrm{2}}+p{\mathrm{NO}}_{\mathrm{3}}^{-})}{c\times S_{\text{a}}\times \left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}}\text{(8)}& {\displaystyle }& {\displaystyle }\mathit{ø}=\mathrm{2}{\left({\displaystyle \frac{p{\mathrm{NO}}_{\mathrm{3}}^{-}}{p{\mathrm{ClNO}}_{\mathrm{2}}+\mathrm{1}}}\right)}^{-\mathrm{1}}\end{array}$$

2.5.2 Parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø

Aerosol liquid water content associated with inorganic species was estimated using the ISORROPIA-II thermodynamic equilibrium model (Nenes et al., 1998; Fountoukis and Nenes, 2007), with input data of ambient NR-PM₁ species, and RH and T at 15 m. The N₂O₅ uptake coefficient and ClNO₂ yield can also be calculated by the parameterization proposed by Bertram and Thornton (2009).

$$\begin{array}{}\text{(9)}& {\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}=Ak\left(\mathrm{1}-{\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{29}\left[{\text{Cl}}^{-}\right]}{\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]}+\frac{\mathrm{0.06}\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]}{\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]}}}\right)\end{array}$$

$$\begin{array}{}\text{(10)}& \mathit{ø}={\left(\mathrm{1}+{\displaystyle \frac{\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]}{\mathrm{483}\left[{\text{Cl}}^{-}\right]}}\right)}^{-\mathrm{1}}\end{array}$$

[H₂O], [${\mathrm{NO}}_{\mathrm{3}}^{-}$], and [Cl⁻] are molar concentrations of liquid water, particle nitrate, and chloride, respectively, and the empirical parameters A $=\mathrm{3.2}\times {\mathrm{10}}^{-\mathrm{8}}$ and $k=\mathrm{1.15}\times {\mathrm{10}}^{\mathrm{6}}\times (\mathrm{1}-e^{-\mathrm{0.13}}[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left]\right)$ are used.

3 Results and discussion

3.1 Overview of N₂O₅ and ClNO₂ measurements

Figure 1 shows the time series of N₂O₅ and ClNO₂, gaseous species of NO, NO₂, and O₃, and meteorological parameters during the field campaign. Both N₂O₅ and ClNO₂ exhibited large day-to-day variability with the 5 min average (±1σ) mixing ratios being 79.2±157.1 and 174.3±262.0 pptv, respectively. Such dramatic variations of N₂O₅ and ClNO₂ are consistent with previous observations in various environments, for example at ground sites in Colorado and London (Bannan et al., 2015; Thornton et al., 2010) and the residual layer at Mt. Tai (Z. Wang et al., 2017). Four nights (i.e., P1, P2, P3, and P4 from 20:00 to 04:30) were selected to investigate the nocturnal chemistry of N₂O₅ and ClNO₂ in this study. The first two nights (P1 and P2) showed much higher mixing ratios of N₂O₅ and ClNO₂ than those during P3 and P4, although the NO_x and O₃ levels during P4 were comparable to those during P2 (Table 1).

Table 1 Summary of average (±1σ) meteorological parameters (RH, T, WS), CIMS species (N₂O₅, ClNO₂), the calculated NO₃, nitrate radical production rate p(NO₃), N₂O₅ reactivity (τ(N₂O₅)⁻¹) and NO₃ reactivity (τ(NO₃)⁻¹), trace gases (O₃, NO₂, NO), and NR-PM₁ species (${\mathrm{NO}}_{\mathrm{3}}^{-}$, Cl⁻) for the entire study and four nighttime periods (i.e., P1, P2, P3, and P4).

The highest N₂O₅ mixing ratio (1.10 ppbv, 5 min average) was observed at 02:15 on 13 June (P2), which is comparable to the previous observation in urban Beijing (1.3 ppbv; H. Wang et al., 2017), but much lower than that in the aged air masses in Hong Kong at ∼ 7.8 ppbv (Brown et al., 2016b). A recent measurement at a suburban site in Beijing impacted by the outflow of urban Beijing air masses also reported consistently high N₂O₅ (1 min maxima 937 pptv; Wang et al., 2018). The mixing ratio of N₂O₅ was also much higher than that in the nocturnal residual boundary layer at Mt. Tai (167 pptv; Z. Wang et al., 2017), indicating potentially significant nighttime N₂O₅ chemistry in highly polluted urban areas. One of the reasons for this could be the high mixing ratios of precursors; for instance, the average O₃ mixing ratios at nighttime were as high as 18–56 ppbv. The maximal N₂O₅ that occurred during P2 rather than the rest of the nights was likely due to insignificant titration of NO during P2, e.g., 0.5 vs. 2.3–15.6 ppbv. The lowest nighttime average of N₂O₅ (∼ 37.8 pptv) was observed during P3 although the NO₂ showed a much higher concentration than those during P2 and P4, indicating the joint influences of precursors (NO₂ and O₃). Fast heterogeneous hydrolysis of N₂O₅ under high RH (∼ 60.5 %) conditions during P3 could be another reason, which was supported by the higher ClNO₂ during P3 than P4.

Similar to N₂O₅, ClNO₂ presented the highest value (1.44 ppbv, 5 min average) before sunrise on 13 June (P2), yet it is lower than the maximum of 2.1 ppbv (1 min average) observed at a rural site located to the southwest of Beijing (Tham et al., 2016) and also the ClNO₂ peak of 2.9 ppbv (1 min average) in suburban Beijing (Wang et al., 2018). These results indicated ubiquitously observed ClNO₂ in the NCP, although high ClNO₂ mixing ratios have also been previously observed in both marine and continental environments in North America, Europe, and Asia (Osthoff et al., 2008; Mielke et al., 2011; Thornton et al., 2010; Phillips et al., 2012; Tham et al., 2014). The average nitrate radical production rate p(NO₃) was 2.8 and 3.6 ppbv h⁻¹ during P1 and P2, respectively, which are both higher than those during P3 and P4 (1.7–2.6; Table 1). This result supports a higher production potential for N₂O₅ during P1 and P2. On average, p(NO₃) was 2.6±2.4 ppbv h⁻¹ at nighttime, indicating more active nocturnal chemistry than previous studies in NCP in terms of radical production rates, for example 1.2±0.9 ppbv h⁻¹ in suburban Beijing, 1.7±0.6 ppbv h⁻¹ in Wangdu, and 0.45±0.40 ppb h⁻¹ at Mt. Tai (Tham et al., 2016; Z. Wang et al., 2017; Wang et al., 2018). We also note that the p(NO₃) was comparable between P4 and P2 (2.6 vs. 2.8 pptv), yet the N₂O₅ and ClNO₂ mixing ratios during P4 were much lower, likely due to the difference in NO levels, i.e., 0.5 vs. 7.1 ppbv. The favorable dispersing meteorological conditions with higher wind speed and lower relative humidity in P4 than in P2 might also be an explanation (Table 1). Our results illustrate that precursors levels, reaction rates, and meteorological conditions can all affect the variability of N₂O₅ and ClNO₂.

Figure 2 Diurnal variations of trace gases (NO, NO₂, O₃), IAP-CIMS species (N₂O₅, ClNO₂), nitrate radical production rate p(NO₃), and NR-PM₁ species (Cl⁻, NO${}_{\mathrm{3}}^{-})$.

The average diurnal variations of trace gases, N₂O₅, ClNO₂, and submicron nitrate and chloride are depicted in Fig. 2. O₃ showed a pronounced peak of 93.3 ppbv between 14:00 and 16:00 corresponding to a minimum mixing ratio of NO₂ (9.1 ppbv). As a consequence, p(NO₃) showed relatively high values around noon with a decrease in the middle of the afternoon owing to the depletion of NO₂ and then reached a maximum of 5.9 ppbv h⁻¹ before sunset. A similar diurnal pattern of p(NO₃) was also observed at a rural site in the autumn in Beijing (H. Wang et al., 2017). Both NO and NO₂ showed pronounced diurnal cycles with lowest concentrations in the afternoon. In addition to the rising boundary layer, the formation of NO_z is another important reason for the low levels of NO_x during this time period in urban Beijing (Sun et al., 2011). Nitrate and chloride also showed lowest concentrations in the late afternoon, mainly due to the evaporative loss under high temperature conditions (Sun et al., 2012).

Figure 3 (a–b) Average reactivity of N₂O₅ (τ(N₂O₅)⁻¹) and NO₃ (τ(NO₃)⁻¹) for different nights (i.e., P1, P2, P3, and P4). The error bar represents the standard deviation. (c) Variations of the nocturnal τ(N₂O₅) as a function of aerosol surface area density (S_a) and (d) variations of the nocturnal τ(N₂O₅) as a function of relative humidity (RH). The data were binned according to S_a (50 µm² cm⁻³ increment) or RH (5 % increment). Mean (triangle), median (horizontal line), 25 and 75th percentiles (lower and upper box), and 10 and 90th percentiles (lower and upper whiskers) are shown for each bin.

N₂O₅ was rapidly formed after sunset. The mixing ratio of N₂O₅ peaked approximately at 22:00 and then remained at a consistently high level (∼ 200–300 pptv) until 03:00. After that, N₂O₅ showed a rapid decrease due to significant titration by NO. Similar loss of N₂O₅ due to the injection of NO-containing air was also reported at sites near urban areas (Brown et al., 2003b). Because NO is predominantly from local emissions as supported by the tight correlation (R²=0.64–0.73, Fig. S3) with black carbon, a tracer for combustion emissions, our results demonstrated that local NO emissions serve as an important scavenger of N₂O₅ before sunrise in urban Beijing. In comparison, the decrease in N₂O₅ due to NO titration only occurred during the second half of the night with low O₃ in suburban Beijing (Wang et al., 2018). This study also found high N₂O₅ after midnight due to the incomplete titration of O₃, for instance ∼ 52.9 ppbv after midnight on 13 June, which is different from previous findings that high N₂O₅ mixing ratios were typically observed before midnight due to the rapid depletion of O₃ (H. Wang et al., 2017; Z. Wang et al., 2017). The high nocturnal mixing ratios of O₃ and NO₂ (Fig. 2) highlight much higher oxidative capacity at night in summer in urban Beijing compared to the other seasons and/or rural locations.

ClNO₂ showed clear nocturnal formation from heterogeneous processing and decreased rapidly after sunrise, mainly due to photolysis (Fig. 2). Note that ClNO₂ peaked at a similar time (21:00–22:00) as that of N₂O₅ without showing a time lag of 1–3 h as previously observed in Jinan (X. Wang et al., 2017), indicating that either particulate Cl⁻ was sufficient for the heterogeneous reactions or other chlorine sources (e.g., HCl) contributed to the formation of ClNO₂ in urban Beijing. According to previous studies, the partitioning of HCl to particulate Cl⁻ could substantially contribute to ClNO₂ formation at urban sites (Thornton et al., 2010; Riedel et al., 2012). In addition, Wang et al. (2018) also speculated that large particulate chloride during the campaign was possibly replenished by gas-phase HCl due to high emissions from human activities. We also found that ClNO₂ was well correlated with chlorine (Cl₂) derived from IAP-CIMS (R²=0.90–0.99) rather than particulate chloride (Cl⁻) (R²=0.01–0.44) at nighttime, indicating that ClNO₂ might act as an intermediate during the formation of Cl₂ under sufficient chloride conditions (Roberts et al., 2008). Indeed, the much lower particulate Cl⁻ than ClNO₂ also indicated other chlorine sources. Therefore, we need simultaneous measurements to further support such a conclusion in this study, e.g., HCl.

Figure 4 Correlations between ClNO₂ and N₂O₅ for four different nights, i.e., P1, P2, P3, and P4. The data are color coded by the hours since sunset. Also shown are the correlation coefficients and slopes.

3.2 Reactivity of N₂O₅ and NO₃

Considering the time needed to meet the steady-state assumption, only the data 2 h after sunset were used to calculate N₂O₅ steady-state lifetime via Eq. (4) (Wagner et al., 2013). High N₂O₅ reactivity was observed and the average τ (N₂O₅)⁻¹ was 0.16–1.58$\times {\mathrm{10}}^{-\mathrm{2}}$ s⁻¹ during these four nights corresponding to a short nighttime N₂O₅ lifetime between 1.1 and 10.7 min (Fig. 3), with τ(N₂O₅)⁻¹ ranging from 0.20 × 10⁻² to 1.46 × 10⁻² s⁻¹ throughout the campaign. Such values are overall consistent with those measured at surface sites and in the nocturnal residual layer in NCP, for example 1.30 × 10⁻² s⁻¹ in Wangdu (Tham et al., 2016) and 1.30–1.40 × 10⁻² s⁻¹ at Mt. Tai (Z. Wang et al., 2017). In comparison, the N₂O₅ loss is much more rapid than that previously reported in southern China (1–5 h; Brown et al., 2016b) and the USA (a few hours; Wagner et al., 2013), mainly due to the high aerosol loading in NCP leading to an enhanced N₂O₅ sink through both indirect and direct pathways. Correspondingly, the average τ(NO₃)⁻¹ values calculated from the inferred NO₃ were 0.02–0.62 s⁻¹ during the four nights, indicating active NO₃ nighttime chemistry through reactions with NO and VOCs in the polluted nocturnal boundary. Note that P2 and P4 showed comparable p(NO₃) (2.8 vs. 2.6 ppbv h⁻¹; Table 1), yet the N₂O₅ reactivity during P4 (1.58 × 10⁻² s⁻¹) was significantly higher than that during P2 (0.16 × 10⁻² s⁻¹), likely due to the higher NO level, and the enhanced N₂O₅ heterogeneous loss might also be an explanation. Consistently, τ(NO₃)⁻¹ showed similar patterns to τ(N₂O₅)⁻¹. Indeed, the N₂O₅ reactivity presented a nonlinear dependence on aerosol surface area (S_a) and relative humidity (Fig. 3c and d). Although P3 showed much higher RH than P4 (60.5 % vs. 28.0 %), the N₂O₅ reactivity was comparable between P3 and P4 (0.014 vs. 0.016 s⁻¹), illustrating the complex heterogeneous process of N₂O₅.

Figure 5 Box plots of (a) Org ∕ SO₄ ratio, (b) LWC, (c) particulate chloride, (d) particulate nitrate, and (e) ClNO₂∕N₂O₅ ratio for each night, i.e., P1, P2, P3, and P4. The mean (triangle), median (horizontal line), 25 and 75th percentiles (lower and upper box), and 10 and 90th percentiles (lower and upper whiskers) are shown.

Figure 3c shows the N₂O₅ lifetime as a function of surface area density (S_a) with the data being binned according to the 50 µm² cm⁻³S_a increment. τ(N₂O₅) decreased rapidly from 11.8 to 2.2 min as S_a increased up to 500 µm² cm⁻³ and then remained at relatively constant levels at S_a>500 µm² cm⁻³. Such an S_a dependence of τ(N₂O₅) is consistent with previous observations in Hong Kong (Brown et al., 2016b). Large variations in τ(N₂O₅) as a function of RH were also observed. As shown in Fig. 3d, the N₂O₅ lifetime decreased by nearly a factor of 5 from 11.3 to 2.2 min as RH increased from 40 % to 50 %. We noticed that the aerosol surface area exhibits an increase as a function of RH at RH > 40 % (Fig. S4). These results suggested that the decrease in τ(N₂O₅) at high RH levels (RH > 40 %) might be caused by increased N₂O₅ uptake rates due to the higher S_a. In addition, the increasing aerosol liquid water content at high RH might be another reason (Fig. S4). Comparatively, the N₂O₅ lifetime showed an increase as a function of RH at RH < 40 %, while the variations in S_a were small, suggesting additional contributions from other factors, for example aerosol loading and composition (Morgan et al., 2015). Considering that the period of this study is relatively short, long-term measurements are needed in future studies to better characterize the parameterizations of τ(N₂O₅) as a function of S_a and RH.

3.3 Relationship between N₂O₅ and ClNO₂

Previous studies have found that N₂O₅ and ClNO₂ were generally positively correlated in predominantly continental air masses, whereas they were negatively correlated in marine air masses with high chloride content (Bannan et al., 2015). Phillips et al. (2012) also reported large variability in N₂O₅ and ClNO₂ correlations and ClNO₂∕N₂O₅ ratios in air masses from continental or marine origins due to the changes in particle Cl⁻. In this study, ClNO₂ was well and positively correlated with N₂O₅ during all four nights (Fig. 4, R²=0.36–0.78), and only slight changes in ClNO₂∕N₂O₅ ratios were observed after sunset. These results are different from previous observations showing large variability in the correlations (Osthoff et al., 2008), which indicates that there are sufficient chloride sources for ClNO₂ formation during this study period. The differences in regression coefficients among the four nights can be explained by different air masses originating from different regions, which were calculated using the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT; NOAA) model (Draxler and Hess, 1997; Fig. S5). For example, ClNO₂ tracked much better with N₂O₅ after midnight (R²=0.69) than before midnight (R²=0.16) during P2 (Fig. S6), suggesting the influence of air masses from different regions (Fig. S5). Comparatively, P4 and P1 showed similar tight correlations between ClNO₂ and N₂O₅ before and after midnight, consistent with their similar back trajectories during the two different periods.

The ClNO₂∕N₂O₅ ratios varied significantly throughout the study ranging from 0.3 to 95.5 (30 min average). The average (±1σ) ratio of ClNO₂∕N₂O₅ was 6.9±7.4, consistent with previous studies in NCP, for example 0.4–131.3 in Jinan and Wangdu (X. Wang et al., 2017; Tham et al., 2016). However, the ratios are substantially higher than those measured in other megacities, e.g., Hong Kong (0.1–2.0; Wang et al., 2016), London (0.02–2.4; Bannan et al., 2015), and Los Angeles, California (0.2–10.0; Mielke et al., 2013). These results indicate ubiquitously high ClNO₂∕N₂O₅ ratios in the NCP, consistent with another measurement in suburban Beijing (Wang et al., 2018), which might result from the high ClNO₂ production rate due to high aerosol loadings. We also note that the relatively low N₂O₅ associated with high N₂O₅ reactivity might be another possible explanation. Furthermore, we compared the ClNO₂∕N₂O₅ ratios with particulate concentrations and compositions during the four nights (Fig. 5). P3 showed the highest median ratio of 9.4, which is much higher than during the other three nights (1.0–3.2). This can be explained by the correspondingly high liquid water content that facilitated N₂O₅ heterogeneous uptake (Morgan et al., 2015). In comparison, the particle chloride concentrations were relatively close during the four nights, with slightly lower concentrations during P4, further supporting the fact that the ClNO₂∕N₂O₅ ratios were independent of particle chloride in this study due to the sufficient chloride source for ClNO₂ production, e.g., HCl gas–particle partitioning. The lower ClNO₂∕N₂O₅ ratios during P2 compared with P1 can be explained by the “nitrate effect”, which suppressed N₂O₅ uptake (Mentel and Wahner, 1999) as P2 showed much higher nitrate concentrations than P1 (4.2 vs. 1.4 µg m⁻³). Note that the ClNO₂∕N₂O₅ ratios were also characterized by a dependence on Org ∕ SO₄ ratios in our campaign, similar to other studies (Evans and Jacob, 2005; Riemer et al., 2009).

Figure 6 Time series of meteorological parameters (RH, T), particulate nitrate (NO${}_{\mathrm{3}}^{-})$, mixing ratios of N₂O₅ and ClNO₂, and aerosol surface area density (S_a) for the selected periods on three nights. The black solid lines are the predicted integration concentrations of NO${}_{\mathrm{3}}^{-}$ and ClNO₂ calculated using the estimated method.

3.4 N₂O₅ uptake coefficient and ClNO₂ production yield

To quantity the relative contributions of different pathways to N₂O₅ loss, three periods with relatively stable air masses and concurrent increases in ClNO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. 6; 20:00–23:00 on 12 June, 20:00–00:00 on 13 June, and 20:00–22:30 on 14 June) were selected for the calculations of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø. A rigorous method as suggested by Phillips et al. (2016) was used in this study. Briefly, the predicted concentrations of ClNO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ were derived by integrating pClNO₂ and p${\mathrm{NO}}_{\mathrm{3}}^{-}$ with average S_a and N₂O₅ over each time step (∼ 15 min) and initial estimations for ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø. The integration was repeated by changing ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø until good agreements between observed and predicted values of ClNO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ were reached. The derived heterogeneous uptake coefficient, ClNO₂ yield, and N₂O₅ loss rate k_d following this method are listed in Table 2.

Table 2 Estimated uptake coefficient of N₂O₅, ClNO₂ production yield, and related parameters for the selected periods on three nights.

The estimated ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values for the three selected periods were 0.017–0.09, which was generally comparable to previous values (0.014–0.092) derived from the steady-state assumption method in the NCP (H. Wang et al., 2017; X. Wang 2017; Z. Wang et al., 2017; Tham et al., 2016) and also consistent with recent measurements (0.012–0.055) using the same method in suburban Beijing (Wang et al., 2018). However, the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ determined in our campaign was 1–2 orders of magnitude higher than obtained in the laboratory (Thornton et al., 2003) and also much higher than those in Hong Kong and Germany (Brown et al., 2016b; Phillips et al., 2016). We also found that the parameterized ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values (0.0014–0.012) determined from Eq. (9) (the Bertram–Thornton parameterization) were significantly lower than the observed values, suggesting that more field measurements are needed to improve the parameterization schemes. Note that ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values appeared to increase with rising relative humidity, which was also observed at other sites (X. Wang et al., 2017; Thornton et al., 2003). For example, ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values increased from 0.019 to 0.090 when RH increased from 21.1 % to 63.6 %. However, the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values were comparable at low RH levels (<40 %; 0.019 vs. 0.017 in Table 2) although RH differed by a factor of 2 (21 % vs. 40 %). These results further supported the fact that the influences of hygroscopic growth on ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ were mainly caused by increasing aerosol liquid water content. The direct N₂O₅ loss rates estimated from the uptake coefficient were in the range of 0.00044–0.0034 s⁻¹, which contributed 7–33 % to the total N₂O₅ loss with the rest being indirect loss. The uncertainty of the direct N₂O₅ loss rate contributions is estimated to be ∼ 40 %, associated with S_a (∼ 30 %), O₃ and NO₂ (∼ 5 %), and N₂O₅ (∼ 17 %). Our results indicated that the fast N₂O₅ loss in the nocturnal boundary in urban Beijing was predominantly from the indirect loss of NO₃ rather than the heterogeneous uptake of N₂O₅, mainly due to active NO₃ reaction in summer. Such a conclusion was different from previous results in autumn in Beijing that found N₂O₅ loss to be dominated by N₂O₅ heterogeneous hydrolysis (69.1 %–98.8 %; H. Wang et al., 2017). Several studies also revealed the importance of heterogeneous N₂O₅ uptake in N₂O₅ loss in the NCP by using steady-state-derived ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (Tham et al., 2016; X. Wang et al., 2017; Z. Wang et al., 2017). While the uncertainties in different analysis methods, e.g., due to product formation rates or the steady-state assumption, the high NO concentration could be an important reason for the dominant N₂O₅ loss pathway. The higher VOC emissions, particularly biogenic emissions (e.g., isoprene and terpene), in summer than in other seasons might be another reason for the differences in the dominant N₂O₅ loss pathway. Indeed, indirect N₂O₅ loss via NO₃ + VOCs was also found to dominate the total loss of N₂O₅ (67 %) in summer in suburban Beijing (Wang et al., 2018). Our results highlight significant nighttime NO_x loss through reactions of NO₃ with VOCs in summer in urban Beijing.

The ClNO₂ yields ø derived for the three cases were 0.35, 0.10, and 0.15, respectively. The production yields in this study are substantially larger than those in urban Jinan (0.014–0.082; X. Wang et al., 2017), yet comparable to those reported at Mt. Tai (0.02–0.90; Z. Wang et al., 2017) and continental Colorado (0.07–0.36; Thornton et al., 2010). However, the significantly lower ø than that in suburban Beijing (0.50–1.0; X. Wang et al., 2017) indicated more effective ClNO₂ production in suburban regions than urban regions to some extent. Indeed, the product of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ø (${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\times \mathit{ø})$ in this study ranged from 0.006–0.009 and was much lower than in X. Wang et al. (2017; 0.008–0.035). We noticed that ø values were much lower than those parameterized from Eq. (10) (0.55–0.97), indicating that the Bertram–Thornton parameterization scheme might overestimate the ClNO₂ yield substantially. Note that ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ might be overestimated, associated with an underestimation of ø if assuming particulate nitrate is completely from N₂O₅ heterogeneous uptake. Possible contribution from gas-phase HNO₃ repartitioning to the particulate phase was not considered, mainly due to the lack of observational data for HNO₃ and NH₃. Indeed, a recent study found that the nocturnal nitrate formation potential by N₂O₅ heterogeneous uptake was comparable to that formed by gas-phase HNO₃ repartitioning in Beijing (H. Wang et al., 2017). In addition, ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\times \mathit{ø}$ was higher on 13 June than the other two days (e.g., 0.009 vs. 0.003–0.006), which might explain the correspondingly higher ClNO₂∕N₂O₅ ratio on this day (on average 8.2 vs. 1.2–1.4). Our results overall suggest fast heterogeneous N₂O₅ uptake and a high ClNO₂ production rate in summer in urban Beijing, which might have great implications for models to improve simulations for nocturnal nitrate and daytime ozone.

4 Conclusions

We present the simultaneous measurement of gas-phase N₂O₅ and ClNO₂ by I-CIMS during the APHH summer campaign to investigate the nocturnal chemistry in urban Beijing. The average (±1σ) mixing ratios of N₂O₅ and ClNO₂ were 79.2±157.1 and 174.3±262.0 pptv, with maximum values of 1.17 and 1.44 ppbv, respectively. Differing from previous studies with negligible N₂O₅ after midnight at surface level, our measurements showed high nocturnal levels of N₂O₅ across the entire night, suggesting a high oxidative capacity in summer in urban Beijing. N₂O₅ and ClNO₂ exhibited clear diurnal variations with significant nocturnal formation due to heterogeneous uptake. The average nighttime nitrate radical production rate p(NO₃) was 2.6±2.4 ppbv h⁻¹, and the τ(N₂O₅)⁻¹ was in the range of 0.20–$\mathrm{1.46}\times {\mathrm{10}}^{-\mathrm{2}}$ s⁻¹, corresponding to a nighttime N₂O₅ lifetime of 1.1–10.7 min. We also observed a decrease in τ(N₂O₅) under high relative humidity (RH > 40 %) conditions due to higher N₂O₅ uptake rates with higher available surface area and liquid water content. N₂O₅ and ClNO₂ were positively correlated, although the ClNO₂∕N₂O₅ ratios changed significantly from 0.3 to 95.5. The high ClNO₂∕N₂O₅ ratios in this study might result from a high ClNO₂ production rate and fast N₂O₅ loss due to the sufficient chloride source supply.

The N₂O₅ uptake coefficients estimated on the basis of the product formation rates of ClNO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ were 0.017–0.09 in this study. Correspondingly, the direct N₂O₅ loss rates via heterogeneous uptake were in the range of 0.00044–0.0034 s⁻¹, contributing 7 %–33 % to the total N₂O₅ loss. Our results indicated that fast N₂O₅ loss in the nocturnal boundary in urban Beijing was mainly due to indirect pathways through NO₃ reactions with NO and VOCs rather than the heterogeneous uptake of N₂O₅. We also noticed that the derived ClNO₂ production yields (0.10–0.35) were substantially lower than those from the Bertram–Thornton parameterization, indicating that future studies are needed to address these discrepancies.