Nitrate formation from heterogeneous uptake of dinitrogen pentoxide during a severe winter haze in southern China

Nitrate (${\mathrm{NO}}_{\mathrm{3}}^{-}$) has become a major component of fine particulate matter (PM_2.5) during hazy days in China. However, the role of the heterogeneous reactions of dinitrogen pentoxide (N₂O₅) in nitrate formation is not well constrained. In January 2017, a severe haze event occurred in the Pearl River Delta (PRD) of southern China during which high levels of PM_2.5 (∼400 µg m⁻³) and O₃ (∼160 ppbv) were observed at a semi-rural site (Heshan) in the western PRD. Nitrate concentrations reached 108 µg m⁻³ (1 h time resolution), and the contribution of nitrate to PM_2.5 was nearly 40 %. Concurrent increases in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ClNO₂ (with a maximum value of 8.3 ppbv at a 1 min time resolution) were observed in the first several hours after sunset, indicating an intense N₂O₅ heterogeneous uptake by aerosols. The formation potential of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ via N₂O₅ heterogeneous reactions was estimated to be between 29.0 and 77.3 µg m⁻³ in the early hours (2 to 6 h) after sunset based on the measurement data, which could completely explain the measured increase in the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration during the same time period. Daytime production of nitric acid from the gas-phase reaction of OH+NO₂ was calculated with a chemical box model built using the Master Chemical Mechanism (MCM v3.3.1) and constrained by the measurement data. The integrated nocturnal nitrate formed via N₂O₅ chemistry was comparable to or even higher than the nitric acid formed during the day. This study confirms that N₂O₅ heterogeneous chemistry was a significant source of aerosol nitrate during hazy days in southern China.

1 Introduction

Severe haze in China has been a major concern of the regulatory and scientific communities in recent years. Nitrate has also been identified as an important component of PM_2.5 during hazy days in both summer and winter (e.g., Huang et al., 2014; Li et al., 2018; Pathak et al., 2009; Zhang et al., 2015). Moreover, the proportion of nitrate in PM_2.5 has steadily increased over the last decade due to the lagged control of NO_x emissions compared to SO₂ (Fu et al., 2014; Geng et al., 2017; Qu et al., 2017; Reuter et al., 2014; X. Wang et al., 2016). As a result, the concentrations of nitrate in PM_2.5 ∕ PM_1.0 have been even higher than those of sulfate during some haze events (Ge et al., 2017; Li et al., 2017; Liu et al., 2015; Yang et al., 2017; Yue et al., 2015).

Nitrate is formed from NO_x during both the daytime and nighttime. During the day, nitric acid (HNO₃) is produced through the gas-phase reaction between OH and NO₂ (Reaction R1), while this pathway is insignificant at night due to very low OH concentrations (e.g., Seinfeld and Pandis, 2016). Nitric acid can react with ammonia (NH₃) to form ammonium nitrate (NH₄NO₃), and an equilibrium can be reached for these three compounds between the gas phase and the particle phase (Reactions R2, R3). During nighttime, the heterogeneous uptake of N₂O₅, which is formed from reactions involving O₃, NO₂, and NO₃, becomes a source of nitrate and also produces gaseous ClNO₂ when chloride-containing aerosol is present (Reactions R4–R7; Finlayson-Pitts et al., 1989). This nitrate formation pathway is only important at night due to the fast photolysis of NO₃ during the day. Compared to the relatively well-understood formation of aerosol nitrate via the OH+NO₂ reaction, the contribution from N₂O₅ heterogeneous reactions has been poorly quantified due to the limited knowledge of key factors controlling the heterogeneous processes, such as the N₂O₅ uptake coefficient (${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) and ClNO₂ yield (${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$) (Brown and Stutz, 2012; Chang et al., 2011).

$$\begin{array}{ll}\text{(R1)}& {\displaystyle }& {\displaystyle }\mathrm{OH}+{\mathrm{NO}}_{\mathrm{2}}+\mathrm{M}\to {\mathrm{HNO}}_{\mathrm{3}}+\mathrm{M}\text{(R2)}& {\displaystyle }& {\displaystyle }{\mathrm{HNO}}_{\mathrm{3}}\left(g\right)+{\mathrm{NH}}_{\mathrm{3}}\left(g\right)\leftrightarrow {\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}\left(s\right)\text{(R3)}& {\displaystyle }& {\displaystyle }{\mathrm{HNO}}_{\mathrm{3}}\left(g\right)+{\mathrm{NH}}_{\mathrm{3}}\left(g\right)\leftrightarrow {\mathrm{NH}}_{\mathrm{4}}^{+}\left(\mathrm{aq}\right)+{\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{aq}\right)\text{(R4)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{3}}\text{(R5)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+M\leftrightarrow {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M\text{(R6)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{VOCs}\to \mathrm{products}{\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\text{or}{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)\\ \text{(R7)}& {\displaystyle }& {\displaystyle }\to (\mathrm{2}-\mathit{\varphi }){\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{aq}\right)+\mathit{\varphi }{\mathrm{ClNO}}_{\mathrm{2}}\left(g\right)\end{array}$$

Model studies initially treated ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ as a constant (0.03 to 0.1) (Dentener and Crutzen, 1993; Makar et al., 1998; Munger et al., 1998; Schaap et al., 2004; Wen et al., 2015; Xue et al., 2014), and later utilized several parameterization schemes of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ based on laboratory investigations of their dependence on aerosol composition and aerosol water content (Anttila et al., 2006; Bertram and Thornton, 2009; Davis et al., 2008; Evans and Jacob, 2005; Riemer et al., 2003, 2009; Roberts et al., 2009). However, recent studies have found a significant discrepancy between the field-derived and the parameterized ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ (McDuffie et al., 2018; Phillips et al., 2016; Tham et al., 2018; X. Wang et al., 2017; Z. Wang et al., 2017; Zhou et al., 2018). These findings suggest that N₂O₅ uptake is more complicated than previously thought, and a better understanding of the uptake process is needed to improve the prediction of nitrate and haze.

In addition to the modeling approach, field measurements of trace gases and aerosol composition have been used to infer the contribution of N₂O₅ heterogeneous chemistry to nitrate formation. Pathak et al. (2009) postulated the importance of N₂O₅ heterogeneous reactions with respect to the high aerosol nitrate observed in Beijing and Shanghai in summertime by examining the variation of nitrate with the change in relative humidity (RH) and the equilibrium between anions and cations in PM_2.5. Pathak et al. (2011) further investigated nitrate formation using a coupled aqueous phase radical mechanism (CAPRAM) and a gas-phase chemistry mechanism (RACM, without ClNO₂chemistry). By constraining the uptake coefficient of N₂O₅ in the range from 0.001 to 0.1, they reproduced the observed enhancement of nitrate and suggested that N₂O₅ uptake by aerosols contributed to 50 % to 100 % of the nighttime increase in nitrate. A similar method was recently used by Wen et al. (2018) to simulate the summertime nitrate formation in the North China Plain (NCP), which demonstrated the dominant contribution of N₂O₅ heterogeneous reactions to nighttime nitrate formation. Based on the observed covariation of nitrate and RH, Wang et al. (2009) speculated that N₂O₅ reactions dominated the nitrate formation on polluted days with high NO₂ and O₃ concentrations in Shanghai. Neither N₂O₅ nor ClNO₂ was measured during these early observation-based studies. A recent study (H. Wang et al., 2017) inferred ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ from the measured N₂O₅ on 4 days in urban Beijing and estimated the lower limit of the formation potential of aerosol nitrate assuming a unity ϕ_ClNO2 because ClNO₂was not measured. Their result showed a comparable contribution to nitrate formation from the N₂O₅ heterogeneous chemistry and from the daytime pathway of the OH+NO₂ reaction.

In the present study, N₂O₅, ClNO₂, and the related chemical and meteorological parameters were measured at a semi-rural site in the Pearl River Delta of southern China from 2 to 15 January 2017. A severe haze event was observed during the field study with PM_2.5 reaching 400 µg m⁻³ and O₃ peaking at 160 ppbv. ClNO₂, which is only known to be produced from N₂O₅ heterogeneous uptake, reached 8.3 ppbv, which is the largest reported value to date and revealed extremely active N₂O₅ chemistry during the abovementioned episode. The concurrent measurements of N₂O₅, ClNO₂, and aerosol nitrate provide better constraints for elucidating nighttime NO₃ ∕ N₂O₅ chemistry and aerosol nitrate formation. An overview of the measurement data was first presented. The nighttime processes that led to the formation of nitrate (e.g., the production of NO₃ and N₂O₅, N₂O₅ uptake coefficient, and ClNO₂ yield) were analyzed. The nighttime formation potential of nitrate was estimated based on these data and compared to the measured increase in nitrate. The daytime production of nitric acid via the OH+NO₂ reaction was calculated based on a box model using the Master Chemical Mechanism (MCM v3.3.1) and compared to the nighttime formation potential of nitrate.

Figure 1 (a) Google map images of the Pearl River Delta in Guangdong Province and the measurement site (Hua Guo Shan). (b) The topography and major roads (shown by number) adjacent to the measurement site.

2 Methods

2.1 Site description

The field observation was conducted at the Guangdong atmospheric supersite, a semi-rural site located at Hua Guo Shan (HGS, 22.728^∘ N, 112.929^∘ E) southwest of the city of Heshan from 2 to 15 January 2017. As shown in Fig. 1, HGS is a hill with a height of 60 m a.s.l. All measurement instruments were located on the fourth floor of a four-story building on the top of the hill. The observation site was located in the western PRD where the economic activity and population density are much lower than the central PRD. There are five main roads near the HGS site, including three national roads (G325, G94, and G15), and two provincial roads (S272 and S270). The hill is covered by subtropical trees and surrounded by similar hills within close proximity; a few residents live at the foot of the hill, and there is some farmland in the area.

2.2 Chemical ionization mass spectrometer

N₂O₅ and ClNO₂ were simultaneously observed using a quadrupole chemical ionization mass spectrometer (CIMS, THS Instruments, Atlanta). The same instrument had been used in several previous studies in southern and northern China (Tham et al., 2016; T. Wang et al., 2016; Z. Wang et al., 2017). The reader can refer to these earlier papers for a detailed description of the measurement principle, calibration, and maintenance procedures. Briefly, ambient N₂O₅ and ClNO₂ are converted to ion clusters of I(N₂O₅)⁻ and I(ClNO₂)⁻ by Iodide ions (I⁻) that are produced by exposing CH₃I ∕ N₂ (0.3 % v∕v) to an alpha radioactive source, 210-Po, and are subsequently detected at 235 and 208 m z⁻¹, respectively. Activated carbon packed in a filter was used to determine the instrument background, which were 10.2±2.2 and 8.9±2.0 Hz on average for N₂O₅ and ClNO₂, respectively. In situ offline calibration was carried out every day for N₂O₅ and every 2 days for ClNO₂ by mixing the respective synthetic standard into humidified zero air (with RH controlled at 60 % in the present study). The N₂O₅ standard was generated by reacting excess NO₂ with O₃ and determined from the decrease of NO₂, and the ClNO₂ was synthesized by the uptake of a known concentration of N₂O₅ on a NaCl slurry (see T. Wang et al., 2016 and Tham et al., 2016 for details). The average sensitivity of N₂O₅ and ClNO₂ was 0.9±0.3 and 0.7±0.2 Hz pptv⁻¹, respectively. The dependence of the sensitivity on the relative humidity was measured during the field study (see Fig. S1) and was used to correct for the RH effect based on the measured ambient RH values. The detection limits of N₂O₅ and ClNO₂ were both 6 pptv (2σ, 1 min-averaged data).

The inlet of the CIMS instrument was set approximately 1.5 m above the roof with 6 m long PFA-Teflon tubing as the sampling line. The total sampling flow was set as 11 standard liters per minute (SLPM). Four SLPM were diverted into the CIMS, the O₃ analyzer, and NO_x analyzer, and the remaining part was evacuated directly from the system. The total residence time was less than 1 s in the sampling system. Following our previous practice, the inlet tubing and fittings were replaced every afternoon and washed in an ultrasonic bath to reduce the influence of particle deposition on the tubing wall. The loss of N₂O₅ on the tubing wall was checked on site by injecting N₂O₅ into the ambient air before and after the tubing replacement; the loss was found to be around 10 % in the“clean” tubing and nearly 40 % by the next afternoon. Because our analysis mainly focused on data from the first few hours of evening, the loss was insignificant and thus was not corrected in our final data. However, this bias could be important in the later period before tube replacement. The uncertainty of the measurement was estimated to be ±25 % for both N₂O₅ and ClNO₂ (T. Wang et al., 2016). The time resolution for the measurement was approximately 10 s, and the derived data were later averaged to a time resolution of 1 min for further analysis.

Table 1 Technique, limit of detection, and uncertainty of measuring instruments for trace gases and aerosols.

2.3 Other measurements

Trace gases of CO, SO₂, O₃, NO_x, total reactive nitrogen (NO_y), nitrous acid (HONO), C2 to C10 non-methane hydrocarbons (NMHCs), oxygenated hydrocarbons (OVOCs), and aerosol chemical composition and number concentrations were also measured. Table 1 summarizes the principle, detection limit and uncertainty of the measuring instruments.

CO was observed using a gas filter correlation analyzer (Thermo Scientific, Model 48i). SO₂ was measured using a pulsed fluorescence analyzer (Thermo Scientific, Model 43i). O₃ was determined using a UV photometric analyzer (Thermo Scientific, Model 49i). NO and NO₂ were detected with a chemiluminescence instrument (Thermo Scientific, Model 42i) with a photolytic converter to convert NO₂ to NO (Xu et al., 2013). NO_y was determined using a chemiluminescence analyzer which was equipped with a molybdenum oxide (MoO) catalytic converter (Thermo Scientific, Model 42i-Y). HONO was detected using a long path absorption photometer (QUMA, Model LOPAP-03) (Xu et al., 2015). NMHCs were determined using an online gas chromatograph (GC) coupled with a flame ionization detector (FID) and a mass spectrometer (MS) (Wang et al., 2014). NMHCs were only measured from 2 to 8 January 2017 due to the maintenance of the GCMS after 8 January. OVOCs (e.g., formaldehyde, acetaldehyde, acetone, and methyl ethyl ketone) were sampled using 2,4-dinitrophenylhydrazine (DNPH) cartridges every 3 h and were later analyzed with a high-performance liquid chromatography (HPLC) system (Cui et al., 2016).

Concentrations of PM_2.5 were detected with a multi-angle absorption photometer (MAAP; Thermo Scientific, Model 5012). The ionic compositions of PM_2.5 were measured with an ion chromatography (GAC-IC) system equipped with a gas and aerosol collector at a time resolution of 30 min (Dong et al., 2012), and the data were also averaged every 1 h to meet the time resolution of other components of PM_2.5. Organic carbon (OC) and elemental carbon (EC) were measured using an online OC ∕ EC analyzer (RT-4, SUNSET) with a time resolution of 1 h (Bauer et al., 2009). A scanning mobility particle sizer (SMPS Model 3936L75, TSI) was used to determine the dry-state particle number size distribution, covering the size range from 16.5 to 1000 nm. The ambient (wet) particle number size distributions were estimated based on a size-resolved kappa-Köhler function considering the variation with relative humidity (Hennig et al., 2005; Liu et al., 2014). In the present study, data with a RH greater than 90 % were excluded due to the large uncertainty of the growth factor at very high RH. The aerosol surface area density was then derived using the ambient particle number size distribution (wet) and an assumption of spherical particles with an estimated uncertainty of around 30 % (Tham et al., 2016; Z. Wang et al., 2017).

Meteorological parameters were measured with a portable weather station (WXT520, Vaisala, Finland), including temperature, relative humidity (RH), wind direction, wind speed, and pressure. A pyranometer (CMP22, Kipp & Zonen B.V., Holland) was used to measure the solar radiation, and the data were then utilized to derive the photolysis frequency of NO₂ based on the method of Trebs et al. (2009).

2.4 Chemical box model

To estimate the daytime formation of nitric acid via the reaction of OH+NO₂, an observation-based chemical box model developed with the latest version of the MCM (v3.3.1) (Jenkin et al., 2003, 2015; Saunders et al., 2003) and an updated chlorine (Cl) radical chemistry module (Xue et al., 2015) was utilized to estimate the mixing ratio of OH radicals and the reaction rate of OH+NO₂. The integrated production of nitric acid during daytime was then calculated based on the simulation results. The box model was constrained with the observation data every 10 min, including the data relating to N₂O₅, ClNO₂, HONO, O₃, NO, NO₂, SO₂, CO, C2 to C10 NMHCs, OVOCs (formaldehyde, acetaldehyde, acetone, and MEK), temperature, aerosol surface area density, and J(NO₂), which were first averaged or interpolated. Average concentrations of NMHC species during the day (07:00 to 17:00) and at night (17:00 to 07:00 of the next day) are shown in Table S1. A function considering the variation of the solar zenith angle (Saunders et al., 2003) was used to calculate the photolysis frequencies of HONO, O₃, and other species in clear sky, which were then corrected with the J(NO₂) values in the real environment. The J(ClNO₂) was treated the same as in Tham et al. (2016). The lifetime of unconstrained species with respect to the physical loss was set as 8 h in a boundary layer with a depth of 1000 m (equivalent to $\mathrm{3.47}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹) in order to avoid their accumulation. The model was run from 00:00 on 3 January to 11:00 on 8 January 2017. To stabilize the intermediate species, the simulation for the first 24 h was repeated six times. Sensitivity tests were carried out by reducing the input concentrations by 10 % to check the deviation of the average daytime (07:00–17:00) rate of the OH+NO₂ reaction. The simulated rate of the OH+NO₂ reaction was most sensitive to HONO, followed by NO_x and OVOCs (see Sect. S1 and Fig. S2 in the Supplement).

Figure 2 Time series of N₂O₅, ClNO₂, components of PM_2.5, and related trace gases and meteorological parameters from 18:40 on 2 January to 11:00 on 15 January 2017. The inset figure shows the variation of the ratio of nitrate to PM_2.5 with an increasing nitrate concentration. The green rectangles in the figure indicate the five days used for detailed analysis.

Figure 3 (a) Surface weather chart at 08:00 LT on 6 January 2017, downloaded from the Hong Kong Observatory website, indicating stagnant conditions. (b) The distribution of PM_2.5 concentrations in the PRD region at 09:00 LT on 6 January 2017. This figure was captured from the following website: http://113.108.142.147:20031/GDPublish/publish.aspx (last access: 17 November 2018).

3 Results and discussion

3.1 Overview of the observation

Figure 2 shows the time series of N₂O₅, ClNO₂, components of PM_2.5, and related trace gases and meteorological parameters from 18:40 on 2 January to 11:00 on 15 January 2017. The average temperature and RH values during the measurement period were 17±4^∘C and 86±14 %, respectively. A severe pollution episode occurred from 3 to 7 January due to stagnant meteorological conditions (Fig. 3a), and the concentrations of most pollutants decreased to very low levels on 9 January and from 12 to 15 January, which corresponded to the change in weather conditions. The most polluted days were 5 and 6 January with the highest PM_2.5 value of 400 µg m⁻³ and the highest O₃ concentration of 160 ppbv. The PM_2.5 data from the PRD regional air quality monitoring network revealed that the HGS site was within the most polluted area during this haze event (Fig. 3b). This pollution event was characterized by concurrent high levels of PM_2.5 and O₃ and was in contrast to the winter haze in north China, which experienced high PM_2.5 values but low O₃ concentrations (e.g., Sun et al., 2016; H. Wang et al., 2018a). The mixing ratios of N₂O₅ and ClNO₂ were up to 3358 and 8324 pptv (1 min time resolution), respectively, indicating active N₂O₅ heterogeneous chemistry.

Figure 4 The covariance of aerosol nitrate and ClNO₂ in the early nighttime (at a 30 min time resolution) for four nights.

Figure 5 Variation of N₂O₅, ClNO₂, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, and trace gases and meteorological conditions during the night from 4 to 5 January 2017 as an example from the five selected nights.

Very high concentrations of aerosol nitrate (up to 108 µg m⁻³; 1 h time resolution) were also observed during the multi-day episode. Nitrate contributed to 24 % of the total PM_2.5 mass concentration on average, which was comparable to that of organic matter ($\mathrm{OM}=\mathrm{1.7}\cdot \mathrm{OC}$, 28 %) and much higher than that of sulfate (16 %) and ammonium (11 %). The contribution of nitrate to the PM_2.5 increased with an increase in the nitrate concentration, and reached nearly 40 % at its peak, indicating that nitrate was a dominant component of the PM_2.5 on the most polluted days. The concentration of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ exhibited a concurrent increase with that of ClNO₂ in the early nighttime from 3 to 4, 4 to 5, 5 to 6, and 9 to 10 January (see Fig. 4), suggesting that N₂O₅ heterogeneous reactions significantly contributed to the formation of nitrate during the night. The measured increases of the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration during these four nights were 17.1, 50.9, 43.3, and 32.7 µg m⁻³, respectively. A similar increase in ClNO₂ was observed from 6 to 7 January, but the composition of the PM_2.5 was not available due to instrument maintenance. Apart from chemical reactions, the evolution of the planetary boundary layer (PBL) also affects the concentrations of trace gas and aerosols. The height of PBL generally decreases after sunset due to the fast decrease in the land temperature, which can lead to the accumulation of primary pollutants (and secondary pollutants) at the surface if significant local sources are present. For example, on the night from 4 to 5 January (see Fig. 5), the CO and NO_y levels increased between 18:00 and 19:00 LT with the enhancement of ClNO₂ and nitrate, indicative of an accumulation of primary emissions; however, after this period of time the primary pollutants decreased for 3 h while ClNO₂ and nitrate continued to increase due to the nighttime chemical process.

In the remainder of this paper, we will focus on the detailed analysis of the abovementioned five nights to investigate the role of N₂O₅ heterogeneous chemistry in nitrate formation.

3.2 N₂O₅ heterogeneous chemistry on the selected nights

3.2.1 Production of NO₃ and N₂O₅

The first step in the nighttime nitrate formation via N₂O₅ chemistry is the production of NO₃ and N₂O₅. To gain insight into the key factors affecting the NO₃ ∕ N₂O₅ chemistry, the variation of N₂O₅ and the production rate of NO₃ were examined in relation to some relevant gases and meteorological parameters on the selected five nights. Figure 5 shows the data for the night from 4 to 5 January as an example. Some common features were identified for all five nights. In general, low wind speed (<2.0 m s⁻¹) at night facilitated the accumulation of air pollutants, and high RH was favorable for N₂O₅ heterogeneous uptake. In addition, high aerosol surface area density provided interfaces for N₂O₅ heterogeneous reactions.

In the first couple of hours after sunset (Fig. 5, red rectangle), N₂O₅ exhibited a peak and then quickly dropped to hundreds of pptv, while nitrate and ClNO₂ concurrently increased, which was indicative of the local production and loss of N₂O₅. NO was below the detection limit during this period. The production rates of NO₃ ($P_{{\mathrm{NO}}_{\mathrm{3}}}=k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right])$ were the fastest just after sunset and decreased gradually due to reduced O₃ levels. There was a period later in the night (22:00 to 01:00) when fresh emissions of NO were observed, and the production of NO₃ was suppressed due to the titration of O₃ by NO. In the later nighttime, NO was below the detection limit (Fig. 5, blue rectangle). During this period, NO₃ and N₂O₅ were produced at moderate rates, and the very low N₂O₅ concentrations (below the detection limit) suggested a fast loss of N₂O₅ probably leading to the local production of ClNO₂ and nitrate, which was not revealed in the observed variations of ClNO₂ and nitrate. The concentrations of ClNO₂ and nitrate during this period fluctuated due to the change in the air masses indicated by the change in SO₂ concentrations and wind speeds.

3.2.2 The N₂O₅ uptake coefficient and ClNO₂ yield

The N₂O₅ uptake coefficient and ClNO₂ yield, in combination with the reactivity of NO₃ with NO and VOCs, determines the loss pathways of NO₃ and N₂O₅. To derive the uptake coefficient of N₂O₅, a method suggested by McLaren et al. (2010) was applied which treated NO₃ and N₂O₅ as a whole ([NO₃]+[N₂O₅]) without assuming that the chemical system was in a steady state. This approach considers that the change of NO₃ and N₂O₅ concentrations is mainly due to NO₃ ∕ N₂O₅ chemistry; thus, it requires that the air mass has relatively stable chemical conditions and is not subject to fresh NO emissions. It also requires that ClNO₂ is produced from the N₂O₅ chemistry and has an increasing trend to derive the yield of ClNO₂. This method is applicable for the early nighttime (Fig. 5, red rectangle; Sect. 3.2.1) for these five nights.

The variation rate of [NO₃]+[N₂O₅] can be calculated by deducting the production rate of [NO₃]+[N₂O₅] with its loss rate as follows:

$$\begin{array}{}\text{(1)}& {\displaystyle \frac{\mathrm{d}\left(\right[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}]+[{\mathrm{NO}}_{\mathrm{3}}\left]\right)}{\mathrm{d}t}}=P_{{\mathrm{NO}}_{\mathrm{3}}}-L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{NO}}_{\mathrm{3}}}\end{array}$$

Table 2 Average N₂O₅ concentration values, N₂O₅ uptake coefficients, ClNO₂ yields, and other related parameters and maximum ClNO₂ concentration values in the early nighttime for the five selected nights.

The loss of [NO₃]+[N₂O₅] is via the reaction of NO₃ with VOCs and N₂O₅ heterogeneous reactions, which can both be expressed as pseudo-first-order losses:

$$\begin{array}{ll}{\displaystyle }{L}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{NO}}_{\mathrm{3}}}& {\displaystyle }=L_{{\mathrm{NO}}_{\mathrm{3}}}+L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\\ \text{(2)}& {\displaystyle }& {\displaystyle }={k^{\prime }}_{{\mathrm{NO}}_{\mathrm{3}}}\left[{\mathrm{NO}}_{\mathrm{3}}\right]+{k^{\prime }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right],\end{array}$$

where $k_{{\mathrm{NO}}_{\mathrm{3}}}^{\prime }$ and $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}^{\prime }$ represent the total first-order rate constants for NO₃ and N₂O₅, respectively. The loss rate of N₂O₅ can then be obtained from Eq. (3):

$$\begin{array}{ll}{\displaystyle }{L}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}& {\displaystyle }=k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}^{\prime }\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]=k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\\ \text{(3)}& {\displaystyle }& {\displaystyle }-{\displaystyle \frac{\mathrm{d}\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{\mathrm{d}t}}-{\displaystyle \frac{\mathrm{d}\left[{\mathrm{NO}}_{\mathrm{3}}\right]}{\mathrm{d}t}}-k_{{\mathrm{NO}}_{\mathrm{3}}}^{\prime }\left[{\mathrm{NO}}_{\mathrm{3}}\right]\end{array}$$

Because NO₃ was not measured, it was calculated by assuming an equilibrium of NO₂–NO₃–N₂O₅ as shown in Eq. (4). High levels of NO would break this equilibrium. Thus, the periods with detected NO were excluded. d[NO₃] ∕ dt and d[N₂O₅] ∕ dt were calculated as the rate of change of NO₃ and N₂O₅, respectively, at a time resolution of 10 min. $k_{{\mathrm{NO}}_{\mathrm{3}}}^{\prime }$ was derived using the measured concentrations of NMHCs as in Eq. (5) by interpolating the data of the NMHCs to a 10 min time resolution. The NO₃ reactivity with VOCs ($k_{\mathrm{NO}\mathrm{3}}^{\prime }$) in the early nighttime ranged from 0.516 to $\mathrm{1.54}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ (Table 2), which was higher than those derived at Mt. TMS in winter 2013 (0.17 to $\mathrm{1.1}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹) (Brown et al., 2016), but lower than those in the North China Plain during the summertime (2 to $\mathrm{57}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹) (Tham et al., 2016; H. Wang et al., 2017, 2018b; Z. Wang et al., 2017). NMHCs were not measured from 9 to 10 January 2017. We used the average $k_{{\mathrm{NO}}_{\mathrm{3}}}^{\prime }$ in the early nighttime from 3 to 4 January as a replacement because these two periods had similar pollution levels for most pollutants. For the later nighttime (Fig. 5, blue rectangle), low levels of N₂O₅ and moderate levels of $P_{{\mathrm{NO}}_{\mathrm{3}}}$ made Eq. (3) inapplicable even though NO was not detected.

$$\begin{array}{}\text{(4)}& {\displaystyle }& {\displaystyle }\left[{\mathrm{NO}}_{\mathrm{3}}\right]={\displaystyle \frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]\cdot K_{\mathrm{eq}}}}\text{(5)}& {\displaystyle }& {\displaystyle }{k^{\prime }}_{{\mathrm{NO}}_{\mathrm{3}}}=\sum k_i\left[{\mathrm{VOC}}_i\right]\end{array}$$

Finally, the uptake coefficient of N₂O₅ was derived using Eq. (6) for every 10 min and averaged for each selected period. In Eq. (6), $C_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ is the mean molecular speed of N₂O₅, and S_a is the aerosol surface area density. The yield of ClNO₂ was derived via dividing the integrated production of ClNO₂ ([ClNO₂]_max) by the integrated loss of N₂O₅ since sunset as Eq. (7).

$$\begin{array}{}\text{(6)}& {\displaystyle }& {\displaystyle }{k^{\prime }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}={\displaystyle \frac{L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}}{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}{C}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}{S}_{\mathrm{a}}{\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\text{(7)}& {\displaystyle }& {\displaystyle }\mathit{\varphi }={\displaystyle \frac{[{\mathrm{ClNO}}_{\mathrm{2}}{]}_{\max }}{\int L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\mathrm{d}t}}\end{array}$$

The relative importance of the NO₃ reactions with VOCs and N₂O₅ heterogeneous reactions can be examined by comparing the values of the loss coefficient of the NO₃ reactions $\left(\frac{{k^{\prime }}_{{\mathrm{NO}}_{\mathrm{3}}}}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]\cdot K_{\mathrm{eq}}}\right)$ and N₂O₅ heterogeneous reactions ($k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}^{\prime }$) (Tham et al., 2016). Based on the calculations, the values of $\frac{{k^{\prime }}_{{\mathrm{NO}}_{\mathrm{3}}}}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]\cdot K_{\mathrm{eq}}}$ were $\mathrm{1.40}\times {\mathrm{10}}^{-\mathrm{5}}$ to $\mathrm{6.07}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ (see Table 2), while those of $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}^{\prime }$ were $\mathrm{3.78}\times {\mathrm{10}}^{-\mathrm{3}}$ to $\mathrm{9.00}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹, which was 2 orders of magnitude higher than $\frac{{k^{\prime }}_{{\mathrm{NO}}_{\mathrm{3}}}}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]\cdot K_{\mathrm{eq}}}$, suggesting that N₂O₅ heterogeneous reactions were the dominant loss pathway for both NO₃ and N₂O₅.

Table 3 Average values of the N₂O₅ loss rate and related parameters for selected periods in the later nighttime.

The average ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ derived for the early night in the five cases are listed in Table 2. The data show that the uptake coefficient ranged from 0.009 to 0.066, which was comparable with previous values derived at Mt. Tai Mo Shan (TMS) in Hong Kong (0.004 to 0.022) (Brown et al., 2016) and in the North China Plain (0.006 to 0.102) (Tham et al., 2016, 2018; H. Wang et al., 2017, 2018b; X. Wang et al., 2017; Z. Wang et al., 2017; Zhou et al., 2018). It is interesting to see a much higher ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ value (0.066) on 3 January than those on other four nights (0.009–0.015), which resulted from higher $P_{{\mathrm{NO}}_{\mathrm{3}}}$ but much lower Sa and relatively low N₂O₅ concentrations on 3 January. We examined known factors affecting the loss of NO₃ and N₂O₅ such as the concentrations of NO, NMHCs, and aerosol compositions, but found no obvious difference between 3 January and the other nights. The yield in this study varied from 0.18 to 0.32, which was similar to most studies in China (Tham et al., 2016, 2018; Z. Wang et al., 2017; Yun et al., 2018; Zhou et al., 2018).

The uncertainty of the above ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ was estimated to be ±45 % due to the measurement uncertainty of N₂O₅ (±25 %), NO₂ (±20 %), O₃ (±5 %), and Sa (±30 %). The uncertainty of ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ was mainly caused by the uncertainty of NO₂ (±20 %), O₃ (±5 %), and ClNO₂ (±25 %) and was estimated to be ±30 %. The correlation between ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$, and the concentrations of aerosol compositions (see Table S2) or RH was investigated, and the results (not shown here) did not indicate any significant dependence of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ or ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ on these parameters.

Figure 6 Comparison between the measured ${\mathrm{NO}}_{\mathrm{3}}^{-}$ increase and the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ formation potential in the early nighttime (periods in Table 2: 3 January 17:40–19:00, 4 January 17:00–22:00, 5 January 17:00–22:00, 6 January 17:00–22:40, and 9 January 19:00–00:20) and in the later nighttime (periods in Table 3: 3–4 January 21:00–05:00, 5 January 01:30–06:50, 5–6 January 23:40–01:10, 6–7 January 23:00–06:00, and 10 January 01:50–03:30).

3.3 Nitrate formation potential p(${\mathrm{NO}}_{\mathrm{3}}^{-}$) through N₂O₅ chemistry

3.3.1 Nighttime p(${\mathrm{NO}}_{\mathrm{3}}^{-}$)

The formation potential of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ through N₂O₅ chemistry is the total amount of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ accumulated from N₂O₅ heterogeneous loss. It can be calculated by deducting the integrated production of ClNO₂ from the integrated loss of N₂O₅ as follows:

$$\begin{array}{ll}{\displaystyle }p\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)& {\displaystyle }=(\mathrm{2}-\mathit{\varphi })\int L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\mathrm{d}t\\ \text{(8)}& {\displaystyle }& {\displaystyle }=\mathrm{2}\int L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\mathrm{d}t-[{\mathrm{ClNO}}_{\mathrm{2}}{]}_{\max }\end{array}$$

In the early nighttime, the average loss rate of N₂O₅ ($L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) ranged from 1.9 to 4.3 ppbv h⁻¹ (Table 2), which was close to the average $P_{{\mathrm{NO}}_{\mathrm{3}}}$ due to the dominance of the N₂O₅ heterogeneous reactions in NO₃ and N₂O₅ loss. Based on the derived N₂O₅ loss rate and the maximum ClNO₂ concentration, the formation potential of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ was derived and ranged from 29.0 to 77.3 µg m⁻³ as shown in Fig. 6. The measured increase of the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration in the early nighttime can be completely explained by the integrated production of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ via the N₂O₅ heterogeneous reactions during the same period.

In the later nighttime, the method described in Sect. 3.2.2 was not valid for calculating the N₂O₅ heterogeneous loss rate as mentioned above. We attempted to estimate the formation potential of nitrate by assuming that the N₂O₅ heterogeneous reactions continued to dominate the loss of NO₃+N₂O₅ in the later nighttime. The $k_{{\mathrm{NO}}_{\mathrm{3}}}^{\prime }$ values in the later nighttime were comparable to those in the early nighttime, and the high RH (close to 100 %) in the later nighttime was favorable for N₂O₅ heterogeneous reactions. We assumed that all NO₃ was quickly consumed by the N₂O₅ heterogeneous reactions, which means that the loss rate of N₂O₅ approximated to the production rate of NO₃ ($L_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\approx P_{{\mathrm{NO}}_{\mathrm{3}}}$). As listed in Table 3, the N₂O₅ loss rates ranged from 0.82 to 1.26 ppbv h⁻¹, which were significantly lower than those derived in the early nighttime. The derived N₂O₅ loss rate here and the yield of ClNO₂ in the early nighttime were used to estimate the formation potential of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in the later nighttime. As shown in Fig. 6, the nitrate produced during these later periods ranged from 7.3 to 40.3 µg m⁻³, which was lower than values in the early nighttime for four nights, indicating that the nighttime nitrate from N₂O₅ chemistry was mainly produced in the early nighttime.

Figure 7 Comparison between the daytime (07:00 to 17:00 LT; assuming that all gas-phase HNO₃ is partitioned into particle phase) and nighttime (17:00 to 07:00 LT of the next day) ${\mathrm{NO}}_{\mathrm{3}}^{-}$ formation potential. The early nighttime of each day represents the periods in Table 2, including 3 January 17:40–19:00, 4 January 17:00–22:00, 5 January 17:00–22:00, 6 January 17:00–22:40, and 9 January 19:00–00:20. The later nighttime of each day represents the periods in Table 3, including 3–4 January 21:00–05:00, 5 January 01:30–06:50, 5–6 January 23:40–01:10, 6–7 January 23:00–06:00, and 10 January 01:50–03:30. The intercomparison of the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ formation potential during the day and night on 9 and 10 January was not conducted due to the lack of NMHC data after 8 January which made the model simulation of OH infeasible during the day on 9 January.

3.3.2 Comparison with the daytime production of HNO₃

During the daytime, the formation of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is mainly from the gas–particle partitioning of the gas-phase HNO₃ formed via the OH+NO₂ reaction. Hence, the daytime formation potential of HNO₃ (p(HNO₃)) can be treated as the upper limit for the locally produced daytime aerosol nitrate. To calculate the daytime p(HNO₃), a box model based on MCM v3.3.1 was used to derive the mixing ratio of OH and the rates of OH+NO₂ as described in Sect. 2.4. This model was previously used in our study at Wangdu in northern China (Tham et al., 2016). The calculated mixing ratios of OH at Wangdu with this model compared well with those observed by the laser-induced fluorescence (LIF) technique (Tan et al., 2017). In the present study, the average daytime OH (07:00 to 17:00) mixing ratios were 1.71 to 3.82×10⁶ molec cm⁻³ from 3 to 7 January, as listed in Table 4, with the maximum values reaching 3.24 to 6.71×10⁶ molec cm⁻³. The detailed results for OH can be found in Fig. S3.

Table 4 Average OH mixing ratio and rate of OH+NO₂ during the daytime (07:00 to 17:00 LT) from 3 to 7 January 2017.

The average production rates of HNO₃ via the OH+NO₂ reaction were 1.40 to 5.21 ppbv h⁻¹ from 3 to 7 January, and the integrated formation potential of HNO₃ during the daytime was 35.7 to 131.8 µg m⁻³, which was comparable to the nighttime p(${\mathrm{NO}}_{\mathrm{3}}^{-}$) that ranged from 69.3 to 102.9 µg m⁻³ (Fig. 7). The nighttime production of nitrate via the heterogeneous uptake of N₂O₅ accounted for 43.8 % to 57.7 % of the total nitrate (${\mathrm{NO}}_{\mathrm{3}}^{-}+{\mathrm{HNO}}_{\mathrm{3}}$) produced in a 24 h period at the site. These results underscored the important role of N₂O₅ heterogeneous chemistry in nitrate formation in this severe winter haze in southern China.

4 Concluding remarks

With the use of concurrent measurements of nitrate, ClNO₂, and related pollutants, this study demonstrates the important contribution of N₂O₅ heterogeneous uptake in nitrate formation. Current chemical transport models have difficulties simulating this nitrate production pathway. Therefore, more research efforts are needed to improve the representations of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and ${\mathit{\varphi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ for the better prediction of nitrate in the models. The observation-based approach presented here can be applied to investigate nitrate formation in other areas.