Atmospheric Δ¹⁷O(NO₃⁻) reveals nocturnal chemistry dominates nitrate production in Beijing haze

The rapid mass increase of atmospheric nitrate is a critical driving force for the occurrence of fine-particle pollution (referred to as haze hereafter) in Beijing. However, the exact mechanisms for this rapid increase of nitrate mass have not been well constrained from field observations. Here we present the first observations of the oxygen-17 excess of atmospheric nitrate $\left({\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\right({\mathrm{NO}}_{\mathrm{3}}^{-}\left)\right)$ collected in Beijing haze to reveal the relative importance of different nitrate formation pathways, and we also present the simultaneously observed ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. During our sampling period, 12 h averaged mass concentrations of PM_2.5 varied from 16 to 323 µg m⁻³ with a mean of (141±88(1SD)) µg m⁻³, with nitrate ranging from 0.3 to 106.7 µg m⁻³. The observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ ranged from 27.5 ‰ to 33.9 ‰ with a mean of (30.6±1.8) ‰, while ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ ranged from −2.5 ‰ to 19.2 ‰ with a mean of (7.4±6.8) ‰. ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$-constrained calculations suggest nocturnal pathways (${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}/{\mathrm{Cl}}^{-}$ and NO₃+HC) dominated nitrate production during polluted days (PM_2.5≥75 µg m⁻³), with a mean possible fraction of 56–97 %. Our results illustrate the potentiality of Δ¹⁷O in tracing nitrate formation pathways; future modeling work with the constraint of isotope data reported here may further improve our understanding of the nitrogen cycle during haze.

1 Introduction

Severe and frequent haze pollution has become a crucial threat for the air quality in the megacity of Beijing and the North China Plain in recent years. The high concentrations of PM_2.5 (particulate matter with an aerodynamic diameter equal or less than 2.5 µm) during severe haze, of which the hourly average can reach 1000 µg m⁻³ (B. Zheng et al., 2015), are harmful to public health by contributing to cardiovascular morbidity and mortality (Cheng et al., 2013; Brook et al., 2010). Nitrate is an important component of PM_2.5, accounting for 1–45 % of PM_2.5 mass in Beijing and the North China Plain (Wen et al., 2015; B. Zheng et al., 2015; G. Zheng et al., 2015). The main formation pathways of atmospheric nitrate, defined herein as gas-phase HNO₃ plus particulate ${\mathrm{NO}}_{\mathrm{3}}^{-}$, in the urban area are summarized in Fig. 1, which includes (i) NO₂ oxidation by OH radicals in the gas phase, (ii) heterogeneous uptake of NO₂ on wet aerosols, (iii) NO₃ radicals reacting with hydrocarbon (HC), and (iv) heterogeneous uptake of N₂O₅ on wet aerosols and chlorine-containing aerosols. Since OH radicals are mainly present in the daytime, while NO₃ radicals and N₂O₅ are mainly present in the nocturnal atmosphere (Brown and Stutz, 2012), NO₂+OH is usually referred to as the daytime nitrate formation pathway, while ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}/{\mathrm{Cl}}^{-}$ and NO₃+HC are referred to as nocturnal formation pathways (Vicars et al., 2013; Sofen et al., 2014). During haze in Beijing, the mixing ratio of daytime OH is modeled to be low (G. Zheng et al., 2015; Rao et al., 2016), while a relatively high mixing ratio of nocturnal N₂O₅ is observed in several studies (Wang et al., 2017a, b; Li et al., 2018); therefore, nocturnal pathways are suggested to be most responsible for the high concentrations of atmospheric nitrate during haze (Su et al., 2017; Pathak et al., 2009, 2011). In addition, the high PM_2.5 concentration and relative humidity during haze in Beijing favor heterogeneous reactions, which renders NO₂+H₂O a potentially significant pathway for nitrate production (J. Wang et al., 2017; Tong et al., 2015; B. Zheng et al., 2015).

Figure 1 Simplified schematic of the main nitrate formation pathways in urban air; “het.” refers to heterogeneous reactions on aerosols.

Nitrogen isotopic composition of nitrate (${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$, wherein δ¹⁵N = ($R_{\mathrm{sample}}/R_{\mathrm{reference}}-\mathrm{1}$), with R representing isotope ratios of ¹⁵N∕¹⁴N in the sample and the reference atmospheric N₂) is useful in tracing the source of its precursor NO_X (Xiao et al., 2015; Beyn et al., 2014; Fang et al., 2011; Hastings et al., 2013). Anthropogenic sources of NO_X such as coal combustion are generally enriched in δ¹⁵N, while natural NO_X sources such as soil emissions or lighting typically have a negative or zero δ¹⁵N signature (Hoering, 1957; Yu and Elliott, 2017; Felix et al., 2012). Therefore highly positive values of observed ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ can be considered as an indicator of anthropogenic combustion (Elliott et al., 2009; Fang et al., 2011), although this judgment may be influenced by isotopic exchange between NO and NO₂ (Freyer et al., 1993; Walters et al., 2016), isotopic fractionations associated with nitrate formation pathways, and isotopic effects occurring during transport, such as deposition of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and HNO₃ partitioning between the gas and particle phase (Freyer, 1991; Geng et al., 2014). The oxygen-17 excess (Δ¹⁷O) of nitrate, defined as ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}={\mathit{\delta }}^{\mathrm{17}}\mathrm{O}-\mathrm{0.52}{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$, wherein δ^XO = ($R_{\mathrm{sample}}/R_{\mathrm{reference}}-\mathrm{1}$), with R representing isotope ratios of ^XO∕¹⁶O in the sample and the reference Vienna Standard Mean Ocean Water and X=17 or 18, is particularly useful in reflecting nitrate formation pathways (Michalski et al., 2003). Atmospheric nitrate from nocturnal reaction pathways has higher Δ¹⁷O than that from daytime OH oxidation at a given Δ¹⁷O(NO₂) (Table 1). And once formed, atmospheric ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ cannot be altered by mass-dependent processes such as deposition during transport (Brenninkmeijer et al., 2003). Previous studies have shown the utility of atmospheric ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in quantifying the relative importance of various nitrate formation pathways (Alexander et al., 2009; Michalski et al., 2003; Patris et al., 2007; Savarino et al., 2013; Vicars et al., 2013). For example, the ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$-constrained box modeling work of Michalski et al. (2003) suggests that more than 90 % of atmospheric nitrate is from nocturnal N₂O₅+H₂O pathways in winter in La Jolla, California, which is reflected by the highest ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ values being observed in winter. In another study, Alexander et al. (2009) use observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ to constrain a 3-D model and found that the daytime NO₂+OH pathway dominates global tropospheric nitrate production, with an annual mean contribution of 76 %.

Table 1 Isotope assumptions of different nitrate formation pathways.

^a The values are calculated on assumptions that bulk Δ¹⁷O(O₃)=26 ‰ (Vicars and Savarino, 2014; Ishino et al., 2017) and Δ¹⁷O(HO₂∕RO₂) = 0 ‰. Δ¹⁷O(RO₂) is equal to 0 ‰ in the troposphere (Morin et al., 2011); in contrast, observations suggest Δ¹⁷O(HO₂) = 1–2 ‰ (Savarino and Thiemens, 1999). However, the difference in calculated ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ between assuming Δ¹⁷O(HO₂) = 0 ‰ and Δ¹⁷O(HO₂) = 2 ‰ is negligible in this study (<0.1 ‰). And the assumption that Δ¹⁷O(HO₂) = 0 ‰ simplifies calculations and is also consistent with previous studies (Michalski et al., 2003; Alexander et al., 2009; Morin et al., 2008; Kunasek et al., 2008; Sofen et al., 2014). α is the proportion of O₃ oxidation in NO₂ production rate, calculated by Eq. (3). ^b Previous studies suggest that in R7 one oxygen atom of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is from H₂O and the other two are from NO₂ (Li et al., 2010; Cheung et al., 2000; Goodman et al., 1999), which will result in ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ = 2∕3Δ¹⁷O(NO₂). ^c R4 and R5 suggest that the central oxygen atom of N₂O₅ (O₂N–O–NO₂) is from NO₃ radicals (O–NO₂), with Δ¹⁷O (‰) $=\mathrm{1.23}\times {\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{O}}_{\mathrm{3}}\right)+\mathrm{9.0}$ ‰. R10 is suggested to occur via O₂N–O–NO₂ (aq.) $\to {\mathrm{NO}}_{\mathrm{2}}^{+}+{\mathrm{NO}}_{\mathrm{3}}^{-}$ and the following ${\mathrm{NO}}_{\mathrm{2}}^{+}+{\mathrm{Cl}}^{-}\to {\mathrm{ClNO}}_{\mathrm{2}}$ (Bertram and Thornton, 2009), so ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ $=\mathrm{1}/\mathrm{3}(\mathrm{1.23}\times {\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{O}}_{\mathrm{3}}\right)+\mathrm{9.0}$ ‰) $+\mathrm{2}/\mathrm{3}{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{2}}\right)={\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}\right)$.

Until now, however, field observations of atmospheric ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ have not been conducted in north China to constrain the relative importance of different nitrate formation pathways during haze. In this work, we present the first observations of atmospheric ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ during Beijing haze from October 2014 to January 2015, and use this observation to examine the importance of nocturnal formation pathways. We also present the signature of simultaneously observed ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$.

2 Materials and methods

2.1 Sampling and atmospheric observations

PM_2.5 filter samples were collected at a flow rate of 1.05 m³ min⁻¹ using a high volume air sampler (model TH-1000C II, Tianhong Instruments Co., Ltd, China). The quartz microfiber filter (Whatman Inc., UK) is pre-combusted at 450 ^∘C for 4 h before sampling. Our sampling period lasted from October 2014 to January 2015, with the collection interval being 12 h (08:00–20:00 LT or 20:00–08:00 LT) for each sample. Blank control samples were also collected. The blank was sampled identically to the real sample except that the collection interval was 1 min. Due to the fact that gaseous HNO₃ is likely to adsorb onto particulate matter already trapped by the filter material (Vicars et al., 2013), the nitrate species collected is likely to include both particulate nitrate and gaseous HNO₃, which is referred to as atmospheric nitrate in previous studies (Vicars et al., 2013; Morin et al., 2009; Michalski et al., 2003) and in this study. The sampling site is at the campus of University of the Chinese Academy of Sciences (40.41^∘ N, 116.68^∘ E; ∼20 m high) in suburban Beijing, about 60 km northeast of downtown Beijing (Fig. 2), which is a supersite set up by HOPE-J³A (Haze Observation Project Especially for Jing–Jin–Ji Area), with various observations being reported (Zhang et al., 2017; Xu et al., 2016; Chen et al., 2015; Tong et al., 2015; He et al., 2018). Hourly concentrations of surface PM_2.5, CO, SO₂, NO₂, and O₃ were observed at Huairou station (40.33^∘ N, 116.63^∘ E) by Beijing Municipal Environmental Monitoring Center, about 10 km from our sampling site. Meteorological data including relative humidity (RH) and air temperature (T) were measured by an automatic weather station (model MetPak, Gill Instruments Limited, UK). Time used in the present study is local time (LT = UTC +8).

Figure 2 A brief map of the sampling site in Beijing. The map scale of base map is 1:1 250 000. Huairou station is set up by the Beijing Municipal Environmental Monitoring Center, where hourly PM_2.5, SO₂, CO, NO₂, and O₃ were observed.

2.2 Measurements of ions and isotopic ratios

Ion concentrations of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Cl⁻ were measured in Anhui Province Key Laboratory of Polar Environment and Global Change in the University of Science and Technology of China. A detailed description of this method can be found in the literature (Ye et al., 2015). Briefly, ions in the PM_2.5 filter sample were extracted with Millipore water (≥18 MΩ) and insoluble substances in the extract were filtered. Then the ion concentrations were analyzed using an ion chromatograph system (model Dionex ICS-2100, Thermo Fisher Scientific Inc., USA). The measured ion concentrations of blank samples were subtracted when determining the ion concentrations of real samples. Typical analytical precision by our method is better than 10 % relative standard deviation (RSD) (Chen et al., 2016).

${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ were measured with a bacterial denitrifier method (Kaiser et al., 2007) in IsoLab at the University of Washington, USA. Briefly, ions in the filter sample were extracted with Millipore water (≥18 MΩ) and the insoluble substances were filtered. ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in each sample was converted to N₂O by the denitrifying bacteria, Pseudomonas aureofaciens. Then N₂ and O₂, which were decomposed from N₂O in a gold tube at 800 ^∘C, were separated using a gas chromatograph. The isotopic ratios of each gas were then measured by a Finnigan Delta-Plus Advantage isotope ratio mass spectrometer. Masses of 28 and 29 from N₂ were measured to determine δ¹⁵N. Masses of 32, 33, and 34 from O₂ were measured to determine δ¹⁷O and δ¹⁸O, and Δ¹⁷O was then calculated. We use international nitrate reference materials, USGS34, USGS35, and IAEANO₃, for data calibration. The uncertainty (1σ) of δ¹⁵N and Δ¹⁷O measurements in our method is 0.4 ‰ and 0.2 ‰, respectively, based on replicate analysis of the international reference materials. All the samples including blank samples were measured in triplicate to quantify the uncertainty in each sample. The blank was subtracted for each sample by using an isotopic mass balance on the basis of isotopic ratios and concentrations of the blank. To minimize the blank effect, samples with blank concentrations being >10 % of their concentrations were not analyzed for isotopic ratios. This ruled out 3 of the total 34 samples, all of which are from non-polluted days (NPD, PM_2.5 < 75 µg m⁻³). In total, isotopic compositions of 7 samples from NPD and 24 samples from polluted days (PD, PM_2.5≥75 µg m⁻³) are reported here.

2.3 Estimate of different nitrate formation pathways based on ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$

The observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ is determined by the relative importance of different nitrate formation pathways and the relative importance of O₃ oxidation in NO_X cycling as shown in Eq. (1):

$$\begin{array}{ll}{\displaystyle }\mathrm{\Delta }& {\displaystyle }{}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)={{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}}_{\mathrm{R}\mathrm{6}}\times f_{\mathrm{R}\mathrm{6}}+{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}}_{\mathrm{R}\mathrm{7}}\times f_{\mathrm{R}\mathrm{7}}+{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}}_{\mathrm{R}\mathrm{8}}\\ \text{(1)}& {\displaystyle }& {\displaystyle }\times f_{\mathrm{R}\mathrm{8}}+{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}}_{\mathrm{R}\mathrm{9}}\times f_{\mathrm{R}\mathrm{9}}+{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}}_{\mathrm{R}\mathrm{10}}\times f_{\mathrm{R}\mathrm{10}},\end{array}$$

where Δ¹⁷O_R6, Δ¹⁷O_R7, Δ¹⁷O_R8, Δ¹⁷O_R9, and Δ¹⁷O_R10 are, respectively, ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ resulting from NO₂+OH, NO₂+H₂O, NO₃+HC, N₂O₅+H₂O, and ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ pathways (Table 1); f_R6, f_R7, f_R8, f_R9, and f_R10 are, respectively, corresponding fractional contributions of the above pathways to nitrate production. Using the Δ¹⁷O assumptions for different pathways in Table 1 and the definition $f_{\mathrm{R}\mathrm{6}}+f_{\mathrm{R}\mathrm{7}}+f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}}=\mathrm{1}$, Eq. (1) is further expressed as

$$\begin{array}{ll}{\displaystyle }& {\displaystyle }{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)/\mathrm{‰}=\mathrm{25}\mathit{\alpha }{f}_{\mathrm{R}\mathrm{6}}+\mathrm{25}\mathit{\alpha }{f}_{\mathrm{R}\mathrm{7}}+\left(\mathrm{25}\mathit{\alpha }+\mathrm{14}\right)\times f_{\mathrm{R}\mathrm{8}}\\ {\displaystyle }& {\displaystyle }+\left(\mathrm{25}\mathit{\alpha }+\mathrm{7}\right)\times f_{\mathrm{R}\mathrm{9}}+\left(\mathrm{25}\mathit{\alpha }+\mathrm{14}\right)\times f_{\mathrm{R}\mathrm{10}}\\ \text{(2)}& {\displaystyle }& {\displaystyle }=\mathrm{25}\mathit{\alpha }+\mathrm{14}\times \left(f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{10}}\right)+\mathrm{7}{f}_{\mathrm{R}\mathrm{9}},\end{array}$$

where α is the proportion of O₃ oxidation in NO₂ production rate, calculated by Eq. (3):

$$\begin{array}{}\text{(3)}& \mathit{\alpha }={\displaystyle \frac{k_{\mathrm{R}\mathrm{1}}\left[\mathrm{NO}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]}{k_{\mathrm{R}\mathrm{1}}\left[\mathrm{NO}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]+k_{\mathrm{R}\mathrm{2}\mathrm{a}}\left[\mathrm{NO}\right]\left[{\mathrm{HO}}_{\mathrm{2}}\right]+k_{\mathrm{R}\mathrm{2}\mathrm{b}}\left[\mathrm{NO}\right]\left[{\mathrm{RO}}_{\mathrm{2}}\right]}}.\end{array}$$

In Eq. (3), k_R1, k_R2a, and k_R2b are, respectively, the reaction rate constants listed in Table 2. To evaluate α, we estimated HO₂ mixing ratios on the basis of empirical formulas between HO₂ and O₃ mixing ratios derived from observations in winter (Kanaya et al., 2007); i.e., $\left[{\mathrm{HO}}_{\mathrm{2}}\right]/\left(\mathrm{pmol}{\mathrm{mol}}^{-\mathrm{1}}\right)=\exp (\mathrm{5.7747}\times {\mathrm{10}}^{-\mathrm{2}}\times [{\mathrm{O}}_{\mathrm{3}}]/(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}})-\mathrm{1.7227})$ during the daytime and $\left[{\mathrm{HO}}_{\mathrm{2}}\right]/\left(\mathrm{pmol}{\mathrm{mol}}^{-\mathrm{1}}\right)=\exp (\mathrm{7.7234}\times {\mathrm{10}}^{-\mathrm{2}}\times [{\mathrm{O}}_{\mathrm{3}}]/(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}})-\mathrm{1.6363})$ at night. Then the RO₂ mixing ratio was calculated as 70 % of HO₂ mixing ratios based on previous studies (Liu et al., 2012; Elshorbany et al., 2012; Mihelcic et al., 2003). As the NO mixing ratio was not observed in our study, we estimated NO mixing ratios following the empirical formulas between NO_X and CO mixing ratios derived from observations in winter Beijing (Lin et al., 2011); i.e., $\left[\mathrm{NO}\right]/\left(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}}\right)=(\left[\mathrm{CO}\right]/(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}})-\mathrm{196})/\mathrm{27.3}-\left[{\mathrm{NO}}_{\mathrm{2}}\right]/\left(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}}\right)$ during daytime and $\left[\mathrm{NO}\right]/\left(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}}\right)=(\left[\mathrm{CO}\right]/(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}})-\mathrm{105})/\mathrm{30.9}-\left[{\mathrm{NO}}_{\mathrm{2}}\right]/\left(\mathrm{nmol}{\mathrm{mol}}^{-\mathrm{1}}\right)$ at night.

Table 2 Reaction expressions for different NO₂ production pathways.

Figure 3 General characteristics of haze events in Beijing (October 2014–January 2015). (a) Time series of PM_2.5 and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations. (b) Time series of nitrogen oxidation ratio (NOR, which is equal to the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ molar concentration divided by the sum of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and NO₂ molar concentration) and Cl⁻ concentrations. (c) Time series of ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and visibility. (d) Time series of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and relative humidity (RH). The error bars in (c, d) are ±1σ of replicate measurements (n=3) of each sample. The khaki shaded area indicates polluted days (PD, PM_2.5≥75 µg m⁻³).

By using Eq. (2), the relative importance of nocturnal formation pathways ($f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}})$ can be written as Eq. (4):

$$\begin{array}{}\text{(4)}& f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}}={\displaystyle \frac{f_{\mathrm{R}\mathrm{9}}}{\mathrm{2}}}+{\displaystyle \frac{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)}{\mathrm{14}\mathrm{‰}}}-\mathrm{1.8}\mathit{\alpha }.\end{array}$$

Equation (4) suggests that the relative importance of nocturnal pathways is solely a function of the assumption of f_R9 at given ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and α. Sincef_R9, f_R8+f_R10, and $f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}}$ should be in the range of 0–1 all the time, f_R9 is further limited to meet Eq. (5):

$$\begin{array}{}\text{(5)}& f_{\mathrm{R}\mathrm{9}}\left\{\begin{array}{l}>\mathrm{0}\\ <\min \left(\mathrm{1},{\displaystyle \frac{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)}{\mathrm{7}\mathrm{‰}}}-\mathrm{3.6}\mathit{\alpha },\mathrm{2}+\mathrm{3.6}\mathit{\alpha }-{\displaystyle \frac{{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)}{\mathrm{7}\mathrm{‰}}}\right)\end{array}\right..\end{array}$$

We estimated the relative importance of nocturnal pathways ($f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}})$ by using concentration-weighted ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ observations and production-rate-weighted α from PD of each haze event rather than each sample due to the lifetime of atmospheric nitrate is typically on the order of day (Liang et al., 1998), larger than our sampling collection interval.

2.4 Simulation of surface N₂O₅ and NO₃ radicals

To see whether the relative importance of nocturnal pathways constrained by ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ can be reproduced by models, we use the standard Master Chemical Mechanism (MCM, version 3.3; http://mcm.leeds.ac.uk/, last access: 3 September 2018) to simulate the mixing ratios of surface N₂O₅ and NO₃ radicals during our sampling period. The input for this modeling work includes (i) 1 h averaged mixing ratios of observed surface CO, NO₂, SO₂, and O₃ and estimated NO (see Sect. 2.3), (ii) observed RH and T, and (iii) the mixing ratios of organic compounds from the literature (Table S1) (Wang et al., 2001; Wu et al., 2016; Rao et al., 2016).

3 Results and discussion

3.1 Overview of observations in Beijing haze

Figure 3 describes general characteristics of haze events during our observations. The 12 h averaged PM_2.5 concentrations, corresponding with filter samples, varied from 16 to 323 µg m⁻³ with a mean of (141±88 (1 SD)) µg m⁻³. In comparison, the Grade II of NAAQS (National Ambient Air Quality Standard) in China is 75 µg m⁻³ for daily PM_2.5. The ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations present similar trends with PM_2.5 levels (Fig. 3a), ranging from 0.3 to 106.7 µg m⁻³ with a mean of (6.1±5.3) µg m⁻³ on NPD (PM_2.5 < 75 µg m⁻³) and (48.4±24.7) µg m⁻³ on PD (PM_2.5≥75 µg m⁻³). Correspondingly, the nitrogen oxidation ratio (NOR, which is equal to the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ molar concentration divided by the sum of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and NO₂ molar concentration), a proxy for secondary transformation of nitrate (Sun et al., 2006), increased from a mean of 0.09±0.05 on NPD to 0.31±0.10 on PD (Fig. 3b). In the residential heating season (Case III–V in November 2014–January 2015, Fig. 3b), Cl⁻ concentrations present similar trends to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ levels, increasing from (0.6±1.0) µg m⁻³ on NPD to (7.9±4.8) µg m⁻³ on PD. However, during Case I–II in October 2014, Cl⁻ concentrations were (3.5±1.6) µg m⁻³ on NPD and (3.5±1.9) µg m⁻³ on PD, showing no significant difference at the 0.01 level (t test). Throughout our observational period, the visibility decreased from (11.4±6.7) km on NPD to (3.1±1.8) km on PD (Fig. 3c), while RH increased from (37±12) % on NPD to (62±12) % on PD (Fig. 3d).

Table 3 Atmospheric ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in aerosols obtained from the literature and this study.

${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ ranged from 27.5 ‰ to 33.9 ‰ with a mean of (29.1±1.3) ‰ on NPD and (31.0±1.7) ‰ on PD (Fig. 3c). Our observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ is in the range of aerosol ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ reported in the literature (Table 3) and wet deposition ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ observed in East Asia (Nelson et al., 2018; Tsunogai et al., 2010, 2016). All our observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ values, whether from the daytime sample (08:00–20:00) or the nighttime sample (20:00–08:00), are larger than 25 ‰, the maximum of ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ that can be produced via NO₂+OH and NO₂+H₂O (Table 1) with the assumption of bulk Δ¹⁷O(O₃)=26 ‰ (Ishino et al., 2017; Vicars and Savarino, 2014). This directly suggests that nocturnal formation pathways (${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}/{\mathrm{Cl}}^{-}$ and NO₃+HC) must contribute to all the sampled nitrate. Given that the lifetime of atmospheric nitrate is typically larger than our sampling collection interval (Vicars et al., 2013), each of our samples is expected to reflect both daytime and nocturnal nitrate production. Not surprisingly, the ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ mean of daytime and nighttime samples is (30.3±1.5) ‰ and (30.9±2.1) ‰, respectively, showing no significant difference at the 0.01 level (t test).

Figure 4 Relationships between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and other parameters. The relationship between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$concentrations (a), PM_2.5 concentrations (b), nitrogen oxidation ratio (NOR, c), visibility (d), relative humidity (RH, e), and ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (f). The dark red dots are samples with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ < 50 µg m⁻³ and the orange dots are samples with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ > 50 µg m⁻³. The black dashed lines are linear least-squares fitting lines for all samples, the dark red solid lines are linear least-squares fitting lines for samples with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ < 50 µg m⁻³, and the orange solid lines are linear least-squares fitting lines for samples with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ > 50 µg m⁻³. The error bars are ±1σ of replicate measurements of each sample.

${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in our observation varied from −2.5 ‰ to 19.2 ‰ with a mean of (7.4±6.8) ‰, which is in the range of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ observed from rainwater in Beijing, China (Zhang et al., 2008), and similar to ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ values observed from aerosols in Germany (Freyer, 1991). Figure 3d shows that ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ varies largely in October 2014. The mean ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ varied from (0.4±1.5) ‰ in the period 08:00 on 18 October–08:00 on 21 October to (10.7±1.4) ‰ in the period 08:00 on 21 October–08:00 on 23 October and then decreased to ($-\mathrm{0.9}\pm \mathrm{2.1}$) ‰ in the period 08:00 on 23 October–08:00 on 26 October, which corresponds to PM_2.5 concentrations being 155±63, 57±19, and (188±51) µg m⁻³ respectively. However, during the residential heating season, relatively high ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (7.6 ‰–19.2 ‰) levels were always observed, both on NPD and PD. This may be related to the high NO_X emission from coal combustion in north China (Wang et al., 2012; Lin, 2012; Zhang et al., 2007).

3.2 Relationships between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and other data

Figure 4 presents the relationships between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations, PM_2.5 concentrations, NOR, visibility, RH, and ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ shows a positive correlation with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations when ${\mathrm{NO}}_{\mathrm{3}}^{-}$ < 50 µg m⁻³ (r=0.81, p<0.01). Similarly, ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ shows a positive correlation with PM_2.5 concentration in Fig. 4b and NOR in Fig. 4c when ${\mathrm{NO}}_{\mathrm{3}}^{-}$ < 50 µg m⁻³ (r=0.71 and r=0.80, p<0.01, respectively). Figure 4d shows that ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ is negatively correlated with visibility in general ($r=-\mathrm{0.66}$, p<0.01). The significant decrease of visibility will largely reduce surface radiation and thereby OH mixing ratios (G. Zheng et al., 2015), which is unfavorable for nitrate production via the NO₂+OH pathway. Since the NO₂+OH pathway produces low ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (Table 1), the decreased importance of the NO₂+OH pathway will conversely increase ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. While the rise of RH accompanying the large increase of PM_2.5 favors nitrate production via the heterogeneous uptake of gases, e.g., N₂O₅ (G. Zheng et al., 2015; B. Zheng et al., 2015), and the heterogeneous uptake of N₂O₅ produces relative high ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (Table 1), the enhanced heterogeneous uptake of N₂O₅ will increase ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ too. Therefore, the decrease of the importance of NO₂+OH and the increase of the importance of the heterogeneous uptake of N₂O₅ should be responsible for the positive correlation between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations. In addition, for samples with ${\mathrm{NO}}_{\mathrm{3}}^{-}$ > 50 µg m⁻³, visibility was always low with narrow variations (2.3±1.0 km), and RH was always high with a narrow range (67±7 %), which may be the reason for the relatively high ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ being observed (31.2±1.7 ‰). Figure 4f shows that ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ is not correlated with ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$.

Figure 5 Estimate of the proportion of O₃ oxidation in NO_X cycling, α. The gray column represents the possible α range determined by ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. The blue dot represents a specific α value calculated by Eq. (3).

Table 4 The possible range of fractional contribution of different nitrate formation pathways during PD of each case estimated on the basis of observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$^a.

^a R6, R7, R8, R9, and R10 are, respectively, NO₂+OH, NO₂+H₂O, NO₃+HC, N₂O₅+H₂O, and ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ pathways.

Figure 6 Estimate of the nocturnal formation pathways. The estimated relative importance of nocturnal formation pathways ($f_{\mathrm{R}\mathrm{8}}+f_{\mathrm{R}\mathrm{9}}+f_{\mathrm{R}\mathrm{10}})$ during PD of each case on the basis of observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (see Sect. 2.3, a) and the simulated mixing ratios of N₂O₅ and NO₃ radicals by MCM (b). R8, R9, and R10 in (a) represent NO₃+HC, N₂O₅+H₂O, and ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ pathways, respectively.

3.3 Estimate of nocturnal formation pathways

Before estimating the relative importance of different nitrate formation pathways, we estimate the proportion of O₃ oxidation in the NO₂ production rate, α. The possible α range can be calculated based on observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. It can be obtained from Table 1 that 25α ‰ < ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ < (25α+14) ‰, so the lower limit of possible α is (${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ −14 ‰) ∕25 ‰. And since ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)\ge \mathrm{27.5}$ ‰ in our observation, the higher limit of α is always 1 for all the samples. Figure 5 presents the possible range of calculated α based on ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. The calculated lower limit of α ranged from 0.56 to 0.81 with a mean of 0.68±0.07, which directly suggests that O₃ oxidation played a dominated role in NO_X cycling during Beijing haze. To estimate the specific α value, chemical kinetics in Table 2 and Eq. (3) were used. Specific α is estimated to range from 0.86 to 0.97 with a mean of (0.94±0.03), which is in the possible range of α value calculated directly based on ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ (Fig. 5) and close to the range of 0.85–1 determined in other midlatitude areas (Michalski et al., 2003; Patris et al., 2007).

Figure 6a shows the estimated relative importance of nocturnal formation pathways (${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}/{\mathrm{Cl}}^{-}$ and NO₃+HC) during PD of each case on the basis of observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. Possible fractional contributions of nocturnal formation pathways range from 49 to 97 %, 58 to 100 %, 60 to 100 %, 45–90 % and 70–100 % on PD of Case I to V, respectively, with a mean of 56–97 %. This directly implies that nocturnal chemistry dominates atmospheric nitrate production in Beijing haze. This finding is consistent with the suggested importance of the heterogeneous uptake of N₂O₅ during Beijing haze by previous studies (Su et al., 2017; Wang et al., 2017b). The other pathways (NO₂+OH and NO₂+H₂O) account for the remaining fraction with a mean possible range of 3–44 %. Since NO₂+OH and NO₂+H₂O produce the same ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ signature in our assumptions (Table 1), we cannot distinguish their fractional contributions purely from the observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in the present study. However, the overall positive correlation between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and RH (r=0.55, p<0.01; Fig. 4e) suggests that the heterogeneous uptake of NO₂ should be less important than the heterogeneous uptake of N₂O₅; otherwise, a negative relationship between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and RH is expected. Our calculations also suggest that the sum of possible fractional contributions of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ and NO₃+HC is in the range of 0–49 %, 17–58 %, 20–60 %, 0–45 %, and 41–70 % on PD of Case I to V, respectively, with a mean of 16–56 % (Table 4), which emphasizes that ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ and NO₃+HC played a unignorable role in nitrate production during Beijing haze. Due to the fact that ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ and NO₃+HC produce the same ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in our assumptions (Table 1), we cannot distinguish their fractional contributions purely from the observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in this study either. However, NO₃+HC should be minor for nitrate production. For example, the 3-D modeling work of Alexander et al. (2009) suggests that the NO₃+HC pathway only accounts for 4 % of global tropospheric nitrate production annually on average, and Michalski et al. (2003) found that the NO₃+HC pathway contributes 1–10 % to nitrate production on the basis of an annual observation at La Jolla, California, with low values in winter. Therefore, in addition to NO₃+HC, ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ is likely to also contribute to nitrate production during haze in Beijing. In support of this, the concentrations of Cl⁻ are as high as (5.5±4.1) µg m⁻³ during PD of all the cases in our observation and the mixing ratios of ClNO₂, an indicator of the ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{Cl}}^{-}$ pathway, reached up to 2.9 nmol mol⁻¹ during a summer observation in suburban Beijing (Wang et al., 2018b) and reached up to 5.0 nmol mol⁻¹ in another modeling work in summer rural Beijing (Wang et al., 2017c).

Figure 6b presents the simulated mixing ratios of surface N₂O₅ and NO₃ radicals during our observational period by using the box model MCM. The 12 h averaged mixing ratios of simulated N₂O₅ ranged from 3 to 649 pmol mol⁻¹, while simulated NO₃ radicals ranged from 0 to 27 pmol mol⁻¹. In comparison, previous observations in Beijing suggest that 5 s averaged N₂O₅ can be as high as 1.3 nmol mol⁻¹ and 30 min averaged NO₃ radicals can be as high as 38 pmol mol⁻¹, with large day-to-day variability (Wang et al., 2015, 2017b). During Case I and II in October, simulated N₂O₅ and NO₃ radicals present similar trends with the observed ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and remain relatively high during PD (346±128 and 9±7 pmol mol⁻¹, respectively, Fig. 6b), which supports the dominant role of nocturnal formation pathways suggested by ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$. However, during Case III–V in the residential heating season, the simulated surface mixing ratios of N₂O₅ and NO₃ radicals remain relatively low during PD (63±80 and <1 pmol mol⁻¹, respectively, Fig. 6b), which seems to be inconsistent with ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ observations. We note that a recent study suggests that the heterogeneous uptake of N₂O₅ is negligible at the surface but larger at higher altitudes (e.g., >150 m) during winter haze in Beijing (Wang et al., 2018a). So during PD of Case III–V in our observational period, large nitrate production via heterogeneous uptake of N₂O₅ may occur aloft rather than at the surface, which leads to the dominant role of nocturnal formation pathways as suggested by ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$.

4 Conclusions

We report the first observation of isotopic composition (Δ¹⁷O and δ¹⁵N) of atmospheric nitrate in Beijing haze. The observed ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ ranged from 27.5 ‰ to 33.9 ‰ with a mean of (30.6±1.8) ‰. ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ ranged largely from −2.5 ‰ to 19.2 ‰ with a mean of (7.4±6.8) ‰. When ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is <50 µg m⁻³, a positive correlation was observed between ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration (r=0.81, p<0.01). This is likely to result from the variation of relative importance of different nitrate formation pathways. Calculations with the constraint of ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ suggest that nocturnal pathways (${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}/{\mathrm{Cl}}^{-}$ and NO₃+HC) dominated nitrate production during polluted days (PM_2.5≥75 µg m⁻³), with a mean possible contribution of 56–97 %. ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ also indicates that O₃ dominated NO oxidation during Beijing haze.