Variation and trend of nitrate radical reactivity towards volatile organic compounds in Beijing, China

Nitrate radical (NO₃) is an important nocturnal atmospheric oxidant in the troposphere that significantly affects the lifetime of pollutants emitted by anthropogenic and biogenic activities, especially volatile organic compounds (VOCs). Here, we used 1 year of VOC observation data obtained in urban Beijing in 2019 to look into the level, composition, and seasonal variation in NO₃ reactivity $(k_{{\mathrm{NO}}_{\mathrm{3}}}$). We show that hourly $k_{{\mathrm{NO}}_{\mathrm{3}}}$ towards measured VOC varied widely from < 10⁻⁴ to 0.083 s⁻¹ with a campaign-average value (± standard deviation) of 0.0032 ± 0.0042 s⁻¹. There was large seasonal difference in NO₃ reactivity towards VOC with averaged values (± standard deviation) of 0.0024±0.0026 s⁻¹ (spring), 0.0067±0.0066 s⁻¹ (summer), 0.0042±0.0037 s⁻¹ (autumn), and 0.0027±0.0028 s⁻¹ (winter). Alkenes such as isoprene and styrene accounted for the majority. Isoprene was the dominant species in spring, summer, and autumn, accounting for 40.0 %, 77.2 %, and 43.2 %, respectively. Styrene only played a leading role in winter, with a percentage of 39.8 %. A sensitivity study shows monoterpenes, the species we did not measure, may account for a large fraction of $k_{{\mathrm{NO}}_{\mathrm{3}}}$. Based on the correlation between the calculated $k_{{\mathrm{NO}}_{\mathrm{3}}}$ and VOC concentrations in 2019, we established localized parameterization schemes for predicting the reactivity by only using a part of VOC species. The historically published VOC data were collected using the parameterization method to reconstruct the long-term $k_{{\mathrm{NO}}_{\mathrm{3}}}$ in Beijing. The lower $k_{{\mathrm{NO}}_{\mathrm{3}}}$ during 2014–2021 compared with that during 2005–2013 may be attributed to anthropogenic VOC emission reduction. Finally, we revealed that NO₃ dominated the nocturnal VOC oxidation, with 83 % of the annual average in Beijing in 2019, which varied seasonally and was strongly regulated by the level of $k_{{\mathrm{NO}}_{\mathrm{3}}}$, nitrogen oxide, and ozone. Our results improve the understanding of nocturnal atmospheric oxidation in urban regions and contribute to our knowledge of nocturnal VOC oxidation and secondary organic pollution.

1 Introduction

A large amount of NO emitted in cities is oxidized into NO₂ by O₃ in the atmosphere (Reaction R1), and NO₂ continues to be oxidized into nitrate radical (NO₃) by O₃ (Reaction R2). NO₃ is the main nocturnal tropospheric oxidant (Brown and Stutz, 2012; Wayne et al., 1991) with a relatively high concentration level at night due to it has rapid loss by photolysis (Reaction R3) and the reaction with NO during the daytime (Stark et al., 2007). These two reactions return NO₃ back to NO_x and thus cannot contribute to effective NO_x removal. In addition, NO₃ reacts with NO₂ to form nitrous pentoxide (N₂O₅) (Reaction R5), and N₂O₅ can be decomposed to NO₃ and NO₂ (Reaction R6), establishing a temperature-dependent equilibrium.

$$\begin{array}{}\text{(R1)}& {\displaystyle }& {\displaystyle }\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\text{(R3)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+hv\to \mathrm{NO}+{\mathrm{O}}_{\mathrm{2}}\text{(R4)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+hv\to {\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}^{\mathrm{1}}\mathrm{D}\text{(R5)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}}\text{(R6)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+M\to {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M\text{(R7)}& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M\to {\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+M\end{array}$$

During the nighttime, there are two kinds of reactions that have a large impact on air pollution and regulate the lifetime and budget of many trace gas species. One is NO₃ oxidizing volatile organic compounds and forming complex products (Reaction R8). The other is NO₃ being transformed into N₂O₅ and removed by heterogeneous hydrolysis (Reaction R9), providing an effective way to remove NO_x and produce nitrate aerosol and nitryl chloride (Brown et al., 2004; Dentener and Crutz, 1993; Osthoff et al., 2008). The competition between Reactions (R8) and (R9) determines the fate of nocturnal nitrogen oxidation chemistry, which leads to the formation of different secondary pollutants (Bertram and Thornton, 2009; Brown et al., 2006). In particular, the degradation of volatile organic compounds (VOCs) by NO₃, especially biogenic VOCs (BVOCs; Ng et al., 2017), has been proven to be related to the formation of organic nitrate and secondary organic aerosols (SOAs) (Goldstein and Galbally, 2009; Kiendler-Scharr et al., 2016).

$$\begin{array}{}\text{(R8)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{VOC}\to \text{ products}\text{(R9)}& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\left(\mathrm{aq}\right)}/{\mathrm{Cl}}^{-}\to {\mathrm{HNO}}_{\mathrm{3}}+\mathit{\phi }{\mathrm{ClNO}}_{\mathrm{2}}\end{array}$$

The high NO₃ concentration and fast reaction rate make NO₃ responsible for the sinking of many unsaturated hydrocarbons at night (Edwards et al., 2017; Ng et al., 2017; Yang et al., 2020). The NO₃ reactivity ($k_{{\mathrm{NO}}_{\mathrm{3}}}$) towards VOC, defined as the consuming capacity of NO₃ by ambient VOC, can be calculated by Eq. (1):

$$\begin{array}{}\text{(1)}& k_{{\mathrm{NO}}_{\mathrm{3}}}=\sum k_i\times \left[{\mathrm{VOC}}_i\right],\end{array}$$

where [VOC_i] is VOC concentrations and k_i is the corresponding reaction rate coefficients. Table S1 in the Supplement gives the reaction rate coefficients of NO₃ with VOC (Atkinson and Arey, 2003). The contribution of VOC to the NO₃ reactivity with respect to different VOC varies greatly, which is caused by the abundance of species and the reaction rate coefficients. Thus, NO₃ reactivity towards VOC is also affected by temperature since temperature affects not only the temperature-dependent reaction rate coefficients but also the VOC emissions in the atmosphere, especially for the emission of biogenic VOCs like isoprene and monoterpenes (Wu et al., 2020), leading to the variations in VOC species that dominate $k_{{\mathrm{NO}}_{\mathrm{3}}}$ towards VOC in different seasons.

Previous works showed that the VOC species that dominate the NO₃ reactivity vary greatly between different regions. In forests and rural areas, such as Pabstthum outside Berlin, Germany, the lush forests emitted a large number of monoterpenes and isoprene, accounting for the majority of $k_{{\mathrm{NO}}_{\mathrm{3}}}$, which ranged from 0.0025 to 0.01 s⁻¹ (Asaf et al., 2009). In semi-arid urban areas such as Jerusalem, Israel, the emissions of BVOCs are lower due to the sparser vegetation, and the maximum of NO₃ reactivity was about 0.01 s⁻¹, in which the phenol, cresol, and some monoolefins emitted by road traffic were the main contributors (Asaf et al., 2009). In urban regions like Houston, USA, industrial emissions, including isoprene and other alkenes, dominated the NO₃ reactivity (Stutz et al., 2010). In the city's suburbs, the $k_{{\mathrm{NO}}_{\mathrm{3}}}$ may be jointly affected by anthropogenic and biogenic volatile organic compounds. For example, the NO₃ reactivity towards VOC in Xianghe, Beijing, China, reached 0.024 ± 0.030 s⁻¹, with a maximum value of 0.3 s⁻¹ and minimum value of 0.0011 s⁻¹. Isoprene, styrene, and 2-butene contributed to most of the $k_{{\mathrm{NO}}_{\mathrm{3}}}$ (Yang et al., 2020).

The above NO₃ reactivities are all calculated by the measurement of VOC concentrations. In addition to this method, an instrument was developed to measure $k_{{\mathrm{NO}}_{\mathrm{3}}}$ in the atmosphere directly (Liebmann et al., 2017). This presented the first direct measurement of NO₃ reactivity in the Finnish boreal forest in 2017. They concluded that the NO₃ reactivity was generally high, with a maximum value of 0.94 s⁻¹, displaying a strong diel variation with a nighttime mean value of 0.11 s⁻¹ and daytime value of 0.04 s⁻¹ (J. Liebmann et al., 2018). In 2018, they presented the direct measurement in and above the boundary layer of a mountain site, with daytime values of up to 0.3 s⁻¹ and nighttime values close to 0.005 s⁻¹ (J. M. Liebmann et al., 2018). Most importantly, the direct measurement revealed the existence of missing NO₃ reactivity in various regions, which indicated the missing NO₃ oxidation mechanisms. These results largely improved the understanding of nighttime chemistry.

Nevertheless, the direct field determination of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ is currently still extremely lacking, especially in urban regions. Until now, most works about the VOC oxidation by NO₃ were usually based on short-term investigations, and the analysis of the nocturnal chemical process or reactivity was carried out based on the data of a few weeks or several months. Studies of nighttime chemistry based on long-term measurement data are very scarce (Vrekoussis et al., 2007; Wang et al., 2023; Zhu et al., 2022). The details of VOC contributions to $k_{{\mathrm{NO}}_{\mathrm{3}}}$ and the relationships between certain VOCs and total NO₃ reactivity over a long timescale are also rarely studied. Our recent work reported that the increasing trend of the NO₃ production rate is caused by anthropogenic emission changes, while the long-term and detailed NO₃ loss budget is still uncertain to some extent (Wang et al., 2023). Here, we attempt to look for insight into the level, variation, and impact of NO₃ reactivity by using 1 year of VOC measurements in an urban site in Beijing; the role of unmeasured VOC species (monoterpenes) in the contributions of NO₃ reactivity is also discussed. The long-term trend of NO₃ reactivity is estimated by collecting the published VOC data and the newly proposed parameterization method. Finally, the nocturnal VOC oxidation by NO₃ during different seasons was further evaluated.

2 Method

2.1 Site description and instrumentation

The measurement was conducted at the campus of Peking University (39^∘99^′ N, 116^∘30^′ E) during the whole year of 2019. The site is situated northeast of the Beijing city center and near two traffic roads, which represent a typical urban and polluted area with fresh, anthropogenic emissions (Wang et al., 2017a). The measurements were made on a building roof with a height of 20 m above the ground. Measurements of VOC concentrations were performed using an automated gas chromatograph equipped with mass spectrometry or flame ionization detectors (GC-MS/FID). The volatile organic compounds were pre-treated by pre-freezing, collected in the deactivated quartz empty capillary at extremely low temperature (−150 ^∘C), heated, and then delivered into the analysis system. After separation by the double chromatographic column, the low-carbon compounds C₂-C₄ were detected by the FID detector, and the high-carbon compounds C₅-C₁₀ were detected by the MS detector. There are 56 kinds of VOC measured in total (listed in Table S1 and the concentrations are depicted in Fig. S1 in the Supplement), in which monoterpene measurements are not valid. NO_x and O₃ were monitored by chemiluminescence (Thermo Scientific, 42i-TLE) and UV photometric methods (Thermo Scientific, 49i), respectively. A tapered element oscillating microbalance analyzer (TianHong, TH-2000Z1) was used to measure the mass concentration of PM_2.5. The quality assurance and quality controls of data were implemented regularly (Chen et al., 2020). Photolysis frequencies were obtained by the Tropospheric Ultraviolet and Visible (TUV) model simulation. Hourly data were processed and used in the following analysis.

2.2 Estimation of monoterpenes

Since the measurement data did not include monoterpenes (MNTs), we therefore use the measured isoprene and modeled concentration ratio of monoterpene to isoprene in the same region of the measurement site (named “factor” in Eq. 2) to estimate the ambient monoterpene concentrations (named “MNT_obs” in Eq. 3). The factor was obtained by the regional model (WRF/CMAQ); more details of the model simulation setup can be found in Mao et al. (2022). Briefly, the regional model CMAQ (Community Multiscale Air Quality) version 5.2 was applied to simulate air quality in eastern China, with a horizontal resolution of 36 km. Specifically, the gas-phase mechanism of SAPRC-07 and aerosol module AERO6 were used. The meteorological fields were provided by Weather Research and Forecasting (WRF) model version 4.2. The biogenic emissions were simulated by the MEGANv2.1 model, which was driven by WRF as well, and the emissions of open burning were estimated with FINN. The MEIC emission inventory for 2019 (obtained via private communication) was used to represent anthropogenic emissions over China, while the emissions in the areas outside China were provided by the REAS v3.2 inventory simulation.

$$\begin{array}{}\text{(2)}& {\displaystyle }\text{Factor }={\displaystyle \frac{\left[{\mathrm{MNT}}_{\mathrm{sim}}\right]}{\left[{\mathrm{ISO}}_{\mathrm{sim}}\right]}}\text{(3)}& {\displaystyle }\left[{\mathrm{MNT}}_{\mathrm{obs}}\right]=\left[{\mathrm{ISO}}_{\mathrm{obs}}\right]\times \text{factor}\end{array}$$

We used the factor to estimate monoterpene levels rather than modeled monoterpene concentrations due to the modeled isoprene being systematically higher than that of the observation (Fig. S2). Thus, the use of the modeled factor may be more reasonable. In Beijing, α-pinene and β-pinene were reported to have the highest abundance among monoterpenes (Cheng et al., 2018), with higher emissions in summer (Wang et al., 2018b; Xia and Xiao, 2019). Therefore, we use a weighted reaction rate coefficient approximated by the average value of α-pinene and β-pinene with NO₃ in the following calculations. Since the emissions of sesquiterpenes in BVOCs are much lower than those of isoprene, monoterpenes, and other BVOCs, we did not consider the contribution of sesquiterpenes to the reactivity. The detailed average diurnal variations in factor are listed in Table S2.

2.3 VOC oxidation rate by NO₃

To study the reaction of NO₃ and VOC during the nighttime, we estimated the NO₃ concentrations by steady-state calculation. This method is widely used to estimate the concentrations of short-lived substances by assuming its production and loss rates are balanced in a specific time range. Given sufficient time, the steady state can be reached for NO₃ at night, in which the production and loss terms are approximately balanced (Brown, 2003; Crowley et al., 2010). Here the production terms of NO₃ are the reaction of NO₂ and O₃, and the loss terms of NO₃ include reactions with VOC, reaction with NO, heterogeneous reaction, and photolysis. The steady-state NO₃ mixing ratios are expressed by Eq. (4) (Brown and Stutz, 2012).

$$\begin{array}{}\text{(4)}& [{\mathrm{NO}}_{\mathrm{3}}{]}_{\text{ss}}={\displaystyle \frac{k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]}{\begin{array}{c}\sum k_i\times \left[{\mathrm{VOC}}_i\right]+k_{\mathrm{NO}+{\mathrm{NO}}_{\mathrm{3}}}\left[\mathrm{NO}\right]\\ +J_{{\mathrm{NO}}_{\mathrm{3}}}+k_{\text{het}}{K}_{\text{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\end{array}}},\end{array}$$

where $J_{{\mathrm{NO}}_{\mathrm{3}}}$ is the sum of the photolysis coefficients of the two photolysis reactions of NO₃. The k_het is the heterogeneous uptake rate of N₂O₅ on the aerosol surface, which can be calculated by Eq. (5).

$$\begin{array}{}\text{(5)}& k_{\text{het}}=\mathrm{0.25}\times \mathit{\gamma }\times S_{\mathrm{a}}\times c,\end{array}$$

where γ is the dimensionless uptake coefficient of N₂O₅ parameterized by Eq. (6) (Evans and Jacob, 2005; Hallquist et al., 2003; Kane et al., 2001), S_a (m² m⁻³) is the aerosol surface area density estimated by the level of PM_2.5 (Wang et al., 2021), and c is the mean molecular velocity of N₂O₅.

$$\begin{array}{}\text{(6)}& \begin{array}{rl}& \mathit{\gamma }=\mathit{\alpha }\times {\mathrm{10}}^{\mathit{\beta }}\\ & \mathit{\alpha }=\mathrm{2.79}\times {\mathrm{10}}^{-\mathrm{4}}+\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{4}}\times \mathrm{RH}\\ & -\mathrm{3.43}\times {\mathrm{10}}^{-\mathrm{6}}\times {\mathrm{RH}}^{\mathrm{2}}+\mathrm{7.52}\times {\mathrm{10}}^{-\mathrm{8}}\times {\mathrm{RH}}^{\mathrm{3}}\\ & \mathit{\beta }=\mathrm{4}\times {\mathrm{10}}^{-\mathrm{2}}\times (T-\mathrm{294})(T>\mathrm{282}K)\\ & \mathit{\beta }=-\mathrm{0.48}(T<\mathrm{282}K)\end{array}\end{array}$$

The reaction rate coefficients of NO₂ and O₃, NO and NO₃, and the equilibrium constant for the forward and reverse Reactions (R4) and (R5) are temperature dependent. We have adopted Jet Propulsion Laboratory (JPL) evaluation reports for the reaction rate coefficients. The time series of hourly related parameters in estimating the steady-state NO₃ and the diurnal cycle of NO₃ concentrations were shown in Figs. S3 and S4, respectively. To compare the VOC oxidation by NO₃ with other oxidants, we estimated OH concentrations by the slope extracted from the measured OH and $J_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}$ (s⁻¹) in northern China (Tan et al., 2017) (Eq. 7), where $J_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}$ used in this study was obtained by the TUV model simulations. The VOC oxidation rate ($R_{{\mathrm{NO}}_{\mathrm{3}}}$) and the ratio of VOC oxidized by NO₃ to the total oxidation rate can be calculated by Eq. (8).

$$\begin{array}{}\text{(7)}& {\displaystyle }\left[\mathrm{OH}\right]=\mathrm{4.1}\times {\mathrm{10}}^{\mathrm{11}}{\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}\times J_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}},\text{(8)}& {\displaystyle }{R}_{{\mathrm{NO}}_{\mathrm{3}}}\approx {\displaystyle \frac{\sum k_i\times \left[{\mathrm{VOC}}_i\right]\left[{\mathrm{NO}}_{\mathrm{3}}\right]}{\begin{array}{c}\sum k_i\times \left[{\mathrm{VOC}}_i\right]\left[\mathrm{OH}\right]+\sum k_i\times \left[{\mathrm{VOC}}_i\right]\left[{\mathrm{NO}}_{\mathrm{3}}\right]\\ +\sum k_i\times \left[{\mathrm{VOC}}_i\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\end{array}}},\end{array}$$

where k_i represents the corresponding reaction rate coefficients of different VOC with oxidants.

3 Results and discussion

3.1 NO₃ reactivity calculated by measured VOC

During the campaign, the hourly $k_{{\mathrm{NO}}_{\mathrm{3}}}$ towards measured VOC (named $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$) varied widely from < 10⁻⁴ to 0.083 s⁻¹ with a campaign-average value (± standard deviation) of 0.0032 ± 0.0042 s⁻¹. The $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ displayed a strong diel variation in the annual average (Fig. S5). In previous studies, the NO₃ reactivity towards VOC was reported to be 0.024 ± 0.030 s⁻¹ on average at a suburban site in summer in northern China (Yang et al., 2020) and highly varied between 0.005–0.3 s⁻¹ at a mountaintop site in summer (J. M. Liebmann et al., 2018). Our result is an order of magnitude lower, which may reflect the huge difference in $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ in different environments and sampling time. It could certainly be attributed to the fact that calculated $k_{{\mathrm{NO}}_{\mathrm{3}}}$ here did not include some species, such as monoterpenes, phenol, and cresol. The diurnal variations in $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ had strong seasonal variability (Fig. S6). The diurnal variations in winter and spring were relatively weak, and in summer and autumn they were strong, with clear peaks at 09:00–10:00 and 15:00 LT (local time), respectively. The $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ in spring, summer, and autumn reached the daily maximum value between 8:00 and 10:00 LT (spring: 0.0034 s⁻¹; summer: 0.0083 s⁻¹; autumn: 0.0057 s⁻¹). In winter, it reached the maximum value of 0.0033 s⁻¹ at about 22:00 LT.

As shown in Fig. 1a, the $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ reached the highest in August and lowest in February, which was largely affected by the level of isoprene and styrene. For example, isoprene contributed ∼ 80 % to the reactivity in August. The $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ towards isoprene reached the maximum in August and the minimum in February, which was consistent with the previously reported change in isoprene concentrations in Beijing (Cheng et al., 2018). The $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ shows a large seasonal difference with the average values (± standard deviation) of 0.0024±0.0026 s⁻¹ (spring), 0.0067±0.0066 s⁻¹ (summer), 0.0042±0.0037 s⁻¹ (autumn) and 0.0027±0.0028 s⁻¹ (winter). Table S3 shows the specific contributions of the top six species to $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ in different seasons. Isoprene was the dominant species, accounting for 40.0 %, 77.2 %, and 43.2 % in spring, summer, and autumn. By comparison, styrene only played a leading role in winter, accounting for 39.8 %. Among the species that contributed to $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ in Beijing, isoprene and styrene contributed the most to the overall $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ (60 %–90 %), followed by cis-2-butene, trans-2-butene, trans-2-pentene, and propylene (5 %–15 %), with other VOCs contributing less than 2 %. Our results are consistent with previous studies in Beijing that $k_{{\mathrm{NO}}_{\mathrm{3}}}$ was mainly contributed to by isoprene (Yang et al., 2020), indicating the critical role of isoprene in NO₃ reactivity in Beijing. From summer to autumn, the dominant species changed from isoprene to styrene, while from winter to spring, the dominant species changed from styrene to isoprene. This indicates AVOCs (anthropogenic volatile organic compounds) and BVOCs (biogenic volatile organic compounds) control $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ alternately. Overall, the $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ was high in summer and autumn and low in winter and spring.

Figure 1 Histograms of monthly averaged $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ (a) and the compositions during the daytime (b) and nighttime (c). The color denotes the contributions of different VOC species. The lines represent the error bars of the reactivity (± standard deviation).

Figure 1b and c shows that the $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ reactivity towards measured VOC displays clear day–night differences in summer and winter, especially in summer. The NO₃ reactivity towards VOC in the daytime reached the value of 0.010 s⁻¹ in July and August, which was much higher than the 0.002 s⁻¹ in the nighttime. The variations were mainly caused by the diel variations in isoprene concentrations. Conversely, the reactivity was higher at night and lower in the daytime in winter, which was due to the high AVOC level in the morning and at night (Lee and Wang, 2006). Specifically, styrene concentrations at night increased significantly in the stable nocturnal boundary layer, resulting in relatively high reactivity.

In urban areas of Beijing, isoprene originates from anthropogenic and biogenic sources, and the anthropogenic sources of isoprene are mainly traffic emissions (Li et al., 2013; Riba et al., 1987; Zou et al., 2015). The isoprene emissions from biogenic sources in Beijing were an order of magnitude larger than those of anthropogenic sources (Yuan et al., 2009). This indicates the concentrations of isoprene at the environmental level in the urban areas of Beijing are not affected by the traffic vehicles but mainly by plants (Cheng et al., 2018). As an aromatic hydrocarbon, styrene originates from both anthropogenic and biogenic sources in the atmosphere (Miller et al., 1994; Mogel et al., 2011; Schaeffer et al., 1996; Tang et al., 2000; Zielinska et al., 1996; Zilli et al., 2001), such as the laminar flame of engine fuel (Meng et al., 2016), industrial production (Radica et al., 2021), and other human activities. The dominant source of styrene in Beijing is the local vehicle emissions (Li et al., 2014). Some vegetation, such as evergreen trees and oleander, can also release natural styrene (Wu et al., 2014); however, due to the dense industrial distribution in the urban area and the much lower level of biogenic styrene compared with isoprene, we believe that the styrene in the atmosphere in Beijing is mainly from anthropogenic origins. It is believed that human activities in winter, such as heating, gasoline, and diesel combustion, increased; meanwhile, the reduction in temperature and radiation resulted in a reduction in biogenic isoprene emissions, explaining the conversion in the dominance of NO₃ reactivity from summer to winter.

The NO₃ reactivity towards MNTs (named as $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_MNTs}}$) was estimated by the method mentioned in Sect. 2.2. After taking MNTs into account, the total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ (named as $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$) was greatly enlarged, with a campaign-average value of 0.0061 ± 0.0088 s⁻¹, resulting in our results being comparable with previous research results. The NO₃ reactivity towards MNTs was higher in autumn and winter and lower in spring and summer (Fig. S7). Considering the corresponding reactivity towards monoterpenes, the total NO₃ reactivity towards VOC changed from summer > autumn > winter > spring to autumn > winter > summer > spring, highlighting the impact of the monoterpene variations on the reactivity. The NO₃ reactivity towards MNTs displayed significant differences between daytime and nighttime (Fig. S7c and d). The reactivity at night in all months was higher than that in the daytime, especially from October to January, highlighting the role of biogenic monoterpenes in nocturnal NO₃ chemistry (Li et al., 2013; Riba et al., 1987). To evaluate the contribution of monoterpenes to the total $k_{{\mathrm{NO}}_{\mathrm{3}}}$, we calculated the fraction (F_MNTs) using Eq. (9).

$$\begin{array}{}\text{(9)}& F_{\mathrm{MNTs}}={\displaystyle \frac{k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_MNTs}}}{k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}}}\end{array}$$

Figure 2a displays the differences between the $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ and $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$. Monoterpenes were very important for NO₃ reactivity, and the F_MNTs varied from 40 % to 80 %, with strong seasonal variations. The MNTs accounted for an NO₃ reactivity of nearly 80 % in winter and spring. In the seasons when isoprene no longer dominated, the measured reactivity accounted for a small fraction, and the corresponding reactivity towards AVOC, such as styrene, was smaller than that of monoterpenes. As shown in Fig. 2b, the measured VOC had high fractions in the daytime and low fractions at night, especially in May and August. The measured VOC in the daytime accounted for more than 60 % of $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$, which was closely related to the increasing concentrations of isoprene in the summer daytime. The reactivity towards MNTs accounted for a large fraction of reactivity at night.

Figure 2 (a) Fractions of the $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$. (b) Fractions of the $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$ divided into daytime (left) and nighttime (right). The colors on the stacked bar plot indicate the different fractions as they are denoted in the legend. The lines represent the monthly averaged variations in the NO₃ reactivity towards MNTs.

3.2 Parameterization of NO₃ reactivity

We examined the correlation of key VOC concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$. Figure S8 gives the case in January, for example. To a certain extent, the variations in $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ were closely linked to the variations in the concentrations of main contributors. It is worth noting that in January, trans-2-butene had a higher correlation coefficient with $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$, which exceeded that of isoprene and styrene. This indicates that higher contributions may not imply a stronger correlation. Figure 3 shows the correlation coefficients and the fitting equations between VOC concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}}}$ in each month (detailed in Table S4). According to the correlation coefficients, we can select the strongest indicator corresponding to a certain month as the variable of the parameterization method. Here we did not import the VOC with small contributions into the parameterization method because these indicators had no practical significance for $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$. In this way, we established the first parameterization method (Method 1) by using the strongest indicator in each month, which can be found in Table S4 (Eq. 10):

$$\begin{array}{}\text{(10)}& {\mathrm{NO}}_{\mathrm{3}}{\text{ reactivity}}_{\text{sim1}}=a\times \left[\mathrm{VOC}\right]+b,\end{array}$$

where a, b, and [VOC] represent the slope, the intercept, and the VOC species concentrations (ppbv) used for parameterization each month, respectively. The correlation coefficients between isoprene concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ were high throughout the year, ranging from 0.67 to 0.98, especially in summer. The correlation coefficients between styrene concentrations and the reactivity reached a maximum in autumn and winter, which gives an indication of the behavior of these two species (isoprene and styrene) in different seasons.

Figure 3 A heat map of the monthly correlation between VOC concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$. Colored blocks indicate different correlations by which the best indicator can be selected for the parameterization method of each month.

Besides the indicator parameterization method, we can also select only the parts of the VOCs that contribute most of $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ as a representative. Here we approximated NO₃ reactivity towards total VOCs to the reactivity towards these top six species: isoprene, styrene, cis-2-butene, trans-2-butene, trans-2-pentene, and propylene. Thus, the second parameterization method (Method 2) can be expressed by Eq. (11):

$$\begin{array}{}\text{(11)}& {\mathrm{NO}}_{\mathrm{3}}{\text{ reactivity}}_{\text{sim2}}=\sum _{i=\mathrm{1}}^{\mathrm{6}}{k}_i\times \left[{\mathrm{VOC}}_i\right],\end{array}$$

where [VOC_i] is the VOC concentrations and k_i is the corresponding reaction rate coefficients with NO₃. It should be noted that this parameterization method of NO₃ reactivity towards VOC may be localized.

To evaluate the effectiveness of the two parameterization methods established above, we estimated the $k_{{\mathrm{NO}}_{\mathrm{3}}}$ on the different timescales and compared them with the determined $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ of all measured VOCs. As shown in Fig. S9, both methods can capture the level of and variations in $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ well, indicating the parametrization feasibility. Method 1 can easily and quickly estimate NO₃ reactivity towards VOCs using a single indicator. In areas where a single VOC species dominates NO₃ reactivity towards VOCs for a long time, such as forest areas, suburbs, and rural areas (BVOC dominant), this method would have a good performance. Method 2 had a better performance, while more VOC species are needed. In urban areas, especially in urban areas where the contributors had different chemodiversity with strong seasonality, this method should be more suitable. Since the two methods lower the bar for estimating NO₃ reactivity by using VOC measurement data, we can investigate the level of NO₃ reactivity using the reported VOC measurement data in the past.

Figure 4 The reported VOC concentrations in Beijing calculated using the reconstructed NO₃ reactivity record from 2005–2021. The averaged NO₃ reactivity calculated by the reported VOC data in each campaign is plotted as the star. The median values of NO₃ reactivity (black dot) in each year show high values during 2005–2013 and relatively low values during 2014–2021. It should be noted that the monoterpenes are not considered here.

We collected the historical measurement data of VOC concentrations in Beijing (Fig. S1 in the Supplement) and estimated NO₃ reactivity using parameterization methods. We found the level of NO₃ reactivity mainly ranged from 0.001 to 0.1 s⁻¹ in Beijing in the past few decades (Fig. 4). During 2014–2020, a large amount of VOC data in urban Beijing was collected in this study and are presented here. We calculated the $k_{{\mathrm{NO}}_{\mathrm{3}\text{\_mea}}}$ using detailed VOC data provided by the literature and estimated the NO₃ reactivity using parameterization methods if the reported data in the literature were limited. As shown in Fig. 4, NO₃ reactivity was relatively low after 2014 compared to previous measurements. We inferred that the level of isoprene during this period may be small since the change in biogenic emissions may not be significant. Thus, we proposed that the lower NO₃ reactivity during the past decade may be attributed to emission reductions regarding anthropogenic VOC. It should be noted that this estimation suffers from uncertainty; nevertheless, this trend and characterization of NO₃ reactivity in Beijing is helpful to understand the nighttime chemistry in Beijing.

After considering MNTs, we updated the parameterization method established before by using the relationship between reactivity and VOC concentrations, including monoterpenes. The updated parameterization Method 1 used the same principle introduced in Sect. 3.2, with fitting slopes changing significantly (Fig. S10). Table S5 shows the correlation coefficients between six key VOC concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}}\text{\_total}}$. The updated Method 2 considered the sum contributions of six VOCs and the estimated MNTs by isoprene concentration. We reevaluated the two updated parameterization methods (single VOC and six VOCs, respectively). Overall, the performance of the two methods is reasonable, and the updated Method 1 is better than that of Method 2 in general (Fig. S11). We evaluated this parameterization using datasets of other years (shown in Fig. S12), and it showed a robust performance.

3.3 Nighttime VOC oxidation

Here we examined the role of NO₃ in VOC oxidation in Beijing in 2019. As shown in Fig. S13, OH oxidized most of VOC during the daytime, with the oxidation rate reaching the maximum value of 0.6 pptv s⁻¹ in the afternoon. Compared with OH, the VOC oxidation rates by O₃ and NO₃ in the daytime were remarkably low. From 18:00 to 06:00 LT, the ratios of VOC oxidized by NO₃ kept above 80 %, and the contribution of O₃ was relatively weak, which is consistent with that reported in regions of high NO_x (Chen et al., 2019; Edwards et al., 2017; Wang et al., 2018a). The VOC oxidation rate by NO₃ presented a single peak at 19:00 LT with a value of 0.25 pptv s⁻¹, which is the same magnitude as that by OH in the daytime, illustrating the importance of NO₃ in VOC oxidation, as shown in the previous studies (Wang et al., 2017a), implying the importance of nocturnal chemistry for organic nitrate and SOA formation.

Figure 5 (a–d) Median diurnal profiles (± standard deviation) of VOC oxidation rate by atmospheric oxidants in different seasons. (e–h) Fractions of VOC oxidation rate by atmospheric oxidants in different seasons. (i–p) Pie charts representing the daytime and nighttime VOC oxidation rate by OH, NO₃, and O₃ during different seasons, with the averaged values and standard deviations also shown.

The VOC oxidation rate by NO₃ and oxidation fractions had strong seasonal variabilities in Beijing. As shown in Fig. 5, the nighttime oxidation rate (summer > spring > autumn > winter) was affected by NO₃ concentrations and the total NO₃ reactivity towards VOC. In summer, the NO₃ oxidation rate presented a single peak, with a maximum value of 0.7 pptv s⁻¹ at 20:00 LT, and it remained around 0.1 pptv s⁻¹ for the rest of the night. The rate at 21:00–05:00 LT was relatively constant. The rate in winter was lower, with the two maximum values of 0.06 pptv s⁻¹ presenting at 19:00 and 04:00 LT, which were lower than the average value of the other three seasons. The results agreed with the previous studies, in which the VOC oxidation rate by NO₃ concentrations was high from 19:00–23:00 LT (Wang et al., 2017b). There was a competition between NO₃ and O₃ in the nighttime VOC oxidation in Beijing. Although the NO₃ oxidation rate at night was higher than that of O₃ throughout the year, the changes in O₃ oxidation rate significantly impacted the ratios of VOC oxidized by NO₃. The ratios of nighttime VOC oxidized by NO₃ in Beijing were higher in autumn, spring, summer, and winter. Although the O₃ concentrations in winter decreased, the competitiveness of NO₃ in VOC oxidation decreased more due to the decline in NO₃ concentrations. The competitiveness of O₃ in VOC oxidation was relatively enhanced, resulting in a significant decline in the ratios of VOC oxidized by NO₃.

Figure 6 Fitting diagrams between the ratios of nighttime VOC oxidized by NO₃ and the concentrations of NO (a), O₃ (b), and NO_x (c). The light pink scattered dots represent the oxidation ratios at different concentrations, and the solid dots represent the median value of each bin of oxidation ratios corresponding to each concentration range. Colored dotted lines represent the fitting results of the solid median dots. The dotted black line in each panel shows a threshold to divide the curve into two regimes. In (a), the regime is divided into NO-limited (< 7 ppbv) and NO-saturated (> 7 ppbv); in (b) and (c), a threshold of 25 ppbv divides the curves into NO_x-limited (O₃) and NO_x-saturated regimes. The results shown in (b) and (c) are representative of low-NO conditions (< 7 ppbv).

3.4 Relationship between O₃ and NO_x and nocturnal VOC oxidation by NO₃

To understand the importance of nighttime VOC oxidized by NO₃, we defined the fraction of VOC oxidation rate by NO₃ to the total oxidation rate as nocturnal VOC oxidation ratio by NO₃ ($R_{{\mathrm{NO}}_{\mathrm{3}}}$, see Sect. 2.3 for its calculation) and explored the relationship between the ratio and the nighttime concentrations of some species (such as O₃, NO_x). It is found that there is a strong nonlinear relationship between them (shown in Fig. 6). The $R_{{\mathrm{NO}}_{\mathrm{3}}}$ had negative correlation coefficients with NO concentrations. With the increase in NO concentrations at night, the ratios decreased exponentially. When the NO concentrations increased under low-NO conditions, it could cause a significant decline in the ratios of VOC oxidized by NO₃. Under high-NO conditions, the ratios were not sensitive to the increase in NO concentrations (Fig. S14), indicating that the nighttime NO concentrations in Beijing effectively and strongly controlled the ratios. This is expected since the increase in NO concentrations controlled the NO₃ loss term and then caused the decrease in NO₃ concentration. When the NO concentrations exceeded a threshold value (7 ppbv), the NO₃ loss was dominated by NO.

The ratios of nighttime VOC oxidized by NO₃ also had a strong nonlinear relationship with O₃ and NO_x concentrations. O₃ concentrations have one positive and one negative contribution to the $R_{{\mathrm{NO}}_{\mathrm{3}}}$. The positive effect is that increasing the O₃ concentration increases the NO₃ production rate, which increases the NO₃ steady-state concentrations and then increase the ratios. The negative is that increasing O₃ concentrations increases the reaction rate between VOC and O₃, which increases the competitiveness of O₃ in terms of VOC oxidation and then decreases the ratios. Figure S14 also shows the relationship between $R_{{\mathrm{NO}}_{\mathrm{3}}}$ and the concentrations of O₃. While O₃ concentrations were below 25 ppbv, the ratios were very sensitive to the O₃ level, which quickly increased with O₃ concentration. The ratio became insensitive to this and remained relatively constant when the O₃ concentrations exceeded 25 ppbv. This can be explained as being due to the O₃ concentrations being low and the NO₃ production rate being more sensitive to the increase in O₃ concentrations. In this case, O₃ mainly affects the ratios positively. When the O₃ concentrations were high, the positive effect of O₃ tended to be constant, indicating that the two opposing effects remained in balance.

When the NO_x concentrations were low (i.e., < 25 ppbv), the $R_{{\mathrm{NO}}_{\mathrm{3}}}$ was less sensitive to NO_x, remaining relatively constant with further increases. The increase in NO₃ loss rates through the N₂O₅ heterogeneous reaction and the NO reaction was believed to be kept in balance with the NO₃ production rate increased by NO₂ concentrations. Under high-NO_x conditions, the ratios sensitively decreased with the increase in NO_x concentrations, which is explained by the increase in NO₃ loss rates by NO, resulting in a decline in the ratios.

To better understand the nonlinear effect of NO₂ and O₃ on the nighttime VOC oxidation, we further explored the effect of O₃ concentration on the ratios existing in different concentrations of NO₂. As shown in Fig. S15, at higher concentrations of NO₂, the threshold of lower O₃ concentrations was required for the $R_{{\mathrm{NO}}_{\mathrm{3}}}$ to become constant, which reflected the coupled influences of NO₂ and O₃ on nighttime VOC oxidation through the nonlinear response and indicated that nocturnal NO₃ chemistry tended to be more dominant in the NO₂-rich environment.

4 Conclusions and implications

In this study, we showed that the NO₃ reactivity towards measured VOC highly varied with big seasonal differences, mainly driven by isoprene concentrations. The top six contributors to the measured NO₃ reactivity towards VOC were isoprene, styrene, cis-2-butene, trans-2-butene, trans-2-pentene, and propylene. Among them, isoprene and styrene contributed most of the reactivity. In addition, monoterpenes are proposed as a significant source of NO₃ reactivity. Recently studies showed that anthropogenic emissions contribute significantly to the ambient MNT concentrations through biomass burning, traffic, and volatile chemical product emissions in the urban regions, it would further enhance the importance of nocturnal NO₃ oxidation (Coggon et al., 2021; Nelson et al., 2021; Peng et al., 2022; Qin et al., 2020; Wang et al., 2022). It should be noted that the estimated contributions of MNTs only considered the biogenic emissions and may represent a lower bias. Thus, we highlight the importance of field observations of MNTs for advancing the understanding of nighttime NO₃ chemistry. In addition, it should be noted that we did not take the contributions of OVOCs (oxygenated volatile organic compounds) into account since the reaction rate coefficients of OVOC with NO₃ are small (Ambrose et al., 2007).

Looking for insight into the trend and evolution of detailed NO₃ chemistry can be intimidating, but it can be helpful to understand the response of the nocturnal chemistry to the emission changes over large timescales. Limited by the non-extensive and non-continuous observations available, we cannot obtain long-term measurements of all VOC species at multiple sites. Since isoprene and styrene are good indicators of NO₃ reactivity in different seasons, at least in urban Beijing, they can be used to estimate the NO₃ reactivity towards VOC to re-establish the long-term trend of NO₃ reactivity in urban regions for further evaluation of its history of nighttime chemistry. We admit that the estimation of the NO₃ reactivity trend might be highly uncertain, but this attempt may be very helpful to determine the level of and overall change in nighttime chemistry.

We showed that NO₃ dominated the nighttime VOC oxidation in Beijing, but the oxidation ratio had a strong nonlinear relationship with O₃ and NO_x concentrations. With the NO₂ concentrations decreasing, the threshold values of O₃ between the sensitive regime and non-sensitive regime tended to increase, indicating that the nighttime oxidation by NO₃ would be more easily affected by the level of O₃ with the implementation of sustained NO_x reductions in the future. The threshold values of O₃ can provide an effective basis for the measures to control nocturnal chemical and secondary organic aerosol pollution in typical urban regions.