Measurement report: Variations and environmental impacts of atmospheric N₂O₅ concentrations in urban Beijing during the 2022 Winter Olympics

The chemistry of nitrate radical (NO₃) and dinitrogen pentoxide (N₂O₅) plays a pivotal role in tropospheric nighttime chemistry. Given their close linkage to precursor variations, emission reduction during the 2022 Beijing Winter Olympics likely affected NO₃ and N₂O₅ behavior. In this study, we measured N₂O₅, NO₂, O₃, etc. during and after the Olympics, and compared pollutant levels as well as the contributions of reaction pathways to the loss of NO₃ and N₂O₅. Throughout the entire observation period, NO₃ production rate averaged 0.5 ± 0.4 ppbv h⁻¹, and the N₂O₅ mixing ratio could reach up to 875 pptv within 1 min, indicating their active production. The relatively long nighttime N₂O₅ lifetime (${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$), with an average of 11.9 ± 11.8 min, suggested a slow N₂O₅ loss rate during winter season. Despite low NO mixing ratio (below 3 ppbv), it dominated NO₃ loss (79.0 %). VOCs oxidation contributed 0.2 %, primarily driven by styrene. During the Olympics, emission reductions led to decreased NO and VOCs, which in turn reduced their reaction with NO₃. The heterogeneous uptake of N₂O₅, another key NO₃ loss pathway – accounted for 20.8 % of NO₃ loss during the Olympics, but this contribution decreased to 10.6 % after the Olympics. This uptake is crucial for nighttime NO₃ removal and would be essential for winter nitrate formation in urban Beijing. Our results highlight that under emission control scenarios, the relative importance of heterogeneous processes in nocturnal NO₃ cycling increases, providing new insights into how emission reduction measures shape nighttime oxidation processes in polluted urban environments.

1 Introduction

Nitrate radical (NO₃) and dinitrogen pentoxide (N₂O₅) play crucial roles in the nocturnal atmospheric chemical cycle, controlling the removal and conversion of nitrogen oxides (NO_x) and volatile organic compounds (VOCs). They significantly contribute to the formation of nitrate and secondary organic aerosols during the nighttime (Crutzen, 1979; Wayne et al., 1991). NO₃ primarily originates from the reaction of NO₂ with O₃ (Reaction R1), while it rapidly establishes a thermodynamic equilibrium (Reaction R2) with N₂O₅. This tight coupling species are frequently considered simultaneously in atmospheric chemistry studies. During daytime, however, the rapid photolysis of NO₃ (Reaction R3) and its reaction with NO (Reaction R4) result in a short NO₃ lifetime (<5 s). Consequently, the concentrations of NO₃ and N₂O₅ usually fall below the detection limit of analytical instruments during daylight hours.

The direct removal pathways of NO₃ include heterogeneous reactions on particulate matter surfaces and gas-phase reactions with NO (Reaction R4) and VOCs (Reaction R5), which can influence the atmospheric lifetimes of nighttime NO_x and VOCs (Ng et al., 2017; Wayne et al., 1991). NO₃ is also capable of reacting with alkenes in an addition reaction and subsequently with O₂ to form peroxy radicals (RO₂), which further generates organic nitric acid, one of the important sources of secondary organic aerosols (Fry and Sackinger, 2012; Hoyle et al., 2007; Pye et al., 2010). The removal pathways of N₂O₅ represent indirect removal pathways for NO₃ chemistry (Reaction R6), primarily involving reactions with water vapor and heterogeneous reactions on cloud droplets or particle surfaces (Brown and Stutz, 2012; Chang et al., 2011).

$$\begin{array}{}\text{(R1)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}\leftrightarrows {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\text{(R3)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{hv}\to {\mathrm{O}}_{\mathrm{2}}+\mathrm{NO}\text{(R4)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}}\text{(R5)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{VOC}\to \mathrm{products}\text{(R6)}& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\mathrm{l}\right)\to \mathrm{2}{\mathrm{HNO}}_{\mathrm{3}}\end{array}$$

In recent years, anthropogenic emission control measures have played a pivotal role in improving air pollution in China with notable declines in NO_x emissions (Li et al., 2020; Zhang et al., 2016). However, NO_x emission intensity remains relatively high (Li et al., 2024). Reactive nitrogen-containing compounds have emerged as a prominent factor in China's complex air pollution scenario (Zhu et al., 2023). With advancements in measurement techniques, several research teams have explored the core processes of reactive nitrogen species in atmospheric pollution, particularly in regions with severe atmospheric pollution such as the North China Plain, the Yangtze River Delta, and the Pearl River Delta (Li et al., 2020; Tham et al., 2016; Wang et al., 2018, 2020, 2024, 2013; Yun et al., 2018). While NO₃ reactivity is typically attenuated under low-temperature winter conditions, thereby restricting its oxidative capacity, multiple studies – including winter campaigns such as Yun et al. (2018) and Yan et al. (2023) – have demonstrated the significance of nocturnal NO₃ chemistry in cold seasons.

Emerging evidence further highlights the sensitivity of nocturnal NO₃ chemistry to emission controls: increases in nocturnal NO₃ production rates enhance nighttime oxidation capacity (Wang et al., 2023a), and urban nocturnal NO₃ concentrations may even experience “explosive” growth under stringent emission reduction policies (Wang et al., 2023b). In the Beijing region specifically, Yan et al. (2023) showed that the contribution of nocturnal nitrogen chemistry to winter haze has increased in recent years. Despite these advances, gaps remain in our understanding how short-term, large-scale emission control measures – such as those implemented during major events – influence the balance between ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ production and loss, and their subsequent impacts on nighttime secondary pollution.

The 2022 Beijing Winter Olympics (BWO) provided a unique opportunity to address this gap. To ensure high air quality during the event, a series of strict emission reduction measures were implemented in Beijing and its surrounding areas, leading to a significant decline in PM_2.5 concentrations (average 24 µg m⁻³) compared to historical levels for the same period (Huang et al., 2024). Given the close linkage between ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ and their precursors (NO₂, O₃, and VOCs), this emission cuts were expected to alter the behavior of NO₃ and N₂O₅.

In this study, we conducted field observations of N₂O₅, NO₂, O₃, NO, VOCs, and meteorological parameters in urban Beijing during (5–20 February 2022) and after (21 February–3 March 2022) the BWO. Our objectives were to: (1) characterize the temporal variations of N₂O₅ and NO₃ in urban Beijing during winter; (2) quantify the contributions of different reaction pathways to NO₃ and N₂O₅ loss; and (3) assess how the BWO emission reduction measures modulated nocturnal ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ chemistry. The findings provide critical insights into the response of nighttime reactive nitrogen chemistry to short-term emission controls, with implications for air quality management in polluted urban environments.

2 Methods

2.1 Site description

Field measurements were conducted from 5 February to 3 March 2022 at an urban site in Beijing. The observation location was situated on the rooftop of the NO. 1 Science Building at Peking University in Beijing (39.99° N, 116.31° E, 61.6 m a.s.l.). As shown in Fig. 1, the location is proximal to the North Fourth Ring Road – one of Beijing's major traffic arteries – and within 1 km of two primary traffic corridors (east-west along the North Fourth Ring Road and north-south along Zhongguancun Street). The surrounding area features mixed land use, including residential complexes (within 500 m) and low-intensity commercial facilities (within 1 km), with no large industrial sources within a 5 km radius. This setting makes the site representative of a typical urban mixed-use area impacted by fresh anthropogenic emissions (e.g., traffic-related NO_x and VOCs), consistent with previous characterizations of this location (Hu et al., 2023; Wang et al., 2017a; Yao et al., 2023).

Sampling inlets were installed 1.5 m above the rooftop, approximately 20 m above ground level. Throughout the measurement period, the prevailing wind direction was predominantly from the northwest, with an average wind speed of 2.0 ± 2.0 m s⁻¹.

Figure 1 Measurement site, surroundings, and wind rose (winter 2022). Base map adapted from https://map.baidu.com/ (last access: 20 September 2025); wind rose generated from on-site meteorological observations.

2.2 Instrument setup

2.2.1 Measurement of NO₃ and N₂O₅

Ambient concentrations of NO₃ and N₂O₅ were determined utilizing an in-house-developed cavity ring-down spectroscopy (CRDS) analyzer, operating at a wavelength of 662 nm (Zhang et al., 2024). The analyzer employs a dual-channel design for simultaneous detection: Channel 1 directly measures NO₃ concentrations under ambient temperature conditions; Channel 2 maintained at 150 °C to thermally decompose N₂O₅ into NO₃, enabling quantification of the total concentration of [NO₃+ N₂O₅].

During this observation campaign, the NO₃-specific detection channel (Channel 1) malfunctioned due to the damage of the mirror, limiting measurements to the combined [NO₃+ N₂O₅] signal from Channel 2. NO₃ concentrations were subsequently derived using the thermodynamic equilibrium relationship between NO₃ and N₂O₅ (Eq. 1 in Sect. 2.3), with input parameters including measured N₂O₅, NO₂ concentrations, and ambient temperature. Under winter conditions (low temperature and relatively high NO₂ levels), the ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ ratio is inherently low (∼1 %), ensuring that [NO₃+ N₂O₅] is dominated by N₂O₅ and derived NO₃ concentrations are reliable.

The limit of detection (LOD) of the CRDS system was calculated as 2.9 pptv, with a measurement uncertainty of ± 13.7 % (Zhang et al., 2024). To ensure measurement accuracy, regular calibrations were performed using a stable dynamic generation system for NO₃ and N₂O₅ standard gases (Zhang et al., 2026). The detailed technical specifications of the instrument are provided in Sect. S1 of the Supplement.

2.2.2 Measurement of other species

Concentrations of NO, NO₂, O₃, VOCs, and meteorological parameters were measured using commercial or well-validated analytical instruments, with details summarized in Table 1. NO and O₃ mixing ratios were measured using commercial instruments, specifically the Model 42i-Y and Model 49i from Thermo Fisher Scientific (USA). NO₂ mixing ratios were observed via a cavity-enhanced absorption spectroscopy (CEAS) (Zhou et al., 2022). Calibrations of these instruments are performed weekly using the standard gases of known concentrations, and the R² of the standard curve for each calibration is greater than 0.99. VOC concentrations were determined using a gas chromatograph equipped with mass spectrometry and flame ionization detectors (Wang et al., 2014). This system measures 99 VOC species with a time resolution of 1 h, LOD range of 1–26 pptv, and accuracy of 0.8 %–6.1 %. Quality control included weekly zero/span checks (using ultra-high-purity nitrogen and a multi-component VOC standard) and a post-campaign full calibration, which confirmed linearity (R²>0.996) and negligible intercepts for all target VOCs. The photolysis rate constants (j-values) were obtained using a spectroradiometer (Metcon CCD-Spectrograph, Garmisch-Partenkirchen, Germany) (Bohn et al., 2008). This instrument quantifies two primary photolysis channels (NO₃+ hv → NO₂ + O(³P) and NO₃ + hv → NO + O₂), with total j(NO₃) calculated as the sum of the two channel-specific rate constants (j(NO₃)_total = j(NO₃)_M + j(NO₃)_R). Meteorological parameters, including wind direction, wind speed, temperature (T), and relative humidity (RH), were monitored utilizing a sensor meteorological measurement system (Metone, USA). The PM_2.5 concentration data were obtained from the Beijing Municipal Ecological and Environmental Monitoring Center (http://www.bjmemc.com.cn/, last access: 20 September 2025). Detailed information about these instruments is listed in Table 1.

Table 1 Species measured in the field work.

2.3 Calculation methods

When N₂O₅ concentrations are obtained, the concentration of NO₃ can be determined by dividing the concentration of N₂O₅ by the equilibrium constant K_eq and the concentration of NO₂ (Osthoff et al., 2006; Wang et al., 2017b), which is specified in Eq. (1).

$$\begin{array}{}\text{(1)}& \left[{\mathrm{NO}}_{\mathrm{3}}\right]={\displaystyle \frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{K_{\mathrm{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}\end{array}$$

Here, K_eq represents the temperature-dependent equilibrium constant established when NO₃ attains steady-state equilibrium with N₂O₅, and is given by $\mathrm{5.50}\times {\mathrm{10}}^{-\mathrm{27}}\times$ exp(10724/T), where T is the temperature in Kelvin (Wang et al., 2024).

The primary source of NO₃ and N₂O₅ is the chemical reaction of NO₂ with O₃. Consequently, the concentrations of NO₂ and O₃ are key factors influencing the production rate of NO₃ (P(NO₃)). This production rate is mathematically represented by Eq. (2) (Brown et al., 2011). Assuming that the formation and loss processes of NO₃ and N₂O₅ are in a state of dynamic equilibrium, the lifetime of N₂O₅, denoted as ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, can be expressed as the ratio of its concentration to the rate of NO₃ production, as determined by Eq. (2) (Brown and Stutz, 2012; Lin et al., 2022; Wang et al., 2017a).

$$\begin{array}{}\text{(2)}& {\displaystyle }P\left({\mathrm{NO}}_{\mathrm{3}}\right)=k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\times \left[{\mathrm{NO}}_{\mathrm{2}}\right]\times \left[{\mathrm{O}}_{\mathrm{3}}\right]\text{(3)}& {\displaystyle }{\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}={\displaystyle \frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{P\left({\mathrm{NO}}_{\mathrm{3}}\right)}}={\displaystyle \frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\cdot \left[{\mathrm{NO}}_{\mathrm{2}}\right]\cdot \left[{\mathrm{O}}_{\mathrm{3}}\right]}}}\end{array}$$

The total reactivity of NO₃ ($k_{{\mathrm{NO}}_{\mathrm{3}}}$) represents the sum of all first-order loss processes for NO₃, including photolysis, reaction with NO, reaction with VOCs, and indirect loss via N₂O₅ heterogeneous uptake. It is calculated using Eq. (4) (Wang et al., 2020): The nocturnal NO₃ loss rate, denoted as L(NO₃), is calculated via Eq. (5).

$$\begin{array}{}\text{(4)}& {\displaystyle }\begin{array}{rl}& k_{{\mathrm{NO}}_{\mathrm{3}}}=j\left({\mathrm{NO}}_{\mathrm{3}}\right)+k_{{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}}\cdot \left[\mathrm{NO}\right]+k_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{VOC}}_i}\\ & \cdot \left[{\mathrm{VOC}}_i\right]+k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\cdot K_{\mathrm{eq}}\cdot \left[{\mathrm{NO}}_{\mathrm{2}}\right]\end{array}\text{(5)}& {\displaystyle }\begin{array}{rl}& L\left({\mathrm{NO}}_{\mathrm{3}}\right)=\sum k_i\left[{\mathrm{VOC}}_i\right]\cdot \left[{\mathrm{NO}}_{\mathrm{3}}\right]+k_{{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}}\\ & \cdot \left[\mathrm{NO}\right]\left[{\mathrm{NO}}_{\mathrm{3}}\right]+k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\cdot \left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]\end{array}\end{array}$$

Here, j(NO₃) denotes the photolysis rate constant for NO₃ decomposition. The rate coefficients $k_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}$ and $k_{{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}}$ correspond to the rate coefficients for reaction Eqs. (1) and (4), respectively, as referenced in Atkinson et al. (2004). The reactivity of NO₃ with VOCs ($k_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{VOC}}_i}$) is characterized by a first order loss rate constant, calculated as the product of the reaction rate constant k_i and the VOC concentrations [VOC_i].

$k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ represents the total first-order loss rate coefficient for the heterogeneous uptake of N₂O₅ at the aerosol surface, which is governed by the uptake coefficient γ (N₂O₅), the aerosol surface area density S_a (µm² cm⁻³), and the mean molecular speed of N₂O₅, c, as described in Eq. (3).

$$\begin{array}{}\text{(6)}& k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}=\mathrm{1}/\mathrm{4}c{S}_{\mathrm{a}}\mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)\end{array}$$

The mean molecular speed c is calculated as $\sqrt{\mathrm{8}RT/\left(\mathit{\pi }M\right)}$, where R is the gas constant (8.314 J mol⁻¹ K⁻¹), T is temperature (K), and M is the molar mass of N₂O₅ (0.108 kg mol⁻¹). γ (N₂O₅) is a critical parameter describing the efficiency of N₂O₅ uptake on aerosol surfaces, influenced by aerosol composition (e.g., organic coatings, nitrate/sulfate content) and meteorological conditions (RH, temperature) (Bertram et al., 2009; Tang et al., 2014; Yu et al., 2020). It was determined using the steady-state method (Brown et al., 2016; Lin et al., 2022; Lu et al., 2022), which relies on linear regression of K_eq [NO₂] $\mathit{\tau }{\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)}^{-\mathrm{1}}$ and 1/4 cS_aK_eq [NO₂] (Eq. 7).

$$\begin{array}{}\text{(7)}& K_{\mathrm{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\mathit{\tau }{\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)}^{-\mathrm{1}}=\mathrm{1}/\mathrm{4}c{S}_{\mathrm{a}}\mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)K_{\mathrm{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]+k_{{\mathrm{NO}}_{\mathrm{3}}}\end{array}$$

Here, the slope of the regression equals γ (N₂O₅), and the intercept equals $k_{{\mathrm{NO}}_{\mathrm{3}}}$. To minimize interference from non-steady-state conditions, data fitting was data fitting was performed under the following constraints:

(1) Meteorological constraint: RH < 70 % (avoiding excessive water vapor interference); (2) Chemical constraints: NO < 1 ppbv (suppressing NO-NO₃ titration), [N₂O₅] > LOD (2.9 pptv, ensuring reliable equilibrium calculations); (2) Timing constraint: Data selected 2–3 h post-sunset (when the NO₃-N₂O₅ equilibrium is most stable). Negative intercepts (physically implausible, arising from $k_{{\mathrm{NO}}_{\mathrm{3}}}$) were excluded, resulting in 23 valid data points for γ (N₂O₅) calculation.

Aerosol surface area density (S_a)

Due to the unavailability of direct particle size distribution measurements, S_a was derived from PM_2.5 concentrations using an empirical formula validated for winter Beijing conditions (Zhang et al., 2022):

$$\begin{array}{}\text{(8)}& S_{\mathrm{a}}=\mathrm{60.03}\times [{\mathrm{PM}}_{\mathrm{2.5}}{]}^{\mathrm{0.62}}\end{array}$$

This formula exhibits a strong linear correlation (R²=0.82) with PM_2.5 and is applicable for PM_2.5 concentrations <200 µg m⁻³ – consistent with the PM_2.5 range observed in this study (average: 24 ± 21 µg m⁻³, maximum: 131 µg m⁻³).

3 Results

3.1 Measurements overview

Figure 2 illustrates time-series variations in the mixing ratios of N₂O₅ and associated trace gases, alongside meteorological parameters, captured during the 2022 Beijing Winter Olympics (BWO) at a temporal resolution of 1 min. Valid data were systematically acquired over a 26-d span, from 5 February to 3 March. In alignment with the 2022 Beijing Winter Olympics timeline, the observation interval was bifurcated into two distinct periods: (1) the Olympic Games Period (OGP; spanning 5–20 February), and (2) the Post-Olympics Period (POP; extending from 21 February to 3 March). Comprehensive statistical metrics for each period are meticulously detailed in Table 2.

Figure 2 Time series for N₂O₅, NO₃, related trace gases, and meteorological data (T and RH) measured in Beijing from 5 February to 3 March 2022.

Table 2 Summary of observed parameters for the two periods (mean ± standard deviation).

3.1.1 Meteorological conditions and PM_2.5

Meteorological conditions differed notably between the OGP and POP, driving variations in pollutant dispersion and chemical reactivity:

•  

  Temperature: Nocturnal temperatures during the OGP were predominantly below freezing (average: −1.4 ± 3.6 °C), while the POP saw a marked warming trend – nocturnal temperatures rose to 3.5 ± 3.5 °C (all-day average: 5.6 ± 3.9 °C, vs. −0.4 ± 3.9 °C in the OGP).

•  

  Relative Humidity (RH): The OGP exhibited higher RH (nocturnal average: 29 ± 13 %) compared to the POP (nocturnal average: 20 ± 4 %). A heavy snowfall event occurred during 13–14 February (OGP), coinciding with peak RH (> 60 %) and a transient increase in PM_2.5 concentration (68 µg m⁻³).

•  

  PM_2.5: The overall average PM_2.5 concentration across the entire observation period was 24 ± 21 µg m⁻³, consistent with the improved air quality during the BWO (Huang et al., 2024). While PM_2.5 levels were similar between the OGP (nocturnal average: 26 ± 2 µg m⁻³) and POP (nocturnal average: 23 ± 2 µg m⁻³), the POP experienced a severe pollution episode with PM_2.5 peaking at 131 µg m⁻³ – likely driven by relaxed emissions and stagnant meteorological conditions.

The aerosol surface area density, a key parameter for N₂O₅ heterogeneous uptake calculations (Eq. 8), was derived from PM_2.5 concentrations. The overall average S_a was 402 ± 215 µm² cm⁻³, with values in the OGP (nocturnal average: 417 ± 208 µm² cm⁻³) slightly higher than in the POP (nocturnal average: 385 ± 205 µm² cm⁻³), reflecting the influence of PM_2.5 and RH-driven aerosol growth.

3.1.2 Precursor gases (NO, NO₂, O₃)

Concentrations of NO_x (NO + NO₂) and O₃ – key precursors for ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ production (Reaction R1) – exhibited distinct differences between the OGP and POP, directly reflecting the impact of emission controls:

•  

  NO: The OGP observed significantly lower NO concentrations compared to the POP – nocturnal NO averaged 1.0 ± 1.2 ppbv (OGP) vs. 4.8 ± 6.0 ppbv (POP). This contrast confirms BWO emission reductions effectively curbed primary NO emissions (e.g., traffic, industry), which further modulated O₃ and NO₂ dynamics.

•  

  NO₂: Inverse to NO, NO₂ concentrations were higher in the POP. Nocturnal NO₂ averaged 20.7 ± 13.1 ppbv in the POP, compared to 14.5 ± 9.3 ppbv in the OGP. The increase in NO₂ during the POP is attributed to enhanced NO oxidation by O₃, driven by higher post-Olympic NO emissions.

•  

  O₃: Nocturnal O₃ levels were substantially higher in the OGP (27.4 ± 10.3 ppbv) than in the POP (19.8 ± 12.1 ppbv), despite similar all-day averages (OGP: 29.9 ± 9.5 ppbv; POP: 26.7 ± 10.6 ppbv). The lower nocturnal O₃ in the POP results from intensified O₃ titration by elevated NO, a process that simultaneously increases NO₂ concentrations. Notably, the overall mean O₃ concentration (28.6 ± 12.8 ppbv) was lower than spring values in Beijing (Wang et al., 2018), consistent with reduced photochemical O₃ production in winter.

The average NO_x concentration (18.2 ± 16.6 ppbv) during the study was also substantially lower than autumn values at this site (typically >30 ppbv) (Li et al., 2022; Wang et al., 2017a), further highlighting the effectiveness of winter emission controls.

3.1.3 N₂O₅ and NO₃ concentrations

N₂O₅ concentrations exhibited significant temporal variability throughout the observation period, with a mean daily value of 86.7 ± 116.5 pptv and a maximum of 874.9 pptv (00:15 LST on 18 February, OGP) – coinciding with moderate NO₂ (14.6 ppbv), O₃ (26.8 ppbv) and extremely low NO (0.4 ppbv) that minimized NO₃ titration.

NO₃ concentrations were derived from the NO₃-N₂O₅ equilibrium (Eq. 1), with a mean value of 0.6 ± 0.7 pptv (maximum: 4.6 pptv). Nocturnal NO₃ levels followed the same trend as N₂O₅: higher in the OGP (0.6 ± 0.6 pptv) than in the POP (0.5 ± 0.6 pptv). This derived NO₃ concentration is notably lower than observations in Shanghai (16 ± 9 pptv) (Wang et al., 2013), likely due to Beijing's lower winter temperatures (which suppress NO₃ production) and higher NO emissions (which enhance NO₃ loss).

3.1.4 NO₃ production rate and N₂O₅ lifetime

The NO₃ production rate, calculated via Eq. (2) as the product of the NO₂ + O₃ reaction rate constant and precursor concentrations, averaged 0.5 ± 0.4 ppbv h⁻¹ across the entire observation period, with a maximum of 2.4 ppbv h⁻¹. This value aligns with winter observations in the Beijing area (0.4 ppbv h⁻¹) (Wang et al., 2021) and summer measurements at Mount Tai (0.45 ± 0.40 ppbv h⁻¹) (Wang et al., 2017c), but is lower than autumn values in Beijing (2.25 ± 2.02 ppbv h⁻¹) (Wang et al., 2017a) and summer measurements in Taizhou (1.2 ± 0.3 ppbv h⁻¹) (Li et al., 2020). The relatively low P(NO₃) in this study is primarily driven by winter's low temperatures, which reduce the NO₂ + O₃ reaction rate constant: for example, at identical NO₂ (15 ppbv) and O₃ (30 ppbv) concentrations, increasing temperature from −1 to 5 °C raises the rate constant from $\mathrm{1.59}\times {\mathrm{10}}^{-\mathrm{17}}$ to $\mathrm{1.94}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molecule⁻¹ s⁻¹, leading to a 19 % increase in P(NO₃) (from 0.70 to 0.83 ppbv h⁻¹).

The N₂O₅ lifetime, a key indicator of N₂O₅ removal efficiency (Eq. 2), averaged 11.9 ± 11.8 min across the study – longer than summer values in Beijing (270 ± 240 s) (Wang et al., 2018) and rural Wangdu (77–172 s) (Tham et al., 2016), but shorter than observations in the Hong Kong boundary layer (Brown et al., 2016). This prolonged winter ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ suggests slower nocturnal ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ loss, consistent with lower winter temperatures and reduced heterogeneous reactivity.

Notably, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ differed significantly between the OGP and POP: the nocturnal mean lifetime was 17.0 ± 17.0 min in the OGP, compared to 11.6 ± 6.8 min in the POP – a ∼5-min reduction. This difference is primarily driven by variations in N₂O₅ concentrations (rather than P(NO₃), which was similar between periods: OGP nocturnal P(NO₃)=0.5 ± 0.2 ppbv h⁻¹; POP = 0.5 ± 0.3 ppbv h⁻¹).

3.2 Mean diurnal variations

Figure 3 displays the average diurnal variations in NO, NO₂, N₂O₅, NO₃, O₃ mixing ratios, and P(NO₃) during the study period. Specifically, panel (a) presents the daily mean patterns for the OGP, whereas panel (b) depicts those for the POP. Notable differences in concentration but similar diurnal trends were observed between the two periods.

Figure 3 Mean diurnal variations in NO, NO₂, N₂O₅, NO₃, O₃ mixing ratios and P(NO₃) during (a) the Olympic Games Period (OGP) and (b) the Post-Olympics Period (POP). Data represent hourly means with error bars indicating the standard deviation; non-physical values <0 (for NO₃) have been excluded.

3.2.1 Diurnal cycles of precursor gases (NO, NO₂, O₃)

The diurnal variations of NO, NO₂, and O₃ exhibit strong interdependencies, consistent with well-documented atmospheric chemical processes (e.g., O₃ titration by NO, NO₂ photolysis) and anthropogenic emission patterns.

Nocturnal NO mixing ratios were substantially lower in the OGP than in the POP, with OGP nighttime values remaining below 2 ppbv (average: 1.0 ± 1.2 ppbv) and POP values frequently exceeding 4 ppbv (average: 4.8 ± 6.0 ppbv). Both periods showed two distinct daily peaks in NO, aligned with morning (06:00–08:00 LST) and evening (18:00–20:00 LST) traffic rush hours – confirming traffic as the primary NO source. The morning peak was particularly pronounced in the POP, reaching 20.4 ppbv at 08:00 LST (vs. 6.4 ppbv at 06:00 LST in the OGP), directly attributable to relaxed post-Olympic traffic emission controls.

NO₂ concentrations displayed an inverse diurnal trend to O₃, with nocturnal levels consistently higher than daytime values (OGP: 14.5 ± 9.3 ppbv nighttime vs. 12.6 ± 8.2 ppbv all-day; POP: 20.7 ± 13.1 ppbv nighttime vs. 18.2 ± 12.3 ppbv all-day). This pattern arises from reduced daytime NO₂ photolysis (NO₂+ hv → NO + O) and enhanced nocturnal NO oxidation. The POP saw higher NO₂ concentrations across all hours, with the nocturnal peak (24.3 ppbv at 21:00 LST) exceeding the OGP peak (15.9 ppbv at 21:00 LST) by ∼ 35 % – a result of elevated NO emissions driving more O₃-to-NO₂ conversion.

O₃ exhibited a classic mid-afternoon peak in both periods, rising gradually after sunrise (07:00 LST) as photochemical production intensified, and peaking between 15:00–16:00 LST (OGP: 39.9 ppbv; POP: 41.2 ppbv). Nocturnal O₃ levels, however, differed sharply: the OGP maintained higher nighttime O₃ (27.4 ± 10.3 ppbv) compared to the POP (19.8 ± 12.1 ppbv), with the POP O₃ concentration dropping to a minimum of 14.6 ppbv at 07:00 LST (vs. 22.2 ppbv in the OGP). This discrepancy stems from intensified O₃ titration by NO in the POP – higher NO concentrations rapidly consume O₃ via NO + O₃→ NO₂ + O₂, reducing the O₃ pool available for NO₃ production (Reaction R1).

3.2.2 Diurnal cycles of NO₃ production rate

P(NO₃) exhibited a strong diurnal pattern tied to the availability of its precursors (NO₂ and O₃) and the suppression of daytime NO₃ loss.

In both periods, P(NO₃) peaked shortly after sunset (19:00 LST), when O₃ concentrations remained relatively high (OGP: 33.3 ppbv; POP: 30.6 ppbv) and NO emissions (and thus NO₃ titration) were still low. The OGP peak P(NO₃) was 0.74 ppbv h⁻¹, slightly lower than the POP peak (0.92 ppbv h⁻¹) – a difference driven by the POP's higher NO₂ concentrations (18.4 ppbv at 19:00 LST vs. 14.2 ppbv in the OGP) offsetting its lower O₃. Throughout the night, P(NO₃) gradually declined in both periods: by 04:00 LST, it dropped to 0.33 ppbv h⁻¹ (OGP) and 0.20 ppbv h⁻¹ (POP), mirroring the nocturnal decrease in O₃.

Notably, P(NO₃) showed a strong first-order exponential decay correlation with NO concentrations (Fig. S2): when NO < 5 ppbv, P(NO₃) decreased sharply with increasing NO (from 1.2 to 0.5 ppbv h⁻¹); when NO > 10 ppbv, P(NO₃) stabilized at < 0.3 ppbv h⁻¹. This confirms NO is a dominant inhibitor of NO₃ production – even small NO increases (e.g., POP rush hours) rapidly consume NO₃ as it forms.

3.2.3 Diurnal cycles of N₂O₅ and NO₃

N₂O₅ and NO₃ exhibited nearly identical diurnal patterns in both periods, reflecting their tight thermodynamic equilibrium (Reaction R2) and shared dependence on precursor availability and loss pathways:

•  

  Post-sunset accumulation: Both species began accumulating rapidly after sunset (18:00 LST), as photolysis (a major daytime NO₃ loss pathway) ceased. They reached peak concentrations around 20:00 LST – shortly after the P(NO₃) peak – with OGP peaks (N₂O₅: 208.2 pptv; NO₃: 1.1 pptv) exceeding POP peaks (N₂O₅: 171.2 pptv; NO₃: 1.0 pptv) by ∼ 22 %. This difference is driven by the OGP's lower NO concentrations, which reduce NO₃ titration (Reaction R4) and allow more N₂O₅ to form via equilibrium.

•  

  Nocturnal decline: After the 20:00 LST peak, N₂O₅ and NO₃ concentrations gradually decreased in the OGP, falling to near-detection limits by sunrise (07:00 LST). The POP, however, showed a steeper decline between 02:00–04:00 LST: N₂O₅ dropped from 94.1 to 61.8 pptv, and NO₃ from 0.6 to 0.3 pptv – attributed to elevated nocturnal NO emissions in the POP (peaking at 9.9 ppbv at 04:00 LST) that accelerate NO₃ loss.

•  

  Morning secondary peak (POP only): A notable secondary peak in N₂O₅ (112.1 pptv at 06:00 LST) and NO₃ (0.5 pptv at 06:00 LST) occurred in the POP, coinciding with a transient increase in O₃ (1.3 ppbv) and decrease in NO (2.9 ppbv) before morning rush hour. This peak is absent in the OGP, likely because lower POP emission controls led to a larger “pre-rush” O₃ pool that drives NO₃ production, while OGP NO emissions remained too low to support such a transient precursor balance.

The daily average variation trends of both N₂O₅ and NO₃ aligned with those reported for the Yangtze River Delta and North China regions (Li et al., 2020; Wang et al., 2022, 2017b). While the chemical conditions in this study bore similarities to those in summer Beijing, the meteorological conditions differed, notably characterized by higher relative humidity during the summer. The average nocturnal N₂O₅ concentration over the observation period was 113.7 ± 103.3 pptv, which was higher than that observed in the Changping area of Beijing (Wang et al., 2018), indicating that the loss process of NO₃ and N₂O₅ in Beijing during winter is more sluggish compared to that in the summer.

4 Discussion

4.1 Factoring influencing N₂O₅ lifetime

RH and S_a are well-recognized as pivotal factors regulating N₂O₅ lifetime in nocturnal atmospheric chemistry, as they directly modulate the efficiency of N₂O₅ heterogeneous uptake – the primary indirect loss pathway for NO₃ (Brown et al., 2017; Lin et al., 2022). The correlation between these parameters and ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ is presented in Fig. 4.

Figure 4 The relationship between ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and S_a as well as RH during the observation period.

4.1.1 Relationship between ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and RH

As shown in Fig. 4a, the correlation between ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and RH exhibits a humidity-dependent dual pattern. At RH < 35 %, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ increased with RH – slight humidity rises softened hydrophobic organic coatings on aerosols (from traffic VOC oxidation), thereby reducing N₂O₅ heterogeneous uptake. RH > 35 %, the heterogeneous uptake rate of N₂O₅ increases, and ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ decreases with increasing RH.

•  

  RH < 35 %: Counterintuitive ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ increases with rising RH. Minimal aerosol liquid water content drives hydrophobic organic components – primarily oxidation products of traffic-related anthropogenic VOCs (AVOCs, e.g., styrene, propylene) – to condense into dense, impermeable coatings on particle surfaces (Bertram et al., 2009; Folkers et al., 2003; McNeill et al., 2006; Tang et al., 2014). These coatings act as a diffusion barrier, preventing N₂O₅ from reaching reactive aqueous sites (e.g., nitrate/sulfate-rich droplets) and lowering the heterogeneous uptake coefficient γ (N₂O₅) (Anttila et al., 2006; Yu et al., 2020). For example, at RH = 25 %, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ averaged 15.5 min, 43 % longer than the 8.9 min observed at RH = 15 %.

•  

  RH > 35 %: ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ decreases with increasing RH (conventional trend). Above 35 % RH, the relationship aligns with physical expectations: ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ declines as RH increases, driven by two synergistic effects. First, hygroscopic growth of aerosols (e.g., ammonium sulfate, sodium chloride) increases S_a, providing more reactive surface sites for N₂O₅ uptake. Second, elevated aerosol liquid water content accelerates N₂O₅ hydrolysis, which becomes the dominant N₂O₅ loss pathway (Brown et al., 2016; Chang et al., 2011). This effect is particularly pronounced when RH > 60 %: during the snowfall events on 13–14 February 2022, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ approached zero (0.8 ± 0.3 min), as high RH (> 85 %) maximized both aerosol growth and hydrolysis efficiency.

Notably, scattered data points in the 30 %–40 % RH range (e.g., ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ ranging from 2 to 33 min at RH = 35 %) suggest interference from transient factors – such as sudden NO spikes or shifts in aerosol organic composition – which obscure the RH-${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ relationship. A more comprehensive discussion of these confounding factors requires consideration of the organic composition of the aerosol.

4.1.2 Relationship between ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and S_a

Figure 4b depicts the dependence of ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ on S_a, reflecting the interplay between S_a and other regulating factors (e.g., RH, organic coatings).

•  

  S_a < 325 µm² cm⁻³: ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ gradually increases with rising S_a. For low S_a values, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ gradually rises from ∼ 10 to 12 min as S_a increases. This non-monotonic pattern is driven by the co-occurrence of low S_a with extremely dry conditions (RH < 25 % for 68 % of data points in this S_a range).

•  

  S_a= 500–1000 µm² cm⁻³: Robust negative correlation. Above a threshold S_a of ∼ 500 µm⁻² cm⁻³, a clear negative correlation emerges: ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ decreases from ∼ 12 to 6 min as S_a increases. This aligns with physical expectations, as higher S_a provides more reactive surface area for N₂O₅ heterogeneous uptake (Lin et al., 2022; Wang et al., 2020; Zhou et al., 2018).

Quantitative discrepancies between our results and summer studies (e.g., Zhou et al., 2018 reported ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ < 5 min at S_a>600 µm² cm⁻³in urban Beijing) are attributed to seasonal differences in aerosol liquid water content. Winter's lower RH (average: 24 ± 12 %) reduces aerosol liquid water content, lowering γ (N₂O₅) and slowing N₂O₅ loss – even at high S_a. This highlights the need for season-specific parameterizations of S_a-${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ relationships in air quality models.

4.2 NO₃ and N₂O₅ loss pathways

To quantify the mechanisms governing NO₃ and N₂O₅ removal, we calculated total NO₃ reactivity via Eq. (4) and dissected the contributions of individual loss pathways. The reaction rate constants for the interaction between VOCs and the oxidizing agent NO₃ were obtained from the literature (Atkinson and Arey, 2003; Brown et al., 2011) or extracted from the National Institute of Standards and Technology database (accessible via http://webbook.nist.gov/chemistry/, last access: 20 September 2025). For certain VOC species where quantitative laboratory reaction rate constants were unavailable, these values were estimated based on the reaction rate constants of analogous species.

4.2.1 NO₃ Loss via VOC oxidation and N₂O₅ uptake

VOC-driven NO₃ loss is negligible in winter urban Beijing, but distinct patterns emerge in the concentrations and reactivity of different VOC categories. Detailed statistical data regarding VOC concentrations (e.g., styrene, isoprene, and other anthropogenic species) and their corresponding NO₃ reaction rates – are provided in Table S1 (Supplement). Time series plots of the concentrations of several highly reactive VOCs (Fig. S3) show that the styrene concentration peaks at 86 pptv, while the isoprene concentration peaks at 96 pptv. Comparative analysis reveals these high-VOC periods coincide with enhanced NO (e.g., NO spikes to 24.8 ppbv on 24 February, POP), suggesting VOCs and NO share a common emission source (traffic exhaust) – consistent with the site's proximity to urban traffic corridors (Sect. 2.1).

•  

  High-concentration AVOCs contribute minimally. The most abundant VOCs – ethane (3.8 ± 1.8 ppbv), propane (2.1 ± 1.3 ppbv), and acetone (1.4 ± 0.8 ppbv) – exhibit extremely low $k_{{\mathrm{NO}}_{\mathrm{3}}}$ (e.g., k(NO₃+ propane) = 9.49×10¹⁵ cm³ molecule⁻¹ s⁻¹ at 298 K (Atkinson and Arey, 2003). As a result, their combined contribution to total VOC-driven NO₃ reactivity is < 5 % ($\mathrm{0.04}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹), emphasizing that high VOC concentration does not equate to strong NO₃ reactivity. When all AVOCs are considered, they dominate NO₃ reactivity (∼ 70.4 % of total VOC-driven NO₃ loss), exceeding the contribution of biogenic VOCs (BVOCs, ∼ 29.6 %) (Fig. S4).

•  

  Reactive VOCs dominate VOC-driven NO₃ loss. Despite their low concentrations, styrene and isoprene account for ∼ 74 % of total VOC-driven NO₃ reactivity (Fig. S4), due to their high $k_{{\mathrm{NO}}_{\mathrm{3}}}$.

•  

  Styrene: Average reactivity $=\mathrm{0.34}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ ($k=\mathrm{1.5}\times {\mathrm{10}}^{\mathrm{12}}$ cm³ molecule⁻¹ s⁻¹), contributing ∼44 % of VOC reactivity. Styrene emissions in Beijing are primarily from vehicle exhaust, with minor contributions from evergreen plant emissions (Li et al., 2014).

•  

  Isoprene: Average reactivity $=\mathrm{0.25}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹, contributing ∼30 % of VOC reactivity. Isoprene has dual sources: traffic exhaust (anthropogenic) and deciduous/evergreen plant emissions (biogenic), with biogenic sources dominating in winter (Cheng et al., 2018; Yuan et al., 2009).

Notably, biogenic VOCs (BVOCs) other than isoprene (e.g., limonene, α-pinene) were not detected, leading to potential underestimation of BVOC reactivity. For example, the rate constant for limonene ($\sim \mathrm{1.6}\times {\mathrm{10}}^{\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹) is $\sim \mathrm{20}\times$ higher than isoprene's, so including it could increase the total VOC reactivity.

γ(N₂O₅) – a key parameter describing the efficiency of N₂O₅ uptake on aerosol surfaces – was calculated via Eq. (7) (steady-state method) with strict data selection, and the calculation results for S_a are presented in Fig. S5. For most of the time, γ(N₂O₅) ranged from 0.01 to 0.12 (average: 0.032 ± 0.049; Table S2), consistent with observations in urban Beijing (0.01–0.09) (Li et al., 2022; Wang et al., 2017a; Xia et al., 2021; Zhou et al., 2018) but higher than rural sites: Wangdu (Hebei), 0.006–0.034 (Tham et al., 2018); Hong Kong boundary layer, 0.014 ± 0.007 (Brown et al., 2016); Rural Germany, 0.028 ± 0.029 (Phillips et al., 2016). The elevated γ(N₂O₅) in our study is attributed to urban aerosols' higher water content and reactive composition (e.g., nitrate, sulfate, and organic acids), which enhance N₂O₅ hydrolysis efficiency (Bertram et al., 2009; Tang et al., 2014).

4.2.2 Temporal Variations in NO₃ Reactivity

To characterize how NO₃ loss dynamics respond to emission controls and transient environmental events, we analyzed the time series of total NO₃ reactivity – the sum of all first-order loss pathways, including reaction with NO, heterogeneous uptake of N₂O₅, oxidation by VOCs, and photolysis (daytime only). This analysis is supported by Fig. 5 (time series of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ and key environmental drivers).

•  

  OGP: Total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ averaged 1.14 s⁻¹, with minimal day-to-day variability. A notable exception occurred on 13 February, when a heavy snowfall event (RH = 71 %, PM_2.5=61 µg m⁻³) triggered a transient spike in $k_{{\mathrm{NO}}_{\mathrm{3}}}$ to 2.35 s⁻¹ – nearly double the OGP average. This spike was driven by enhanced N₂O₅ heterogeneous uptake (Sect. 4.1.1), as high RH increased aerosol liquid water content and reactive surface sites.

•  

  POP: Total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ surged to 3.06 s⁻¹ (2.7× higher than OGP), driven by a 3.7× increase in NO reactivity (from 0.81 to 3.00 s⁻¹; Table 3). The elevated NO reactivity aligns with post-Olympic NO emission rebound (Sect. 3.1.2), which intensified NO₃ titration (Reaction R4) and crowded out N₂O₅ uptake.

Figure 5 Time series variation of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ (reactions with NO and VOCs, heterogeneous uptake of N₂O₅ and photolysis of NO₃).

Figure 5 also captures the response of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ to transient NO spikes – critical drivers of non-steady-state NO₃ loss. For example, on 24 February (POP), a sudden NO burst (24.8 ppbv, Fig. S6) caused total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ to jump from 1.3 to 26.5 s⁻¹ within 30 min, with no corresponding change in RH or S_a. This confirms that NO can override the effects of meteorological factors on $k_{{\mathrm{NO}}_{\mathrm{3}}}$ in winter urban environments.

Table 3 Statistics of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ across various pathways and time periods.

To dissect the drivers of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$ variation, Table 3 presents the contributions of individual reactivity components (NO reaction, N₂O₅ uptake, VOC oxidation) for both periods:

•  

  OGP (Table 3): Reactivity was dominated by two pathways. (1) NO reaction: Contributed 0.81 s⁻¹ (71.1 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), reflecting moderate NO emissions under Olympic controls. (2) N₂O₅ uptake: Contributed 0.32 s⁻¹ (28.1 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), with the 13 February snowfall event pushing this contribution to 86 % (2.35 s⁻¹ ). VOC oxidation remained negligible at $\mathrm{0.8}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ (< 0.1 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), consistent with winter's low VOC emissions and low NO₃-VOC reaction rates (Sect. 4.2.1). For instance, even the styrene contributed only ∼44 % of total VOC reactivity, which remained orders of magnitude lower than NO-driven reactivity.

•  

  POP (Table 3): A dramatic shift in reactivity partitioning occurred. (1) NO reaction: Exploded to 3.00 s⁻¹ (98.0 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), a 3.7× increase from the OGP. This was driven by post-Olympic NO emissions, which intensified NO₃ titration and crowded out other loss pathways. (2) N₂O₅ uptake: Plummeted to 0.06 s⁻¹ (2.0 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), an 81 % decrease from the OGP. The decline stemmed from lower POP RH (19 % vs. 27 % in OGP), which reduced aerosol liquid water content and suppressed N₂O₅ hydrolysis (Reaction R6). This RH-dependent hydrolysis inhibition is further validated by Fig. S7 (Supplement): the figure presents the correlation between N₂O₅ hydrolysis rate and RH during the POP, showing a strong positive linear relationship (R²=0.81). The reduced hydrolysis efficiency directly limited N₂O₅'s role as an indirect NO₃ sink, contributing to its diminished share of NO₃ loss in the POP. VOC oxidation increased slightly to $\mathrm{1.4}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ (<0.1 % of total $k_{{\mathrm{NO}}_{\mathrm{3}}}$), reflecting a modest rebound in anthropogenic VOC emissions (Table 2: total VOCs = 19.68 ppbv vs. 16.02 ppbv in OGP) but remained functionally irrelevant to NO₃ loss.

The combined analysis of Fig. 5 (total trend) and Table 3 reveals two critical findings:

•  

  Emission controls rewire reactivity partitioning: Olympic NO_x reductions reduced NO's dominance as a NO₃ sink, allowing N₂O₅ uptake to emerge as a significant secondary pathway. Relaxing controls reversed this shift, reestablishing NO as the near-exclusive NO₃ loss mechanism.

•  

  Extreme events disrupt baseline reactivity: High-RH events (e.g., snowfall) and NO spikes can temporarily alter reactivity partitioning, but their effects are transient – baseline dynamics remain governed by long-term emission conditions.

4.2.3 NO₃ loss budget

Figure 6 illustrates the diurnal variation and relative contributions of NO₃ loss pathways, with distinct differences between the OGP and POP that reflect the impact of Olympic emission controls.

•  

  OGP: Balanced NO and N₂O₅ uptake pathways. NO dominated NO₃ loss (79.0 %), but N₂O₅ uptake emerged as a significant secondary pathway (20.8 %), with VOC oxidation contributing <0.2 %. The N₂O₅ uptake pathway peaked at 19:00 LST (0.37 ppbv h⁻¹), coinciding with high [N₂O₅] (149.9 pptv). This contribution is comparable to winter observations in urban Beijing (Li et al., 2022).

•  

  POP: NO dominates NO₃ loss. NO's contribution to NO₃ loss rose to 89.4 %, with a peak loss rate of 2.04 ppbv h⁻¹ at 22:00 LST – driven by post-Olympic NO emissions that increased significantly (Table 2). In contrast, N₂O₅ uptake declined to 10.6 %, as lower RH reduced γ (N₂O₅) and S_a reactivity. Notably, the POP's NO₃ loss rate (1.61 ppbv h⁻¹) was 30 % higher than the OGP's (1.14 ppbv h⁻¹), confirming that relaxed emissions accelerated nocturnal NO₃ removal.

Compared to summer studies (Lin et al., 2022), winter's low VOC reactivity and high NO emissions make NO the unambiguous primary NO₃ sink in urban Beijing. This seasonal contrast underscores the need for season-specific air quality management strategies – prioritizing NO_x reduction in winter and VOC reduction in summer.

Figure 6 Mean daily variation and reactivity share of different loss pathways.

4.3 Linkage to Olympic Emission Controls and Precursor Dynamics

The 2022 Beijing Winter Olympics provided a unique “natural experiment” to quantify how short-term, large-scale emission controls modulate nocturnal NO₃-N₂O₅ chemistry. Below, we dissect the impacts of these controls on precursor concentrations and loss pathway hierarchies, and explore the interacting roles of NO₂ and O₃ in shaping NO₃-N₂O₅ dynamics.

4.3.1 Impact of Emission Controls on NO₃-N₂O₅ Chemistry

The Olympic emission control measures – including traffic restrictions (e.g., odd-even license plate policy), industrial shutdowns, and reduced coal combustion – induced significant changes in precursor concentrations and NO₃-N₂O₅ behavior.

•  

  Precursor modulation: OGP emissions of NO_x and VOCs were substantially lower than the POP. Nocturnal NO decreased by 79 % (1.0 vs. 4.8 ppbv), and NO₂ by 30 % (14.5 vs. 20.7 ppbv). Nocturnal total VOCs decreased by 18 % (16.02 vs. 19.68 ppbv), with reactive AVOCs (styrene) declining by 40 %.

  Lower NO emissions weakened its role as a “NO₃ scavenger,” allowing more NO₃ to partition into N₂O₅ via Reaction (R2). This explains why the OGP's nocturnal [N₂O₅] (137.6 pptv) was 41 % higher than the POP's (97.8 pptv), despite similar NO₃ production rates (P(NO₃)= 0.5 ppbv h⁻¹ for both periods).

•  

  Loss pathway shift: Reduced NO emissions elevated the relative importance of N₂O₅ uptake in NO₃ loss – its contribution increased from 10.6 % (POP) to 20.8 % (OGP). This shift demonstrates that emission controls can “rewire” nocturnal loss hierarchies, making heterogeneous processes more significant as primary pollutant emissions decline. This finding extends previous studies (Xia et al., 2020; Zhou et al., 2018 which focused on ClNO₂ formation but did not quantify N₂O₅'s role under low-NO conditions.

4.3.2 Precursor (NO₂, O₃) Influences on NO₃-N₂O₅ Dynamics

NO₂ and O₃, the primary precursors of NO₃ via Reaction (R1), exert dual and interactive controls on NO₃-N₂O₅ chemistry that depend on emission conditions.

•  

  NO₂: Equilibrium driver and precursor tradeoff. NO₂ plays two conflicting roles: it is both a precursor for NO₃ (via Reaction R1) and a partner in the NO₃-N₂O₅ equilibrium (via Reaction R2). During the OGP, higher nocturnal NO₂ (14.5 ppbv) shifted the equilibrium toward N₂O₅, as low NO prevented rapid NO₃ loss. This created a “N₂O₅ surplus,” with [N₂O₅] exceeding the POP's by 41 %. In contrast, the POP's higher NO₂ (20.7 ppbv) paired with elevated NO (4.8 ppbv) created a “dual sink” effect: more NO₃ was produced via Reaction (R1), but immediately titrated by NO via Reaction (R4) – limiting N₂O₅ accumulation. This tradeoff highlights NO₂'s context-dependent role in NO₃-N₂O₅ dynamics.

•  

  O₃: Production regulator and persistence enhancer. OGP's higher nocturnal O₃ (27.4 vs. 19.8 ppbv in the POP) initially boosted NO₃ production (P(NO₃)= 0.5 ppbv h⁻¹), but lower NO prevented rapid NO₃ loss. This “NO₃ surplus” prolonged N₂O₅ lifetime: the OGP's nocturnal ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (17.0 min) was 46 % longer than the POP's (11.6 min). This indirect effect of O₃ – enhancing N₂O₅ persistence by supporting NO₃ production without accelerating loss – has not been fully quantified in previous winter studies, emphasizing the need to consider O₃ alongside NO_x in nocturnal chemistry models.

4.4 Broader Atmospheric Implications

Our findings advance understanding of winter urban nocturnal chemistry and provide critical insights for air quality management in polluted regions like Beijing. Three key implications emerge:

•  

  Emission control efficacy and regional nitrate transport. Olympic controls demonstrated that reducing NO_x (not just VOCs) can enhance N₂O₅ accumulation – potentially extending the lifetime of reactive nitrogen and increasing regional nitrate transport. N₂O₅ is a stable reservoir species that can be transported long distances before hydrolyzing to form nitrate aerosols; thus, increased N₂O₅ under NO_x reduction may shift winter nitrate pollution from local to regional scales. This suggests that future NO_x mitigation strategies should consider regional coordination to address long-range transport of reactive nitrogen.

•  

  Model parameterization improvements. Our results provide two critical constraints for air quality models, which often underestimate winter N₂O₅ chemistry.

•  

  S_a threshold: S_a exerts significant control over ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ only when S_a>500 µm⁻² cm⁻³; below this threshold, organic coatings and NO dominate.

•  

  γ (N₂O₅) range: The average γ(N₂O₅) of 0.032 ± 0.049 (with values up to 0.22 under high RH) is higher than the constant γ(N₂O₅) = 0.02 (Chang et al., 2011) often used in models. Incorporating these season-specific parameters will improve predictions of winter nitrate formation.

•  

  Winter mitigation priority: NO_x over VOCs. Despite their high reactivity, VOCs contribute <0.5 % of NO₃ loss in winter urban Beijing – far less than NO (79.0 %–89.4 %). This confirms that NO_x (not VOCs) should be prioritized for mitigating winter nocturnal nitrogen pollution. For example, further reducing traffic-related NO emissions (a major source in urban Beijing) would not only lower direct NO pollution but also enhance N₂O₅ uptake – a pathway that converts reactive nitrogen to nitrate, which is less toxic and more easily removed via wet deposition.

5 Summary and conclusions

This study conducted continuous field observations of N₂O₅, NO₃, and their precursor species (NO, NO₂, O₃, VOCs) in urban Beijing from 5 February to 3 March 2022, covering the 2022 Beijing Winter Olympics (BWO). By analyzing pollutant variations, quantifying the contributions of ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ loss pathways, and linking observations to BWO emission control measures, we clarified the response of winter nocturnal reactive nitrogen chemistry to short-term anthropogenic emission reductions.

During the observation period, P(NO₃) averaged 0.5 ± 0.4 ppbv h⁻¹, with N₂O₅ mixing ratios peaking at 875 pptv (1-min resolution) and derived NO₃ concentrations reaching a maximum of 4.6 pptv; ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ averaged 11.9 ± 11.8 min, longer than summer values in Beijing due to slower winter N₂O₅ loss driven by low temperatures and reduced heterogeneous reactivity. BWO emission controls significantly modulated precursor concentrations: nocturnal NO (1.0 ± 1.2 ppbv) and total VOCs (16.02 ± 7.74 ppbv) in the OGP were 79 % and 18 % lower than in the POP, respectively, while nocturnal O₃ was 38 % higher in the OGP (27.4 ± 10.3 ppbv vs. 19.8 ± 12.1 ppbv in the POP) as reduced NO minimized O₃ titration – these changes directly led to 41 % higher nocturnal N₂O₅ concentrations in the OGP (137.6 ± 112.7 pptv vs. 97.8 ± 90.3 pptv in the POP).

RH and S_a exerted context-dependent control over ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$: at RH < 35 %, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ increased with RH as slight humidity rises softened hydrophobic organic aerosol coatings (derived from traffic VOC oxidation) and reduced N₂O₅ heterogeneous uptake; at RH > 35 %, ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ decreased with RH due to hygroscopic aerosol growth and enhanced N₂O₅ hydrolysis, approaching zero during snowfall events (RH > 85 %). For S_a, a threshold of ∼ 500 µm⁻² cm⁻³ was identified – below this value, organic coatings and NO dominated ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$; above it, S_a became the primary regulator, with ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ decreasing as S_a increased.

NO was the dominant NO₃ sink in both periods, though its contribution varied with emission controls: it accounted for 79.0 % of NO₃ loss in the OGP, with N₂O₅ heterogeneous uptake (20.8 %) as a significant secondary pathway, while its contribution rose to 89.2 % in the POP (driven by 3.8× higher NO emissions) and N₂O₅ uptake declined to 10.6 % (due to lower RH reducing aerosol reactivity). The N₂O₅ heterogeneous uptake coefficient (γ(N₂O₅)) averaged 0.032 ± 0.049 in the OGP, higher than rural sites due to urban aerosols' higher water content and reactive components (e.g., nitrate, sulfate). Despite the high reactivity of species like styrene and isoprene, VOC oxidation contributed <0.2 % to NO₃ loss in both periods, confirming its negligible role in winter NO₃ dynamics in urban Beijing.

These findings hold key implications for air quality management: BWO NO_x reductions enhanced N₂O₅ accumulation, potentially extending reactive nitrogen lifetime and shifting winter nitrate pollution from local to regional scales – highlighting the need for regional coordination in NO_x mitigation; the identified S_a threshold (500 µm² cm⁻³) and γ(N₂O₅) range (0.01–0.12) provide critical constraints for air quality models, which often rely on oversimplified ${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and γ (N₂O₅) parameters; and given NO's dominance in NO₃ loss and N₂O₅ dynamics, NO_x (not VOCs) should be prioritized for winter nocturnal nitrogen pollution control in Beijing – reducing traffic-related NO emissions would simultaneously lower direct pollution and enhance N₂O₅ uptake, promoting nitrate removal via wet deposition.