Amplified role of potential HONO sources in O₃ formation in North China Plain during autumn haze aggravating processes

Co-occurrences of high concentrations of PM_2.5 and ozone (O₃) have been frequently observed in haze-aggravating processes in the North China Plain (NCP) over the past few years. Higher O₃ concentrations on hazy days were hypothesized to be related to nitrous acid (HONO), but the key sources of HONO enhancing O₃ during haze-aggravating processes remain unclear. We added six potential HONO sources, i.e., four ground-based (traffic, soil, and indoor emissions, and the NO₂ heterogeneous reaction on ground surface (Het_ground)) sources, and two aerosol-related (the NO₂ heterogeneous reaction on aerosol surfaces (Het_aerosol) and nitrate photolysis (Phot_nitrate)) sources into the WRF-Chem model and designed 23 simulation scenarios to explore the unclear key sources. The results indicate that ground-based HONO sources producing HONO enhancements showed a rapid decrease with height, while the NO + OH reaction and aerosol-related HONO sources decreased slowly with height. Phot_nitrate contributions to HONO concentrations were enhanced with aggravated pollution levels. The enhancement of HONO due to Phot_nitrate on hazy days was about 10 times greater than on clean days and Phot_nitrate dominated daytime HONO sources (∼ 30 %–70 % when the ratio of the photolysis frequency of nitrate (J_nitrate) to gas nitric acid ($J_{{\mathrm{HNO}}_{\mathrm{3}}}$) equals 30) at higher layers (>800 m). Compared with that on clean days, the Phot_nitrate contribution to the enhanced daily maximum 8 h averaged (DMA8) O₃ was increased by over 1 magnitude during the haze-aggravating process. Phot_nitrate contributed only ∼ 5 % of the surface HONO in the daytime with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 but contributed ∼ 30 %–50 % of the enhanced O₃ near the surface in NCP on hazy days. Surface O₃ was dominated by volatile organic compound-sensitive chemistry, while O₃ at higher altitudes (>800 m) was dominated by NO_x-sensitive chemistry. Phot_nitrate had a limited impact on nitrate concentrations (<15 %) even with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120. These results suggest the potential but significant impact of Phot_nitrate on O₃ formation, and that more comprehensive studies on Phot_nitrate in the atmosphere are still needed.

1 Introduction

Nitrous acid (HONO) is an important source of the hydroxyl radical (OH) through its photolysis (Reaction R1), and contributes ∼ 20 %–80 % of primary OH production (Alicke et al., 2002; Hendrick et al., 2014; Kim et al., 2014).

$$\begin{array}{}\text{(R1)}& \mathrm{HONO}+hv\to \mathrm{NO}+\mathrm{OH}.\end{array}$$

Although 40 years have passed since the first detection of HONO in the atmosphere (Perner and Platt, 1979), the sources of HONO (especially daytime) and the dynamic parameters of HONO formation mechanisms are still not well understood (Ge et al., 2021). Current air quality models with the default gas-phase reaction (the reverse reaction of Reaction R1) always significantly underestimate HONO observations, resulting in low atmospheric oxidation capacity and in underestimation of secondary pollutants such as ozone (O₃) (Li et al., 2010, 2011; Sarwar et al., 2008; Zhang et al., 2016, 2019a).

HONO sources can be generally classified into three categories, i.e., direct emissions and homogeneous and heterogeneous reactions. Direction emissions are mainly from traffic (Kramer et al., 2020; Kurtenbach et al., 2001; Liao et al., 2021), soil (Kubota and Asami, 1985; Oswald et al., 2013; Wu et al., 2019; Xue et al., 2021), biomass burning (Cui et al., 2021; Rondon and Sanhueza, 1989; Theys et al., 2020), and indoor combustion processes (Klosterkother et al., 2021; Liu et al., 2019; Pitts et al., 1985). The reaction of nitric oxide (NO) with OH (Pagsberg et al., 1997; Stuhl and Niki, 1972) is usually thought to be the dominant homogeneous reaction and is significant during daytime, but may be neglected at night due to low OH concentrations, other minor homogeneous HONO sources including nucleation of NO₂, H₂O, and NH₃ (Zhang and Tao, 2010), via the photolysis of ortho-nitrophenols (Bejan et al., 2006; Chen et al., 2021; Lee et al., 2016), via the electronically excited NO₂ and H₂O (Crowley and Carl, 1997; Dillon and Crowley, 2018; Li et al., 2008) and via HO₂•H₂O + NO₂ reaction (Li et al., 2015, 2014; Ye et al., 2015). The heterogeneous reactions mainly include nitrogen dioxide (NO₂) hydrolysis and reduction reactions on various humid surfaces (Finlayson-Pitts et al., 2003; Ge et al., 2019; Gómez Alvarez et al., 2014; Ma et al., 2013; Marion et al., 2021; Sakamaki et al., 1983; Tang et al., 2017; W. Yang et al., 2021) and nitrate photolysis (Phot_nitrate) (Romer et al., 2018; Ye et al., 2016a, b; Zhou et al., 2003), and are usually considered the main contributors to HONO concentrations in the atmosphere.

Among these potential HONO sources, the photolysis of nitrate to produce HONO in the atmosphere has received extensive attention over the past few years, and the Phot_nitrate frequency (J_nitrate) is still debated (Gen et al.., 2022). In laboratory studies, some researchers (Bao et al., 2018; Ye et al., 2016a, 2017) showed that Phot_nitrate was an important HONO source, the measured J_nitrate was 1–3 orders larger than the gas nitric acid (HNO₃) photolysis frequency ($J_{{\mathrm{HNO}}_{\mathrm{3}}}$) and could reach up to 10⁻⁴ s⁻¹. Furthermore, a number of substances including humic acid (Yang et al., 2018), sulfate (Bao et al., 2020), and TiO₂ (Xu et al., 2021) might enhance the reaction significantly; while Shi et al. (2021) found that the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio was <10 when using suspended submicron particulate sodium and ammonium nitrate rather than PM_2.5 samples. In field studies combined with model simulations, Kasibhatla et al. (2018) compared NO_x observations from the Cape Verde Atmospheric Observatory with GEOS-Chem (Goddard Earth Observing System-Chemistry) model simulations and reported a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 25–50; Romer et al. (2018) reported a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of <30 based on observations of NO_x (= NO + NO₂) and HNO₃ over the Yellow Sea and a box model simulation, while larger $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (e.g., 300) were inconsistent with the observed NO_x to HNO₃ ratios. Adopting a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of ∼ 120 could greatly improve daytime surface HONO simulations (contributed ∼ 30 %–40 % of noontime HONO) by using the Community Multiscale Air Quality model (CMAQ) in the Pearl River Delta (Fu et al., 2019) or a box model in the Yangtze River Delta (Shi et al., 2020), whereas a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 produced negligible HONO in clean periods (∼ 2 %) and slightly higher HONO in heavy haze periods (∼ 8 %) in the North China Plain (NCP) by using a box model (Xue et al., 2020) and ∼ 1 % by using CMAQ in urban Beijing (Zhang et al., 2021). Recently, Zheng et al. (2020) evaluated the effect of three $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (1, 10, and 100) on heterogeneous sulfate formation by using CMAQ and large uncertainties of simulated sulfate concentrations were reported. The most widely adopted $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios were 1–30 or 100–120 with large uncertainties, and thus more efforts are needed to better understand the Phot_nitrate impact on atmospheric oxidation capacity and on concentrations of HONO and other secondary pollutants.

A number of potential HONO sources (e.g., direct emissions, NO₂ heterogeneous reactions, and Phot_nitrate) have been coupled into several air quality models (An et al., 2013; Fu et al., 2019; Guo et al., 2020; Li et al., 2010, 2011; Sarwar et al., 2008; Tang et al., 2015; Xu et al., 2006; Zhang et al., 2019a, b, 2021, 2022; J. Zhang et al. 2020) to improve HONO simulations. The improved HONO sources can produce more OH, which is favorable for the formation of O₃ (Fu et al., 2019; Guo et al., 2020; Li et al., 2010; Xing et al., 2019; Zhang et al., 2016, 2019a, 2022). O₃ can directly damage plants and threaten human health (Avnery et al., 2011a, b; Feng et al., 2015, 2019, 2022; Mills et al., 2007, 2018; Richards et al., 1958; Selin et al., 2009; Wilkinson et al., 2012; Zhao et al., 2021), and an increasing trend of O₃ concentrations in China has been widely reported in recent years (S. Chen et al., 2020; Li et al., 2020; Lu et al., 2020; Ma et al., 2016; Maji and Namdeo, 2021), making O₃ pollution a severe concern. A co-occurrence of high PM_2.5 and O₃ concentrations has been frequently reported in China over the past few years, with researchers speculating a significant role of HONO in producing O₃ enhancements (Feng et al., 2021; Fu et al., 2019; Tie et al., 2019; K. Yang et al., 2021). Nevertheless, current knowledge on the HONO difference in O₃ formation during clean and hazy days is still unclear, especially the relative contribution of each potential HONO source to O₃ enhancements during haze-aggravating processes with a co-occurrence of high PM_2.5 and O₃ concentrations.

In this study, time series of pollutants including HONO, O₃, and nitrate were collected in NCP during 11–31 October 2018, in which high concentrations of PM_2.5 accompanied by high O₃ concentrations were found at least twice during haze events. The specific role of each potential HONO source in O₃ formation is explored during these haze events by coupling the potential HONO sources into the Weather Research and Forecasting model with Chemistry (WRF-Chem, Grell et al., 2005). The relative contribution of each potential HONO source to surface-averaged and vertically averaged concentrations of HONO and O₃ are quantified and the uncertainty in key potential HONO sources (e.g., J_nitrate) is discussed, in order to find the key HONO sources resulting in O₃ enhancements in NCP at different pollution levels (especially during haze-aggravating processes).

2 Data and methods

2.1 Observation data

The field observation was carried out during 11–31 October 2018, and the observation site was located on the west campus of Beijing University of Chemical Technology (BUCT, 116^∘18^′37^′′ E, 39^∘56^′56^′′ N) in Beijing. BUCT is an urban site close to the third ring road of Beijing, with extensive human activities, including vehicle emissions. Instruments were set up on the fifth floor of the main teaching building. HONO was measured with a home-made water-based long-path absorption photometer (Y. Chen et al., 2020). A dual-channel absorption system was deployed to subtract the potential interferences, e.g., NO₂ hydrolysis. A set of on-line commercial analyzers (Thermo 48i, 42i, 49i, 43i) was used for measurements of CO, NO_x, O₃, and SO₂. Specifically, the 42i used a molybdenum NO₂-to-NO converter, and there would be an NO₂ overestimation for the conversion of HONO, HNO₃, or other NO_y. Considering the relatively lower concentration compared with NO₂, the impact would be minor. The chemical composition of PM_2.5 was analyzed with a Time-of-Flight Aerosol Chemical Speciation Monitor (ToF-ACSM, Aerodyne). ToF-ACSM was developed by Fröhlich et al. (2013) for non-refractory PM_2.5 measurement. Details on its usage can be found in Liu et al. (2020), where ionization efficiency calibration of nitrate was performed using 300 nm dry NH₄NO₃ every month during the observation period. An online single-photon ionization time-of-flight mass spectrometer (SPI-ToF-MS, Hexin) was used for the detection of a large variety of volatile organic compounds (VOCs) (Gao et al., 2013). Surface observations of O₃, NO₂, PM_2.5, and PM₁₀ at 95 sites in NCP were obtained from https://quotsoft.net/air/ (last access: 3 March 2022​​​​​​​), issued by the China Ministry of Ecology and Environment; surface meteorological observations at 284 sites in NCP were taken from the National Climatic Data Center, China Meteorological Administration (Fig. 1).

Figure 1 Domains of WRF-Chem used in this study (a), and the locations of one HONO observation site (orange dot in urban Beijing), 95 environmental monitoring (PM_2.5, NO₂ and O₃) sites (dark pink dots), and 284 meteorological observation sites (black dots) in domain 2 (b).

Vertical HONO observations were not available during the period 11–31 October 2018 at the BUCT site, and we therefore used the observed vertical HONO concentrations from Meng et al. (2020) in urban Beijing in December 2016 to evaluate our simulation of vertical HONO concentrations, which were also used by Zhang et al. (2021) in their CMAQ evaluation.

2.2 Model description

The improved WRF-Chem model (version 3.7.1), which included six potential HONO sources, i.e., traffic (E_traffic), soil (E_soil), and indoor (E_indoor) emissions, Phot_nitrate in the atmosphere, and NO₂ heterogeneous reactions on aerosol (Het_aerosol) and ground (Het_ground) surfaces (Zhang et al., 2019a), was used in this study. Phot_nitrate was newly added in WRF-Chem (Reaction R2) following the work of Fu et al. (2019), Ye et al. (2017), and Zhou et al. (2003):

$$\begin{array}{}\text{(R2)}& p{\mathrm{NO}}_{\mathrm{3}}+hv\to \mathrm{0.67}\mathrm{HONO}+\mathrm{0.33}{\mathrm{NO}}_{\mathrm{2}}.\end{array}$$

For Het_aerosol and Het_ground, laboratory studies suggest that these heterogeneous reactions of NO₂ to HONO are of first order in NO₂ (Aumont et al., 2003; Finlayson-Pitts et al., 2003; Saliba et al., 2000):

$$\begin{array}{}\text{(R3)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}{k}_{\mathrm{a}},\text{(R4)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}{k}_{\mathrm{g}}.\end{array}$$

The first-order rate constants for aerosol (k_a) and ground (k_g) surface reactions are calculated as:

$$\begin{array}{}\text{(1)}& {\displaystyle }{k}_{\mathrm{a}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\times v_{{\mathrm{NO}}_{\mathrm{2}}}\times \left({\displaystyle \frac{S}{V}}\right)\times \mathit{\gamma },\text{(2)}& {\displaystyle }{k}_{\mathrm{g}}={\displaystyle \frac{f\times v_{\mathrm{d}}}{H}},\end{array}$$

where $v_{{\mathrm{NO}}_{\mathrm{2}}}$ is the mean molecular speed of NO₂, $\frac{S}{V}$ is the surface-to-volume ratio for aerosols, γ is the reactive uptake coefficient of aerosols, f is the proportion of deposited NO₂ reaching the surface in participating HONO formation, v_d is the dry deposition velocity of NO₂, and H is the first model layer height above the ground (∼ 35 m). It should be noted that not 100 % (50 % is commonly accepted) of the participating NO₂ could be converted to HONO in Reactions (R3) and (R4), and thus k_a and k_g were multiplied by 0.5 in the final calculation of HONO heterogeneous formation via NO₂.

The two factors γ and f were improved from previous studies (Li et al., 2010; Liu et al., 2014; Zhang et al., 2019a) and calculated by:

$$\begin{array}{}\text{(3)}& {\displaystyle }\mathit{\gamma }=\mathrm{5}\times {\mathrm{10}}^{-\mathrm{6}}\times \left(\mathrm{1}+{\displaystyle \frac{\mathrm{SR}}{\mathit{\alpha }}}\right),\text{(4)}& {\displaystyle }f=\mathrm{0.08}\times \left(\mathrm{1}+{\displaystyle \frac{\mathrm{SR}}{\mathit{\alpha }}}\right),\end{array}$$

where SR denotes solar radiation (W m⁻²), α is an adjusted parameter and set as 100 (W m⁻²), and thus γ and f become continuous functions during the whole day (γ and f enhanced by 10 times and reached 5 × 10⁻⁵ and 0.8 when SR reached 900 W m⁻² at noontime, respectively).

The physical and chemical schemes used in this study are given in Table 1. Two domains were adopted, domain one contains 82 × 64 grid cells with a horizontal resolution of 81 km, and domain two contains 51 × 51 grid cells with a horizontal resolution of 27 km (Fig. 1), both with 17 vertical layers encompassing from the surface to 100 hPa. The observational sites are shown in the right panel of Fig. 1, including one HONO observation site (the orange dot in urban Beijing), 95 observation sites of PM_2.5, NO₂, and O₃ (pink dots), and 284 meteorological monitoring sites (black dots).

Table 1 Physical and chemical options in WRF-Chem used in this study.

The anthropogenic emissions in East Asia in 2010 were taken from the MIX emission inventory (Li et al., 2017) (http://www.meicmodel.org/, last access: 3 March 2022), including both gaseous and aerosol species, i.e., SO₂, NO_x, CO, VOCs, NH₃, PM₁₀, PM_2.5, BC, OC, and CO₂, and were provided monthly by five sectors (power, industry, residential, transportation, and agriculture) at a resolution of 0.25^∘ × 0.25^∘. VOC emissions were speciated into model-ready inputs according to the MOZART chemical mechanism to build the WRF-Chem emission files. The anthropogenic emissions in China were replaced by employing the MEIC 2016 (the Multi-resolution Emission Inventory for China) developed by Tsinghua University. The NH₃ emissions in China were from Dong et al. (2010), biomass burning emissions were from Huang et al. (2012), and biogenic emissions were calculated using the Model of Emissions of Gases and Aerosols from Nature (MEGAN) (Guenther et al., 2012). Due to the sharp reduction in anthropogenic emissions in recent years, the default emission inventory was systematically overestimated in autumn of 2018, especially for SO₂ and PM_2.5 concentrations. Based on the comparison of simulations and observations (the urban Beijing site plus the other 95 pollutant-monitoring sites in NCP), we cut off 80 % of SO₂ emissions, 50 % of NH₃ emissions, 30 % of toluene emissions, and 50 % of PM_2.5 and PM₁₀ emissions. The cut-off emissions are largely close to the emission reductions in east China during the period 2013–2017 (Zhang and Geng, 2019). The revised emissions significantly improved regional PM_2.5 simulations in NCP (Fig. S1), and the simulations of gases and PM_2.5 in urban Beijing (Fig. S2).

The National Centers for Environmental Prediction (NCEP) 1^∘ × 1^∘ final reanalysis data (FNL) (https://rda.ucar.edu/datasets/ds083.2/, last access: 3 March 2022, National Centers for Environmental Prediction et al., 2000) were used in this study to obtain the meteorological initial and boundary conditions every 6 h. The global simulations of MOZART-4 (https://www.acom.ucar.edu/wrf-chem/mozart.shtml, last access: 3 March 2022) were used as the chemical initial and boundary conditions (every 6 h).

In total, 23 simulation scenarios were performed in this study (Table 2), in which the base case only considered the default homogeneous reaction (OH + NO → HONO), case 6S contained six potential HONO sources while cases A, B, C, D, E, and F contained each of the six potential HONO sources, respectively. The other 15 cases (A_double, A_half, … , Nit_120, D_NO₂, and D_HONO) were used to evaluate the uncertainties of the six potential HONO sources (Table 2). All of the cases were simulated with a spin-up of 7 d. J_nitrate and $J_{{\mathrm{HNO}}_{\mathrm{3}}}$ denote the photolysis frequency of nitrate and gas nitric acid in the atmosphere, respectively. The enhancement factor for F_double was 1.25 instead of 2.0 to avoid the production rate of HONO from NO₂ reaching the surface exceeding 100 %. The 0.33NO₂ in D_NO₂ or 0.67HONO in D_HONO referred to the assumed Phot_nitrate products in Reaction (R2).

Table 2 Simulation scenarios designed in this study.

3 Results

3.1 Comparison of simulations and observations

3.1.1 Meteorological factors

The statistical metrics of simulated meteorological parameters at 284 sites in NCP including air temperature (T), relative humidity (RH), and wind speed (WS) were comparable with the modeling results reported by other researchers (Table 3). The simulated wind direction (WD) bias within 45^∘ accounted for ∼ 56 %, and the bias within 90^∘ accounted for ∼ 80 %, suggesting that the simulated WD captured the main observed WD.

Table 3 Performance metrics (index of agreement (IOA), RMSE, and MB (mean bias)) of WRF-Chem simulated air temperature, relative humidity, wind speed, and direction at 284 meteorological sites in the North China Plain during 11–31 October 2018. The definitions of the metrics used in this study are given in Sect. S1.

3.1.2 Pollutant concentrations at the BUCT site

Time series of the observational data at the BUCT site are shown in Fig. 2, the gray-shaded periods stand for three haze-aggravating processes, while the cyan-shaded period denotes typical clean days. The largest hourly observations of O₃ (∼ 50–75 ppb) and PM_2.5 (∼ 100–200 µg m⁻³) were both relatively higher on hazy days than on clean days, especially for the first two haze events (the O₃ concentrations in the third haze event were relatively lower due to the higher NO_x concentrations in the urban area).

Figure 2 Comparison of simulated (Base and 6S cases) and observed hourly concentrations of PM_2.5, nitrate, NO₂, HONO, and O₃ (a–e), and the hourly enhanced concentrations of O₃ (ΔO₃) (f) caused by the six potential HONO sources (6S minus Base) at the BUCT site during 11–31 October 2018.

The observed PM_2.5 and nitrate trends at the BUCT site were well simulated (Fig. 2a and b), and NO₂ simulations generally agreed with the observations (Fig. 2c). The promotion effect of the six potential HONO sources on the formation of secondary aerosols leads to an increase in concentrations of PM_2.5 and nitrate for case 6S, despite nitrate consumption through Phot_nitrate (Li et al., 2010; Qu et al., 2019; Fu et al., 2019; Zhang et al., 2019a, 2021); detailed nitrate variation caused by each of the six potential HONO sources in case 6S is presented in Fig. S3. The overestimation of nitrate could be partially caused by the uncertainties in the anthropogenic emission inventory, e.g., the overestimation of NO_x emissions (Fig. 2c). The inadequate understanding of the nitrate formation mechanism could also be related to nitrate simulation bias, which was also found in some related studies using CMAQ (Fu et al., 2019; Zhang et al., 2021).

Hourly and diurnal HONO simulations at the BUCT site (Figs. 2d and 3a) were significantly improved in the 6S case (mean of 1.47 ppb) compared with the base case (mean of 0.05 ppb). The normalized mean bias (NMB) was remarkably reduced to −14.22 % (6S) from −97.11 % (Base), and the index of agreement (IOA) was improved significantly to 0.80 (6S) from 0.45 (Base) (Fig. 2d). The underestimation of the simulated HONO (6S) on 15 and 22 October was mainly caused by the earlier scavenging of pollutants at the BUCT site in the model used (Fig. 2a and d).

Figure 3 Comparison of diurnal mean simulations (Base and 6S cases) and observations of HONO during the study period (a) and O₃ during the first two haze events at the BUCT site (b) and O₃ averages at the 95 NCP monitoring sites during the study period (c); the relative contributions of each of the six potential HONO sources and the reaction of OH with NO to surface HONO concentrations for the 6S case at the BUCT site (d), at the 95 monitoring sites (e), and in the whole NCP region (f). The calculated 24 h mean HONO concentrations and DMA8 O₃ concentrations are given in panels a–c.

As for O₃, noticeable improvements were found at the BUCT site after considering the six potential HONO sources, especially on hazy days (Fig. 2e and f). The mean bias (MB) was improved to −3.61 ppb (6S) from −7.09 ppb (Base), and the IOA was improved to 0.86 (6S) from 0.78 (Base) (Fig. 2e). In particular, the 6S case significantly enhanced daytime hourly O₃ by 15–35 ppb compared with the base case, and the simulated O₃ was very close to the observations on hazy days (Fig. 2e). Larger daytime O₃ enhancements were accompanied by higher PM_2.5 concentrations during haze-aggravating processes, while on clean days the daytime-enhanced O₃ due to the potential HONO sources was mostly <5 ppb (Fig. 2e and f). The diurnal O₃ pattern during the first two haze-aggravating processes is presented in Fig. 3b. Significant improvements in daily maximum 8 h (10:00–17:59) averaged (DMA8) O₃ (18.8 ppb) occurred at the BUCT site after considering the six potential HONO sources, and the NMB of DMA8 O₃ was remarkably improved to −2.38 % (6S) from −47.14 % (Base).

The relative contribution of each HONO source near the surface at the BUCT site for the 6S case is shown in Fig. 3d. Briefly, Het_ground was the largest source during daytime and nighttime (∼ 50 %–70 %), consistent with the results of Zhang et al. (2021). Phot_nitrate ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{30}$) and the NO + OH reaction contributed similarly ∼ 1 %–12 % during daytime. The contribution of E_traffic was significant during nighttime (∼ 10 %–20 %) but small during daytime (<5 %). The contribution of Het_aerosol to HONO concentrations was minor (∼ 2 %–3 %) during daytime and ∼ 6 %–10 % at nighttime. E_soil could be neglected while the contribution of E_indoor was close to that of E_traffic in urban Beijing. The relative contribution of the potential HONO sources in this study was comparable to the results reported by Fu et al. (2019) when using CMAQ, except for the contribution of Phot_nitrate due to the different $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (30 in our study and ∼ 120 in Fu et al., 2019).

3.1.3 Pollutant concentrations in NCP

The 95-site-averaged hourly simulations and observations of O₃, NO₂, and PM_2.5 during the study period are shown in Fig. 4. The six potential HONO sources significantly improved hourly O₃ simulations, remarkably enhanced the daily maximum O₃ by ∼ 5–10 ppb during 11–25 October, and by ∼ 2–4 ppb during 26–31 October (Fig. 4a and b). The simulations of NO₂ agreed well with the observations, and the mean concentrations were 22.55 (Base), 21.62 (6S), and 20.74 (Obs) ppb (Fig. 4c). The PM_2.5 simulations generally followed the observed PM_2.5 trend but were overestimated by ∼ 8 µg m⁻³, with averaged concentrations of 49.94 (Base), 53.30 (6S), and 45.31 (Obs) µg m⁻³ (Fig. 4d), respectively.

Figure 4 Comparison of 95-site-averaged hourly simulations (Base and 6S cases) and observations of O₃ (a), NO₂ (c), PM_2.5 (d), and O₃ enhancements due to the six potential HONO sources (6S minus Base case) (b) in the North China Plain during 11–31 October 2018.

The 95-site-averaged diurnal simulations and observations of O₃ are presented in Fig. 3c. O₃ simulations showed a remarkable improvement when the six potential HONO sources were considered. The six potential HONO sources produced a mean enhancement of 5.7 ppb in DMA8 O₃ and improved the NMB to −7.16 % from −20.32 % at the 95 sites in NCP. The 95-site-averaged diurnal simulations and observations of NO₂ and PM_2.5 during the study period are demonstrated in Fig. S4. NO₂ simulations generally followed the observed trend but were underestimated from 04:00 to 16:00 and overestimated after 18:00 (Fig. S4a), PM_2.5 simulations agreed with the observed diurnal pattern but were overestimated for both cases during the whole day (Fig. S4b).

The relative contribution of each HONO source near the surface at the 95 NCP sites for the 6S case is shown in Fig. 3e. Het_ground was the dominant source during daytime and nighttime (∼ 70 %–80 %). Phot_nitrate ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{30}$) and the NO + OH reaction nearly equaled and contributed ∼ 2 %–8 % during daytime (∼ 5 % on average). The contribution of E_traffic was significant during nighttime (∼ 10 %–15 %) but small during daytime (<3 %). The contribution of Het_aerosol to HONO concentrations was <3 % during daytime and <10 % at nighttime. E_soil contributed ∼ 3 % at nighttime but could be neglected at daytime. The contribution of E_indoor was too small to be noticed at the 95 NCP sites, implying that this source was noticeable only in megacities. The relative contribution of each HONO source in the whole NCP region (all grid cells in domain two except for the seas) is presented in Fig. 3f. The results were quite similar to those of the 95 sites (Fig. 3e), which were representative for the whole NCP region. To further understand the role of potential HONO sources in haze-aggravating processes in regional O₃ concentrations, the 95-site-averaged surface/vertical HONO concentrations and their impacts during a typical haze event (19–21 October) and a clean period (27–29 October) were analyzed and are presented in the following sections.

3.2 Spatial distribution of enhanced DMA8 O₃ by potential HONO sources

3.2.1 General patterns of enhanced DMA8 O₃

Figure S5 shows surface-averaged and zonal-averaged DMA8 O₃ enhancements due to the six potential HONO sources in NCP during the study period (11–31 October) and three haze events (12–14, 18–21, and 24–25 October). The overall surface DMA8 O₃ enhancement decreased gradually from south (6–10 ppb) to north (2–6 ppb) (Fig. S5a) and could reach 10–20 ppb under unfavorable meteorological conditions during haze events (Fig. S5b–d). For the first two haze events, the anti-cyclone in the Shandong peninsula carried pollutants being transported from the southeastern NCP to the western (108–112^∘ E) and northern (39–41^∘ N) NCP, and the six potential HONO sources led to a DMA8 O₃ enhancement of 10–20 (Fig. S5b) and 10–15 ppb (Fig. S5c) in Beijing, respectively. For the third haze event, two air masses converged to form a transport channel from south to north. The O₃ enhancement caused by the six potential HONO sources reached 10–18 ppb in the southern NCP and decreased to 6–10 ppb in the northern NCP along the transport channel. Vertically, the DMA8 O₃ enhancements were 2–8 ppb during the whole period (Fig. S5e) and increased to 6–12 ppb in these haze events (Fig. S5f–h). The enhanced O₃ near the surface (0–100 m) was slightly smaller than that at higher altitude (Fig. S5f–h), due mainly to the stronger titration of O₃ by NO near the surface. These results demonstrate that the six potential HONO sources significantly enhanced surface and vertical O₃ concentrations in NCP, especially during haze events.

3.2.2 Enhanced DMA8 O₃ during a typical haze-aggravating process and a clean period

Figure 5 demonstrates surface-averaged and zonally averaged DMA8 O₃ enhancements due to the six potential HONO sources in NCP during a typical haze-aggravating process (19–21 October 2018) and a clean period (27–29 October 2018). The increasing trend of DMA8 O₃ enhancements can be clearly seen from 19 to 21 October near the surface and in the vertical direction. During the haze-aggravating process, the surface DMA8 O₃ enhancements were ∼ 2–10 ppb (19 October), ∼ 6–12 ppb (20 October), and ∼ 8–15 ppb (21 October), respectively; the vertical DMA8 O₃ enhancements were ∼ 4–7 ppb (19 October), ∼ 6–10 ppb (20 October), and ∼ 8–15 ppb (21 October), respectively. While during clean days, the surface/vertical DMA8 O₃ enhancements were usually <4 ppb. The six potential HONO sources significantly enhanced surface and vertical O₃ concentrations in NCP during haze-aggravating processes. The detailed role of the potential HONO sources in vertical HONO concentrations and their impacts are presented in the next section.

Figure 5 Surface-averaged (a1–a3, c1–c3) and zonal-averaged (b1–b3, d1–d3) DMA8 O₃ enhancements due to the six potential HONO sources in the North China Plain during a typical haze-aggravating process (19–21 October 2018) and a clean period (27–29 October 2018). The dashed line denotes the latitude of the BUCT site.

3.3 Vertical variations of the six potential HONO sources and their impacts

3.3.1 Six potential HONO sources and their impacts on HONO concentrations

A number of studies have conducted vertical HONO observations abroad (Kleffmann et al., 2003; Ryan et al., 2018; Sörgel et al., 2011; VandenBoer et al., 2013; Villena et al., 2011; Wang et al., 2020; Wong et al., 2011, 2012; Zhang et al., 2009) and in China (Meng et al., 2020; Wang et al., 2019; Xing et al., 2021; Zhu et al., 2011). A decreasing trend of HONO with height was mostly observed in these studies, and our simulations also reproduced this vertical variation and were comparable to another model simulation by Zhang et al. (2021), who used CMAQ (Fig. S6). For an in-depth understanding of the role of each HONO source considered in HONO concentrations at different heights, we assessed the contributions of each potential HONO source to HONO concentrations at different heights (Fig. 6) during 11–31 October 2018.

Figure 6 The 95-site-averaged daytime/nighttime HONO concentrations/enhancements at different heights for the NO + OH reaction (a1 and a2) and each of the six potential HONO sources (b1–g1 and b2–g2) during 11–31 October 2018. The error bar denotes the uncertainties of each potential HONO source in HONO concentrations (Table 2). The right panel denotes the approximate height of each vertical layer above the ground.

Generally, the impacts of ground-based potential HONO sources (E_traffic, E_soil, E_indoor, and Het_ground) on HONO concentrations decreased rapidly with height, while the NO + OH reaction and aerosol-related HONO sources (Phot_nitrate and Het_aerosol) decreased slowly with height (Fig. 6). During daytime the NO + OH reaction, Phot_nitrate, and Het_ground were the three main HONO sources, while during nighttime E_traffic, Het_aerosol, and Het_ground were the three main contributors to HONO concentrations (Fig. 6). The HONO concentrations via the NO + OH reaction and Phot_nitrate were higher during daytime. The impact of E_soil in the NCP was small; nevertheless, Xue et al. (2021) found strong soil HONO emissions in NCP agricultural fields after fertilization, suggesting that this source may have a significant enhancement on regional HONO and secondary pollutants in crop-growing seasons.

The comparison of HONO concentrations/enhancements during a haze-aggravating process and a clean period is shown in Figs. 7 and 8. Generally, daytime HONO concentrations increased during haze-aggravating processes and were higher than concentrations on clean days. Het_ground was the dominant source of the surface HONO on both hazy and clean days and contributed 80 %–90 % of daytime averaged HONO concentrations (Fig. 8); however, this reaction occurred only on the ground surface, thus its relative contribution decreased with height, especially during haze-aggravating processes (Fig. 8). Although the contribution of the NO + OH reaction to daytime HONO was small near the surface, its relative contribution to HONO increased with height, especially on clean days (Fig. 8). As for Phot_nitrate, a much larger enhancement was found on hazy days compared with clean days. On clean days the daytime enhanced HONO by Phot_nitrate was only 1–3 ppt in general, and its contribution to daytime HONO was usually <10 %. During the haze-aggravating process, however, the enhanced HONO concentration by Phot_nitrate was about 10 times higher than that on clean days and Phot_nitrate became the dominant HONO source (∼ 30 %–70 %) at higher altitude, and both HONO concentrations and contributions by Phot_nitrate increased with the air pollution aggravation (Figs. 7a–c, 8a–c). The contributions of direct emission sources were small and decreased when PM_2.5 increased, compared with the heterogeneous reactions. Higher concentrations of NO₂, nitrate, and PM_2.5 favored heterogeneous formation of HONO, while direct emission sources were relatively invariable under different pollution levels.

Figure 7 The 95-NCP-site-averaged daytime HONO concentrations at different heights when the NO + OH reaction and the six potential HONO sources were included for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f). The numbers in black in the first column of each graph are for Phot_nitrate, and the numbers in gray in the second column are for Het_ground.

Figure 8 The 95-NCP-site-averaged relative contributions of the NO + OH reaction and each of the six potential HONO sources to daytime HONO concentrations at different heights for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f). The numbers in blue in the first column of each graph are for the NO + OH reaction, the numbers in black in the second column are for Phot_nitrate, the numbers in white in the third column are for Het_aerosol, and the numbers in gray in the fourth column are for Het_ground).

Our results show that nitrate concentrations increased with the haze-aggravating processes (Fig. 2b), and as a positive feedback effect, the elevated nitrate could in turn enhance HONO formation and further enhance the atmospheric oxidation capacity during daytime. Considering J_nitrate is still unclear, sensitivity tests were conducted and are presented in the discussion section.

3.3.2 Enhanced OH and its production rate

Figure 9 demonstrates daytime variations in OH production (P(OH)) and loss (L(OH)) rates near the surface and in the vertically averaged layer (from the ground to a height of 2.5 km) at the 95 NCP sites for the Base and 6S cases during 11–31 October 2018. A significant enhancement of $P/L$(OH) can be found near the surface and vertically; the six potential HONO sources accelerated OH production and loss rates remarkably near the surface and noticeably in the vertical layers considered.

Figure 9 Diurnal mean variations in OH production (P(OH)) and loss (L(OH)) rates including major production and loss reactions near the surface and in the vertically averaged layer (from the ground to a height of 2.5 km) at the 95 NCP sites for the Base and 6S cases during 11–31 October 2018.

Near the surface, daytime P(OH) and L(OH) were significantly enhanced by ∼ 320 % for the 6S case (mean was 5.27 ppb h⁻¹) compared with the base case (mean was 1.26 ppb h⁻¹). For the base case, the daytime P(OH) via the photolysis of HONO and O₃ was 0.09 and 0.09 ppb h⁻¹, respectively, while the daytime L(OH) via the NO + OH reaction was 0.11 ppb h⁻¹, and the net contribution of HONO photolysis to P(OH) was −0.02 ppb h⁻¹. After adding the six potential HONO sources in case 6S, the daytime P(OH) via the photolysis of HONO and O₃ was 1.81 and 0.10 ppb h⁻¹, respectively, the daytime L(OH) via the NO + OH reaction was 0.48 ppb h⁻¹, and the net contribution of HONO photolysis to P(OH) reached 1.33 ppb h⁻¹. HONO photolysis was the main source of the primary formation of OH, while the secondary formed OH via the reaction of HO₂+NO (3.14 ppb h⁻¹) was the dominant source of the total OH formation.

Vertically, daytime P(OH) or L(OH) was enhanced by ∼ 105 % for the 6S case (mean was 2.21 ppb h⁻¹) compared with the base case (mean was 1.08 ppb h⁻¹). For the base case, the daytime P(OH) via the photolysis of HONO and O₃ was 0.06 and 0.10 ppb h⁻¹, respectively, while the daytime L(OH) via the NO + OH reaction was 0.07 ppb h⁻¹, and the net contribution of HONO photolysis to P(OH) was −0.01 ppb h⁻¹. After coupling the six potential HONO sources in case 6S, the daytime P(OH) via the photolysis of HONO and O₃ and via the HO₂ + NO reaction was 0.48, 0.12 and 1.52 ppb h⁻¹, respectively, the daytime L(OH) via the NO + OH reaction was 0.15 ppb h⁻¹, and the net contribution of HONO photolysis to P(OH) was 0.33 ppb h⁻¹.

Figure 10 shows the linear relationships between daytime-averaged P(OH) and PM_2.5 concentrations and between daytime-averaged OH and PM_2.5 concentrations from the ground to a height of 2.5 km at the 95 NCP sites during 11–31 October 2018. Both P(OH) for the two cases (Base and 6S) and the enhanced P(OH) due to the six potential HONO sources showed a strong positive correlation (r>0.8) with PM_2.5 concentrations at the 95 NCP sites, because Het_aerosol, Het_ground, and Phot_nitrate were significantly increased with the elevated pollution level. The enhanced P(OH) for the 6S case reached 0.043 ppb h⁻¹ per 1 µg m⁻³ of a PM_2.5 enhancement. Similarly, a high positive correlation (r>0.6) was found between OH and PM_2.5 concentrations; the OH concentrations and enhancements due to the six potential HONO sources were both higher on hazy days than those on clean days, and the enhancement of OH reached 3.62 × 10⁴ molec cm⁻³ per 1 µg m⁻³ of PM_2.5 for case 6S. These results are consistent with a recent field study reported by Slater et al. (2020), who found that the OH observed in haze events was elevated in central Beijing during November–December 2016. Furthermore, two observations confirmed the key role of HONO in producing primary OH despite the relatively lower photolysis frequency in haze-aggravating processes (Slater et al., 2020; Tan et al., 2018), consistent with our simulations (Fig. S7 shows the relationship between surface PM_2.5 and photolysis frequencies of NO₂, HONO, and HNO₃ in this study).

Figure 10 The linear relationships between daytime-averaged P(OH) and PM_2.5 concentrations (a) and between daytime-averaged OH and PM_2.5 concentrations (b) from the ground to a height of 2.5 km at the 95 NCP sites during 11–31 October 2018.

Figures 11 and 12 show detailed comparisons of P(OH) and OH enhancements during a haze-aggravating process and a clean period. It can be seen that both P(OH) and OH were enhanced on hazy days compared with clean days, and P(OH) and OH increased with the aggravated haze pollution. Among the six potential HONO sources, Het_ground was the largest contributor to the enhanced P(OH) and OH near the surface, but its contribution was relatively stable under different pollution levels and was rapidly reduced with height on both hazy and clean days; the contribution induced by Phot_nitrate was remarkably increased in haze-aggravating processes and was about 10 times higher than that on clean days; Het_aerosol also increased with the pollution levels but with relatively small values, while the impact of other three direct emission sources of HONO was quite small.

Figure 11 The 95-NCP-site-averaged daytime P(OH) for the base case and the enhancements due to the six potential HONO sources for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f). The numbers in black in the first column of each graph are for Phot_nitrate, and the numbers in gray in the second column are for Het_ground.

Figure 12 The 95-NCP-site-averaged daytime OH concentrations for the base case and the enhancements due to the six potential HONO sources for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f). The numbers in black in the first column of each graph are for Phot_nitrate, and the numbers in gray in the second column are for Het_ground.

3.4 Enhanced DMA8 O₃

Figure 13 demonstrates the linear relationship between DMA8 O₃ enhancements and daytime PM_2.5 concentrations in each vertical layer and the averaged vertical layer for the 11 layers considered at the 95 NCP sites during 11–31 October 2018. A good correlation (r>0.8) between DMA8 O₃ enhancements and daytime PM_2.5 concentrations in the vertical averaged layer (similar reasons for the strong positive correlation between the enhanced P(OH) and PM_2.5 concentrations shown above) suggests that the enhanced O₃ due to the six potential HONO sources was larger on polluted days and increased during the haze-aggravating processes. The enhanced DMA8 O₃ was <2 ppb when PM_2.5 was <20 µg m⁻³ and was >10 ppb when PM_2.5 was >60 µg m⁻³ on average, with a mean DMA8 O₃ enhancement of 0.24 ppb per 1 µg m⁻³ of PM_2.5.

Figure 13 The linear relationship between DMA8 O₃ enhancements and daytime PM_2.5 concentrations in each vertical layer (a) and the averaged vertical layer for the 11 layers considered (b) at the 95 NCP sites during 11–31 October 2018.

Figure 14 shows the 95-NCP-site-averaged DMA8 O₃ enhancements due to the six potential HONO sources for a typical haze-aggravating process during 19–21 October and a clean period during 27–29 October 2018. A significant enhancement of DMA8 O₃ can be found during the haze-aggravating process compared with that during clean days. The enhanced DMA8 O₃ was ∼ 5.5 ppb (19 October), ∼ 7 ppb (20 October), and ∼ 10 ppb (21 October), during the haze-aggravating process, while it was usually ∼ 2 ppb on clean days.

Figure 14 The 95-NCP-site-averaged DMA8 O₃ enhancements due to the six potential HONO sources for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f). The numbers in black in each graph are for Phot_nitrate, the numbers in purple are for Het_aerosol, and the numbers in gray are for Het_ground.

On clean days, Het_ground was the dominant contributor (∼ 1.5–2 ppb) to the enhanced DMA8 O₃ among the six potential HONO sources; the contribution of Phot_nitrate to the enhanced DMA8 O₃ was ∼ 0.1–0.4 ppb, while that of the other four sources was minor. In the comparison between the haze-aggravating process (19–21 October) and clean days, the DMA8 O₃ enhancements induced by Het_ground were doubled and reached ∼ 3–4 ppb; the contribution of Phot_nitrate to the enhanced DMA8 O₃ substantially increased and reached ∼ 2–4.5 ppb (19 October), ∼ 3–6 ppb (20 October),and ∼ 5–10 ppb (21 October). Het_aerosol showed an increasing contribution to the enhanced DMA8 O₃ during the haze-aggravating process (∼ 0.3 ppb on 19 October, ∼ 0.4 ppb on 20 October, and ∼ 0.7 ppb on 21 October), while the impacts of the other three direct emission sources (E_traffic, E_soil, and E_indoor) on the enhanced DMA8 O₃ were minor.

3.5 Vertical variations of O₃-NO_x-VOC sensitivity

Based on the results presented in the previous section, Phot_nitrate significantly enhanced the DMA8 O₃ 10-fold in the vertical layers considered (especially at elevated heights) during polluted events, although previous studies have not fully discussed this. To better understand its role in vertical O₃ formation, the O₃-NO_x-VOC sensitivity was analyzed by using the P(H₂O₂)$/P$(HNO₃) ratio proposed by Sillman (1995), which is more suitable than the concentration ratio of H₂O${}_{\mathrm{2}}/$HNO₃ because of the large dry deposition velocity of the two gases in the troposphere (Sillman, 1995). A transition point of P(H₂O₂)$/P$(HNO₃)=0.35 was suggested by Sillman (1995); when P(H₂O₂)$/P$(HNO₃) was <0.35, O₃ shows VOC-sensitive chemistry (increasing VOC concentrations can significantly elevate O₃ levels) and when P(H₂O₂)$/P$(HNO₃) was >0.35, O₃ tends to NO_x-sensitive chemistry (increasing NO_x concentrations can significantly elevate O₃ levels).

Figure 15 demonstrates the 95-NCP-site-averaged P(H₂O₂)$/P$(HNO₃) ratio at each vertical layer for the 6S case for a typical haze-aggravating process during 19–21 October and a clean period during 27–29 October 2018. A clearly opposite O₃ sensitivity appeared between the lower layers (VOC sensitive) and the higher layers (NO_x sensitive) on both clean and hazy days, and the transition point usually appeared at the eighth layer (∼ 600–800 m).

Figure 15 The 95-NCP-site-averaged P(H₂O₂)$/P$(HNO₃) ratio at each vertical layer for the 6S case for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f).

The Phot_nitrate reaction is assumed to produce HONO and NO_x (Zhou et al., 2003; Romer et al., 2018; Gen et al., 2022). This reaction not only enhances OH concentrations via HONO photolysis, but also directly releases NO_x back into the troposphere. Considering the NO_x-sensitive O₃ chemistry at higher layers (>800 m), elevating OH and NO_x concentrations are both favorable for O₃ formation, especially in haze-aggravating processes with abundant nitrate (detailed vertically enhanced O₃ production/loss rates induced by Phot_nitrate are shown in Fig. S8).

The specific role of the HONO or NO₂ produced via the Phot_nitrate reaction (Reaction R2) in DMA8 O₃ enhancements was further analyzed and is shown in Fig. 16. The produced NO₂ and HONO jointly promoted O₃ formation and increased DMA8 O₃ concentrations. From the surface to ∼ 1200 m (Level 9), the DMA8 O₃ enhancements for case D_HONO was ∼ 5 times those for case D_NO₂, while at ∼ 2000 m (Level 11) the DMA8 O₃ enhancements for case D_HONO was ∼ 2 times those for case D_NO₂. A balance exists between the propagation of the free radical interconversion cycle and the rate of termination of the cycle for the O₃ formation chemistry (Gligorovski et al., 2015). Considering the 0.67 and 0.33 yields (ratio of 2) for the two products, we could conclude that the impact of produced HONO on O₃ enhancements was larger than that of produced NO₂ near the surface, while at higher altitude (>2000 m) the impacts of the two products were similar.

Figure 16 The 95-NCP-site-averaged DMA8 O₃ enhancements due to nitrate photolysis with three product scenarios (cases D_NO₂, D_HONO and D) for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f).

4 Discussion

4.1 Vertical variations of potential HONO sources

The relative contribution of potential HONO sources near the surface, corresponding to the first model layer (0 to ∼ 35 m) in our simulation, was quantified in previous modeling studies (Fu et al., 2019; Xue et al., 2020; Zhang et al., 2021); however, for those potential HONO sources, their relative contributions to HONO concentrations near and above the surface should be different. Based on our results (Figs. 7 and 8), the effects of aerosol-related HONO sources would be severely underestimated on hazy days when only focused on surface HONO, especially for Phot_nitrate. Near the surface in NCP, the daytime contribution of Phot_nitrate to HONO concentrations on hazy days was only ∼ 4 %–6 %, but this source contributed ∼ 35 %–50 % of the enhanced DMA8 O₃ (Fig. 14a–c); above the eighth layer (∼ 800 m), this source contributed ∼ 50 %–70 % of HONO concentrations and ∼ 50 %–95 % of the enhanced DMA8 O₃ (Fig. 14a–c).

A recent observation in urban Beijing reported vertical HONO concentrations from three heights above the ground and found that extremely high HONO concentrations occurred at 120 m (∼ 5 ppb) and 240 m (∼ 3 ppb) rather than near the surface (∼ 1.2 ppb) during 12:00 on a typical hazy day (W. Q. Zhang et al., 2020). The observation was unusual at noontime under strong convection conditions, inconsistent with those during most of the previous observations indicating a HONO decreasing trend with height, especially with the observational results of Zhu et al. (2011) and Meng et al. (2020) as well as the simulated results of Zhang et al. (2021) and our results in Fig. S6 at the same observational site. The contributions of different HONO sources at each layer were analyzed by using a box model, but ∼ 80 %–90 % of the noontime HONO at higher layers could not be explained by the known HONO formation mechanisms (W. Q. Zhang et al., 2020). The box model neglected the vertical convection, and thus the ground-related HONO sources had no contribution to HONO concentrations at the higher layers; therefore, their HONO simulations were actually underestimated compared with our results and those from the studies by Wong et al. (2011) and Zhang et al. (2021).

4.2 Uncertainties of $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios and their impacts

4.2.1 Uncertainties of $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios in DMA8 O₃ enhancements

Based on our results, Het_ground and Phot_nitrate were the two major contributors to the enhanced DMA8 O₃, especially for Phot_nitrate on hazy days with higher PM_2.5 concentrations. The uncertainties of Phot_nitrate (four $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios) in O₃ enhancements were analyzed and are shown in Fig. 17 (The uncertainties of Het_ground are presented in Sect. S2). During the haze-aggravating process, the enhanced DMA8 O₃ near the surface increased from ∼ 0.3 to ∼ 0.5 ppb, from ∼ 0.9 to ∼ 2 ppb, from ∼ 2 to ∼ 6 ppb, and from ∼ 5 to ∼ 12 ppb, with the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio being 1, 7, 30, and 120, respectively, and the enhanced O₃ increased with altitude. On clean days, the impact of Phot_nitrate on O₃ enhancements was small (<1 ppb) even with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120.

Figure 17 The 95-NCP-site-averaged DMA8 O₃ enhancement induced by nitrate photolysis with four $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (1, 7, 30, and 120) for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f).

4.2.2 Uncertainties of $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios in nitrate concentrations

We found considerable enhancements in O₃ concentrations induced by Phot_nitrate, yet it is still unclear that to what extent Phot_nitrate could influence nitrate concentrations. The overall nitrate concentrations for the base case and the nitrate enhancements induced by the potential HONO sources decreased with rising altitude except for Phot_nitrate (Fig. S9a). Het_ground enhanced nitrate concentrations by ∼ 1.5 µg m⁻³ near the surface and the enhancements decreased to <0.5 µg m⁻³ above the eighth model layer (∼ 800 m); the nitrate enhancements due to Het_aerosol and E_traffic near the surface were ∼ 0.2 and ∼ 0.1 µg m⁻³, respectively, and were <0.1 and <0.04 µg m⁻³ above the sixth model layer (∼ 500 m). For Phot_nitrate, the overall impact of four $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios on nitrate concentrations is shown in Fig. S9b; a smaller $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 1 or 7 had a limited impact on nitrate concentrations of ∼ 0–0.05 µg m⁻³, a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 slightly decreased nitrate concentrations by ∼ 0.2 µg m⁻³, while the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120 decreased vertical nitrate concentrations by ∼ 0.3–0.8 µg m⁻³. The relative nitrate changes caused by Phot_nitrate were calculated by the differences between four cases of added Phot_nitrate (cases Nit_1, Nit_7, D, and Nit_120) and the base case (Fig. S9c). The vertical nitrate concentrations were reduced by ∼ 0 %–0.4 % ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{1}$), ∼ 0 %–2 % (7), ∼ 2 %–5 % (30), and ∼ 10 %–14 % (120) at the 95 NCP sites, meaning that the Phot_nitrate impact on vertical nitrate concentrations is limited (<5 %) when adopting a relatively small $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio (<30) (Fig. S9c).

Romer et al. (2018) found a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 10 or 30 had a much larger effect on HONO than on HNO₃, and Phot_nitrate accounted for an average of 40 % of the total production of HONO, and only 10 % of HNO₃ loss with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 10 (Fig. 5 in Romer et al., 2018), consistent with our study. From the production rate of gas HNO₃ ($P_{{\mathrm{HNO}}_{\mathrm{3}}}$) in Fig. S10, we find that an increase in the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio for Phot_nitrate simultaneously enhances the HNO₃ production rate, and is favorable for nitrate formation via the reaction between HNO₃ and NH₃. Nitrate consumption is mitigated by the faster nitrate formation, and this is the main reason for less perturbation of the nitrate budget influenced by Phot_nitrate.

Figure 18 shows the detailed relative changes of nitrate caused by Phot_nitrate during a typical haze-aggravating process and a clean period (corresponding concentrations are shown in Fig. S11). The percentage nitrate reduction was usually smaller on hazy days than on clean days, mainly due to the slightly weaker photolysis frequency during pollution events (Fig. S7). The nitrate reduction was <5 % when adopting a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 on both clean and hazy days and was <15 % in most cases even when the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio reached 120.

Figure 18 The 95-NCP-site-averaged relative changes of nitrate with four $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (1, 7, 30, and 120) compared with the base case for a typical haze-aggravating process during 19–21 October (a–c) and a clean period during 27–29 October 2018 (d–f).

4.2.3 Possible ranges of the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio

From the above discussion, we find that the enhanced OH and O₃ due to Phot_nitrate are significant during haze-aggravating processes, and the exact value of the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio requires more study.

Figure 19 shows the diurnal patterns of surface-averaged and vertically averaged simulations of the Phot_nitrate frequency with four different $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$​​​​​​​ ratios at the 95 NCP sites during the study period. The Phot_nitrate frequency at 12:00 was 3.7 × 10⁻⁷, 2.6 × 10⁻⁶, 1.1 × 10⁻⁵, and 4.5 × 10⁻⁵ s⁻¹ when adopting a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 1, 7, 30, and 120, respectively. The corresponding vertically averaged Phot_nitrate frequency was slightly larger (∼ 10 %) and was 4.2 × 10⁻⁷, 2.9 × 10⁻⁶, 1.3 × 10⁻⁵, and 5.0 × 10⁻⁵ s⁻¹, respectively. Adopting a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 in the 6S case, with the corresponding J_nitrate of 1.1–1.3 × 10⁻⁵ s⁻¹, produced ∼ 30 %–50 % of the enhanced O₃ near the surface on hazy days (Fig. 14), and ∼ 70 %–90 % of the enhanced O₃ at higher layers (>800 m).

Figure 19 Diurnal patterns of surface-averaged (a) and vertically averaged (b) simulations of the nitrate photolysis frequency with four different $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (1, 7, 30, 120) at the 95 NCP sites during the study period. The nitrate photolysis frequencies at 12:00 are shown in each graph.

The reported values of J_nitrate from previous studies are summarized in Table 4. The experimental J_nitrate values have been controversial over the past two decades and are still being debated. In our simulations for the 6S case, Phot_nitrate contributed from ∼ 1 % (clean days) to ∼ 5 % (hazy days) to surface HONO during daytime when using the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 in NCP, consistent with <8 % at a rural site in NCP reported by Xue et al. (2020) and ∼ 1 % in urban Beijing reported by Zhang et al. (2021) using the same ratio; however, the increasing contribution of Phot_nitrate to HONO concentrations with rising altitude based on our simulations (Figs. 7 and 8) has not been discussed in previous research. Furthermore, we found that the overall Phot_nitrate impact on OH and O₃ would be severely underestimated if the Phot_nitrate contribution to vertical HONO was excluded.

Table 4 Summary of studies on the nitrate photolysis frequency (J_nitrate) ($J_{{\mathrm{HNO}}_{\mathrm{3}}}$ denotes the photolysis frequency of gas HNO₃).

MBL: marine boundary layer; ABL: atmospheric boundary layer.

A larger $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120 for Phot_nitrate (4.5–5.0 × 10⁻⁵ s⁻¹ at 12:00) produced ∼ 25 %–30 % of noontime HONO in NCP in our study (Fig. S12), comparable to 30 %–40 % in previous modeling studies (Fu et al., 2019; Shi et al., 2020) when using the $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 118.57 (8.3 × 10${}^{-\mathrm{5}}/\mathrm{7}$ × 10⁻⁷). In haze-aggravating processes, the contribution of Phot_nitrate ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{120}$) to the DMA8 O₃ enhancements reached ∼ 5–10 ppb near the surface and ∼ 8–20 ppb above the 10th model layer (Fig. 17), these enhancements were extremely large. In a previous modeling study by Fu et al. (2020), the daytime surface O₃ simulations were systematically overestimated by ∼ 5 ppb in NCP in winter (Fig. S4 in Fu et al., 2020); the inclusion of Phot_nitrate ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{118.57}$) in their study might have caused the overestimation. From the above, a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120 or a J_nitrate value of ∼ 4–5 × 10⁻⁵ s⁻¹ is possibly overestimated. When adopting the maximum J_nitrate value of 10⁻⁴ s⁻¹ reported by Ye et al. (2016a) and Bao et al. (2018), we reasonably speculate that O₃ simulations will be significantly overestimated, especially at higher altitude with NO_x-sensitive O₃ chemistry (Fig. 15).

Romer et al. (2018) and Kasibhatla et al. (2018) suggested that a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 or smaller would be more suitable, being about the minimum value reported by Ye et al. (2016a) and Bao et al. (2018). This ratio has shown significant influence on the O₃ simulations in haze-aggravating processes in this study. The lack of photo-catalyzer in suspended submicron particulate sodium and ammonium nitrate may cause a lower $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio (<10), as reported by Shi et al. (2021), and thus more chamber experiments need to be conducted by using the particles collected in the real atmosphere. Choosing a larger J_nitrate value might cover up other ground-based unknown HONO sources, creating an illusion of good model simulations of daytime HONO, but resulting in an overestimation of O₃ concentrations. Considering the uncertainties of NO_x or VOC emissions, which also significantly impact O₃ simulations, more studies are needed to find the exact value of J_nitrate in the real atmosphere.

4.3 Interactions between heterogeneous HONO sources

Form the comparison of nitrate budget induced by the six potential HONO sources in Figs. S3 and S9, we find that Het_ground led to a significant increase in nitrate concentrations. In the real atmosphere, the NO₂ heterogeneous reactions and the Phot_nitrate reaction occur simultaneously, whereas the sensitivity tests considered only one specific HONO source for each case and neglected their interactions, leading to the underestimation of the Phot_nitrate impact to some extent. When this is taken into consideration, the Phot_nitrate impact on atmospheric oxidants and secondary pollutants would be even larger, especially during the haze-aggravating process.

Phot_nitrate would in turn change NO_x concentrations to some extent. From the 95-site-averaged NO₂ concentrations shown in Fig. 20, we find that Phot_nitrate slightly increased NO₂ concentrations on hazy days. The elevated NO₂ concentration could enhance HONO formation via the NO₂ heterogeneous reactions; nevertheless, due to the high background NO₂ concentrations in NCP (up to ∼ 40 ppb at nighttime), the increment of NO₂ and the enhanced HONO formation from NO₂ caused by Phot_nitrate were small (<10 %), but might have a larger impact on NO_x budgets in clean regions. From the above, a positive feedback relationship between the NO₂ heterogeneous reactions and the Phot_nitrate reaction was found, and these multi-processes worsen the air quality during haze-aggravating processes.

Figure 20 Comparison of 95-site-averaged simulations of NO₂ concentrations for the base case and four cases with different $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratios (1, 7, 30, and 120) (a), and the corresponding NO₂ variations (b) compared with the base case in the North China Plain during 11–31 October 2018.

5 Conclusions

In this study, three direct emission sources, the improved NO₂ heterogeneous reactions on aerosol and ground surfaces, and particulate nitrate photolysis in the atmosphere were included in the WRF-Chem model to explore the key HONO sources producing O₃ enhancements during typical autumn haze-aggravating processes with co-occurrence of high PM_2.5 and O₃ in NCP. The six potential HONO sources produced a significant enhancement in surface HONO simulations and improved the mean HONO concentration at the BUCT site to 1.47 ppb from 0.05 ppb (improved the NMB to −14.22 % from −97.11 % and the IOA to 0.80 from 0.45). The improved HONO significantly enhanced the atmospheric oxidation capacity near the surface and at elevated heights, especially on hazy days, resulting in rapid formation of and significant improvements in O₃ during haze-aggravating processes in NCP. Although the photolysis frequency is usually lower during hazy days, higher concentrations of NO₂, PM_2.5, and nitrate favored HONO formation via heterogeneous reactions, leading to stronger atmospheric oxidation capacity. The major results include:

1. For the surface HONO in NCP, Het_ground was the largest source during daytime and nighttime (∼ 50 %–80 %); the contribution of Phot_nitrate ($J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{30}$) to surface HONO concentrations was close to that of the NO + OH reaction during daytime (∼ 1 %–12 %) and was ∼ 5 % for daytime average; the contribution of E_traffic was important during nighttime (∼ 10 %–20 %) but small during daytime (<5 %); the contribution of Het_aerosol was minor (∼ 2 %–3 %) in the daytime and <10 % at nighttime; the contribution of E_soil was <3 %, and E_indoor could be neglected. Vertically, the HONO enhancements due to ground-based potential HONO sources (E_traffic, E_soil, E_indoor, and Het_ground) decreased rapidly with height, while the NO + OH reaction and aerosol-related HONO sources (Phot_nitrate and Het_aerosol) decreased with height much slower. The enhanced HONO due to Phot_nitrate on hazy days was about 10 times larger than on clean days and became the dominant HONO source (∼ 30 %–70 % when $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{30}$) at higher layers, and both HONO concentrations and Phot_nitrate contributions increased with the aggravated pollution levels.

2. Near the surface, daytime OH production/loss rates were significantly enhanced by ∼ 320 % for the 6S case (mean of 5.27 ppb h⁻¹) compared with the base case (mean of 1.26 ppb h⁻¹); vertically, daytime OH production/loss rates were enhanced by ∼ 105 % for the 6S case (mean of 2.21 ppb h⁻¹) compared with the base case (mean of 1.08 ppb h⁻¹). The enhanced OH production rate and OH due to the six potential HONO sources both showed a strong positive correlation with PM_2.5 concentrations at the 95 NCP sites, with a slope of 0.043 ppb h⁻¹ per 1 µg m⁻³ of PM_2.5 and 3.62 × 10⁴ molec cm⁻³ per 1 µg m⁻³ of PM_2.5 from the surface to the height of 2.5 km for case 6S, respectively. The atmospheric oxidation capacity (e.g., OH) was enhanced in the haze-aggravating process.

3. A strong positive correlation (r>0.8) between enhanced O₃ by the six potential HONO sources and PM_2.5 concentrations was found in NCP, and nitrate photolysis was the largest contributor to the enhanced DMA8 O₃ on hazy days. Vertically, the enhanced DMA8 O₃ was <2 ppb when PM_2.5 was <20 µg m⁻³, and it was >10 ppb when PM_2.5 was >60 µg m⁻³ on average, with a slope of 0.24 ppb DMA8 O₃ enhancement per 1 µg m⁻³ of PM_2.5. The surface-enhanced DMA8 O₃ was ∼ 5.5 ppb (19 October), ∼ 7 ppb (20 October), and ∼ 10 ppb (21 October) during a typical haze-aggravating process, while it was usually ∼ 2 ppb on clean days. The contribution of Phot_nitrate to the enhanced DMA8 O₃ was increased by over 1 magnitude during the haze-aggravating process (up to 5–10 ppb) compared with that on clean days (∼ 0.1–0.5 ppb), and reached ∼ 2–4.5 ppb (19 October), ∼ 3–6 ppb (20 October), and ∼ 5–10 ppb (21 October) during a typical haze-aggravating process vertically.

4. Surface O₃ was controlled by VOC-sensitive chemistry, while O₃ at higher altitude (>800 m) was controlled by NO_x-sensitive chemistry in NCP during autumn. The nitrate photolysis reaction enhanced OH and NO_x concentrations, and both favored O₃ formation at high altitude, especially in haze-aggravating processes with abundant nitrate. The produced HONO rather than the produced NO₂ through nitrate photolysis had a stronger promotion of O₃ formation near the surface, but the impacts of the two products on O₃ enhancements were similar at higher altitude (∼ 2000 m).

5. Nitrate photolysis only contributed ∼ 5 % of the surface HONO in the daytime with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 30 (∼ 1 × 10⁻⁵ s⁻¹) but contributed ∼ 30 %–50 % of the enhanced O₃ near the surface in NCP on hazy days. The photolysis of nitrate had a limited impact on nitrate concentrations (reduced by <5 % with $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{30}$, and <15 % even with a $J_{\mathrm{nitrate}}/J_{{\mathrm{HNO}}_{\mathrm{3}}}$ ratio of 120), due mainly to the simultaneously enhanced atmospheric oxidants favoring the formation of HNO₃ and nitrate. Choosing a larger J_nitrate value might cover up other ground-based unknown HONO sources, but overestimate vertical sources of HONO as well as NO_x and O₃ concentrations; thus, more studies are needed to find the exact value of J_nitrate in the real atmosphere.