The ambient PM_2.5 was collected on Teflon or quartz filters during fall–winter seasons at five representative sites, i.e., Beijing, Wangdu, Xinxiang, Guangzhou, and Changji, which are shown in Fig. 1a and described in detail in the Supplement. These cities are located in the North China Plain (NCP), with Beijing as an urban site and Wangdu as a rural one; central China; the Pearl River Delta (PRD) region; and northwestern China, respectively. The sampling flow rates ranged from 16.7 to 1050 L min⁻¹, the sampling times from 9 to 23 h, and the overall sampling volumes of air from 8 to 1450 m³ to collect a very wide range of particulate nitrate loadings. The comparison experiments between Teflon and quartz filters were conducted, and no significant differences in HONO production rates from particulate nitrate photolysis were found (T < 0.01). The sampling settings employed in Wangdu were designed to quantify the shadowing effect (Fig. 1b). In Wangdu, PM_2.5 was collected at a flow rate of 16.7 L min⁻¹ with four channels (A, B, C, and D). Channels A and B were set for daytime (08:00–17:00 LT) and nighttime (18:00–07:00 LT) PM_2.5 samples, respectively, and the other two channels were for “all-day” PM_2.5 samples (including the timings 08:00–17:00 and 18:00–07:00 LT). A total of 158 effective PM_2.5 samples were obtained in this study. These aerosol filter samples were labeled and stored at -20 °C in the freezer.

Fractions with a given surface area from each filter sample were used to perform photochemical reaction experiments and an analysis of aerosol chemical components. For each PM_2.5 sample, fractions with a given surface area were rinsed with deionized water and then sonicated for 15 min. The quantity of water-soluble ions, including Na⁺, NH4+, K⁺, Mg²⁺, Ca²⁺, Cl⁻, NO3-, and SO42-, were measured using ion chromatography (IC; Thermo Scientific Dionex ICS-2100). To measure the values of carbon components, including those of organic carbon (OC) and elemental carbon (EC), part (0.5024 cm²) of each filter was detected using a thermal–optical carbon analyzer (DRI (Desert Research Institute) Model 2015). The concentration of OM was obtained by multiplying the OC concentration by a factor of 1.6 (Li et al., 2021). The PM_2.5 concentration was estimated using the sum of all the water-soluble ions and carbon components. The surface concentration of PM_2.5 and its components on aerosol filters was calculated by dividing the absorbed loading by the geometric area of the aerosol filter sample (µg cm⁻²).

A custom-made cylindrical quartz vessel was used as the photochemical flow reactor (Fig. 1c). The diameter of the reactor was 10 cm, and the depth was 2.5 cm, with a cell volume of ∼ 200 mL. A xenon lamp (300 W) was placed 20 cm above the reactor as the light source. The light was filtered with a Pyrex sleeve to remove heat-generating infrared light. The effective light intensity in the center of the flow reactor, where aerosol samples were placed, was measured (by a calibrated optical power meter) to be about 0.5 times higher (1.5 kW m⁻²) than that at noon under tropical conditions on the ground (with a solar elevation angle of 0°). Synthetic air, composed of ultrahigh-purity nitrogen and ultrahigh-purity oxygen mixed at a ratio of 79 : 21, was used as the carrier gas. The relative humidity (RH) in the airflow was adjusted using a water bubbler and monitored with an online RH sensor (HMT130, Vaisala). The aerosol filter sample was exposed to the solar simulator radiation for 20 min. The photochemical reaction experiment for each sample was repeated 2–3 times with different fractions from the same sample. The gaseous product (i.e., HONO) released during the experiment was flushed out of the reactor by the carrier gas and was detected online by a custom-built HONO analyzer, which had been used in several measurements previously (W. Zhang et al., 2020; Li et al., 2021).

The production rates (nmol h⁻¹) of HONO from particulate nitrate photolysis (PHONO) were calculated from their time-integrated signals above the baseline over the period of light exposure: 1PHONO=Fg×60Vm(t2-t1)∫t1t2CHONOdt, where Fg (L min⁻¹) is the flow rate of the carrier gas; Vm (24.5 L mol⁻¹) is the molar volume of gas at 25 °C and under 1 atm of pressure; t1 and t2 (minutes) are the starting and ending times of the irradiation, respectively; and CHONO (parts per billion) is the online-measured concentration of HONO. With a flow rate of 2.5 L min⁻¹, the residence time in the reaction system was around ∼ 5 s. The photolytic loss of HONO was less than 5 %; thus, no correction was made in the calculation of HONO production.

The photolysis rate constant of particulate nitrate leading to HONO production (JNO3--HONO; s⁻¹) was calculated using the following equation: 2JNO3--HONO=PHONONNO3-×3600, where NNO3- (moles) is the amount of NO3- in the tested PM_2.5 sample. In principle, the photolysis rate constant should be calculated based on the amount of NO3- that is reachable by the irradiation. However, the amount of light-reachable NO3- in the PM_2.5 sample was hard to quantify. In this work, the deviation of JNO3--HONO due to the overestimation of the amount of NO3- under light irradiation, referred to as the shadowing effect, will be corrected in Sect. 3.1.

HONO production occurring within the first 20 min of irradiation during the photochemical experiment was investigated using PM_2.5 samples collected from five typical sites in China. Figure 2a shows a typical profile of the changes in HONO concentration in the reaction system. When the light was turned on, HONO concentration in the reactor increased immediately, before leveling off and slightly decaying afterwards. After the light was turned off, HONO generation stopped immediately, and the signal nearly returned to its baseline level. Previous works have revealed that the decay of HONO generation during light exposure periods does not result from the evaporation loss of particulate nitrate (Ye et al., 2017) but is mainly related to the inhomogeneity of particulate nitrate's photochemical reactivity or the consumption of reactive electron donors (Bao et al., 2018). HONO production from the photochemical reactions of particulate nitrate was significantly influenced by ambient environmental conditions (i.e., light intensity and RH). As shown in Fig. 2b, with the increase in light intensity, PHONO gradually increased, with PHONO at a light intensity of 3.85 kW m⁻² being approximately twice that at 1.50 kW m⁻². Previous works have found that the formation of HONO is negligible at low RH levels (< 5 %) and increases at intermediate RH levels (15 %–75 %), before decreasing at RH levels greater than 90 % (Bao et al., 2018). Here, we found that PHONO climbed to its highest when the RH was around 65 % (Fig. 2c). In this work, the photochemical reactions on different aerosol samples were all conducted under the same environmental conditions (an RH of 65 %, a temperature of 20 °C, and a light intensity of 1.50 kW m⁻²).

As expected, PHONO increased with particulate nitrate loadings in different sampling locations (Fig. S1 in the Supplement); however, it is interesting to note that PHONO did not increase or somewhat decreased under conditions of very high NO3- loading. This phenomenon has also been observed in other works (Ye et al., 2017; Bao et al., 2018). Previous works suggest that this may be attributed to the shadowing effect of particles under heavy aerosol loading conditions on the filters. The particulate nitrate underneath the aerosol filters may receive less UV light because of the presence of particles in the upper layers, inhibiting the photolysis of particulate nitrate (Ye et al., 2017). Assuming that the sampling time of all aerosol filter samples was the same, the aerosol loading on the filters collected under polluted conditions was much higher than that collected under clean conditions. Thus, the reported PHONO values for the aerosol filters collected under polluted ambient conditions would have been underestimated with heavy aerosol particle loading. To verify and quantify the underestimation of PHONO due to the shadowing effect, we collected two sets of filters in Wangdu (set A (daytime and nighttime filters) and set B (all-day filters); Fig. 1b). Theoretically, the all-day set should share the same NO3- loading and chemical composition as the sum of the daytime and nighttime filters; thus, the sum of PHONO during daytime (PdaytimeHONO) and that during nighttime (PnighttimeHONO) should be equal to PHONO during the all-day period (Pall-dayHONO), without considering the shadowing effect. A total of 20 pairs of comparative photochemical experiments were conducted, and the comparison of PHONO between these two sets of filters is shown in Fig. 3a. We found that the discrepancy between Pall-dayHONO and PdaytimeHONO+PnighttimeHONO widened with the increase in surface PM_2.5 concentration. To quantify the shadowing effect, we introduced a parameter called the “light screening coefficient” (LSC) to describe the decreasing efficiency of light penetration into the particles with increasing PM_2.5 loadings. The equations are expressed as follows: 3PtheoryHONO=PdaytimeHONO+PnighttimeHONO,4LSC=PobservedHONO/PcorrectedHONO=Pall-dayHONO/PtheoryHONO,

where PobservedHONO represents the observed production rate of HONO from particulate nitrate photolysis during the photochemical experiment and PcorrectedHONO represents the corrected value of PHONO after quantifying the shadowing effect. As shown in Fig. 3b, when the PM_2.5 surface concentration (dPM_2.5) was low, the LSC was almost equal to 1, indicating that the shadowing effect was negligible. With the increase in PM_2.5 loading, the value of the LSC declined to less than 65 %. In general, a significant negative correlation existed between the LSC and dPM_2.5, except when dPM_2.5 was higher than 200 µg cm⁻² (Fig. 3b). In this experiment, we assumed that the daytime and nighttime PM_2.5 samples were both single-layered. However, with the increase in air pollution, the filters in each pair of comparative experiments may already have exhibited the shadowing effect; thus, the sum of PdaytimeHONO and PnighttimeHONO would have been underestimated. Therefore, when quantifying the shadowing effect, the LSC data with PM_2.5 loadings higher than 200 µg cm⁻² were excluded. Correlations between the LSC and the surface concentrations of major chemical components of PM_2.5, such as EC (dEC), OC (dOC), and NO3- (dNO3-), were conducted (Fig. 3c–e). A significant correlation was found between the LSC and the carbonaceous components, especially EC (R2 = 0.73), which was one of the most important light-absorbing species in PM_2.5, indicating that the shadowing effect was mainly related to the light-absorbing components in PM_2.5. The relationship between the LSC and dEC was established as follows: 5dEC>5.5µgm-2: LSC=1.11–0.02×dEC,dEC≤5.5µgm-2: LSC=1. When dEC ≤ 5.5 µg m⁻², the shadowing effect can be ignored, and when dEC > 5.5 µg m⁻², PHONO can be corrected using the observed PHONO values and the LSC, which is estimated using the fitting equation with dEC. Previous works have found that heavy loads of carbonaceous particles can turn these filters a dark-brown color. The UV light is unlikely to be transmitted efficiently through the dark layer to the particulate nitrate underneath, thus inhibiting the generation of HONO from the photolysis of particulate nitrate (Ye et al., 2017). In consideration of the potential shadowing effect for the daytime and nighttime filters in each pair of comparative experiments, the observed PdaytimeHONO and PnighttimeHONO values would be underestimated, and the uncertainty in the LSC should be considered at high PM_2.5 loadings. To evaluate this uncertainty, the observed PdaytimeHONO and PnighttimeHONO values were recalculated and corrected to the theoretical single-layered condition based on Eqs. (4) and (5). As shown in Fig. S2, with the increase in PM_2.5 surface concentration, the deviations between the LSC and the corrected values enlarged. However, it is noted that the deviation was still lower than 20 % when the PM_2.5 surface concentration was around 200 µg cm⁻². For example, for the aerosol sample collected on 4 December 2023 in Wangdu, the PM_2.5 surface concentration was 173.57 µg cm⁻², and the deviation was 15.74 %, which is acceptable in this work.

There were 158 filter samples collected from five representative cities in China, and the average concentrations of PM_2.5 and its chemical composition from these filters showed significant spatial characteristics, as shown in Fig. 4. During the sampling period, OM was the most abundant species in PM_2.5 across most regions, except in the northwestern city of Changji. NO3- was the dominant inorganic component in the NCP (Beijing and Wangdu) and central China (Xinxiang), while SO42- showed the highest contribution in the PRD region (Guangzhou) and northwestern China (Changji). The values of JNO3--HONO for these PM_2.5 samples were calculated with Eq. (2), with PHONO corrected using Eqs. (4) and (5), and are summarized in Fig. 4 and Table 1. The median and mean (± 1 standard deviation) of the corrected JNO3--HONO values were 1.55 × 10⁻⁵ and 1.57 (± 2.14) × 10⁻⁵ s⁻¹ in Beijing, 1.68 × 10⁻⁵ and 1.75 (± 2.83) × 10⁻⁵ s⁻¹ in Wangdu, 0.69 × 10⁻⁵ and 0.78 (± 0.48) × 10⁻⁵ s⁻¹ in Xinxiang, 3.04 × 10⁻⁵ and 3.31 (± 1.15) × 10⁻⁵ s⁻¹ in Guangzhou, and 0.38 × 10⁻⁵ and 0.39 (± 0.25) × 10⁻⁵ s⁻¹ in Changji, respectively. The maximum JNO3--HONO values for these cities ranged from 0.91 × 10⁻⁵ s⁻¹ for Changji to 1.96 × 10⁻⁴ s⁻¹ for Wangdu. These values are in a range comparable to values previously reported for aerosol samples, such as 1.22 × 10⁻⁵ to 4.84 × 10⁻⁴ s⁻¹ for China – reported by Bao et al. (2018) using an RH of 60 %, a temperature of 25 °C, and an irradiation time of 15 min – and 6.2 × 10⁻⁶ to 5.0 × 10⁻⁴ s⁻¹ (the sum of HONO production and NO_x production, with an average HONO / NO_x production ratio of ∼ 2) for the US – reported by Ye et al. (2017) using an RH of 50 %, a temperature of 20 (± 1) °C, and an irradiation time of 10 min. It is interesting to note that the highest average JNO3--HONO value was from Guangzhou, which was characterized by the lowest PM_2.5 and NO3- concentrations among the observed cities. As for the other cities with high PM_2.5 concentrations, such as Changji and Xinxiang, the corrected JNO3--HONO values were comparatively low. According to the National Ambient Air Quality Standard of China (GB3095-2012), daily PM_2.5 averages for Guangzhou can meet the Level-II standard of 75 µg m⁻³ while exceeding the Level-I standard (35 µg m⁻³). Here, we defined PM_2.5-polluted days as days with a daily mean PM_2.5 value exceeding 35 µg m⁻³. As shown in Fig. 5, the distribution of the corrected JNO3--HONO values on clean days was generally more dispersed and greater than on polluted days, except in the case of Guangzhou. The average value of JNO3--HONO for Guangzhou under air-polluted conditions was slightly higher than that under clean conditions and much higher than the values for other cities. Because the influence of the shadowing effect has been corrected to some degree, the spatial and temporal changes in JNO3--HONO presented in this work should be mainly related to the varied chemical and physical properties of PM_2.5 samples collected from different atmospheric environments.

The determined JNO3--HONO values were closely associated with the aerosol's chemical and physical characteristics, especially the coexisting organic components, and were distributed around the curve as expressed by Eq. (6). This is the first effort to explore the photolysis of particulate nitrate in aerosol samples collected from different typical regions of China. The enhanced formation of HONO from the photolysis of particulate nitrate can contribute significantly to the atmospheric oxidation capacity. To assess the photolysis of particulate nitrate as a daytime HONO source, the noontime source strength of HONO (SHONO) through this mechanism in the air column within the planetary boundary layer can be calculated using the following equation (Ye et al., 2017): 7SHONO(10-5molh-1m-2)=0.67×NO3-(µmolm-3)×10-6×JNO3--HONO×BLH×3600, or 8SHONO(ppbvh-1)=0.67×NO3-(ppbv)×JNO3--HONO×3600, where BLH refers to the boundary mixing height (meters). Here, we assume a typical BLH of 1000 m. Based on the daily measured NO3- and corrected JNO3--HONO values for each city, the SHONO values derived from Eq. (7) or Eq. (8) during the observation period are shown in Table 1. It was found that, even though JNO3--HONO on polluted days was much lower than that on clean days, due to the apparent higher NO3- concentration, the corresponding SHONO values were about twice the average on clean days. The calculated SHONO values ranged from 0.03 × 10⁻⁵ to 0.88 × 10⁻⁵ mol h⁻¹ m⁻² (0.01–0.2 ppbv h⁻¹), with a mean value of 0.36 × 10⁻⁵ mol h⁻¹ m⁻² (0.08 ppbv h⁻¹), comparable to or higher than that for other HONO sources (Bhattarai et al., 2019; Wang et al., 2023; Ye et al., 2017). For example, the soil HONO emission flux was measured to be in the range of 1.81 × 10⁻⁶ to 4.55 × 10⁻⁶ mol h⁻¹ m⁻² in soil not treated with nitrogen fertilizer (Bhattarai et al., 2019). The mean value of SHONO during the observation period was highest in Wangdu (0.42 × 10⁻⁵ mol h⁻¹ m⁻² and 0.10 ppbv h⁻¹) and Guangzhou (0.41 × 10⁻⁵ mol h⁻¹ m⁻² and 0.09 ppbv h⁻¹), followed by Xinxiang (0.35 × 10⁻⁵ mol h⁻¹ m⁻² and 0.08 ppbv h⁻¹), Beijing (0.22 × 10⁻⁵ mol h⁻¹ m⁻² and 0.05 ppbv h⁻¹), and Changji (0.13 × 10⁻⁵ mol h⁻¹ m⁻² and 0.03 ppbv h⁻¹). Even though the PM_2.5 and NO3- concentrations were lowest in Guangzhou, SHONO was much higher here than in other cities with air pollution. It should be noted that the SHONO value calculated with the daily changing NO3- and JNO3--HONO values from this work was much lower than the value reported by Bao et al. (2018) (0.78 ppbv h⁻¹), who applied the average NO3- value (6.64 µg m⁻³ (2.62 ppbv)) and the JNO3--HONO range (1.22 × 10⁻⁵ to 4.84 × 10⁻⁴ s⁻¹) to simulate SHONO (0.12–4.57 ppbv h⁻¹). Other works, such as Fu et al. (2019) and Gu et al. (2022a), applied the mean value of JNO3--HONO (8.3 × 10⁻⁵ s⁻¹) and the observed NO3- concentration to calculate SHONO. However, due to the significant decrease in JNO3--HONO along with the increase in NO3-, the SHONO values calculated with mean NO3- or JNO3--HONO values are largely overestimated, thus directly influencing the identification of HONO sources. For example, JNO3--HONO was at its highest in Wangdu on 23 November 2023, with a value of 19.6 × 10⁻⁵ s⁻¹, while the corresponding NO3- concentration was low (0.39 µg m⁻³). If the average NO3- concentration (12.53 µg m⁻³, equivalent to 4.53 ppbv) and the maximum JNO3--HONO value were applied, the determined SHONO value would be 9.56 × 10⁻⁵ mol h⁻¹ m⁻² (2.14 ppbv h⁻¹), which is about 30 times higher than the actual result (0.07 ppbv h⁻¹). Therefore, we suggest estimating SHONO with the observed concentration of NO3- and the JNO3--HONO value derived from the parameterization equation with OC / NO3-, thereby reducing the large uncertainties and improving estimations of the HONO budget.

On the basis of daily average concentrations of NO3- and OC extracted from a Chinese high-resolution PM_2.5 component simulation concentration dataset (the CAQRA-aerosol dataset (15 km × 15 km); https://www.capdatabase.cn, last access: 28 May 2024) (Kong et al., 2024), JNO3--HONO and SHONO can be estimated using Eqs. (6) and (8), respectively. As shown in Fig. 9, significant spatiotemporal changes in NO3-, OC, JNO3--HONO, and SHONO were demonstrated in the fall–winter seasons from 2013 to 2022 in China. The high JNO3--HONO values were concentrated in the clean environments (e.g., the Tibetan Plateau region, the southern Xinjiang basin, the Yunnan–Guizhou Plateau, and the Sichuan Basin), followed by the air-polluted regions (e.g., the NCP, the Fenhe–Weihe basin, northeastern China, and the PRD). From 2013 to 2022, with OC decreasing significantly and NO3- staying stable or even increasing, JNO3--HONO showed a downward trend in most regions. Although the JNO3--HONO values for polluted regions were comparatively lower than those for clean environments, the higher values of SHONO were mostly distributed in these polluted regions due to the much higher NO3- concentration. However, it should be noted that the photolysis of particulate nitrate contributed only a small fraction to the needed daytime HONO source in these polluted regions, with values such as 1.26–3.82 ppbv h⁻¹ for the cities in the North China Plain (Hou et al., 2016; Wang et al., 2017; Lian et al., 2022; Li et al., 2018), 0.75 ppbv h⁻¹ for western China (Huang et al., 2017), and 0.77–4.90 ppbv h⁻¹ for southern China (Li et al., 2012; Su et al., 2008). We note that uncertainties still exist in our simulations. Given the paucity of field measurements of HONO production from aerosol samples obtained in clean environments, the deviation of JNO3--HONO derived from the parameterization in this work may be large in these regions. Additionally, the concentrations of NO3- and OC extracted from the CAQRA-aerosol dataset with regard to clean environments were around the mean deviation level. Therefore, more field observations and simulation experiments should be conducted in these clean regions in the future to enrich and improve the parametric equations of JNO3--HONO and to further evaluate the contribution of nitrate photolysis to the formation of HONO in different regions of China.