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# A diurnal story of Δ17O($$\rm{NO}_{3}^{-}$$) in urban Nanjing and its implication for nitrate aerosol formation

## Abstract

Inorganic nitrate production is critical in atmospheric chemistry that reflects the oxidation capacity and the acidity of the atmosphere. Here we use the oxygen anomaly of nitrate (Δ17O($$\rm{NO}_{3}^{-}$$)) in high-time-resolved (3 h) aerosols to explore the chemical mechanisms of nitrate evolution in fine particles during the winter in Nanjing, a megacity of China. The continuous Δ17O($$\rm{NO}_{3}^{-}$$) observation suggested the dominance of nocturnal chemistry (NO3 + HC/H2O and N2O5 + H2O/Cl) in nitrate formation in the wintertime. Significant diurnal variations of nitrate formation pathways were found. The contribution of nocturnal chemistry increased at night and peaked (72%) at midnight. Particularly, nocturnal pathways became more important for the formation of nitrate in the process of air pollution aggravation. In contrast, the contribution of daytime chemistry (NO2 + OH/H2O) increased with the sunrise and showed a highest fraction (48%) around noon. The hydrolysis of N2O5 on particle surfaces played an important role in the daytime nitrate production on haze days. In addition, the reaction of NO2 with OH radicals was found to dominate the nitrate production after nitrate chemistry was reset by the precipitation events. These results suggest the importance of high-time-resolved observations of Δ17O($$\rm{NO}_{3}^{-}$$) for exploring dynamic variations in reactive nitrogen chemistry.

## Introduction

Nitrate ($$\rm{NO}_{3}^{-}$$) and its precursor NOx (NOx = NO + NO2) play a crucial role in atmospheric chemical processes and the formation of PM2.5, fine particles with diameter less than 2.5 μm1,2. Tropospheric NOx oxidation drives the formation of ozone (O3) and recycle of hydroxyl radicals (OH) that control the atmospheric self-cleansing capacity3. Majority of NOx emitted from various sources are finally converted into nitric acid (HNO3) and organic nitrate (e.g., RONO2) through atmospheric oxidation processes by oxidants (e.g., O3, OH, HO2, and RO2)4. HNO3 lowers the pH of the precipitation and increases the risk of forming acid rain5. Furthermore, HNO3 easily be transformed into nitrate particles through atmospheric reactions with alkaline ammonia that in turn influence the chemical composition and the size of existing particles, affecting the formation of clouds and precipitation as well3,6. RONO2 can partition into the particle phase (RONO2(p)) and then is removed from the atmosphere by deposition to the surface or through hydrolysis to form inorganic nitrate and alcohols7,8. Atmospheric nitrate in gas phase (HNO3(g)), liquid phase (HNO3(aq)) and particulates ($$\rm{NO}_{3}^{-}$$(p)) are eventually removed through wet/dry deposition. Thus investigating the mechanism of NOx-$$\rm{NO}_{3}^{-}$$ conversion is important to the study of atmospheric chemistry.

The conversion of NOx to $$\rm{NO}_{3}^{-}$$ is a combination of the NOx cycle (Supplementary Note 1) and nitrate production processes. During the day, OH radical is easily generated under the strong sunlight and HNO3(g) is then formed through the NO2 + OH reaction9. NO2 can be hydrolyzed on surfaces to produce HNO3(aq)10, which was found to be a weak source of nitrate formation on severe haze days in winter in the North China Plain (NCP)11,12. In addition, NO2 can also react with O3 to form NO3 radicals and then NO3 directly reacts with hydrocarbon (HC) and dimethylsulfide (DMS) or be hydrolyzed on surfaces to produce HNO313,14,15. This reaction occurred at night because NO3 radical is easily photolyzed to NO2 under sunlight16. And the contribution of NO3 + DMS is small in non-coastal areas due to the low mixing ratio of DMS17. Dinitrogen pentoxide (N2O5), a nocturnal NOx reservoir, can react on airborne particle surface to produce only HNO3(aq) or both $$\rm{NO}_{3}^{-}$$(p) and nitryl chloride (ClNO2)18. Other potential formation mechanisms of nitrate particles, like the hydrolysis of organic nitrates (RONO2) and halogen nitrates (XNO3), might be important in coastal regions or the rainforest areas like Amazonia13.

$${{{\mathrm{NO}}}}_{\mathrm{2}}\,+\, {\mathrm{OH}}\, +\, {\mathrm{M}} \to {{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}\,+\,{{{\mathrm{M}}}}$$
(1)
$${{{\mathrm{2NO}}}}_{{{\mathrm{2}}}}\,+\,{{{\mathrm{H}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{surface}}}}} \right) \to {{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}\left( {{{{\mathrm{liquid}}}}} \right)\,+\,{{{\mathrm{HONO}}}}$$
(2)
$${{{\mathrm{NO}}}}_{{{\mathrm{2}}}} \,+ \,{{{\mathrm{O}}}}_{{{\mathrm{3}}}} \to {{{\mathrm{NO}}}}_{{{\mathrm{3}}}} \,+\, {{{\mathrm{O}}}}_{{{\mathrm{2}}}}$$
(3)
$${{{\mathrm{NO}}}}_{{{\mathrm{3}}}}\, + \,{{{\mathrm{HC/DMS}}}} \to {{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}\, +\, {{{\mathrm{Others}}}}$$
(4)
$${{{\mathrm{NO}}}}_{{{\mathrm{3}}}} \,+ \,{{{\mathrm{H}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{surface}}}}} \right) \to {{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}\left( {{{{\mathrm{liquid}}}}} \right) \,+ \,{{{\mathrm{OH}}}}$$
(5)
$${{{\mathrm{NO}}}}_{{{\mathrm{2}}}} \,+ \,{{{\mathrm{NO}}}}_{{{\mathrm{3}}}} \leftrightarrow {{{\mathrm{N}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}_{{{\mathrm{5}}}}$$
(6)
$${{{\mathrm{N}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}_{{{\mathrm{5}}}} \,+\, {{{\mathrm{H}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{surface}}}}} \right) \to {{{\mathrm{2HNO}}}}_{{{\mathrm{3}}}}\left( {{{{\mathrm{liquid}}}}} \right)$$
(7)
$${{{\mathrm{N}}}}_{{{\mathrm{2}}}}{{{\mathrm{O}}}}_{{{\mathrm{5}}}} + {{{\mathrm{Cl}}}}^{{{\mathrm{ - }}}}\left( {{{{\mathrm{surface}}}}} \right) \to {{{\mathrm{NO}}}}_{{{\mathrm{3}}}}^{{{\mathrm{ - }}}}\left( {{{{\mathrm{particle}}}}} \right) + {{{\mathrm{ClNO}}}}_{{{\mathrm{2}}}}$$
(8)

In the past, NO2 + OH photochemical reaction and N2O5 hydrolysis have been widely considered as the main pathways of nitrate formation worldwide13,19. However, NO3 + HC reaction was reported to be an important pathway for nitrate formation in industrial regions due to the extensive emissions of hydrocarbons (HCs) from anthropogenic sources14. Previous studies suggested that N2O5 uptake in aerosols and clouds was the dominant nitrate production pathway during intense haze events under low temperatures and minimal sunlight conditions20,21. Some laboratory studies suggested that the hydrolysis of NO2 and NO3 was not important for HNO3 formation because of its low reaction probability22,23,24. A recent model simulation found that NO2 hydrolysis was a neglected source of nitrate formation on haze days in Beijing winter11. And the heterogeneous reactions of NO3 and N2O5 on the aerosol surface have been pointed out to dominate the particulate nitrate formation on polluted days in urban Shanghai based on the high-time resolution observation25. Platt et al.26 also pointed out that the lifetimes for NO3 radicals were shorter than 1 min in the presence of fog, which indicated a fast reaction of N2O5 or NO3 with liquid water droplets.

Triple oxygen isotope (16O, 17O, and 18O) analysis of atmospheric nitrate is a powerful technique used to identify nitrate formation pathways19,27. The only exception to the mass-dependent oxygen isotope fractionation rule (δ17O = 0.52 × δ18O)28 occurs during O3 production (heavy oxygen isotopes are equally enriched). This isotope fractionation that appears independent of relative mass differences is termed as mass-independent fractionation and is quantified by Δ17O = δ17O − 0.52 × δ18O29. The Δ17O signature of O3 is transferred through oxidation reactions to other oxygen-bearing compounds (e.g., NO2, NO3, and N2O5) and the Δ17O of these atmospheric species acts as a marker of the influence of O3 in their chemical formation. Δ17O of atmospheric nitrate (the Δ17O of compound X is expressed as Δ17O(X) in this paper. Δ17O($$\rm{NO}_{3}^{-}$$) normally shows positive values from 12 to 43‰30 due to the oxygen atom transfer from O3 to $$\rm{NO}_{3}^{-}$$ during the NOx oxidation. Moore and Semmens31 reported a large range of Δ17O(O3) (20–40‰). Modeling studies that seek to simulate the propagation of Δ17O in the atmosphere typically assume a Δ17O(O3) value of 25–35‰19. However, the Δ17O of tropospheric O3 has been observed to average at 26 ± 1‰32,33. Except for O3, the Δ17O values of all the oxygen atoms that may be incorporated into nitrate (i.e., water vapor, OH radical, and HO2 (ROx)) are close to 0‰34,35,36,37,38,39. Thus Δ17O($$\rm{NO}_{3}^{-}$$) actually reflects the fraction of O3 derived oxygen atoms incorporated into $$\rm{NO}_{3}^{-}$$, which varies depending on the nitrate formation pathways. In recent years, the use of Δ17O(NO3-) in revealing reactive nitrogen chemistry in China has gotten considerable attention. He et al.20 found that nocturnal reactions (including NO3 + HC and N2O5 uptake) dominated nitrate formation along with high ambient humidity and weak sunlight during polluted days in Beijing. Fan et al.40 suggested nocturnal chemistry contributed to nitrate production equally with NO2 + OH/H2O at ground level, but dominated the nitrate production in the air aloft (260 m) under higher O3 and aerosol liquid water content (ALWC) conditions based on tower observation. The average fractions of NO2 + OH and N2O5 hydrolysis were estimated to be 43 and 52% of nitrate production over the Himalayan-Tibetan Plateau41.

Although many modeling and observation studies focused on the variation of nitrate production influenced by factors such as clean versus haze days11,42,43, it’s necessary to explore the diurnal variation of nitrate production pathways which can provide us new insights into the dynamic variations in nitrate chemistry. Many field measurements showed large differences in oxidants (e.g., O3, OH, and HO2)44,45 and meteorology (e.g., solar radiation and boundary layer height)46,47 between daytime and nighttime in urban areas, which probably caused the different nitrate chemical processes at different times of the day. Huang et al.48 found that the aqueous-phase processes played an important role in nitrate production during the nighttime in the NCP. Kuang et al.49 suggested that the prevailing NH3 morning spikes on the NCP significantly influenced nitrate formation and atmospheric chemistry. Tan et al.50 highlighted that the HNO3 production was less efficient throughout the boundary layer than that was observed in the surface layer. Liu et al.51 found that NO2 + OH reaction played a pivotal role in the daytime formation of nitrate at moderate relative humidity (RH). However, this is a lack of investigation of the diurnal variations of nitrate formation mechanisms based on the multiple oxygen isotopes observations, which can further provide direct evidence to understand the dynamic nitrate chemistry in the real atmosphere.

In this study, Δ17O($$\rm{NO}_{3}^{-}$$) measurements were conducted in high-time-resolved winter aerosols collected during a haze event in Nanjing, a megacity in eastern China. The contribution of each nitrate formation pathway was evaluated based on the combination of Δ17O($$\rm{NO}_{3}^{-}$$) observations and the Bayesian model. The diurnal variations of nitrate production pathways were assessed and the differences between these pathways during clean and haze days were also explained.

## Results and discussion

### Temporal variation of chemical species, meteorological conditions, and Δ17O of nitrate

The PM2.5 mass concentrations ranged from 19.3 to 263.7 μg m3 with an average value of 105.4 ± 61.7 μg m3 (Fig. 1a). The mass concentration of nitrate varied from 3.3 to 68.7 μg m3 (Fig. 2a). The first few sampling days (January 14th 2:00 to 16th 8:00) were classified as “clean days” based on low PM2.5 levels (39.0 ± 13.6 μg m3). After January 21st 8:00, PM2.5 showed consecutively high values (> 75 μg m3) and increased up to 271.7 μg∙m−3 on January 25th. Time period from January 21st 8:00 to 27th 2:00 was defined as a haze period (PM2.5 > 75 μg m−3) according to the Grade II of NAAQS (National Ambient Air Quality Standard) in China. The severe haze ended when the majority of PM2.5 was scavenged by the precipitation on January 27th. Visibility was relatively high (4.0 ± 0.7 km) during the clean days and extremely low (≈1 km) during the most severe haze period (January 24th to 26th) (Fig. 1a). Three precipitation events (less than 4 mm for each) were observed on January 14th, 25th, and 27th, resulting in the decrease of PM2.5 levels with fractions of 52–82% (Fig. 1a). Air temperature varied from −1.1 to 12.8 °C and was negatively correlated (r = −0.56, p < 0.001) with RH, which ranged from 19 to 84% (Fig. 1b). The wind speed was less than 3.7 m∙s1 and was either from the north or east to south (Fig. 1c). RH was used to estimate the trend of planetary boundary layer height (PBLH) using the Clausius–Claperyron Equation (Supplementary Note 2). The obtained PBLH was higher in the daytime (865 ± 528 m) and lower at night (770 ± 458 m) (Fig. 2d).

The mixing ratio of O3 ranged from 0.5 to 37.3 ppb and was higher during the day compared to the night (Fig. 2b). The extremely low O3 concentrations (<10 ppb) were observed in the most severe haze period (January 24th to 26th). NO2 concentrations ranged from 6.9 to 84.3 ppb with an average value of 28.2 ± 17.4 ppb and CO concentrations varied from 0.1 to 2.2 ppm (Fig. 2c). The $$\rm{NO}_{3}^{-}$$ mass concentration was correlated with both CO (r = 0.87, p < 0.01) and NO2 (r = 0.72, p < 0.01) during the sampling period. Nitrogen oxidation ratio (NOR = [$$\rm{NO}_{3}^{-}$$]/([NOx] + [$$\rm{NO}_{3}^{-}$$]), a proxy for the secondary formation of nitrate52) varied between 0.08 and 0.54 without significant diurnal variation. Δ17O($$\rm{NO}_{3}^{-}$$) ranged from 23.4 to 39.3‰ (Fig. 2a), with a weighted average value of 30.5‰. These values are within the range of most previous observations (12–43‰)30,43,53. Especially, the Δ17O($$\rm{NO}_{3}^{-}$$) values in PM2.5 in this study were similar with those observed during winter in Beijing (30.6 ± 1.8‰)20 and Shanghai (20.5–31.9‰)54, but higher than those in winter in Taiwan province (23 ± 5‰)53. In this work, Δ17O($$\rm{NO}_{3}^{-}$$) were similar during clean (24.0–34.4‰) and haze days (23.4–33.6‰).

Contrary to most investigating days, extremely high Δ17O($$\rm{NO}_{3}^{-}$$) at noon were observed on January 17th, 18th, 19th, and 27th (Fig. 2a). In the case on January 17th, the nitrate aerosols possessed a Δ17O value of 39.3‰, which exceeded the terminal value of O3 (~39‰) produced in the troposphere (Eq. (17)). This suggests that the tropospheric produced NO3- could not completely explain this enhanced Δ17O($$\rm{NO}_{3}^{-}$$) value. Previously, such high Δ17O($$\rm{NO}_{3}^{-}$$) values have been found in polar areas and high-altitude localities like Nepal Climate Observatory-Pyramid (5079 m a.s.l.), where the stratospheric intrusion of O3 and nitrate with high Δ17O values frequently occurred in winter and spring seasons38,41,55,56,57,58. Thus, the high Δ17O($$\rm{NO}_{3}^{-}$$) value on January 17th might be attributed to a mixed source from the tropospheric and stratospheric intrusion of O3 and nitrate. In urban areas, the daily Δ17O($$\rm{NO}_{3}^{-}$$) has been observed more than 35‰ in the polluted upper air (260 m a.s.l.) in Beijing winter40. There were other possible explanations for the high Δ17O($$\rm{NO}_{3}^{-}$$) values around noontime: the oxidation pathways of HNO3 during the current period and the external input of nitrate through vertical/horizontal air mass transport. The variation of PBLH was similar on January 17th, 18th, and 19th; PBLH was lower (~500 m) at night and increased to higher values (1500–2500 m) at noon. During the nighttime, large anthropogenic-emitted pollutants (e.g., NOx, VOCs, CO) reached above the top of the nocturnal boundary layer and nitrate was produced in the residual layer without sinking59,60,61. Then, the increased PBLH during the day promoted the mixture of materials in the boundary layer at noon, allowing nitrate transport from the top of the PBLH to the surface layer (Supplementary Fig. 1). This suggested the high Δ17O($$\rm{NO}_{3}^{-}$$) might be related to vertical air mass transport. Vertical air mass transport increased the fraction of nitrate produced above the boundary layer at night and decreased the contribution of nitrate produced in the surface layer during the day. In that case, the nitrate produced at night (such as through NO3 + HC pathway) with high Δ17O($$\rm{NO}_{3}^{-}$$) was collected at noon. In particular, a high concentration of Ca2+ was found with the increase of PBLH on January 19th (Supplementary Fig. 2). The footprints of nitrate aerosols at noon on January 19th from the FLEXPART model (Supplementary Note 3 and Supplementary Fig. 3) suggested that the dust air was affected by air mass transport from southeast of the sampling site where some chemical industries and steel plants located and nitrate particles might be formed in the process of region transport. On the contrary, the PBLH was relatively low (~ 400–700 m) on January 27th, but the high wind speed (3.3 m s1) at noon might also bring the nitrate with a high Δ17O value from northeast to the sampling site. Without considering the four abnormal days with extremely high values of Δ17O($$\rm{NO}_{3}^{-}$$) around noontime, the Δ17O($$\rm{NO}_{3}^{-}$$) values at night (17:00–5:00 on the next day, 31.0 ± 2.6‰) were significantly higher (p-value = 0.002, Supplementary Table 1) than those during the day (5:00–17:30, 29.3 ± 3.0‰). This suggested the differences in relative contributions of photochemical and nocturnal reactions to nitrate formation during the day and night. In addition, nitrate concentration and Δ17O($$\rm{NO}_{3}^{-}$$) decreased significantly after the three precipitation events on January 14th, 25th, and 27th in this study, suggesting the important role of reaction with depleted Δ17O signature on the formation of nitrate after air cleaning by wet deposition.

### The diurnal variation of nitrate production

Observations of Δ17O($$\rm{NO}_{3}^{-}$$) and estimated α were applied to quantify the contribution of each nitrate formation pathway using the Bayesian model. The α values ranged from 0.61 to 0.97 with higher values during the day (0.95 ± 0.04) and lower values at night (0.87 ± 0.11) (Supplementary Fig. 4), suggesting the significance of O3 participation in NO oxidation during the sampling period. On the other hand, our α values were similar to those (0.85–1) for other midlatitude regions19. The α value is affected by the relative amount of O3 and HO2/RO2 in NOx cycling. And the low O3 concentrations (<1 ppb) were found when the α values were at a low level (~0.6) (Supplementary Fig. 4). The relative contributions of (P1: NO2 + OH/H2O, ƒP1), (P2: NO3 + HC/H2O and N2O5 + Cl, ƒP2), and (P3: N2O5 + H2O, ƒP3) to diurnal nitrate formation in Nanjing city are showed in Fig. 3 and Supplementary Fig. 5. On average, the ƒP1, ƒP2, and ƒP3 were 38 ± 10%, 27 ± 10%, and 35 ± 20% during the sampling period, which indicated the dominant role of nocturnal chemistry in nitrate formation during the winter in Nanjing. Our result was similar to the previous results in Beijing winter40. The average contributions of P1, P2, and P3 were 44 ± 21, 22 ± 16, and 34 ± 10% during the day, and 39 ± 19, 25 ± 17, and 36 ± 7% at night, respectively.

Significant diurnal variations of nitrate formation mechanisms were observed in this work (Fig. 4). The NO2 + OH/H2O fraction increased to the highest (48 ± 20%) around noon (11:00–14:00) and decreased to the lowest (28 ± 16%) at midnight (23:00–2:00). The significant increase in the NO2 + OH/H2O fraction during the day was predictable due to the diurnal pattern of OH radical concentration observed in previous studies62,63. The diurnal variation of ambient RH was contrary to the NO2 + OH/H2O fraction, suggesting that NO2 hydrolysis was not an essential reaction for the formation of nitrate in this work. In contrast, the increases in the relative fractions of the P2 and P3 pathways were observed at night, which peaked (34 ± 16% for P2 and 38 ± 6% for P3) at midnight and decreased to the lowest (20 ± 19% for P2 and 32 ± 7% for P3) at noon. As the precursors of NO3 and N2O5, NO2 and O3 showed different diurnal patterns (Fig. 4). The NO2 concentration levels were higher at night than during the day. In this case, the enriched NO2 atmosphere and dark environment were responsible for generating NO3 and N2O5 at night without being photolysis62,64. This has been proved by some previous studies65,66. A recent observational study in Nanjing found that the high level of volatile organic components (VOCs) concentrations in January 2015, which were emitted by various industrial sources nearby67. Thus, the active NO3 + HC reaction was considered as an important formation mechanism of particulate nitrate in Nanjing, especially at night. At the same time, peroxyl radicals (HO2/RO2) can be produced from the reaction of NO3 with hydrocarbons. A previous study suggested the reaction rate of NO3 radical with selected hydrocarbons (e.g., isobutene and trans-2-butene) at night was slightly higher than that during the day in the winter68. However, the reaction of O3 with hydrocarbons can also produce peroxyl radicals and the daytime reaction rate of O3 with hydrocarbons was much higher than the nighttime reaction rate68. As shown in Fig. 4, O3 concentrations during the day were much higher than those at night. This would cause the nighttime HO2/RO2 production to be much lower than the daytime production of HO2/RO2, which has been proved in many previous studies69,70. Besides, the higher RH values at night could facilitate the nitrate formation through heterogeneous processes (e.g., NO3 hydrolysis and N2O5 uptake)71. Consequently, our results suggested that the nocturnal chemistry (including NO3 + HC/H2O and N2O5 + Cl/H2O) dominated the nitrate formation at night, while the NO2 + OH/H2O pathway and nocturnal reactions contributed equally to nitrate production during the day in this study.

In this work, both daytime and nocturnal chemistry contributed to nitrate formation at different times of the day. Daytime NO3 and N2O5 chemistry is generally regarded as less important due to rapid NO3 photolysis and the titration reaction initiated by NO. A previous study showed that there was also a certain amount of NO3 radical during the day compared with the night in cold seasons due to the weak sunlight65. The daytime production rate of NO3 was found to be large because of the elevated NO2 and O3 concentrations in Taizhou of the Yangzi River Plain72. The N2O5 and NO3 concentrations are very low during the daytime, however, both species exhibited non-neglected (even high) concentrations in urban cities, especially during the PM haze events. This resulted in high contributions of nocturnal mechanisms to nitrate formation during the day73. In addition, the global lifetime of atmospheric inorganic nitrate is on the order of 3–4 d74, both the accumulated nitrate (i.e., the old nitrate produced prior to the current sampling period) and fresh nitrate (i.e., the new nitrate produced during the current sampling period) were collected in the high-time-resolved (3 h) samples and had impacts on Δ17O($$\rm{NO}_{3}^{-}$$). This meant that the Δ17O($$\rm{NO}_{3}^{-}$$) collected at noon was influenced by the nitrate production pathways of fresh nitrate and the nitrate generated during the previous night. On the other hand, the variation of NO2 formation mechanism also had impacts on Δ17O($$\rm{NO}_{3}^{-}$$) and then the estimated results75. During the day, a large quantity of NO2 was produced through the NOx cycle and had Δ17O(NO2) = αΔ17O($${\rm{O}}_{3}^{\ast}$$)19. After sunset, NO2 was mainly produced with the absence of NO2 photolysis and the NOx cycle was not able to complete. Only half of the oxygen atoms in each NO2 molecule was oxidized by O3 or HO2/ROx, the other one was from the NO emitted at night with Δ17O(NO) ≈ 0‰76. Thus NO2 produced at night was expected to have Δ17O(NO2) = 1/2αΔ17O($${\rm{O}}_{3}^{\ast}$$). In a recent observational study in Grenoble77, the Δ17O(NO2) values showed a large diurnal cycle peaking in the late morning (9:00–12:00) at 39.2‰ and decreasing at night until 20.5‰ at 00:00–5:00. In our calculation, the Δ17O(NO2) = αΔ17O($${\rm{O}}_{3}^{\ast}$$) was used to estimate the formation pathways for the daytime and nighttime samples. As discussed, a great portion of NO2 produced at night had Δ17O(NO2) = 1/2αΔ17O($${\rm{O}}_{3}^{\ast}$$). However, the Δ17O($$\rm{NO}_{3}^{-}$$) of the nighttime samples were a lot beyond the range of Δ17O(HNO3) of each pathway at night calculated by using Δ17O(NO2) = 1/2αΔ17O($${\rm{O}}_{3}^{\ast}$$) (Supplementary Fig. 6). Since the atmospheric lifetime of NOx near the surface against nighttime oxidation to nitrate was typically greater than 24 h13, most nitrate formed during the nighttime would form from NO2 that reached photochemical equilibrium during the previous day. Consequently, the Δ17O(NO2) and the Δ17O(HNO3) in each nitrate formation pathway might be overestimated. And the contribution of the pathway that has higher Δ17O($$\rm{NO}_{3}^{-}$$) (NO3 + HC/H2O and N2O5 uptake) might be underestimated to varying degrees, especially at night. Despite all the complicated variations of reactions, our results strongly suggested the higher contribution of NO2 + OH pathway during the day and nocturnal chemistry at night.

As shown in Fig. 3, nocturnal processes contributed the major fractions to nitrate formation on haze days. The average contributions of P1, P2, and P3 were 38, 25, and 36% on haze days, respectively. This result was very different from that during clean days, in which P1, P2, and P3 contributed 47, 21, and 32% to nitrate production, respectively. To understand the diurnal formation mechanisms of nitrate aerosols under different pollution conditions in Nanjing, the fractions of the different pathways to nitrate formation at the different times of the day under clean and haze air conditions are shown in Fig. 5. On clean days (January 14th 2:00 to 16th 8:00), there was no obvious discrepancy in nitrate formation from 5:00 to 20:00, but an apparent difference was found at 23:00–2:00. The average contribution of NO2 + OH/H2O oxidation was 50% at 5:00–20:00, dropping to 38% at 23:00–2:00. In contrast, the average contributions of NO3 + HC/H2O and N2O5 + Cl pathway and N2O5 + H2O pathway were 19 and 30% at 5:00–20:00 and increased to 25 and 38% at 23:00–2:00. However, the diurnal variation of nitrate formation on haze days was more obvious than that on clean days. On haze days (January 21st 8:00 to 27th 2:00), the fractions of NO2 + OH/H2O pathway to nitrate production gradually increased from 27% at 5:00 to 51% at noon and then decreased with sunset until the lowest (27%) at midnight. Nevertheless, the contribution of NO3 + HC/H2O and N2O5 + Cl pathway decreased with sunrise, which from 40% at 5:00 to the lowest (15%) around noon and increased to 32% at 23:00. The contribution of N2O5 + H2O pathway showed a similar diurnal variation to NO3 + HC/H2O and N2O5 + Cl pathway, but kept a relatively stable level (32–41%) as a whole. The fractions of NO3 + HC/H2O and N2O5 + Cl/H2O showed a significant positive correlation (r = 0.81, p < 0.01) with NO2 concentrations on haze days but no correlation on clean days, suggesting that large emissions of gas precursors like NOx might significantly affect the nitrate formation in the haze events. On haze days, the daytime RH values were much lower than those at night, but the fractions of N2O5 + H2O pathway were still at a high level during the day. This suggested the important role of the hydrolysis of N2O5 on particle surfaces in nitrate production in the heavily polluted atmosphere even during the daytime.

### The effect of air cleaning for resetting the nitrate chemistry

As mentioned above, Δ17O($$\rm{NO}_{3}^{-}$$) of the 3 h samples were affected by both accumulated nitrate produced prior to the current sampling period and fresh nitrate produced during the current sample period. Fortunately, three precipitation events happened on January 14th, 25th, and 27th during the sampling period (Fig. 2b), eliminating the effect of Δ17O($$\rm{NO}_{3}^{-}$$) buffering caused by nitrate accumulation. After the precipitation event on January 14th, the concentrations of nitrate and tracer gases (NO2 and CO) were at the lowest levels (Fig. 2c) during the entire period accompanied with the lower wind speeds until January 16th (Fig. 1c). Therefore, the formation mechanisms quantified by the Δ17O($$\rm{NO}_{3}^{-}$$) of high-time resolved aerosols after the precipitation were closer to the current nitrate production in the ambient atmosphere. At the beginning of this period, the Δ17O($$\rm{NO}_{3}^{-}$$) showed low values and averaged at 26.1 ± 1.8‰ from January 14th 2:00 to January 15th 11:00 (Fig. 2a). On average, the NO2 + OH pathway and N2O5 + H2O pathway contributed 70 ± 10 and 24 ± 8% to nitrate production (Fig. 3), respectively. At the same time, O3 concentrations remained in a stable level (20 ± 2 ppb) from January 14th 2:00 to January 15th 11:00 (Fig. 2b), which indicated the low NO level after the rainfall limited the reaction of NO with O3 to form NO2 and then the photolysis of NO2 by daylight. Although the contributions of nocturnal pathways (NO3 + HC/H2O and N2O5 + H2O/Cl) showed higher fractions at night than those during the day, the nitrate aerosols collected at night were mainly formed through NO2 + OH reaction. The low NOx and atmospheric pollutants (e.g., CO, VOCs) levels in the air after the precipitation reduced the nitrate production rates through NO3 + HC and N2O5 hydrolysis reactions at night. And some nitrate formed through NO2 + OH reaction during the day would be collected by the nighttime samples. Interestingly, the Δ17O($$\rm{NO}_{3}^{-}$$) suddenly increased on January 15th 2:00 and averaged at 33.7 ± 0.9‰ during January 15th 2:00–16th 8:00 (Fig. 2a). The $$\rm{NO}_{3}^{-}$$, NO2, and CO concentrations increased gradually and O3 began to show significant diurnal variation (Fig. 2). Nocturnal pathways contributed a total of 80% to nitrate formation (Fig. 3). These results suggested that the active photochemical reactions dominated the nitrate production under the strong sunlight in the clean atmosphere and nocturnal chemistry played a key role in the formation of nitrate pollution.

The other case of Δ17O($$\rm{NO}_{3}^{-}$$) decline occurred before the rain on January 25th. It is notable that both $$\rm{NO}_{3}^{-}$$ (11 µg m3) and the Δ17O($$\rm{NO}_{3}^{-}$$) (~6‰) suddenly decreased after the constant southeast wind turned to the north (Figs. 1c and 2a). The change of wind direction indicated the transport of air masses from the north, which blocked the continuous influence of the original air masses. In this case, we inferred that the decrease of Δ17O(NO3-) before the precipitation resulted from the transport of cleaner air masses and the rainfall continued to scavenge the accumulated nitrate. Therefore, the nitrate collected after the transport of clean air masses and/or the precipitation were mostly newly formed in the atmosphere, the whole system of nitrate chemistry was reset and nitrate accumulation restarted. In other words, Δ17O($$\rm{NO}_{3}^{-}$$) values after the precipitation were able to reveal the quick variation of nitrate production in the atmosphere. This typical event was affected by the combination of precipitation and the clean air transport, resulting in a rapid decrease of Δ17O($$\rm{NO}_{3}^{-}$$) (over 10‰ in 15 h) during the severe haze on January 25th. Δ17O($$\rm{NO}_{3}^{-}$$) was steady around 30–33‰ and suddenly decreased to 23.4‰ after the sunset on January 24th. It showed the minimum value at noon on January 25th and gradually increased back to more than 30‰ after sunset on January 25th (Fig. 2a). Both nitrate and NO2 showed a similar tendency with Δ17O($$\rm{NO}_{3}^{-}$$), the accumulated nitrate was effectively washed out by the precipitation78,79 accompanied with the sudden increase of NOR (from 0.2 to 0.55). This indicated a decreasing fraction of cumulative $$\rm{NO}_{3}^{-}$$ and an increasing contribution of fresh nitrate with low Δ17O($$\rm{NO}_{3}^{-}$$) in this precipitation event. The time period before the precipitation went through the most severe haze in the whole sampling period. The low wind speed and stable wind direction (Fig. 1c) suggested that the sampling site was controlled by aged local air masses that moved back and forth in the direction of north and south with consecutive nitrate accumulation since January 23rd. As we illustrated in the previous section, cumulative nitrate has an impact on buffering the Δ17O($$\rm{NO}_{3}^{-}$$) on haze days. Thus the steady Δ17O($$\rm{NO}_{3}^{-}$$) before the precipitation and the large contribution of nocturnal formation pathways were observed during the nitrate accumulation in the severe haze (Fig. 3). In addition, HNO3, N2O5, and other soluble species were scavenged by the rain, and NO2 and CO were much more likely to be diluted by a relatively clean air mass from the north suburb due to the change of wind direction (Fig. 1c). Both the precipitation and the transport of clean air mass helped to reset the whole system of nitrate chemistry. The formation mechanism quantified by the Δ17O($$\rm{NO}_{3}^{-}$$) of high-time resolved aerosols after this precipitation event also pointed out the dominant contribution of NO2 + OH to nitrate formation.

Another precipitation event happened on January 27th. In this case, the Δ17O($$\rm{NO}_{3}^{-}$$) firstly increased after the rainfall during January 27th 2:00–8:00 and then a largely decline of Δ17O($$\rm{NO}_{3}^{-}$$) was observed during January 27th 14:00–18:00. The high wind speed and stable wind direction suggested that this sampling period was controlled by transported air masses in the direction of east where some chemical industries located. This meant that although rainfall effectively cleared the air of pollutants, a high value (~36‰) of Δ17O($$\rm{NO}_{3}^{-}$$) was recorded firstly due to the timely replacement of external nitrates formed by NO3 + HC pathway. Then $$\rm{NO}_{3}^{-}$$ and Δ17O($$\rm{NO}_{3}^{-}$$) rapidly decreased to 3.3 µg m3 and 24.6‰, representing another reset of nitrate chemistry by the rainfall at 14:00 on January 27th. All the three cases discussed above indicated the important role of NO2 + OH pathway in nitrate production after the air cleaning by precipitation events.

The analysis of diurnal variation of nitrate production based on the Δ17O($$\rm{NO}_{3}^{-}$$) of high-time-resolved (3 h) aerosols was first conducted during a haze period in Nanjing, a megacity of China. An easy and fast approach was deployed to assess the NOx oxidation process, which reduced the inaccuracy of models to the greatest extent with the constraint of Δ17O($$\rm{NO}_{3}^{-}$$) observation. The effect of nitrate accumulation on buffering the Δ17O($$\rm{NO}_{3}^{-}$$) on haze days and the cleansing effect for resetting nitrate chemistry was significant for understanding the variation of nitrate production. Thus previous studies of nitrate formation mechanisms based on the daily Δ17O($$\rm{NO}_{3}^{-}$$) observation might have overestimated the contribution of nocturnal pathways.

Although significantly diurnal variations of nitrate formation pathways based on Δ17O($$\rm{NO}_{3}^{-}$$) observation were found in this work, we must acknowledge the uncertainties of the diurnal variation on the contribution of nitrate formation pathways due to the absence of the studies on the nighttime NO emissions and NO2–NO isotope exchange. That requires the enlargement of synchronous studies about triple oxygen isotopes of high-time-resolved atmospheric nitrate and NO/NO2. Because neither the variation nor the extremum contribution of each pathway could be noticed in lower time-resolved samples such as aerosols collected more than 12 h in previous studies, therefore, it is necessary to study the Δ17O($$\rm{NO}_{3}^{-}$$) atmospheric nitrate in gas phase and in particles to get a more complete understanding of atmospheric nitrate formation mechanism in future studies.

## Methods

### Sampling and atmospheric observation

PM2.5 samples were collected from January 14th to 28th, 2015 in Nanjing, China (Supplementary Fig. 7). The sampling site was in the agrometeorological station located on the campus of Nanjing University of Information Science and Technology (32°12'57“N, 118°44'50“E). It was close to a busy road and within the largest industrial complex in Nanjing. Aerosol samples were collected on pre-combusted quartz-fiber filters every 3 h using a high-volume aerosol sampler (KC1000, Qingdao, China) at a flow rate of 1 ± 0.001 m3 min−1. A field blank was obtained by placing the blank filter on the filter holder for 10 min without pumping. After sampling, all filters were wrapped in aluminum foil, sealed in air-tight polyethylene bags, and stored at −26 °C for later chemical analysis. The details of measurements of pollutant gases, meteorological data, chemical species, and oxygen isotopes of the nitrate are described in the Supporting Information (Supplementary Note 5 and Supplementary Table 2).

### Evaluation of nitrate formation mechanism

The observed Δ17O($$\rm{NO}_{3}^{-}$$) values were used to calculate the contribution of each formation pathway based on isotope mass balance27. The Δ17O($$\rm{NO}_{3}^{-}$$) can be expressed as:

$${{\Delta }}^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{NO}}}}_{{{\mathrm{3}}}}^{{{\mathrm{ - }}}}} \right) = \sum {{\Delta }}^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}} \right)_{{{j}}}{{{\ \times f}}}_{{{{\mathrm{Pi}}}}}$$
(9)

where Δ17O($$\rm{NO}_{3}^{-}$$) was the Δ17O value of total nitrate, Δ17O(HNO3)j is the Δ17O value of HNO3 produced by pathway j, fj is the mole fraction of nitrate produced by j HNO3 formation pathway. Since all the oxygen sources incorporated into nitrate except for O3, (i.e., water vapor, OH radical, and HO2 (ROx)) were reported to have Δ17O ≈ 0‰34,35,36,37,38,39. Δ17O(HNO3) value of each pathway can be derived from Δ17O(NO2) and written in terms of only Δ17O($${\rm{O}}_{3}^{\ast}$$) (Eqs. (10)–(12))80. Δ17O($${\rm{O}}_{3}^{\ast}$$) is the Δ17O value of the terminal oxygen atom of O3, which transfers to the products during oxidation reactions (Supplementary Table 3)81:

$$\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}} \right)_{{{{\mathrm{NO2 + OH/H2O}}}}}\, = \, {{{\mathrm{2/3\alpha }}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right)$$
(10)
$$\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}} \right)_{{{{\mathrm{NO3 + HC/H2O}}}}\,{{{\mathrm{and}}}}\,{{{\mathrm{N2O5 + Cl - }}}}} \, = \, {{{\mathrm{2/3\alpha }}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right){{{\mathrm{ + 1/3}}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right)$$
(11)
$$\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{HNO}}}}_{{{\mathrm{3}}}}} \right)_{{{{\mathrm{N2O5 + H2O}}}}} \, = \, {{{\mathrm{2/3\alpha }}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right){{{\mathrm{ + 1/6}}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right)$$
(12)

The α factor is the mole fraction of NO oxidized by O3 (Supplementary Note 1). When the NOx cycle achieves at the photochemical steady-state, Δ17O(NO2) could be expressed as:

$$\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{NO}}}}_{{{\mathrm{2}}}}} \right) = {{{\mathrm{\alpha }}}}\Delta ^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_3^ \ast } \right)$$
(13)

The α factor could be calculated by considering the reaction constants of these three chemical reactions and the concentrations of the corresponding oxidants19:

$$\alpha = k_{R1} \times \left[ {{{{\mathrm{NO}}}}} \right] \times \left[ {{{{\mathrm{O}}}}_3} \right]/(k_{R1} \times \left[ {{{{\mathrm{NO}}}}} \right] \times \left[ {{{{\mathrm{O}}}}_3} \right] + k_{R2} \times \left[ {{{{\mathrm{NO}}}}} \right] \times \left[ {{{{\mathrm{HO}}}}_2 \cdot } \right] + k_{R3} \times \left[ {{{{\mathrm{NO}}}}} \right] \times \left[ {{{{\mathrm{RO}}}}_2 \cdot } \right])$$
(14)

where the reaction constants kR1, kR2 and kR3 are 3.0 × 1012 × e(−1500/T), 3.5 × 1012 × e(270/T) and 3.5 × 1012 × e(270/T) (cm3 molecule1 s1) and T is the ambient temperature (K)82,83. Due to the lack of HO2 and RO2 observation, the HO2 mixing ratios were estimated by the empirical formulas established in an urban city, in which HO2 was a function of O384. The RO2 concentrations were estimated by the HO2 concentrations multiplying 0.85985.

$$\left[ {{{{\mathrm{HO}}}}_2 \cdot } \right]/{{{\mathrm{ppt = exp}}}}\left( {5.7747 \times 10^{ - 2}\left[ {{{{\mathrm{O}}}}_3} \right]\left( {{{{\mathrm{ppb}}}}} \right)-1.7227} \right) \, {{{\mathrm{for}}}}\,{{{\mathrm{daytime}}}}$$
(15)
$$\left[ {{{{\mathrm{HO}}}}_2 \cdot } \right]/{{{\mathrm{ppt = exp}}}}\left( {7.7234 \times 10^{ - 2}\left[ {{{{\mathrm{O}}}}_3} \right]\left( {{{{\mathrm{ppb}}}}} \right)-1.6363} \right) \, {{{\mathrm{for}}}}\,{{{\mathrm{nighttime}}}}$$
(16)

Ozone’s terminal atoms are isotopically enriched relative to the central one (isotopic asymmetry)86,87,88. Laboratory experiments89 suggested that Δ17O($${\rm{O}}_{3}^{\ast}$$) is linearly correlated with the Δ17O value of bulk ozone (Δ17O(O3)) when the Δ17O(O3) is in the range of 20–40‰ by:

$${{\Delta }}{}^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_{{{\mathrm{3}}}}^ \ast } \right) = {{{\mathrm{1}}}}{{{\mathrm{.5 \times }}}}\Delta {}^{{{{\mathrm{17}}}}}{{{\mathrm{O}}}}\left( {{{{\mathrm{O}}}}_{{{\mathrm{3}}}}} \right)$$
(17)

Based on the observations of tropospheric O332,33, Δ17O(O3) was assumed to average at 26 ± 1‰ in this study, yielding a Δ17O($${\rm{O}}_{3}^{\ast}$$) value of ~39‰. The calculated α values and Δ17O(HNO3) in each formation pathway were showed in Supplementary Fig. 4. The endmember values of Δ17O(HNO3)NO2+OH/H2O, Δ17O(HNO3)NO3+HC/H2O and N2O5+Cl− and Δ17O(HNO3)N2O5+H2O were 15.98–25.22‰, 28.98–38.22‰, and 22.48–31.72‰, respectively. Then the contribution of each nitrate formation pathway and the uncertainty in each pathway could be quantified using the Bayesian model (Supplementary Note 4)21,90.

## Data availability

All the data used in this paper are available from the Open Science Framework (https://osf.io/5d7qy/, https://doi.org/10.17605/OSF.IO/5D7QY).

## Code availability

The codes are available upon request from the corresponding author Yan-Lin Zhang: dryanlinzhang@outlook.com.

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## Acknowledgements

This study is supported by the National Natural Science Foundation of China (grant nos. 42192512 and 41977305) and the National Key Research and Development Program of China (grant no. 2017YFC0212704).

## Author information

Authors

### Contributions

Y.-L.Z. designed the experiments. W.Z., M.-Y.F., J.L., Y.-L.Z., and G.M. conceived and organized this paper. W.Z., X.L., F.C., and M.B. conducted the aerosol collection and the measurements of meteorological parameters. W.Z., H.F., J.L., and B.P.W. conducted the measurement of triple oxygen isotopes, Y.H. run the FLEXPART model, M.-Y.F. and Y.-L.Z. prepared the manuscript with contributions from all co-authors.

### Corresponding author

Correspondence to Yan-Lin Zhang.

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### Competing interests

The authors declare no competing interests.

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## Supplementary information

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Supplementary Information for A diurnal story of ∆17O(NO3-) in urban Nanjing and its implication for nitrate aerosol formation

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Zhang, YL., Zhang, W., Fan, MY. et al. A diurnal story of Δ17O($$\rm{NO}_{3}^{-}$$) in urban Nanjing and its implication for nitrate aerosol formation. npj Clim Atmos Sci 5, 50 (2022). https://doi.org/10.1038/s41612-022-00273-3

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• DOI: https://doi.org/10.1038/s41612-022-00273-3