The isotope analysis requires at least 5 nmol of equivalent N in 5 mL solution (i.e., the molar concentration of NO3+NH4≥1 µM N), so the FTIR measurements provide a quantitative reference to infer the concentration of dissolved N-containing species. Ten sets of aerosol samples with higher N-containing functional group concentration under distinct weather conditions were selected for the δ15N and δ18O isotope analysis of N-containing species (181202D/N, 181213N, 181214D/N, 181215D, 181220N, 181221D, 181222D, 181222N). If the predicted concentration of one filter was too low, two to four filters collected on the same day with adjacent size bins were put together in a bottle during the rinsing process to ensure sufficient concentration for isotope analysis. Filter samples were cut in half and soaked into 30 mL Milli-Q water (resistivity=18.2 MΩ at 25 ∘C) and underwent a 30 min ultrasonication to dissolve the water-soluble ions into the solution. Afterward, the extracted solution was filtered through a 0.22 µm Millipore syringe filter and then preserved in a high-density polyethylene (HDPE) bottle. The samples were analyzed for the δ15N of total nitrogen (TN) and nitrate + nitrite (NN), and the δ18O of NN by the bacterial “denitrifier method” as stated by Sigman et al. (2001), Casciotti et al. (2002), and updated by Weigand et al. (2016). For the TN analysis, the oxidation process of adding potassium persulfate in NaOH solution was to oxidize NH4+ and other N-containing species in a reduced state into NO3- before bacterial digestion. The isotope 15N/14N and 18O/16O was measured using a gas chromatography–isotope ratio mass spectrometer (GC–IRMS) composed of a GC column system coupled with Thermo MAT 253 Plus 10 kV IRMS. The international standard IAEA-NO3 (δ15N=4.7 ‰, δ18O=+25.61 ‰) and USGS 34 (δ15N=-1.8 ‰, δ18O=-27.93 ‰) were applied for δ15N and δ18O calibration (Bohlke et al., 2003). In each batch of measurement, three to five duplicates of standards and bacteria blank were used to ensure the efficiency of bacterial conversion and the stability of mass spectroscopy. The detail of isotope ratio measurement is described in the Supplement.

Ammonium is a major N-containing component in aerosols as part of TN. Since the concentration of water-soluble TN minus NN correlates well (R2=0.7764) with the measured NH4+ concentration from FTIR (slope is close to 1 with a small interception as shown in Fig. S4), the water-soluble TN minus NN can be regarded as NH4+. Therefore, the δ15N of ammonium can be derived by assuming the collected aerosol mainly comprised of nitrate, nitrite and ammonium with negligible other N forms such as organic nitrogen (Wu et al., 2021). The δ15N of NH4+ can be calculated using Eq. (3) as follows: 3δ15NNH4+=δ15NTN×MTN-δ15NNN×MNNMTN-MNN, where MTN and MNN are the molarities of total nitrogen (TN) and nitrate plus nitrite (NN) of the sample solution, respectively. If organic nitrogen is considered, a slightly higher δ15N of NH4+ than the current reported values can be expected because organic nitrogen might be related to NOx and was reported as a lower δ15N (≤-5 ‰) than nitrate (Wu et al., 2021). Additionally, since the aerosol nitrite concentration is mostly negligible based on ion-chromatography (IC) analysis of PM10, NN is assumed to be in NO3- form, i.e., δ15N of NO3-≈δ15NNN.

A Bayesian mixing model, MixSIAR (Stock and Semmens, 2016), was applied to assess the contribution of multiple aerosol sources. The MixSIAR is a statistical model applying Bayesian inference to infer the posterior probability of mixture sources by analyzing its tracer composition, such as stable isotope or fatty acids (Stock et al., 2018). The studied tracers are assumed to transfer from sources to the mixture through a conserved mixing process integrating the observed variability. In this study, the observed mass-weighted δ15N of NH4+ and NO3- for each sampling period was used as prior information of the mixture. For simplification, the source data adopted the results of Savard et al. (2017) as summarized in Table 1 by assuming that the δ15N of NH4+ and NO3- was directly related to their emission sources, either single source or mixture from those sources. The source data for the MixSIAR analysis include δ15N of NH4+ from traffic, chemical and metal industries, feedlots, fertilizer plants, and coal-fired power plants (CFPPs), and δ15N of NO3- from traffic, chemical and metal industries, fertilizer plants and oil refinery, and CFPPs. The source of the gas compressors was not considered in this study.

The functional group concentration of NH4+ (1.00 µgm-3) and NO3- (0.25 µgm-3) during non-foggy daytime was higher than that in non-foggy nighttime (0.56 and 0.04 µgm-3, respectively) as shown in Table 2, and SO42- and BC also have approximately 1.5 times higher concentration during non-foggy daytime. The greater daytime concentration might link to the upstream transportation of urban pollutants by valley wind combined with the sea breeze (Chen et al., 2021). The sampling site is mostly below the boundary layer height during daytime and above the boundary layer height during nighttime. Once the wind direction changes into mountain wind accompanying land breeze, the cleaner upper-stream air dilutes the pollutants in the Xitou forest area.

The daytime concentration of NH4+ and NO3- was 2 to 4 times higher in the foggy period than that in the non-foggy period (Table 2). The mass distribution seems to shift to a larger size bin (0.56–1.8 µm) for NH4+ as shown in Fig. 2c, while NO3- in Fig. 2d also has a significantly high concentration for the 0.56–1.8 µm size bin during the foggy period. Higher ammonium nitrate concentration might result from the stronger boundary layer inversion on foggy days. When the boundary inversion gets stronger in the Xitou area, the moisture transportation by upwelling turbulence is weakened. Therefore, water vapor could accumulate in the lower atmosphere, promoting fog formation and prolonging fog lifetime (Hsieh, 2019). Furthermore, the weakened upward transport could also accumulate pollutants in the lower boundary layer, causing a higher observed concentration. The enhanced concentration of black carbon (BC), a primary aerosol component with limited chemical reactions in the atmosphere, during foggy periods (Table 2 and Fig. S5) can further reveal the inference of the boundary layer on aerosol concentration.

The observed mass distribution of NH4+ shifting slightly to a larger size mode on foggy days is likely due to the hygroscopic growth of aerosols. According to a previous calculation with the observed dry and wet aerosol size distribution in Xitou, NH4+-containing aerosol has a hygroscopicity parameter of 0.21 ± 0.01 (Chen et al., 2021). The hygroscopic growth of aerosol from averaged RH of 80 % under non-foggy circumstances to over 99 % during the foggy period could lead to a larger wet aerosol size. Extra-high NO3- concentration of 0.56–1 µm aerosol was observed during foggy periods accompanied by the high NH4+ concentration in that size bin (Fig. 2d). In foggy periods, the higher water content of aerosol promotes an aqueous phase reaction of HNO3 uptake on aerosols, and the higher concentration of NH4+, more than 2×[SO42-], gives extra neutralizing cation to stabilize the NO3- as suggested by Chen et al. (2021).

Figure 3a shows the δ15N value of aerosol NH4+ as a function of geometric-averaged particle diameter. The δ15N varies from -3.70 ‰ to +21.39 ‰, and the average mass-weighted δ15N value is +11.95 ‰ with a standard deviation of 2.65 ‰. The δ15N of 0.32–1 µm aerosols is in the range of +7.16 ‰ to +18.64 ‰, relatively higher than that of the larger and smaller size bins. The increasing and then decreasing trend of NH4+ δ15N with aerosol size was also observed in Beijing (Pan et al., 2016, 2018b) but was approximately 12 ‰ lower. This offset probably results from the different emission sources or the partitioning processes. Overall, the processes forming aerosol NH4+ may lead to the size-differentiated δ15N.

The daytime δ15N of NH4+ is mostly greater than the nighttime one as summarized in Table 3, likely resulting from the different sources, such as transportation of high δ15N NH3 from urban rush-hour traffic or industrial sources by sea breeze combined with the valley wind. As the mountain wind dominates after sunset, available NH3 might be attributed to the daytime residual (having lower δ15N due to the fractionation that happened during daytime) or the local biogenic sources having a lower δ15N.

Fog varies the mass size distribution among components and can affect the isotopic ratio. Under foggy daytime conditions, the δ15N value of larger size aerosols (PM1-10-NH4+) was more likely to be the extension of 0.56–1 µm with a value up to 21.39 ‰, higher than that of non-foggy days. As stated in Sect. 3.1, high NH3 concentration can promote the partition of HNO3 under foggy conditions. The observed flat trend of δ15N at diameter ≥0.56 µm might result from the hygroscopic particle growth of NH4+ from the 0.56–1 µm size bin aerosols. As NH4+ is likely to deliquesce to the liquid phase under high RH conditions, the gas–liquid phase transition could accompany isotope equilibrium fractionation for most aqueous particles (Walters et al., 2018). The NH3-rich and high RH conditions might cause the NH3 partition to condensed phase and favor higher δ15N during equilibrium-fractionation processes (Pan et al., 2018b). On non-foggy days, having a relatively lower concentration with more acidic properties (indicating NH3 limited), a higher portion of NH3 might participate in the aerosol phase to lead to a lower δ15N-NH4+ toward the original δ15N-NH3.

The δ15N value of NO3- as a function of size bin shown in Fig. 3b ranges from -1.07 ‰ to +6.64 ‰, with a mass-weighted mean value of +2.98 ‰ and a standard deviation of 1.20 ‰. This value agrees with other studies measured in Asia or the Pacific Ocean in the winter to spring period (-1 ‰ ± 3 ‰ in spring by Guha et al., 2017; 2.0 ‰ ± 0.4 ‰ in spring and 8.6 ‰ ± 0.4 ‰ in winter by Kim et al., 2019; 3.1 ‰ ± 1.1 ‰ in winter by Kawashima, 2019). As stated in Sect. 3.1.2, nitrate significantly contributes to the submicrometer particles during foggy daytime in addition to the usual peak over the supermicrometer particles for all conditions (Fig. 2). The nitrate can be divided into two groups, PM1-10-NO3- for particle size in the range of 1 to 10 µm and PM1-NO3- for particle diameter less than 1 µm, for further discussion. For a given sampling period, PM1-NO3- has lower δ15N (-1.07 ‰ to +3.19 ‰) than PM1-10-NO3- (+1.85 ‰ and +6.64 ‰), likely due to different formation processes. The PM1-10-NO3- might be formed through the reaction of HNO3 or NO2 with the coarse particles comprising NaCl or dust (Evans et al., 2004; Hoffman et al., 2004) during the transport from the coast through the urban region and further to Xitou. Therefore, a higher δ15N NO3- participates in the aerosol phase through isotopic equilibrium fractionation with lower δ15N HNO3(g) or NO2 gas molecules remaining in the air (Walters and Michalski, 2015). In contrast, PM1-NO3- occurs only on foggy days, probably forming in the mountain region with high water content and available NH3. The available HNO3(g) for PM1 is from the residual NOx (after reacting with coarse-mode particles at the upper stream) and has lower δ15N than PM1-10-NO3-. The PM1-NO3- formed through the aqueous-phase reaction under high NH4+ with effective gas-phase HNO3 uptake might have a limited isotopic selection leading to a low δ15N of NO3- under foggy conditions.

The sample of 181221D is a special case with higher δ15N values. It might result from the recorded agricultural activities nearby, including fertilizing and mowing. The fertilizer generates NOx with higher δ15N (Savard et al., 2017), which indicates that the agricultural activities might cause higher δ15N values than on other days.

The δ18O of NO3- ranged from +53.90 ‰ to +79.81 ‰ (Fig. 3c), with a half-day period mass-weighted average of +72.66 ‰ and a standard deviation of 3.42 ‰. The results are within the observed δ18O range in cool seasons over the Mount Lulin site in Taiwan (69 ‰ ± 15 ‰ reported by Guha et al., 2017) and in the typical range of other studies (averaged value from 70.9 ‰ to 83.8 ‰) (Savarino et al., 2007; Wankel et al., 2010; Fan et al., 2020; Sun et al., 2020). The relatively higher δ18O compared to summer samples (32 ‰ ± 13 ‰ reported by Guha et al., 2017) indicates that more NO3- precursors (i.e., NOx) were formed by O3 oxidation whether it was further oxidized through OH oxidation of NO2 or N2O5 hydrolysis pathways (from +72.5 ‰ to +101.67 ‰, detailed description in the Supplement). The slightly lower daytime δ18O (+69.67 ‰ to +72.52 ‰ based on half-day average) compared to nighttime samples (+74.82 ‰ to +79.81 ‰) as shown in Table S1 indicates that peroxyl radicals might partially participate in the daytime photo-oxidation processes or relatively lower δ18O of OH, leading to a lower δ18O in nitrate aerosols during daytime as stated in other studies (Gobel et al., 2013; Hastings et al., 2003; Fang et al., 2011).

For PM1, the δ18O of 0.32–0.56 µm NO3- under foggy conditions (+53.90 ‰ and +66.13 ‰ for 14 and 15 December daytime samples, respectively) is relatively lower than that over larger sizes (e.g., +75.65 ‰ and +73.98 ‰ of 0.56–1 µm), suggesting the formation pathway difference. The concentration of 0.32–0.56 µm NO3- is relatively lower than that of 0.56–1 µm or PM1-10, and it might be attributed to ambient air mass near the observation site. Because the fine particles are more acidic (Chen et al., 2021), NO3- can frequently exchange with gas-phase HNO3 to reveal the local δ18O of NO3-. The peroxyl radicals derived from the photo-oxidation of biogenic volatile organic compounds (BVOCs) at the Xitou forest area might be active oxidants locally for fine-mode organic nitrate (RONO2 or ROONO2) and HNO3 from NO+RO2→NO2+RO and NO2+OH→HNO3 oxidation to have a lower δ18O of NO3- (description in the Supplement). On the other hand, the higher δ18O of 0.56–1 µm NO3- is likely formed from the growth of smaller particles and aqueous-phase reactions such as HNO3 partition, which could be neutralized by excess NH4+ at an earlier stage to be less influenced by peroxyl radicals. Furthermore, the PM1-10-NO3- are mainly produced near the urban regions via the reactions of HNO3 or NOx with sea salt, i.e., HNO3+NaCl(p)→HCl(g)+NaNO3(p) or 2NO2+NaX(p)→XNO(g)+NaNO3(p) (X = Cl or Br, (p) represents particle phase), which may also produce NO3- with a higher δ18O because most O atoms of NO3- might be from O3 during the fast NO↔NO2 conversion processes (Gobel et al., 2013).