Supporting Information (SI)

Song et al.

Text S1. Calculation the fractional contributions of P1, P2 and P3 to NO3-

O3 is only source of anomalous 17O in NO3-, and is a conservative non-mass

dependent parameter compared with 15N and 18O isotopes (Michalski et al., 2012). Thus, the fractional contributions of P1, P2, and P3 (fP1, fP2, fP3; %) to the NO3

- of PM2.5 can be estimated by a Δ17O isotope mass-balance method (Eq. S1).

Δ17O-NO3- = [Δ17O-NO3

-]P1 × fP1 +[Δ17O-NO3-]P2 × fP2 + [Δ17O-NO3

-]P3 × fP3 (Eq. S1),

where fP1 + fP2 + fP3 = 1, and Δ17O-NO3- is the observed value in our study. The [Δ17O-

NO3-]P1, [Δ17O-NO3

-]P2, and [Δ17O-NO3-]P3 endmember values for each observation

were calculated using Eqs. (S2-S4) according to Alexander et al (2009).

[Δ17O-NO3-]P1 (‰) = 2/3A × Δ17O-O3

* (Eq. S2),

[Δ17O-NO3-]P2 (‰) = 2/3A × Δ17O-O3

* + 1/3Δ17O-O3* (Eq. S3),

[Δ17O-NO3-]P3 (‰) = 1/3A × Δ17O-O3

* + 1/2(2/3A × Δ17O-O3* + 1/3Δ17O-O3

*) (Eq. S4),

The Δ17O-O3* values in Eqs. S2-S4 averaged 34.7±3.0‰ (mean ± SD), its uncertainty

has been included by using scattered values reported in literature sources (Alexander et al., 2009; Vicars et al., 2012; Vicars & Savarino 2014).

The A value is the proportional contribution of O3 among the NO oxidation values (R1R3). The A values were estimated by considering the reaction constants of R1, R2, R3, and concentrations of corresponding oxidants (Eq. S5) (Alexander et al., 2009).

A = KR1×[O3]×[NO]/(KR1×[O3]×[NO]+KR2×[NO]×[HO2·]+KR3×[NO]×[RO2·]) (Eq. S5),

For the A value, the uncertainties were mainly from the reaction constants of KR1, KR2 and KR3, and the mixing ratios of HO2 and RO2, where reaction constants of KR1= 3.0×10-12 ×e (-1500/T), KR2=3.3×10-12 ×e (270/T) and KR3 = KR2 (unit: cm3 molecule-1 s-1) (Kunasek et al., 2008; Sander et al., 2006). The uncertainties in KR1, KR2 and KR3

values were associated with the temperature according to the empirical equation (Kunasek et al., 2008; Sander et al., 2006). In this study, the daily mean temperature was used (Fig. S2), with no need to consider its variation because our samples were also based on daily values.

The HO2 mixing ratios were estimated according to empirical formulae (Kanaya et al., 2007), which so far are available only for winter and summer (Eqs. S6-S7).

[HO2·]/pptv = exp (5.7747 × 10-2 [O3] (ppbv) -1.7227) for daytime in winter (Eq. S6),

[HO2·]/pptv = exp (7.7234 × 10-2 [O3] (ppbv) -1.6363) for nighttime in winter (Eq. S7),

Due to the similar latitudes of Beijing and Tokyo in East Asia, their O3 concentrations and temporal variations are comparable (Yoshino et al., 2012; Akimoto et al., 2015; Wang et al., 2015). Accordingly, we considered that the empirical relationship between O3 and HO2 concentrations established in Tokyo of Japan

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101112131415161718192021222324

2526272829303132

333435

36

37383940

(Kanaya et al., 2007) were applicable for estimating the HO2 concentrations in Beijing in China. Standard deviations of each variable in the above calculations were considered and estimated by the Monte Carlo method. In the above calculations, we also evaluated the uncertainty of estimated HO2 values for Beijing using the ratio of estimated HO2 to observed HO2 values from Tokyo (mean ± SD = 0.964 ± 0.409; Kanaya et al., 2007) and the Monte Carlo method (Fig. S4).

The relationship between RO2 and HO2 concentrations has been established for Beijing, showing a mean ratio of 0.859 ± 0.388 (mean ± SD) (Liu et al., 2012), which also allowed us to evaluate the uncertainty of estimated RO2 values for Beijing using the Monte Carlo method (Fig. S4).

[NO] is not needed for the calculations of A values.

A = KR1×[O3]×[NO]/(KR1×[O3]×[NO]+KR2×[NO]×[HO2·]+KR3×[NO]×[RO2·])

= KR1×[O3] / (KR1×[O3] + KR2× [HO2·] + KR3×[RO2·]) (Eq. S8),

To calculate the mixing ratios of HO2 and RO2 (see detailed in Eqs. S6-S7), the standard deviations of each variable in the calculations were estimated by the Monte Carlo method and were finally propagated into the uncertainties of the A values. Each of the daily A values had a standard deviation (Fig. S5). The propagated standard deviation (SD) of each Δ17O endmember value (Eqs. S2-S4) was estimated by the Monte Carlo method (Figs. S6 & S7). Finally, the mean ± SD of Δ17O endmember values for three pathways were input to the SIAR model.

In this study, estimated A values varied from 0.894±0.114 to 0.967±0.049 for all of the observations, averaging 0.949±0.066 during day time and 0.928±0.086 during the night time (Fig. S5). These results indicated that the conversion of NO to NO2 was mainly oxidized by O3 during the sampling period in Beijing. These values were generally similar to those (0.85-1.00) estimated for other mid-latitude regions (Patris et al., 2007; Alexander et al., 2009). Using the A values, we calculated the [Δ17O-NO3

-]P1, [Δ17O-NO3-]P2, and [Δ17O-NO3

-]P3 endmember values for each observation based on Eqns (S2-S4) (Figs. S6 & S7).

Then, the three endmember values were used to calculate values of fP1, fP2 and fP3 by Stable Isotope Analysis in R (i.e., the SIAR model; the detailed calculation method is provided in the Supporting Information (Text S3)) to run the Δ17O-NO3

- data during the day and at night (Fig. 1d), which can output the standard deviation for corresponding calculations. In particular, the SIAR model allows us to input the mean ± SD of source Δ17O values and also a group of PM2.5 Δ17O-NO3

- values in flexible time periods. Therefore, the standard deviation of the source contributions for PM2.5 during the day and at night was obtained (Fig. 2).

Text S2. ε(NO2→NO3-) values of NO2 oxidation to NO3- based on δ18O-NO3

- calculationAtmospheric NO2 is first converted to HNO3 through two dominant reactions (i.e., reactions of NO2 with OH· (P1) and N2O5 with H2O (P3)) and HNO3 is then converted to NO3

-(p) (Walters & Michalski, 2016; Zong et al., 2017; Chang et al., 2018). The product of the N2O5 pathway (P3) is NO3

-, but the product of P1 is first gaseous nitric acid (HNO3), then NO3

-. The 15N signatures of gaseous nitric acid (15N-HNO3(g)) did differ from those of particulates NO3

- (15N-NO3-) that were measured during the same

time at the same sites. Based on the available data, 15N-NO3- values were higher by

41424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586

9.8 ± 3.5‰ in Jülich of Cermany (Freyer 1991), 2.7 ± 1.2‰ in New York, Pennsylvania, and Ohio of UAS (Elliott et al., 2009), 6.2 ± 5.6‰ in Alberta of Canada (Savard et al., 2017), 5.3 ± 2.6‰ in Yurihonjo of Japan (Kawashima 2014), 3.0 ± 3.5‰ in Rishiri of Japan (Nelson et al., 2018), and 3.5 ± 4.5‰ in Sapporo of Japan than corresponding 15N-HNO3(g) values, showing a total difference (total (HNO3↔NO3-)) of 5.1 ± 4.1‰. Therefore, the total(HNO3↔NO3-) value represents the 15N difference between total NO3

- produced by P1 and P3 pathways and HNO3(g) that contributed only by P1. The real 15N differences between NO3

- and HNO3(g) for P1 (real(HNO3↔NO3-)) can be estimated by Eq. S9.

real(HNO3↔NO3-) = total(HNO3↔NO3-) / fP1 (Eq. S9),

Then, the overall ε(NO2→NO3-) values for P1 can be calculated by Eq. S10.

εP1(NO2→NO3-) = εP1(NO2→HNO3) + P1-real(HNO3↔NO3-) (Eqn S10),

Finally, the ε(NO2→NO3-) value for all two pathways of atmospheric NO2 conversion to NO3

-(p) can be calculated by Eq. S11.

ε(NO2→NO3-) = fP1 × εP1(NO2→NO3-) + fP3 × εP3(NO2→NO3-) (Eq. S11),

in which fP1 + fP3 = 1, and εP1(NO2→NO3-) and εP3(NO2→NO3-) values are isotope fractionations during the above two reactions.

Since both reactions of NO2 with OH· and N2O5 with H2O are exchange reactions, both εP1(NO2→NO3-) and εP3(NO2→NO3-) values reflect isotope equilibrium effects in the respective reactions. The εP1(NO2→HNO3) values can be calculated using the following mass-balance equation (Walters & Michalski 2016).

εP1(NO2→HNO3) = 1000 × ((15αNO2/NO - 1) (1 - fNO2) / ((1 - fNO2) + (15αNO2/NO × fNO2)), (Eq. S12),

where the 15αNO2/NO value is the equilibrium isotope fractionation factor between NO2 and NO, which is a temperature-dependent function (see Eq. S14), and fNO2 is the fraction of NO2 relative to total NOx. The fNO2 values were 0.34 ± 0.27 in winter in Beijing (Liu & Zhu, 2013; Hu et al., 2016), which integrated the day/night variations of photochemistry. The standard deviations of fNO2 were estimated by the Monte Carlo method and were finally propagated into the uncertainties of the ε(NO2→HNO3) values. Similarly, the εP3(NO2→HNO3) values can be calculated from the following equation (Walters & Michalski 2016).

εP3(NO2→NO3-) = 1000 × (15αN2O5/NO2 - 1), (Eq. S13),

in which 15αN2O5/NO2 refers to the equilibrium isotope effects between N2O5 and NO2, which is a temperature-dependent function (see Eqn S11). The 15αNO2/NO and 15αN2O5/NO2 in Eqns S12 and S13 (expressed the 15αX/Y) were calculated by Eq. S14:

1000 (15αX/Y-1) = A / T4 × 1010 + B / T3 × 108

+ C / T2 × 106

+ D / T × 104 (Eq. S14),

where A = 3.847, B = -7.680, C = 6.003 and D = -0.118 for 15αNO2/NO; and A = 1.004, B = -2.525, C = 2.718 and D = 0.135 for 15αN2O5/NO2 (Walters & Michalski 2015). In this study, the temperature (T) is shown in Fig. S2.

The fP1 and fP3 values were determined using the 18O fractionations of the above two reactions (Walters & Michalski 2016; Zong et al., 2017; Chang et al., 2018), which can be expressed in Eq. S15.

δ18O-NO3- = [δ18O-NO3

-]OH × fOH + [δ18O-NO3-]N2O5 × fN2O5, (Eq. S15),

87888990919293949596979899

100101102103104105106107108109110111112113114115116117118119120121122123124125126127128

where fOH + fN2O5 = 1. The [δ18O-NO3-]OH value was calculated by the following

equations (Eq. S16).

[δ18O-NO3-]OH = 2/3 × [δ18O-NO2]OH + 1/3 × [δ18O-OH]OH, (Eq. S16),

where the [δ18O-NO2]OH and [δ18O-OH]OH values were calculated by Eq. S17 and Eq. S18, respectively.

[δ18O-NO2]OH=1000×(18αNO2/NO - 1)×(1-fNO2)/((1-fNO2)+(18αNO2/NO×fNO2))+[δ18O-NOx] (Eq. S17),

[δ18O-OH]OH = (δ18O-H2O) + 1000 × (18αOH/H2O - 1), (Eq. S18),

In Eq. S17 and Eq. S18, the 18αNO/NO2 and 18αOH/H2O (expressed as the 18αX/Y) values were calculated using the following equation (Eq. S19).1000(18αX/Y-1) = A / T4 × 1010 + B / T3

× 108 + C / T2

× 106 + D / T × 104, (Eq. S19),

where A = -0.04129, B = 1.1605, C = -1.8829 and D = 0.74723 for 18αNO/NO2; and A = 2.1137, B = -3.8026, C = 2.2653 and D = 0.5941 for 18αH2O/OH (Walters & Michalski 2016). In our study, the temperature (T) data are shown in Fig. S2.

The [δ18O-NO3-]N2O5 values in Eqn S15 were calculated using Eq. S20.

[δ18O-NO3-]N2O5 = 5/6 × (δ18O-N2O5) + 1/6 × (δ18O-H2O), (Eq. S20),

In Eq. S20, the δ18O-H2O values were estimated as the δ18O values of tropospheric water vapor (-12.5±17.6‰; Walters & Michalski, 2016), and the δ18O-N2O5 values were 126.4±7.1‰ (Walters & Michalski, 2016).

The standard deviations of each variable in the above calculations were estimated by the Monte Carlo method and were finally propagated into the uncertainties of the ε(NO2→HNO3) values. These ε(NO2→HNO3) values were considered the δ18O-NO3

- based calculation (ε18O-based). Zong et al (2017) found that the model results with 0.52 times the ε18O-based value had the highest probability distribution of all of the source contributions and were considered to be the final solution in their study. In our study, we also regarded this situation as a possibility and considered ε18O-based × 0.52.

Text S3. Estimating proportional contributions of major NOx sources and oxidation pathways to NO3

- in PM2.5

The fractional contributions (%) of major sources and formation pathways to NO3- in

PM2.5 were estimated using the SIAR model. This model uses a Bayesian framework to establish a logical prior distribution based on the Dirichlet distribution (Evans et al., 2000) and then determines the probability distribution for the contribution of each source and pathway to the mixture (Parnell & Jackson 2008). The model can substantially incorporate the uncertainties associated with multiple sources/pathways, fractionations, and measured isotope signatures of sources and mixture (Moore & Semmens 2008). The SIAR model has been designed primarily for food-web analysis in ecological settings (Parnell et al., 2010), but it has been applied to aquatic environments as well (Xue et al., 2012). Recently, it was also used to quantify the contributions of major emissions to atmospheric reactive nitrogen in atmospheric sciences (Liu et al., 2017; Wang et al., 2017). In our estimates, uncertainties associated with the source analysis were derived from the δ15N variabilities of major NOx sources (mean±SD δ15N values of each source were used as input; Table S1) and the δ15N variabilities of fractionations and NO3

- in PM2.5 (all replicate data of the explored time period (either day or night) were used as input; Fig. 1e). Uncertainties

129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172

associated with the pathway analysis were derived from the Δ17O variabilities of major NO3

- formation pathways (mean±SD Δ17O values of each pathway were input; Fig. S7) and the Δ17O variabilities of NO3

- in PM2.5 (all replicate data of the explored time period (either day or night) were used as input; Fig. 1d). Thus, variabilities have been incorporated into the analysis and are expressed in the percentage values output from the model.

By defining a set of N mixture measurements on J isotopes with K source contributors, the mixing model can be expressed as follows (Parnell et al., 2010):

where Xij is the isotope value j of the mixture i, in which i = 1, 2, 3,…, N and j = 1, 2, 3,…, J; Sjk is the source value k on isotope j (k = 1, 2, 3,…, K) and is normally distributed with mean μjk and standard deviation ωjk; Fk is the proportion of source k estimated by the SIAR model; cjk is the fractionation factor for isotope j on source k and is normally distributed with mean λjk and standard deviation τjk; and εij is the residual error representing the additional unquantified variation between individual mixtures and is normally distributed with mean 0 and standard deviation σj. A detailed description of this model can be found in Moore & Semmens (2008), Jackson et al. (2009) and Parnell et al. (2010) To estimate the contributions of major NOx sources (using δ15N) and formation pathways (using Δ17O) to NO3

- in the PM2.5 samples in Beijing, one isotope (j = 1) (δ15N or Δ17O) and four potential NOx sources or three potential formation pathways (see P1-P3 detailed in the main text), δ15N-NO3

- or Δ17O-NO3

- values of PM2.5 (either day or night ) were analyzed in the SIAR model. The percentage data (n=10000) output from the SIAR model for each analysis were used for mean±SD values.

173174175176177178179180

181182183184185186187188189190191192193194195196

Figure S1. The molar ratios of NO2- to (NO2

- +NO3-) in PM2.5.

197198199

Figure S2. Temperature and concentrations of atmospheric CO, NO2, and O3 from January 4-13, 2015 at an urban site in Beijing.

200

201202

203

Figure S3. Concentrations of NH4+, SO4

2-, Cl-, Na+, K+, Mg2+, and Ca2+ in PM2.5 collected during the day and at night from January 4-13, 2015 at an urban site in Beijing.

204

205

206207208

209

Figure S4. Estimated HO2 and RO2 mixing ratios during the day and at night from January 4-13, 2015 at an urban site in Beijing. Mean ± SD values are shown.

210

211

212213

214

215

Figure S5. Estimated proportional contributions (A values) of O3 oxidation in NOx

cycle during the day and at night from January 4-13, 2015 at an urban site in Beijing. Mean ± SD values are shown.

216

217218219

220

221

Figure S6. Δ17O values of NO3- in PM2.5 (NO3

-, red dot), NO3- produced by the OH·

pathway (P1, up triangle), the HC pathway (P2, square), and the N2O5 pathway (P3, down triangle) during the day and at night from January 4-13, 2015 at an urban site in Beijing. Mean ± SD values are shown.

222

223224225226227

228

229

Figure S7. Δ17O values of NO3- produced by the OH· pathway (P1), the HC pathway

(P2), and the N2O5 pathway (P3) during the day and at night from January 4-13, 2015 at an urban site in Beijing. Mean ± SD values are shown.

Figure S8. Backward trajectory frequencies during the sampling period.

230231232

233234

235

Table S1. δ15N values of major NOx emission sources for urban sites. Different lowercase letters above the mean values indicate significant differences in δ15N values between four NOx emission sources (p<0.05).

Sources n　 δ15N values /‰ 　

References　Mean SD Min Max 　NOx from

coal combustion 28 14.5a 4.4 9.5 25.6 Felix et al.,

2012

NOx from biomass burning 24 　 1.0b 4.1 -7.2 12 　 Fibiger &

Hastings 2016

NOx from vehicle

exhausts 26 -3.2c 6.8 -19.1 9.8 Walters et al., 2015

NOx from microbial N

cycle23 -30.3d 9.4 -48.9 -8.5

Felix et al., 2013; Felix & Elliott 2014; Li & Wang

2008

236237238239

240

Table S2. Values of observed δ15N-NO3- and Δ17O-NO3

-, fractions of P1, P2 and P3, and parameters used for calculation of epsilons, epsilons of each formation pathways, and δ15N-NOx values in day-time and night-time values.

ParametersDay-time values 　 Night-time valuesMean SD 　 Mean SD

Δ17O-NO3- / ‰ 28 1.4 28 2.6

fP1 (%) 31 11 28 12

fP2 (%) 34 11 37 12

fP3 (%) 35 20 35 1815αNO2/NO - 1 0.044668 0.000655 0.046193 0.00072715αN2O5/NO2 - 1 0.030318 0.000439 0.031343 0.000489

εP1(NO2→NO3-) / ‰ 28.3 3.8 28.73 3.7

εP2(NO2→NO3-) / ‰ -14.3 14.9 -13.9 14.7

εP3(NO2→NO3-) / ‰ 30.3 0.4 31.1 0.5

ε17O-based(NO2→NO3-) / ‰ 14.5 6.9 13.9 7.2

δ15N-NO3- / ‰ 17.8 2.7 　 14.7 3.5

δ15N-NOx / ‰ 3.3 7.6 0.8 8.0

241242243

244245

References

Akimoto, H., Mori, Y., Sasaki, K., Nakanishi, H., Ohizumi, T., Itano, Y., 2015. Analysis of monitoring data of ground-level ozone in japan for long-term trend during 1990–2010: causes of temporal and spatial variation. Atmos. Environ. 102(9), 302-310.

Alexander, B., Hastings, M. G., Allman, D. J., Dachs, J., Thornton, J. A. & Kunasek, S. A., 2009. Quantifying atmospheric nitrate formation pathways based on a global model of the oxygen isotopic composition (Δ17O) of atmospheric nitrate. Atmos. Chem. Phys. 9, 5043-5056.

Chang, Y., Zhang, Y., Tian, C., Zhang, S., Ma, X., Cao, F., Liu, X., Zhang, W., Kuhn, T., Lehmann, M. F., 2018. Nitrogen isotope fractionation during gas-to-particle conversion of NOx to NO3

-

in the atmosphere – implications for isotope-based NOx source apportionment, Atmos. Chem. Phys., 18, 11647-11661.

Elliott, E. M., Kendall, C., Boyer, E. W., Burns, D. A., Lear, G. G., Golden, H. E., Harlin, K., Bytnerowicz, A., Butler, T. J., Glatz, R., 2009. Dual nitrate isotopes in dry deposition: Utility for partitioning NOx source contributions to landscape nitrogen deposition. J. Geophys. Res., 114, G04020.

Evans, J. S. B. T., Handley, S. J., Perham, N., Over, D. E., Thompson, V. A., 2000. Frequency versus probability formats in statistical word problems. Cognition, 77(3), 197-213.

Felix, J. D., Elliott, E. M., 2014. The isotopic composition of passively collected nitrogen dioxide emissions: Vehicle, soil and livestock source signatures. Atmos. Environ. 92, 359-366.

Felix, J. D., Elliott, E. M., Gish, T. J., Mcconnell, L. L., Shaw, S. L., 2013. Characterizing the isotopic composition of atmospheric ammonia emission sources using passive samplers and a combined oxidation-bacterial denitrifier isotope ratio mass spectrometer method. Rapid. Commun. Mass. Spectrom. 27, 2239-2246.

Felix, J. D., Elliott, E. M., Shaw, S. L, 2012. The isotopic composition of coal-fired power plant NOx: The influence of emission controls and implications for global emission inventories. Environ. Sci. Technol. 46, 3528-3535

Fibiger, D. L., Hastings, M. G., 2016. First measurements of the nitrogen isotopic composition of NOx from biomass burning. Environ. Sci. Technol. 50, 11569-11574.

Freyer, H.D., 1991. Seasonal variation of 15N/14N ratios in atmospheric nitrate species. Tellus B. 43(1), 30-44.

Hu, W., Hu, M., Hu, W., Jimenez, J. L., Yuan, B., Chen, W., Wang, M., Wu, Y. S., Chen, C., Wang, Z. B., Peng, J. F., Zeng, L. M., Shao, M. 2016. Chemical composition, sources, and aging process of submicron aerosols in Beijing: contrast between summer and winter. J. Geophys. Res.: Atmos. 121(4), 1955-1977.

Jackson, A. L., Inger, R., Bearhop, S., Parnell, A., 2009. Erroneous behaviour of mixsir, a recently published bayesian isotope mixing model: a discussion of moore & semmens (2008). Ecol. Lett. 12(3), E1-E5.

Kanaya, Y., Cao, R., Akimoto, H., Fukuda, M., Komazaki, Y., Yokouchi, Y., Koike, M., Tanimoto, H., Takegawa, N., Kondo, Y., 2007. Urban photochemistry in central Tokyo: 1. Observed and modeled OH and HO2 radical concentrations during the winter and summer of 2004. J. Geophy. Res.-Atmos. 112.

Kawashima, H. 2014. Formation mechanism and source apportionment of ammonium and nitrate ions in aerosol using nitrogen isotopes. Earozoru Kenkyu, 29, 110–116.

Kunasek, S. A., Alexander, B., Steig, E. J., Hastings, M. G., Gleason, D. J., Jarvis, J. C., 2008. Measurements and modeling of Δ17O of nitrate in snowpits from Summit, Greenland. J. Geophy. Res.-Atmos. 113.

Li, D. J., Wang, X. M., 2008. Nitrogen isotopic signature of soil-released nitric oxide (NO) after

246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292

fertilizer application. Atmos. Environ. 42, 4747–4754.

Liu, J. & Zhu, T., 2013. NOx in Chinese Megacities. Disposal of Dangerous Chemicals in Urban Areas and Mega Cities, Springer Netherlands, 249-263.

Liu, X. Y., Xiao, H. W., Xiao, H. Y., Song, W., Sun, X. C., Zheng, X. D., Liu, C. Q., Koba, K., 2017. Stable isotope analyses of precipitation nitrogen sources in Guiyang, Southwestern China. Environ. Pollut. 230, 486-494.

Liu, Z., Wang, Y., Gu, D., Zhao, C., Huey, L., Stickel, R., Liao, J., Shao, M., Zhu, T., Zeng, L., 2012. Summertime photochemistry during CAREBeijing-2007: ROx budgets and O3 formation. Atmos. Chem. Phys. 12, 7737-7752.

Michalski G., Bhattacharya S.K., Mase D. F., 2012. Oxygen Isotope Dynamics of Atmospheric Nitrate and Its Precursor Molecules. In: Baskaran M. (eds) Handbook of Environmental Isotope Geochemistry. Advances in Isotope Geochemistry. Springer, Berlin, Heidelberg.

Moore, J. W. & Semmens, B. X., 2008. Incorporating uncertainty and prior information into stable isotope mixing models. Ecol. Lett. 11, 470–480.

Nelson, D. M., Tsunogai, U., Ding, D., Ohyama, T., Komatsu, D. D., Nakagawa, F., Noguchi, I., Yamaguchi, T., 2018. Triple oxygen isotopes indicate urbanization affects sources of nitrate in wet and dry atmospheric deposition, Atmos. Chem. Phys., 18, 6381-6392.

Parnell, A. & Jackon, A. SIAR: Stable isotope analysis in R Available from: http://cran.r-project.org/web/packages/siar/index.html (accessed 10.12.08), (2008).

Parnell, A. C., Inger, R., Bearhop, S., Jackson, A. L., 2010. Source partitioning using stable isotopes: coping with too much variation. PLOS ONE, 5, e9672.

Patris, N., Cliff, S. S., Quinn, P. K., Kasem, M., Thiemens, M. H., 2007. Isotopic analysis of aerosol sulfate and nitrate during ITCT‐2k2: Determination of different formation pathways as a function of particle size. J. Geophy. Res.-Atmos. 112.

Sander, S. P., Friedl, R. R., Golden, D. M., Kurylo, M. J., Moortgat, G. K., Wine, P. H., 2006. Chemical kinetics and photochemical data for use in atmospheric studies evaluation number 15. JPL Publication09-31, 97–4(2000), 1135-1151.

Savard, M. M., Cole, A., Smirnoff, A., Vet, R., 2017. δ15N values of atmospheric N species simultaneously collected using sector-based samplers distant from sources – isotopic inheritance and fractionation. Atmos. Environ. 162, 11-22.

Vicars, C. & Savarino, J., 2014. Quantitative constraints on the 17O-excess (Δ17O) signature of surface ozone: ambient measurements from 50°N to 50°S using the nitrite-coated filter technique. Geochim. Cosmochim. Ac. 135, 270-287.

Vicars, W. C., Bhattacharya, S. K., Erbland, J., Savarino, J., 2012. Measurement of the 17O-excess (Δ17O) of tropospheric ozone using a nitrite-coated filter. Rapid Commun. Mass Sp. 26, 1219-1231.

Walters, W. W., & Michalski, G., 2015. Theoretical calculation of nitrogen isotope equilibrium exchange fractionation factors for various NOy molecules. Geochim. Cosmochim. Ac. 164(7), 284-297.

Walters, W. W., & Michalski, G., 2016. Theoretical calculation of oxygen equilibrium isotope fractionation factors involving various NOy molecules, OH, and H2O and its implications for isotope variations in atmospheric nitrate. Geochim. Cosmochim. Ac. 191, 89-101.

Walters, W. W., Goodwin, S. R., Michalski, G., 2015. The Nitrogen stable isotope composition (15N) of vehicle emitted NOx. Environ. Sci. Technol. 49, 2278-2285.

Wang, Y. L., Liu, X. Y., Song, W., Yang, W., Han, B., Dou, X. Y., Zhao, X. D., Song, Z. L., Liu, C. Q., Bai, Z. P., 2017. Source appointment of nitrogen in PM2.5 based on bulk δ15N signatures and a Bayesian isotope mixing model. Tellus B. B69, 1299672.

293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339

Wang, Z. S., Li, Y. T., Chen, T., Zhang, D. W., Sun, F., Wei, Q., Dong, X., Sun, R, W., Huan, N., Pan, L. B., 2015. Ground-level ozone in urban Beijing over a 1-year period: temporal variations and relationship to atmospheric oxidation. Atmos. Res. 164-165, 110-117.

Xue, D., De Baets, Van Cleemput, O., Hennessy, C., Berglund, M. and Boeckx, P., 2012. A Bayesian isotope mixing model to estimate proportional contributions of multiple nitrate sourcesinsurface water. Environ. Pollut. 161, 43-49.

Yoshino, A., Nakashima, Y., Miyazaki, K., Kato, S., Suthawaree, J., Shimo, N., Matsunaga, S., Chatani, S., Apel, E., Greenberg, J., Guenther, A., Ueno, H., Sasaki, H., Hoshi, J., Yokota, H., Ishii, K., Kajii, Y., 2012. Air quality diagnosis from comprehensive observations of total OH reactivity and reactive trace species in urban central Tokyo. Atmos. Environ. 49, 51-59.

Zong, Z., Wang, X., Tian, C. G., Chen, Y. J., Fang, Y. T., Zhang, F., Li, C., Sun, J. Z., Li, J., Zhang, G., 2017. First assessment of NOx sources at a regional background site in North China using isotopic analysis linked with modeling. Environ. Sci. Technol. 51(11), 5923-5931.

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