Nitrogen isotope fractionation during gas-particle conversion of NO x to 1 NO 3in the atmosphere – implications for isotope-based NO x source 2 apportionment

23 Atmospheric fine-particle (PM2.5) pollution is frequently associated with the formation 24 of particulate nitrate (pNO3 ), the end product of the oxidation of NOx gases (=NO+NO2) 25 in the upper troposphere. The application of stable nitrogen (N) (and oxygen) isotope 26 analyses of pNO3 to constrain NOx source partitioning in the atmosphere requires the 27 knowledge of the isotope fractionation during the reactions leading to nitrate formation. 28 Here we determined the δN values of fresh pNO3 (δN-pNO3 ) in PM2.5 at a rural site 29 in Northern China, where atmospheric pNO3 can be attributed exclusively to biomass 30 burning. The observed δN-pNO3 (12.17±1.55‰; n=8) was much higher than the N 31 isotopic source signature of NOx from biomass burning (1.04±4.13‰). The large 32 difference between δN-pNO3 and δN-NOx (Δ(δ N)) can be reconciled by the net N 33 isotope effect (ԑN) associated with the gas-particle conversion from NOx to NO3 . For 34 the biomass-burning site, a mean ԑN (≈ Δ(δ N)) of 10.99±0.74‰ was assessed through 35 a newly-developed computational quantum chemistry (CQC) module. ԑN depends on 36 the relative importance of the two dominant N isotope exchange reactions involved 37 (NO2 reaction with OH versus hydrolysis of dinitrogen pentoxide (N2O5) with H2O), 38 and varies between regions, and on a diurnal basis. A second, slightly higher CQC39 based mean value for ԑN (15.33±4.90‰) was estimated for an urban site with intense 40 traffic in Eastern China, and integrated in a Bayesian isotope mixing model to make 41 isotope-based source apportionment estimates for NOx at this site. Based on the δ N 42 values (10.93±3.32‰, n=43) of ambient pNO3 determined for the urban site, and 43 considering the location-specific estimate for ԑN, our results reveal that the relative 44 contribution of coal combustion and road traffic to urban NOx are 32±11% and 68±11%, 45 respectively. This finding agrees well with a regional bottom-up emission inventory of 46 NOx. Moreover, the variation pattern of OH contribution to ambient pNO3 formation 47 calculated by the CQC module is consistent with that simulated by the Weather 48 Research and Forecasting model coupled with Chemistry (WRF-Chem), further 49 confirming the robustness of our estimates. Our investigations also show that, without 50 the consideration of the N isotope effect during pNO3 formation, the observed δN51 2 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-385 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 8 May 2018 c © Author(s) 2018. CC BY 4.0 License.

Emissions of NO x occur mostly in the form of NO (Seinfeld and Pandis, 2012; Leighton, 1961).During daytime, transformation from NO to NO 2 is rapid (few minutes) and proceeds in a photochemical steady state, controlled by the oxidation of NO by O 3 to NO 2 and the photolysis of NO 2 back to NO (Leighton, 1961): where M is any non-reactive species that can take up the energy released to stabilize O. NO x oxidation to HNO 3 is governed by the following equations.HNO 3 then reacts with gas-phase NH 3 to form ammonium nitrate (NH 4 NO 3 ) aerosols.If the ambient relative humidity (RH) is lower than the efflorescence relative humidity (ERH) or crystallization relative humidity (CRH), solidphase NH 4 NO 3 (s) is formed (Smith et al., 2012;Ling and Chan, 2007): If ambient RH exceeds the ERH or CRH, HNO 3 and NH 3 dissolve into the aqueous phase (aq) (Smith et al., 2012;Ling and Chan, 2007): While global NO x emissions are well constrained, individual source attribution and their local or regional role in particulate nitrate formation are difficult to assess due to the short lifetime of NO x (typically less than 24 h) and the high degree of spatiotemporal heterogeneity with regards to the ratio between gas-phase HNO 3 and particulate NO − 3 (pNO − 3 ) (Duncan et al., 2016;Lu et al., 2015;Zong et al., 2017;Zhang et al., 2003).Given the conservation of the nitrogen (N) atom between NO x sources and sinks, the N isotopic composition of pNO − 3 can be related to the different origins of the emitted NO x and thus provides valuable information on the partitioning of the NO x sources (Morin et al., 2008).Such a N isotope balance approach works best if the N isotopic composition of various NO x sources display distinct 15 N/ 14 N ratios (reported as δ 15 N = 15 N/ 14 N sample −( 15 N/ 14 N) N 2 ( 15 N/ 14 N) N 2 × 1000).
Along the same lines, in this study, the average δ 18 O value of pNO − 3 in Nanjing was 83.0±11.2‰ (see Discussion section), suggesting that pNO − 3 formation is dominated by the pathways of "OH + NO 2 " and the heterogeneous hydrolysis of N 2 O 5 .
δ 15 N-based source apportionment of NO x requires knowledge of how kinetic and equilibrium isotope fractionation may impact δ 15 N values during the conversion of NO x to nitrate (Freyer, 1978;Walters et al., 2016).If these isotope effects are considerable, they may greatly limit the use of δ 15 N values of pNO − 3 for NO x source partition (Walters et al., 2016).Previous studies did not take into account the potentially biasing effect of N isotope fractionation, because they assumed that changes in the δ 15 N values during the conversion of NO x to nitrate are minor (without detailed explanation) (Kendall et al., 2007;Morin et al., 2008;Elliott et al., 2007) or relatively small (e.g., +3 ‰) (Felix and Elliott, 2014;Freyer, 2017).However, a field study by Freyer et al. (1993) has indicated that N isotope exchange may have a strong influence on the observed δ 15 N values in atmospheric NO and NO 2 , implying that isotope equilibrium fractionation may play a significant role in shaping the δ 15 N of NO y species (the family of oxidized nitrogen molecules in the atmosphere, including NO x , NO 3 , NO − 3 , peroxyacetyl nitrate, etc.).The transformation of NO x to nitrate is a complex process that involves several different reaction pathways (Walters et al., 2016).To date, few fractionation factors for this conversion have been determined.Recently, Walters and Michalski (2015) and Walters et al. (2016) used computational quantum chemistry methods to calculate N isotope equilibrium fractionation factors for the exchange between major NO y molecules and confirmed theoretical predictions that 15 N isotopes get enriched in the more oxidized form of NO y and that the transformation of NO x to atmospheric nitrate (HNO 3 , NO 3 (aq), NO 3 (g)) continuously increases the δ 15 N in the residual NO x pool.
As a consequence of its severe atmospheric particle pollution during the cold season, China has made great efforts to-ward reducing NO x emissions from on-road traffic (e.g., improving emission standards, higher gasoline quality, vehicle travel restrictions) (Li et al., 2017).Moreover, China has continuously implemented denitrogenation technologies (e.g., selective catalytic reduction) in the coal-fired power plants sector since the mid-2000s and has been phasing out small inefficient units (Liu et al., 2015).Monitoring and assessing the efficiency of such mitigation measures, and optimizing policy efforts to further reduce NO x emissions, require knowledge of the vehicle-and power-plant-emitted NO x to particulate nitrate in urban China (Ji et al., 2015;Fu et al., 2013;Zong et al., 2017).In this study, the chemical components of ambient fine particles (PM 2.5 ) were quantified, and the isotopic composition of particulate nitrate (δ 15 N-NO − 3 , δ 18 O-NO − 3 ) was assessed in order to elucidate ambient NO x sources in the city of Nanjing in eastern China.We also investigated the potential isotope effect during the formation of nitrate aerosols from NO x and evaluated how disregard of such N isotope fractionation can bias N-isotope-mixingmodel-based estimates on the NO x source apportionment for nitrate deposition.

Field sampling
In this study, PM 2.5 aerosol samples were collected on precombusted (450 • C for 6 h) quartz filters (25 × 20 cm) on a day-night basis, using high-volume air samplers at a flow rate of 1.05 m 3 min −1 in Sanjiang and Nanjing (Fig. 1).After sampling, the filters were wrapped in aluminum foil, packed in air-tight polyethylene bags and stored at −20 • C prior to further processing and analysis.Four blank filters were also collected.They were exposed for 10 min to ambient air (i.e., without active sampling).PM 2.5 mass concentration was analyzed gravimetrically (Sartorius MC5 electronic microbalance) with a ±1 µg precision before and after sampling (at 25 • C and 45 % ± 5 % during weighing).
The Sanjiang campaign was performed during a period of intensive burning of agricultural residues between 8 and 18 October 2013, to examine if there is any significant difference between the δ 15 N values of pNO − 3 and NO x emitted from biomass burning.The Sanjiang site (in the following abbreviated as SJ; 47.35 • N, 133.31 • E) is located at an ecological experimental station affiliated with the Chinese Academy of Sciences located in the Sanjiang Plain, a major agricultural area predominantly run by state farms in northeastern China (Fig. 1).Surrounded by vast farm fields and bordering far-eastern Russia, SJ is situated in a remote and sparsely populated region, with a harsh climate and rather poorly industrialized economy.The annual mean temperature at SJ is close to the freezing point, with daily minima ranging between −31 and −15 • C in the coldest month, January.As a consequence of the relatively low tem- 3 data from the literature (see also Table S4).peratures (also during summer), biogenic production of NO x through soil microbial processes is rather weak.SJ is therefore an excellent environment in which to collect biomassburning-emitted aerosols with only minor influence from other sources.
The Nanjing campaign was conducted between 17 December 2014 and 8 January 2015 with the main objective to examine whether N isotope measurements can be used as a tool to elucidate NO x source contributions to ambient pNO − 3 during times of severe haze.Situated in the lower Yangtze River region, Nanjing is, after Shanghai, the second-largest city in eastern China.The aerosol sampler was placed at the rooftop of a building on the Nanjing University of Information Science and Technology campus (in the following abbreviated as NJ; 18 m a.g.l.; 32.21 • N, 118.72 • E; Fig. 1), where NO x emissions derive from both industrial and transportation sources.
For isotopic analyses of aerosol nitrate, aerosol subsamples were generated by punching 1.4 cm disks out of the filters.In order to extract the NO − 3 , sample discs were placed in acid-washed glass vials with 10 ml deionized water and placed in an ultra-sonic water bath for 30 min.Between one and four disks were used for NO x extraction, dependent on the aerosol NO − 3 content of the filters, which was determined independently.The extracts were then filtered (0.22 µm) and analyzed the next day.N and O isotope analyses of the extracted/dissolved aerosol nitrate ( 15 N/ 14 N, 18 O/ 16 O) were performed using the denitrifier method (Sigman et al., 2001;Casciotti et al., 2002).Briefly, sample NO − 3 is converted to nitrous oxide (N 2 O) by denitrifying bacteria that lack N 2 O reductase activity (Pseudomonas chlororaphis ATCC 13985; formerly Pseudomonas aureofaciens, referred to below as such).N 2 O is extracted, purified and analyzed for its N and O isotopic composition using a continuous-flow isotope ratio mass spectrometer (Thermo Finnigan Delta + , Bremen, German).Nitrate N and O isotope ratios are reported in the conventional δ notation with respect to atmospheric N 2 and Vienna standard mean ocean water, respectively.Analyses are calibrated using the international nitrate isotope standard IAEA-N3, with a δ 15 N value of 4.7 ‰ and a δ 18 O value of 25.6 ‰ (Böhlke et al., 2003).The blank contribution was generally lower than 0.2 nmol (as compared to 20 nmol of sample N).Based on replicate measurements of standards and samples, the analytical precision for δ 15 N and δ 18 O was generally better than ±0.2 ‰ and ±0.3 ‰ (1σ ), respectively.
The denitrifier method generates δ 15 N and δ 18 O values of the combined pool of NO − 3 and NO − 2 .The presence of substantial amounts of NO − 2 in NO − 3 samples may lead to errors with regards to the analysis of δ 18 O (Wankel et al., 2010).We refrained from including a nitrite-removal step, because nitrite concentrations in our samples were always < 1 % of the NO − 3 concentrations.In the following δ 15 N NO x and δ 18 O NO x are thus referred to as nitrate δ 15 N and δ 18 O (or δ 15 N NO 3 and δ 18 O NO 3 ).
In the case of atmospheric or aerosol nitrate samples with comparatively high δ 18 O values, δ 15 N values tend to be overestimated by 1-2 ‰ (Hastings et al., 2003) if the contribution of 14 N 14 N 17 O to the N 2 O mass 45 signal is not accounted for during isotope ratio analysis.For most natural samples, the mass-dependent relationship can be approximated as δ 17 O ≈ 0.52 × δ 18 O, and the δ 18 O can be used for the 17 O correction.Atmospheric NO − 3 does not follow this relationship but inhabits a mass-independent component.Thus, we adopted a correction factor of 0.8 instead of 0.52 for the 17 O-to-18 O linearity (Hastings et al., 2003).

Calculation of N isotope fractionation value (ε N )
As we described above, the transformation process of NO x to HNO 3 or NO − 3 involves multiple reaction pathways (see also Fig. S1 in the Supplement) and is likely to undergo isotope equilibrium exchange reactions.The measured δ 15 N-NO − 3 values of aerosol samples are thus reflective of the combined N isotope signatures of various NO x sources (δ 15 N-NO x ) plus any given N isotope fractionation.Recently, Walter and Michalski (2015) used a computational quantum chemistry approach to calculate isotope exchange fractionation factors for atmospherically relevant NO y molecules; based on this approach, Zong et al. (2017) estimated the N isotope fractionation during the transformation of NO x to pNO − 3 at a regional background site in China.Here we adopted, and slightly modify, the approach by Walter and Michalski (2015) and Zong et al. (2017), and assumed that the net N isotope effect ε N (for equilibrium processes A ↔ B: 3 ) in this study unless otherwise specified) during the gas-to-particle conversion from NO x to pNO − 3 formation ) can be considered a hybrid of the isotope effects of two dominant N isotopic exchange reactions: where γ represents the contribution from isotope fractionation by the reaction of NO x and photochemically produced OH to form HNO 3 (and pNO − 3 ), as shown by ε ).The remainder is formed by the hydrolysis of N 2 O 5 with aerosol water to generate HNO 3 (and ).Assuming that kinetic N isotope fractionation associated with the reaction between NO x and OH is negligible, ε N ( NOx ↔pNO − 3 ) OH can be calculated based on mass-balance considerations: where 15 α NO 2 /NO is the temperature-dependent (see Eq. 7 and Table S1 in the Supplement) equilibrium N isotope fractionation factor between NO 2 and NO, and f NO 2 is the fraction of NO 2 in the total NO x .f NO 2 ranges from 0.2 to 0.95 (Walters and Michalski, 2015).Similarly, assuming a negligible kinetic isotope fractionation associated with the reac- 3 ) H 2 O can be computed from the following equation: where 15 α N 2 O 5 /NO 2 is the equilibrium isotope fractionation factor between N 2 O 5 and NO 2 , which also is temperaturedependent (see Eq. 7 and Table S1).
Following Walter and Michalski (2015) and Zhong et al. ( 2017), γ can then be approximated based on the O isotope fractionation during the conversion of NO x to pNO − 3 : represent the O isotope effects associated with pNO − 3 generation through the reaction of NO x and OH to form HNO 3 , and the hydrolysis of N 2 O 5 on a wetted surface to form HNO 3 , respectively.ε O ( NOx ↔pNO − 3 ) OH can be further expressed as can be determined as follows: where 18 where A, B, C and D are experimental constants (Table S1 in the Supplement) over the temperature range of 150-450 K (Walters and Michalski, 2015;Walters et al., 2016;Walters and Michalski, 2016;Zong et al., 2017).Based on Eqs. ( 4)-( 7) and measured values for δ 18 O-pNO − 3 of ambient PM 2.5 , a Monte Carlo simulation was performed to generate 10 000 feasible solutions.The error between predicted and measured δ 18 O was less than 0.5 ‰.The range (maximum and minimum) of computed contribution ratios (γ ) was then integrated in Eq. ( 1) to generate an estimate range for the nitrogen isotope effect ε N (using Eqs.2-3).δ 15 N-pNO − 3 values can be calculated based on ε N and the estimated δ 15 N range for atmospheric NO x (see Sect. 2.4).

Bayesian isotope mixing model
Isotopic mixing models allow estimating the relative contribution of multiple sources (e.g., emission sources of NO x ) within a mixed pool (e.g., ambient pNO − 3 ).By explicitly considering the uncertainty associated with the isotopic signatures of any given source, as well as isotope fractionation during the formation of various components of a mixture, the application of Bayesian methods to stable isotope mixing models generates robust probability estimates of source proportions and is often more appropriate when targeting natural systems than simple linear mixing models (Chang et al., 2016a).Here the Bayesian model MixSIR (a stable isotope mixing model using sampling, importance and resampling) was used to disentangle multiple NO x sources by generating potential solutions of source apportionment as true probability distributions, which has been widely applied in a number of fields (e.g., Parnell et al., 2013;Phillips et al., 2014;Zong et al., 2017).Details on the model frame and computing methods are given in Sect.S1 in the Supplement.
Here, coal combustion (13.72 ± 4.57 ‰), transportation (−3.71 ± 10.40 ‰), biomass burning (1.04 ± 4.13 ‰) and biogenic emissions from soils (−33.77±12.16‰) were considered to be the most relevant contributors of NO x (Table S2 and Sect.S2).The δ 15 N of atmospheric NO x is unknown.However, it can be assumed that its range in the atmosphere is constrained by the δ 15 N of the NO x sources and the δ 15 N of pNO − 3 after equilibrium fractionation conditions have been reached.Following Zong et al. (2017), δ 15 N-NO x in the atmosphere was determined by performing iterative model simulations, with a simulation step of 0.01 times the equilibrium fractionation value based on the δ 15 N-NO x values of the emission sources (mean and standard deviation) and the measured δ 15 N-pNO − 3 of ambient PM 2.5 (Fig. S2).

Sanjiang in northern China
The δ 15 N-pNO − 3 and δ 18 O-pNO − 3 values of the eight samples collected from the Sanjiang biomass burning field experiment ranged from 9.54 ‰ to 13.77 ‰ (mean: 12.17 ‰) and 57.17 ‰ to 75.09 ‰ (mean: 63.57‰), respectively.In this study, atmospheric concentrations of levoglucosan quantified from PM 2.5 samples collected near the sites of biomass burning in Sanjiang vary between 4.0 and 20.5 µg m −3 , 2 to 5 orders of magnitude higher than those measured during non-biomass-burning season (Cao et al., 2017(Cao et al., , 2016)).Levoglucosan is an anhydrosugar formed during pyrolysis of cellulose at temperatures above 300 • C (Simoneit, 2002).Due to its specificity for cellulose combustion, it has been widely used as a molecular tracer for biomass burning (Simoneit et al., 1999;D. Liu et al., 2013;Jedynska et al., 2014;Liu et al., 2014).Indeed, the concentrations of levoglucosan and aerosol nitrate in Sanjiang were highly correlated (R 2 = 0.64; Fig. 2a), providing compelling evidence that particulate nitrate measured during our study period was predominately derived from biomass burning emissions.

Nanjing in eastern China
The mass concentrations mean max min ± 1σ, n = 43 of PM 2.5 and pNO − 3 measured in Nanjing were 122.1 227.8 39.0 ± 47.9 and 17.8 45.2  4.0 ± 10.3 µg m −3 , respectively.All PM 2.5 concentrations exceeded the Chinese Air Quality Standards for daily PM 2.5 (35 µg m −3 ), suggesting severe haze pollution during the sampling period.The corresponding δ 15 N-pNO − 3 values (raw data without correction) ranged between 5.39 ‰ and 17.99 ‰, indicating significant enrichment in 15 N relative to rural and coastal marine atmospheric NO − 3 sources (Table S4).This may be due to the prominent contribution of fossil-fuel-related NO x emissions with higher δ 15 N values in urban areas (Elliott et al., 2007;Park et al., 2018).

Sanjiang campaign: theoretical calculation and field validation of N isotope fractionation during pNO − 3 formation
To be used as a quantitative tracer of biomass-combustiongenerated aerosols, levoglucosan must be conserved during its transport from its source, without partial removal by reactions in the atmosphere (Hennigan et al., 2010).The mass concentrations of non-sea-salt potassium (nss-K + = K + − 0.0355 × Na + ) is considered as an independent/additional indicator of biomass burning (Fig. 2b).The association of elevated levels of levoglucosan with high nss-K + concentrations underscores that the two compounds derived from the same proximate sources and thus that aerosol levoglu-  S3.

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cosan in Sanjiang was indeed pristine and represented a reliable source indicator that is unbiased by altering processes in the atmosphere.Moreover, in our previous work (Cao et al., 2017), we observed that there was a much greater enhancement of atmospheric NO − 3 compared to SO 2− 4 (a typical coal-related pollutant).This additionally points to biomass burning, and not coal-combustion, as the dominant pNO − 3 source in the study area, making SJ an ideal "quasi-singlesource" environment for calibrating the N isotope effect during pNO − 3 formation.Our δ 18 O-pNO − 3 values are well within the broad range of values in previous reports (Zong et al., 2017;Geng et al., 2017;Walters and Michalski, 2016).However, as depicted in Fig. 3, the δ 15 N values of biomass-burning-emitted NO − 3 fall within the range of δ 15 N-NO x values typically reported for emissions from coal combustion, whereas they are significantly higher than the well-established values for δ 15 N-NO x emitted from the burning of various types of biomass (mean: 1.04 ± 4.13 ‰; range: −7 to +12 ‰) (Fibiger and Hastings, 2016).Turekian et al. (1998) conducted laboratory tests involving the burning of eucalyptus and African grasses, and determined that the δ 15 N of pNO − 3 (around 23 ‰) was 6.6 ‰ higher than the δ 15 N of the burned biomass.This implies significant N isotope partitioning during biomass burning.In the case of complete biomass combustion, by mass balance, the first gaseous products (i.e., NO x ) have the same δ 15 N as the biomass.Hence any discrepancy between the pNO − 3 and the δ 15 N of the biomass can be attributed to the N isotope fractionation associated with the partial conversion of gaseous NO x to aerosol NO − 3 .Based on the computational quantum chemistry (CQC) module calculations, the N isotope fractionation ε N mean max min ± 1σ determined from the Sanjiang data was 10.99 12.54  10.30 ± 0.74 ‰.After correcting the primary δ 15 N-pNO − 3 values under the consideration of ε N , the resulting mean δ 15 N of 1.17 2.98  −1.89 ± 1.95 ‰ is very close to the N isotopic signature expected for biomass-burning-emitted NO x (1.04 ± 4.13 ‰) (Fig. 3) (Fibiger and Hastings, 2016).S2).See Table S3 for the information regarding sample ID.
The much higher δ 15 N-pNO − 3 values in our study compared to reported δ 15 N-NO x values for biomass burning can easily be reconciled when including N isotope fractionation during the conversion of NO x to NO − 3 .Put another way, given that Sanjiang is an environment where we can essentially exclude NO x sources other than biomass burning at the time of sampling, the data nicely validate our CQC-module-based approach to estimating ε N .3 formation 4.2 Source apportionment of NO x in an urban setting using a Bayesian isotopic mixing model Due to its high population density and intensive industrial production, the Nanjing atmosphere was expected to have high NO x concentrations derived from road traffic and coal combustion (Zhao et al., 2015).However, the raw δ 15 N-pNO − 3 values (10.93 ± 3.32 ‰) fell well within the variation range of coal-emitted δ 15 N-NO x (Fig. 3).It is tempting to conclude that coal combustion is the main, or even sole, pNO − 3 source (given the equivalent δ 15 N values), yet this is very unlikely.The data rather confirm that significant isotope fractionation occurred during the conversion of NO x to NO − 3 and that, without consideration of the N isotope effect, traffic-related NO x emissions will be markedly underestimated.
In the atmosphere, the oxygen atoms of NO x rapidly exchanged with O 3 in the "NO-NO 2 " cycle (see Reactions R1-R3) (Hastings et al., 2003), and the δ 18 O-pNO − 3 values are determined by its production pathways (Reactions R4-R7), rather than the sources of NO x (Hastings et al., 2003).Thus, δ 18 O-pNO − 3 can be used to gain information on the pathway of conversion of NO x to nitrate in the atmosphere (Fang et al., 2011).In the computational quantum chemistry module used here to calculate isotope fractionation, we assumed that two-thirds of the oxygen atoms in NO − 3 derive from O 3 and one-third from q OH in the q OH generation pathway (Reaction R4) (Hastings et al., 2003); correspondingly, five-sixths of the oxygen atoms then derived from O 3 and one-sixth from q OH in the "O 3 -H 2 O" pathway (Reactions R5-R7).The assumed range for δ 18 O-O 3 and δ 18 O-H 2 O values were 90 ‰-122 ‰ and −25 ‰-0 ‰, respectively (Zong et al., 2017).The partitioning between the two possible pathways was then assessed through Monte Carlo simulation (Zong et al., 2017).The estimated range was rather broad, given the wide range of δ 18 O-O 3 and δ 18 O-H 2 O values used.Nevertheless, the theoretical calculation of the average contribution ratio (γ ) for nitrate formation in Nanjing via the reaction of NO 2 and q OH is consistent with the results from simulations using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) (Fig. 4; see Sect.S3 for details).A clear diurnal cycle of the mass concentration of nitrate formed through q OH oxidation of NO 2 can be observed (Fig. S3), with much higher concentrations between 12:00 and 18:00.This indicates the importance of photochemically produced q OH during daytime.Yet, throughout our sampling period in Nanjing, the average pNO − 3 formation by the heterogeneous hydrolysis of N 2 O 5 (12.6 µg mm −3 ) exceeded pNO − 3 formation by the reaction of NO 2 and q OH (4.8 µg mm −3 ), even during daytime, consistent with recent observations during peak pollution periods in Beijing (Wang et al., 2017).Given the production rates of N 2 O 5 in the atmosphere are governed by ambient O 3 concentrations, reducing atmospheric O 3 levels appears to be one of the most important measures to take for mitigating pNO − 3 pollution in China's urban atmospheres.
In Nanjing, dependent on the time-dependent, dominant pNO − 3 formation pathway, the average N isotope fractionation value calculated using the computational quantum chemistry module varied between 10.77 ‰ and 19.34 ‰ (15.33 ‰ on average).Using the Bayesian model MixSIR, the contribution of each source can be estimated, based on the mixed-source isotope data under the consideration of prior information at the site (see Sect.S1 for detailed information regarding model frame and computing method).As described above, theoretically, there are four major sources potentially contributing to ambient NO x : road traffic, coal combustion, biomass burning and biogenic soil.As a start, we tentatively integrated all four sources into MixSIR (data not shown).The relative contribution of biomass burning to the ambient NO x (median value) ranged from 28 % to 70 % (average 42 %), representing the most important source.The primary reason for such apparently high contribution by biomass burning is that the corrected δ 15 N-pNO − 3 values of −4.29 0.42 −10.32 ± 3.66 ‰ are relatively close to the N isotopic signature of biomass-burning-emitted NO x (1.04 ± 4.13 ‰) compared to the other possible sources.Based on δ 15 N alone, the isotope approach can be ambiguous if there are more than two sources.The N isotope signature of NO x from biomass burning falls right in between the spectrum of plausible values, with highest δ 15 N for emissions from coal combustion on the one end and much lower values for automotive and soil emissions on the other, and will be similar to a mixed signature from coal combustion and NO x emissions from traffic.We can make several evidence-based presumptions to better constrain the emission sources in the mixing model analysis: (1) when sampling at a typical urban site in a major industrial city in China, we can assume that the sources of road traffic and coal combustion are dominant, while the contribution of biogenic soil to ambient NO x should have minimal impact or can be largely neglected (Zhao et al., 2015);

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(2) there is no crop harvest activity in eastern China during the winter season.Furthermore, deforestation and combustion of fuelwood have been discontinued in China's major cities (Chang et al., 2016a).Therefore, the contribution of biomass-burning-emitted NO x during the sampling period should also be minor.Indeed, Fig. S4 shows that the mass concentration of biomass-burning-related pNO − 3 is not correlated with the fraction of levoglucosan that contributes to OC, confirming a weak impact of biomass burning on the variation of pNO − 3 concentration during our study period.In a second, alternative and more realistic scenario, we excluded biomass burning and soil as a potential source of NO x in MixSIR (see above).As illustrated in Fig. 5a, assuming that NO x emissions in urban Nanjing during our study period originated solely from road traffic and coal combustion, their relative contribution to the mass concentration of pNO − 3 is 12.5 ± 9.1 µg m −3 (or 68 ± 11 %) and 4.9 ± 2.5 µg m −3 (or 32 ± 11 %), respectively.These numbers agree well with a city-scale NO x emission inventory established for Nanjing recently (Zhao et al., 2015).Nevertheless, on a nation-wide level, relatively large uncertainties with regards to the overall fossil fuel consumption and fuel types propagate into large uncertainties of NO x concentration estimates and predictions of longer-term emission trends (Li et al., 2017).Current emission-inventory estimates (Jaegle et al., 2005;Zhang et al., 2012;Liu et al., 2015;Zhao et al., 2013) suggest that in 2010 NO x emissions from coal-fired power plants in China were about 30 % higher than those from transportation.However, our isotope-based source apportionment of NO x clearly shows that in 2014 the contribution from road traffic to NO x emissions, at least in Nanjing (a city that can be considered representative for most densely populated areas in China), is twice that of coal combustion.In fact, due to changing economic activities, emission sources of air pollutants in China are changing rapidly.For example, over the past several years, China has implemented an extended portfolio of plans to phase out its old-fashioned and small power plants, and to raise the standards for reducing industrial pollutant emissions (Chang, 2012).On the other hand, China continuously experienced double-digit annual growth in terms of auto sales during the 2000s, and in 2009 it became the world's largest automobile market (X.Liu et al., 2013;Chang et al., 2017Chang et al., , 2016b)).Recent satellite-based studies have successfully analyzed the NO x vertical column concentration ratios for megacities in eastern China and highlighted the importance of transportation-related NO x emissions (Reuter et al., 2014;Gu et al., 2014;Duncan et al., 2016 al., 2017).Moreover, long-term measurements of the ratio of NO − 3 to non-sea-salt SO 2− 4 in precipitation and aerosol jointly revealed a continuously increasing trend in eastern China throughout the latest decade, suggesting decreasing emissions from coal combustion (X.Liu et al., 2013;Itahashi et al., 2018).Both coal-combustion-and road-traffic-related pNO − 3 concentrations are highly correlated with their corresponding tracers (i.e., SO 2 and CO, respectively), confirming the validity of our MixSIR modeling results.With justified confidence in our Bayesian isotopic model results, we conclude that previous estimates of NO x emissions from automotive/transportation sources in China based on bottom-up emission inventories may be too low.

Previous δ 15 N-NO −
3 -based estimates on NO x sources Stable nitrogen isotope ratios of nitrate have been used to identify nitrogen sources in various environments in China, often without large differences in δ 15 N between rainwater and aerosol NO − 3 (Kojima et al., 2011).In previous work, no consideration was given to potential N isotope fractionation during atmospheric pNO − 3 formation.Here, we reevaluated 700 data points of δ 15 N-NO − 3 in aerosol (−0.77 ± 4.52 ‰; n = 308) and rainwater (3.79 ± 6.14 ‰; n = 392) from 13 sites that are located in the area of mainland China and the Yellow, East China and South China seas (Fig. 1), extracted from the literature (see Table S4 for details).To verify the potentially biasing effects of neglecting N isotope fractionation (i.e., testing the sensitivity of ambient NO x source contribution estimates to the effect of N isotope fractionation), the Bayesian isotopic mixing model was applied (a) to the original NO − 3 isotope data set and (b) to the corrected nitrate isotope data set, accounting for the N isotope fractionation dur-ing NO x transformation.All 13 sampling sites are located in non-urban areas; therefore, apart from coal combustion and on-road traffic, the contributions of biomass burning and biogenic soil to nitrate need to be taken into account.
Although most of the sites are located in rural and coastal environments, when the original data set is used without the consideration of N isotope fractionation in the Bayesian isotopic mixing model, fossil-fuel-related NO x emissions (coal combustion and on-road traffic) appear to be the largest contributor at all the sites (data are not shown).This is particularly true for coal combustion: everywhere except for the sites of Dongshan islands and Mt.Lumin, NO x emissions seem to be dominated by coal combustion.Very high contribution from coal combustion (on the order of 40 %-60 %) particularly in northern China may be plausible and can be attributed to a much larger consumption of coal.Yet, rather unlikely, the highest estimated contribution of coal combustion (83 %) was calculated for Beihuang Island (a full-year sampling on a costal island that is 65 km north of Shandong Peninsula and 185 km east of the Beijing-Tianjin-Hebei region) and not for mainland China.While Beihuang may be an extreme example, we argue that, collectively, the contribution of coal combustion to ambient NO x in China as calculated on the basis of isotopic analyses in previous studies without the consideration of N isotope fractionation represents overestimates.
As a first step towards a more realistic assessment of the actual partitioning of NO x sources in China in general (and coal-combustion-emitted NO x in particular), it is imperative to determine the location-specific values for ε N .Unfortunately, without δ 18 O-NO − 3 data on hand, or data on meteorological parameters that correspond to the 700 δ 15 N-NO − 3 values used in our meta-analysis, it is not possible to esti-  6, the estimates of the source partitioning are sensitive to the choice of ε N .Whereas, with increasing ε N , estimates on the relative contribution of on-road traffic and biomass burning remained relatively stable, estimates for coal combustion and biogenic soil changed significantly, in opposite directions.More precisely, depending on ε N , the average estimate of the fractional contribution of coal combustion decreased drastically from 43 % (ε N = 0 ‰) to 5 % (ε N = 20 ‰) (Fig. 6), while the contribution from biogenic soil to NO x emissions increased in a complementary way.Given the lack of better constraints on ε N for the 13 sampling sites, it cannot be our goal here to provide a robust revised estimate on the partitioning of NO x sources throughout China and its neighboring areas.But we have very good reasons to assume that disregard of N isotope fractionation during pNO − 3 formation in previous isotope-based source apportionment studies has likely led to overestimates of the relative contribution of coal combustion to total NO x emissions in China.For what we would consider the most conservative estimate, i.e., lowest calculated value for the N isotope fractionation during the transformation of NO x to pNO − 3 (ε N = 5 ‰), the approximate contribution from coal combustion to the NO x pool would be 28 %, more than 30 % less than N-isotope-mixing-model-based estimates would yield without consideration of the N isotope fractionation (i.e., ε N = 0 ‰) (Fig. 6).

Conclusion and outlook
Consistent with theoretical predictions, δ 15 N-pNO − 3 data from a field experiment where atmospheric pNO − 3 formation could be attributed reliably to NO x solely from biomass burning revealed that the conversion of NO x to pNO − 3 is associated with a significant net N isotope effect (ε N ).It is imperative that future studies, making use of isotope mixing models to gain conclusive constraints on the source partitioning of atmospheric NO x , consider this N isotope fractionation.The latter will change with time and space, depending on the distribution of ozone and OH radicals in the atmosphere and the predominant NO x chemistry.The O isotope signatures of pNO − 3 is mostly chemistry (and not source) driven (modulated by O isotope exchange reactions in the atmosphere), and thus O isotope measurements do not allow addressing the ambiguities with regards to the NO x source that may remain when just looking at δ 15 N values alone.However, δ 18 O in pNO − 3 will help in assessing the relative importance of the dominant pNO − 3 formation pathway.Simultaneous δ 15 N and δ 18 O measurements of atmospheric nitrate thus allow reliable information on ε N and in turn on the relative importance of single NO x sources.For example, for Nanjing, which can be considered representative for other large cities in China, dual-isotopic and chemicaltracer evidence suggest that on-road traffic and coal-fired power plants, rather than biomass burning, are the predominant sources during high-haze pollution periods.Given that the increasing frequency of nitrate-driven haze episodes in China, our findings are critically important in terms of guiding the use of stable nitrate isotope measurements to evaluate the relative importance of single NO x sources on regional scales and for adapting suitable mitigation measures.Future assessments of NO x emissions in China (and elsewhere) should involve simultaneous δ 15 N and δ 18 O measurements of atmospheric nitrate and NO x at high spatiotemporal resolution, allowing us to more quantitatively reevaluate former N-isotope-based NO x source partitioning estimates.
Data availability.Data are available from the corresponding author on request.We prefer not to publish the software for calculating the nitrogen isotope fractionation factor and estimating nitrate source attribution at the present stage in order to avoid compromising the future of ongoing software registration.Readers can download the software through the website http://www.atmosgeochem.com/(last access: 1 August 2018) after the completion of software registration.

Figure 1 .
Figure 1.Location of the sampling sites Sanjiang and Nanjing.The black dots indicate the location of sampling sites (sites are located in the area of mainland China and the Yellow, East China and South China seas) with δ 15 N-NO −3 data from the literature (see also TableS4).
Figure 2. (a) Correlation analysis between the mass concentrations of levoglucosan and aerosol nitrate during the Sanjiang sampling campaign; (b) variation of fractions of various inorganic species (MSA − stands for methyl sulphonate) during day-night samplings at Sanjiang between 8 and 18 October 2013 (sample ID 1 to 8).The higher relative abundances of nss-K + and Cl − are indicative of a biomass-burningdominated source.For sample ID information and exact sampling dates, refer to TableS3.

Figure 3 .
Figure 3. Original δ 15 N values (δ 15 N ini ) for pNO − 3 , calculated values for the N isotope fractionation (ε N ) associated with the conversion of gaseous NO x to pNO − 3 and corrected δ 15 N values (δ 15 N corr ; 15 N ini minus ε N ) of pNO − 3 for each sample collected during the Sanjiang sampling campaign.The colored bands represent the variation range of δ 15 N values for different NO x sources based on reports from the literature (TableS2).See TableS3for the information regarding sample ID.

Figure 4 .
Figure 4. Comparison between the theoretical calculation and WRF-Chem simulation of the average contribution ratio (γ ) for nitrate formation in Nanjing via the reaction of NO 2 and photochemically produced q OH.
Figure 5. (a) Time-series variation of coal combustion and road traffic contribution to the mass concentrations of ambient pNO − 3 in Nanjing, as estimated through MixSIR; (b) correlation analysis between the mass concentrations of coal-combustion-related pNO − 3 and SO 2 ; (c) correlation analysis between the mass concentrations of road-traffic-related pNO − 3 and CO.

Figure 6 .
Figure 6.Estimates of the relative importance of single NO x sources (mean ±1σ ) throughout China based on the original δ 15 N-NO − 3 values extracted from the literature (ε N = 0 ‰) and under consideration of significant N isotope fractionation during NO x transformation (ε N = 5 ‰, 10 ‰, 15 ‰ or 20 ‰).
(Zong et al., 2017) OH/H 2 O represent the equilibrium O isotope fractionation factors between NO 2 and NO between and OH and H 2 O, respectively.The range of δ 18 O-H 2 O can be approximated using an estimated tropospheric water vapor δ 18 O range of −25 ‰ to 0 ‰.The δ 18 O values for NO 2 and N 2 O 5 range from 90 ‰ to 122 ‰(Zong et al., 2017).15α NO 2 /NO , 15 α N 2 O 5 /NO 2 , 18 α NO 2 /NO and 18 α OH/H 2 O in these equations are dependent on the temperature, which can be expressed as www.atmos-chem-phys.net/18/11647/2018/Atmos.Chem.Phys., 18, 11647-11661, 2018 11652 Y. Chang et al.: Nitrogen isotope fractionation during NO x to pNO − 3 formation Chang et al.:Nitrogen isotope fractionation during NO x to pNO − 3 formation 11657 mate the ε N values through the abovementioned CQC module.As a viable alternative, we adopted the approximate values for ε N as estimated in Sanjiang (10.99 ‰) and Nanjing (15.33 ± 4.90 ‰).As indicated in Fig.