Nitrogen isotope fractionation during gas-to-particle conversion of NOx to NO3- in the atmosphere – implications for isotope-based NOx source apportionment

Abstract

Atmospheric fine-particle (PM${}_{\mathrm{2.5}}$) pollution is frequently associated with the formation of particulate nitrate ($p{\mathrm{NO}}_{\mathrm{3}}^{-}$), the end product of the oxidation of ${\mathrm{NO}}_x$ gases (NO $+$ ${\mathrm{NO}}_{\mathrm{2}}$) in the upper troposphere. The application of stable nitrogen (N) (and oxygen) isotope analyses of$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ to constrain ${\mathrm{NO}}_x$ source partitioning in the atmosphere requires knowledge of the isotope fractionation during the reactions leading to nitrate formation. Here we determined the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values of fresh$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ (${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$) in PM${}_{\mathrm{2.5}}$ at a rural site in northern China, where atmospheric$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ can be attributed exclusively to biomass burning. The observed ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ ($\mathrm{12.17}\pm \mathrm{1.55}$ ‰; $n=\mathrm{8}$) was much higher than the N isotopic source signature of ${\mathrm{NO}}_x$ from biomass burning ($\mathrm{1.04}\pm \mathrm{4.13}$ ‰). The large difference between ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ ($\mathrm{\Delta }$(${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$)) can be reconciled by the net N isotope effect (${\mathit{\epsilon }}_{\mathrm{N}}$) associated with the gas–particle conversion from ${\mathrm{NO}}_x$ to${\mathrm{NO}}_{\mathrm{3}}^{-}$. For the biomass burning site, a mean${\mathit{\epsilon }}_{\mathrm{N}}(\approx \mathrm{\Delta }({\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\left)\right)$ of $\mathrm{10.99}\pm \mathrm{0.74}$ ‰ was assessed through a newly developed computational quantum chemistry (CQC) module. ${\mathit{\epsilon }}_{\mathrm{N}}$ depends on the relative importance of the two dominant N isotope exchange reactions involved (${\mathrm{NO}}_{\mathrm{2}}$ reaction with OH versus hydrolysis of dinitrogen pentoxide (${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$) with ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$) and varies between regions and on a diurnal basis. A second, slightly higher CQC-based mean value for${\mathit{\epsilon }}_{\mathrm{N}}$ ($\mathrm{15.33}\pm \mathrm{4.90}$ ‰) was estimated for an urban site with intense traffic in eastern China and integrated in a Bayesian isotope mixing model to make isotope-based source apportionment estimates for ${\mathrm{NO}}_x$ at this site. Based on the${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values ($\mathrm{10.93}\pm \mathrm{3.32}$ ‰; $n=\mathrm{43}$) of ambient$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ determined for the urban site, and considering the location-specific estimate for ${\mathit{\epsilon }}_{\mathrm{N}}$, our results reveal that the relative contribution of coal combustion and road traffic to urban ${\mathrm{NO}}_x$ is 32 % $\pm$ 11 % and 68 %$\pm$ 11 %, respectively. This finding agrees well with a regional bottom-up emission inventory of ${\mathrm{NO}}_x$. Moreover, the variation pattern of OH contribution to ambient $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation calculated by the CQC module is consistent with that simulated by the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem), further confirming the robustness of our estimates. Our investigations also show that, without the consideration of the N isotope effect during$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation, the observed${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ at the study site would erroneously imply that ${\mathrm{NO}}_x$ is derived almost entirely from coal combustion. Similarly, reanalysis of reported${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ data throughout China and its neighboring areas suggests that ${\mathrm{NO}}_x$ emissions from coal combustion may be substantively overestimated (by $>\mathrm{30}$ %) when the N isotope fractionation during atmospheric $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation is neglected.

Introduction

Nitrogen oxides (${\mathrm{NO}}_x$ $=$ NO $+$ ${\mathrm{NO}}_{\mathrm{2}}$) are among the most important molecules in tropospheric chemistry. They are involved in the formation of secondary aerosols and atmospheric oxidants, such as ozone (${\mathrm{O}}_{\mathrm{3}}$) and hydroxyl radicals (OH), which control the self-cleansing capacity of the atmosphere (Galloway et al., 2003; Seinfeld and Pandis, 2012; Solomon et al., 2007). The sources of ${\mathrm{NO}}_x$ include both anthropogenic and natural origins, with more than half of the global burden ($\sim \mathrm{40}$ Tg N yr${}^{-\mathrm{1}}$) currently attributed to fossil fuel burning (22.4–26.1 Tg N yr${}^{-\mathrm{1}}$) and the rest primarily derived from nitrification/denitrification in soils (including wetlands; $\mathrm{8.9}\pm \mathrm{1.9}$ Tg N yr${}^{-\mathrm{1}}$), biomass burning ($\mathrm{5.8}\pm \mathrm{1.8}$ Tg N yr${}^{-\mathrm{1}}$), lightning (2–6 Tg N yr${}^{-\mathrm{1}}$) and oxidation of ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ in the stratosphere (0.1–0.6 Tg N yr${}^{-\mathrm{1}}$) (Jaegle et al., 2005; Richter et al., 2005; Lamsal et al., 2011; Price et al., 1997; Yienger and Levy, 1995; Miyazaki et al., 2017; Duncan et al., 2016; Anenberg et al., 2017; Levy et al., 1996). The main/ultimate sinks for ${\mathrm{NO}}_x$ in the troposphere are the oxidation to nitric acid (${\mathrm{HNO}}_{\mathrm{3}\left(\mathrm{g}\right)}$) and the formation of aerosol-phase particulate nitrate ($p{\mathrm{NO}}_{\mathrm{3}}^{-}$) (Seinfeld and Pandis, 2012), the partitioning of which may vary on diurnal and seasonal timescales (Morino et al., 2006).

Emissions of ${\mathrm{NO}}_x$ occur mostly in the form of NO (Seinfeld and Pandis, 2012; Leighton, 1961). During daytime, transformation from NO to ${\mathrm{NO}}_{\mathrm{2}}$ is rapid (few minutes) and proceeds in a photochemical steady state, controlled by the oxidation of NO by ${\mathrm{O}}_{\mathrm{3}}$ to ${\mathrm{NO}}_{\mathrm{2}}$ and the photolysis of ${\mathrm{NO}}_{\mathrm{2}}$ back to NO (Leighton, 1961): $$\begin{array}{}& {\displaystyle }& {\displaystyle }\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}⟶{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}},& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+hv⟶\mathrm{NO}+\mathrm{O},& {\displaystyle }& {\displaystyle }\mathrm{O}+{\mathrm{O}}_{\mathrm{2}}\stackrel{M}{⟶}{\mathrm{O}}_{\mathrm{3}},\end{array}$$ where $M$ is any non-reactive species that can take up the energy released to stabilize O. ${\mathrm{NO}}_x$ oxidation to ${\mathrm{HNO}}_{\mathrm{3}}$ is governed by the following equations. During daytime, $${\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+\mathrm{OH}\stackrel{M}{⟶}{\mathrm{HNO}}_{\mathrm{3}}.$$ During nighttime: $$\begin{array}{}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}⟶{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}},& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}\stackrel{M}{⟶}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}},& {\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\left(\mathrm{surface}\right)}\stackrel{\mathrm{aerosol}}{⟶}\mathrm{2}{\mathrm{HNO}}_{\mathrm{3}}.\end{array}$$ ${\mathrm{HNO}}_{\mathrm{3}}$ then reacts with gas-phase ${\mathrm{NH}}_{\mathrm{3}}$ to form ammonium nitrate (${\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}$) aerosols. If the ambient relative humidity (RH) is lower than the efflorescence relative humidity (ERH) or crystallization relative humidity (CRH), solid-phase ${\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}$(s) is formed (Smith et al., 2012; Ling and Chan, 2007): $${\displaystyle }{\displaystyle }{\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}\rightleftharpoons {\mathrm{HNO}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NH}}_{\mathrm{3}}\left(\mathrm{g}\right).$$ If ambient RH exceeds the ERH or CRH, ${\mathrm{HNO}}_{\mathrm{3}}$ and ${\mathrm{NH}}_{\mathrm{3}}$ dissolve into the aqueous phase (aq) (Smith et al., 2012; Ling and Chan, 2007): $${\displaystyle }{\mathrm{HNO}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NH}}_{\mathrm{3}}\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{aq}\right)+{\mathrm{NH}}_{\mathrm{4}}^{+}\left(\mathrm{aq}\right).$$ While global ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ (typically less than 24 h) and the high degree of spatiotemporal heterogeneity with regards to the ratio between gas-phase ${\mathrm{HNO}}_{\mathrm{3}}$ and particulate ${\mathrm{NO}}_{\mathrm{3}}^{-}$ ($p{\mathrm{NO}}_{\mathrm{3}}^{-}$) (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 ${\mathrm{NO}}_x$ sources and sinks, the N isotopic composition of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ can be related to the different origins of the emitted ${\mathrm{NO}}_x$ and thus provides valuable information on the partitioning of the ${\mathrm{NO}}_x$ sources (Morin et al., 2008). Such a N isotope balance approach works best if the N isotopic composition of various ${\mathrm{NO}}_x$ sources display distinct ${}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}$ ratios (reported as ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ $=$ $\frac{{\left({}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}\right)}_{\mathrm{sample}}-({}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}{)}_{{\mathrm{N}}_{\mathrm{2}}}}{{\left({}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}\right)}_{{\mathrm{N}}_{\mathrm{2}}}}\times \mathrm{1000})$. The ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ of coal-fired power plant ($+\mathrm{10}$ ‰ to $+\mathrm{25}$ ‰) (Felix et al., 2012, 2013; Heaton, 1990), vehicle ($+\mathrm{3.7}$ ‰ to $+\mathrm{5.7}$ ‰) (Heaton, 1990; Walters et al., 2015; Felix and Elliott, 2014; Felix et al., 2013; Wojtal et al., 2016) and biomass burning ($-\mathrm{7}$ ‰ to $+$12 ‰) emissions (Fibiger and Hastings, 2016), for example, is generally higher than that of lightning ($-\mathrm{0.5}$ ‰ to $+\mathrm{1.4}$ ‰) (Hoering, 1957) and biogenic soil ($-\mathrm{48.9}$ ‰ to $-\mathrm{19.9}$ ‰) emissions (Li and Wang, 2008; Felix and Elliott, 2014; Felix et al., 2013), allowing the use of isotope mixing models to gain insight on the ${\mathrm{NO}}_x$ source apportionment for gases, aerosols and the resulting nitrate deposition ($-\mathrm{15}$ ‰ to $+\mathrm{15}$ ‰) (Elliott et al., 2007, 2009; Zong et al., 2017; Savarino et al., 2007; Morin et al., 2008; Park et al., 2018; Altieri et al., 2013; Gobel et al., 2013). In addition, because of mass-independent fractionation during its formation (Thiemens, 1999; Thiemens and Heidenreich, 1983), ozone possesses a strong isotope anomaly (${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}$ $\approx$ ${\mathit{\delta }}^{\mathrm{17}}\mathrm{O}$ $-$ $\mathrm{0.52}\times {\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$), which is propagated into the most short-lived oxygen-bearing species, including ${\mathrm{NO}}_x$ and nitrate. Therefore, the oxygen isotopic composition of nitrate (${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$, ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}$) can provide information on the oxidants involved in the conversion of ${\mathrm{NO}}_x$ to nitrate (Michalski et al., 2003; Geng et al., 2017). Knopf et al. (2006, 2011) and Shiraiwa et al. (2012) have shown that ${\mathrm{NO}}_{\mathrm{3}}$ can be taken up efficiently by organic (e.g., levoglucosan) aerosol and may dominate oxidation of aerosol in the polluted urban nighttime (Kaiser et al., 2011). Globally, theoretical modeling results show that nearly 76 %, 18 % and 4 % of annual inorganic nitrate are formed via pathways/reactions involving OH, ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$, and dimethyl sulfide or hydrocarbons, respectively (e.g., Alexander et al., 2009). The stable O isotopic composition of atmospheric nitrate is a powerful proxy for assessing which oxidation pathways are important for converting ${\mathrm{NO}}_x$ into nitrate under changing environmental conditions (e.g., polluted, volcanic events, climate change). Along the same lines, in this study, the average ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ value of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ in Nanjing was $\mathrm{83.0}\pm \mathrm{11.2}$ ‰ (see Discussion section), suggesting that $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation is dominated by the pathways of “OH $+$ ${\mathrm{NO}}_{\mathrm{2}}$” and the heterogeneous hydrolysis of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$.

${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$-based source apportionment of ${\mathrm{NO}}_x$ requires knowledge of how kinetic and equilibrium isotope fractionation may impact ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values during the conversion of ${\mathrm{NO}}_x$ to nitrate (Freyer, 1978; Walters et al., 2016). If these isotope effects are considerable, they may greatly limit the use of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ for ${\mathrm{NO}}_x$ 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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values during the conversion of ${\mathrm{NO}}_x$ to nitrate are minor (without detailed explanation) (Kendall et al., 2007; Morin et al., 2008; Elliott et al., 2007) or relatively small (e.g., $+\mathrm{3}$ ‰) (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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values in atmospheric NO and ${\mathrm{NO}}_{\mathrm{2}}$, implying that isotope equilibrium fractionation may play a significant role in shaping the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of ${\mathrm{NO}}_y$ species (the family of oxidized nitrogen molecules in the atmosphere, including ${\mathrm{NO}}_x$, ${\mathrm{NO}}_{\mathrm{3}}$, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, peroxyacetyl nitrate, etc.). The transformation of ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_y$ molecules and confirmed theoretical predictions that ${}^{\mathrm{15}}\mathrm{N}$ isotopes get enriched in the more oxidized form of ${\mathrm{NO}}_y$ and that the transformation of ${\mathrm{NO}}_x$ to atmospheric nitrate (${\mathrm{HNO}}_{\mathrm{3}}$, ${\mathrm{NO}}_{\mathrm{3}}$(aq), ${\mathrm{NO}}_{\mathrm{3}}$(g)) continuously increases the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ in the residual ${\mathrm{NO}}_x$ pool.

As a consequence of its severe atmospheric particle pollution during the cold season, China has made great efforts toward reducing ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ emissions, require knowledge of the vehicle- and power-plant-emitted ${\mathrm{NO}}_x$ 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${}_{\mathrm{2.5}}$) were quantified, and the isotopic composition of particulate nitrate (${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$) was assessed in order to elucidate ambient ${\mathrm{NO}}_x$ sources in the city of Nanjing in eastern China. We also investigated the potential isotope effect during the formation of nitrate aerosols from ${\mathrm{NO}}_x$ and evaluated how disregard of such N isotope fractionation can bias N-isotope-mixing-model-based estimates on the ${\mathrm{NO}}_x$ source apportionment for nitrate deposition.

Methods

Field sampling

In this study, PM${}_{\mathrm{2.5}}$ aerosol samples were collected on precombusted ($\mathrm{450}$ ${}^{\circ }$C for 6 h) quartz filters ($\mathrm{25}\times \mathrm{20}$ cm) on a day–night basis, using high-volume air samplers at a flow rate of 1.05 m${}^{\mathrm{3}}$ min${}^{-\mathrm{1}}$ in Sanjiang and Nanjing (Fig. 1). After sampling, the filters were wrapped in aluminum foil, packed in air-tight polyethylene bags and stored at $-\mathrm{20}$ ${}^{\circ }$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${}_{\mathrm{2.5}}$ mass concentration was analyzed gravimetrically (Sartorius MC5 electronic microbalance) with a $\pm \mathrm{1}$ $\mathrm{\mu }$g precision before and after sampling (at 25 ${}^{\circ }$C and $\mathrm{45}\mathit{\%}\pm \mathrm{5}$ % during weighing).

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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ data from the literature (see also Table S4).

[Figure omitted. See PDF]

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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_x$ emitted from biomass burning. The Sanjiang site (in the following abbreviated as SJ; 47.35${}^{\circ }$ N, 133.31${}^{\circ }$ 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 $-\mathrm{31}$ and $-\mathrm{15}$ ${}^{\circ }$C in the coldest month, January. As a consequence of the relatively low temperatures (also during summer), biogenic production of ${\mathrm{NO}}_x$ through soil microbial processes is rather weak. SJ is therefore an excellent environment in which to collect biomass-burning-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 ${\mathrm{NO}}_x$ source contributions to ambient $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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${}^{\circ }$ N, 118.72${}^{\circ }$ E; Fig. 1), where ${\mathrm{NO}}_x$ emissions derive from both industrial and transportation sources.

Laboratory analysis

The mass concentrations of inorganic ions (including ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{Cl}}^{-}$, ${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Ca}}^{\mathrm{2}+}$, ${\mathrm{Mg}}^{\mathrm{2}+}$ and ${\mathrm{Na}}^{+}$), carbonaceous components (organic carbon, or OC; elemental carbon, or EC) and water-soluble organic carbon were determined using an ion chromatograph (761 Compact IC, Metrohm, Switzerland), a thermal-optical OC–EC analyzer (RT-4 model, Sunset Laboratory Inc., USA) and a total organic carbon analyzer (Shimadzu, TOC-VCSH, Japan), respectively. Importantly, levoglucosan, a molecular marker for the biomass combustion aerosols, was detected using a Dionex^™ ICS-5000${}^{+}$ system (Thermo Fisher Scientific, Sunnyvale, USA). Chemical aerosol analyses, including sample pre-treatment, analytical procedures, protocol adaption, detection limits and experimental uncertainty were described in detail in our previous work (Cao et al., 2016, 2017).

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 ${\mathrm{NO}}_{\mathrm{3}}^{-}$, 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 ${\mathrm{NO}}_x$ extraction, dependent on the aerosol ${\mathrm{NO}}_{\mathrm{3}}^{-}$ content of the filters, which was determined independently. The extracts were then filtered (0.22 $\mathrm{\mu }$m) and analyzed the next day. N and O isotope analyses of the extracted/dissolved aerosol nitrate (${}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}$, ${}^{\mathrm{18}}\mathrm{O}{/}^{\mathrm{16}}\mathrm{O}$) were performed using the denitrifier method (Sigman et al., 2001; Casciotti et al., 2002). Briefly, sample ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is converted to nitrous oxide (${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$) by denitrifying bacteria that lack ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ reductase activity (Pseudomonas chlororaphis ATCC 13985; formerly Pseudomonas aureofaciens, referred to below as such). ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ 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 $\mathit{\delta }$ notation with respect to atmospheric ${\mathrm{N}}_{\mathrm{2}}$ and Vienna standard mean ocean water, respectively. Analyses are calibrated using the international nitrate isotope standard IAEA-N3, with a ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ value of 4.7 ‰ and a ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ 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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ was generally better than $\pm \mathrm{0.2}$ ‰ and $\pm \mathrm{0.3}$ ‰ ($\mathrm{1}\mathit{\sigma }$), respectively.

The denitrifier method generates ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ values of the combined pool of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$. The presence of substantial amounts of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ samples may lead to errors with regards to the analysis of ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ (Wankel et al., 2010). We refrained from including a nitrite-removal step, because nitrite concentrations in our samples were always $<\mathrm{1}$ % of the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations. In the following ${\mathit{\delta }}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_x}$ and ${\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{{\mathrm{NO}}_x}$ are thus referred to as nitrate ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ (or ${\mathit{\delta }}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ and ${\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{{\mathrm{NO}}_{\mathrm{3}}}$).

In the case of atmospheric or aerosol nitrate samples with comparatively high ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ values, ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values tend to be overestimated by 1–2 ‰ (Hastings et al., 2003) if the contribution of ${}^{\mathrm{14}}{\mathrm{N}}^{\mathrm{14}}{\mathrm{N}}^{\mathrm{17}}\mathrm{O}$ to the ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ mass 45 signal is not accounted for during isotope ratio analysis. For most natural samples, the mass-dependent relationship can be approximated as ${\mathit{\delta }}^{\mathrm{17}}\mathrm{O}$ $\approx$ $\mathrm{0.52}\times {\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$, and the ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ can be used for the ${}^{\mathrm{17}}\mathrm{O}$ correction. Atmospheric ${\mathrm{NO}}_{\mathrm{3}}^{-}$ 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 ${}^{\mathrm{17}}\mathrm{O}$-to-${}^{\mathrm{18}}\mathrm{O}$ linearity (Hastings et al., 2003).

Calculation of N isotope fractionation value (${\mathit{\epsilon }}_{\mathrm{N}}$)

As we described above, the transformation process of ${\mathrm{NO}}_x$ to ${\mathrm{HNO}}_{\mathrm{3}}$ or ${\mathrm{NO}}_{\mathrm{3}}^{-}$ involves multiple reaction pathways (see also Fig. S1 in the Supplement) and is likely to undergo isotope equilibrium exchange reactions. The measured ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ values of aerosol samples are thus reflective of the combined N isotope signatures of various ${\mathrm{NO}}_x$ sources (${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$) 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 ${\mathrm{NO}}_y$ molecules; based on this approach, Zong et al. (2017) estimated the N isotope fractionation during the transformation of ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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 ${\mathit{\epsilon }}_{\mathrm{N}}$ (for equilibrium processes $A\leftrightarrow B$: ${\mathit{\epsilon }}_{A\leftrightarrow B}=\left(\frac{{\left(\text{heavy isotope/light isotope}\right)}_A}{{\left(\text{heavy isotope/light isotope}\right)}_B-\mathrm{1}}\right)\cdot \mathrm{1000}\mathrm{‰}$; ${\mathit{\epsilon }}_{\mathrm{N}}$ refers to ${\mathit{\epsilon }}_{{\mathrm{N}}_{({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-})}}$ in this study unless otherwise specified) during the gas-to-particle conversion from ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation $(\mathrm{\Delta }{\left({\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\right)}_{p{\mathrm{NO}}_{\mathrm{3}}^{-}-{\mathrm{NO}}_x}={\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}-{\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x\approx {\mathit{\epsilon }}_{\mathrm{N}})$ can be considered a hybrid of the isotope effects of two dominant N isotopic exchange reactions: $$\begin{array}{cc}{\displaystyle }& {\displaystyle }{\mathit{\epsilon }}_{\mathrm{N}}=\mathit{\gamma }\times {\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}+\left(\mathrm{1}-\mathit{\gamma }\right)\times {\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\\ & {\displaystyle }& {\displaystyle }=\mathit{\gamma }\times {\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}+\left(\mathrm{1}-\mathit{\gamma }\right)\times {\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}},\end{array}$$ where $\mathit{\gamma }$ represents the contribution from isotope fractionation by the reaction of ${\mathrm{NO}}_x$ and photochemically produced OH to form ${\mathrm{HNO}}_{\mathrm{3}}$ (and $p{\mathrm{NO}}_{\mathrm{3}}^{-}$), as shown by ${\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}\left({\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}\right)$. The remainder is formed by the hydrolysis of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ with aerosol water to generate ${\mathrm{HNO}}_{\mathrm{3}}$ (and $p{\mathrm{NO}}_{\mathrm{3}}^{-}$), namely, ${\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}$ $\left({\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\right)$. Assuming that kinetic N isotope fractionation associated with the reaction between ${\mathrm{NO}}_x$ and OH is negligible, ${\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}$ can be calculated based on mass-balance considerations: $$\begin{array}{l}{\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}={\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}={\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_{\mathrm{2}}\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}\\ =\mathrm{1000}\times \left[{\displaystyle \frac{\left({}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}-\mathrm{1}}\right)\left(\mathrm{1}-f_{{\mathrm{NO}}_{\mathrm{2}}}\right)}{\left(\mathrm{1}-f_{{\mathrm{NO}}_{\mathrm{2}}}\right)+\left({}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}}\times f_{{\mathrm{NO}}_{\mathrm{2}}}\right)}}\right],\end{array}$$ where ${}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}}/\mathrm{NO}$ is the temperature-dependent (see Eq. 7 and Table S1 in the Supplement) equilibrium N isotope fractionation factor between ${\mathrm{NO}}_{\mathrm{2}}$ and NO, and $f_{{\mathrm{NO}}_{\mathrm{2}}}$ is the fraction of ${\mathrm{NO}}_{\mathrm{2}}$ in the total ${\mathrm{NO}}_x$. $f_{{\mathrm{NO}}_{\mathrm{2}}}$ ranges from 0.2 to 0.95 (Walters and Michalski, 2015). Similarly, assuming a negligible kinetic isotope fractionation associated with the reaction ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ $+$ ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ $+$ aerosol $\to$ 2${\mathrm{HNO}}_{\mathrm{3}}$, ${\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}$ can be computed from the following equation: $$\begin{array}{l}{\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}={\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}=\\ {\mathit{\epsilon }}_{{\mathrm{N}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}=\mathrm{1000}\times \left({}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}/{\mathrm{NO}}_{\mathrm{2}}}-\mathrm{1}\right)\end{array},$$ where ${}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}/{\mathrm{NO}}_{\mathrm{2}}}$ is the equilibrium isotope fractionation factor between ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ and ${\mathrm{NO}}_{\mathrm{2}}$, which also is temperature-dependent (see Eq. 7 and Table S1).

Following Walter and Michalski (2015) and Zhong et al. (2017), $\mathit{\gamma }$ can then be approximated based on the O isotope fractionation during the conversion of ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$: $$\begin{array}{l}{\mathit{\epsilon }}_{{\mathrm{O}}_{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}}=\mathit{\gamma }\times {\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}\\ +\left(\mathrm{1}-\mathit{\gamma }\right)\times {\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\\ =\mathit{\gamma }\times {\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}+\left(\mathrm{1}-\mathit{\gamma }\right)\times {\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\end{array},$$ where ${\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}$ and ${\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}$ represent the O isotope effects associated with $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ generation through the reaction of ${\mathrm{NO}}_x$ and OH to form ${\mathrm{HNO}}_{\mathrm{3}}$, and the hydrolysis of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ on a wetted surface to form ${\mathrm{HNO}}_{\mathrm{3}}$, respectively. ${\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}$ can be further expressed as $$\begin{array}{l}{\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{\mathrm{OH}}}}={\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}={\displaystyle \frac{\mathrm{2}}{\mathrm{3}}}{\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_{\mathrm{2}}\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}\\ +{\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}{\mathit{\epsilon }}_{{\mathrm{O}}_{{\left(\mathrm{NO}\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{\mathrm{OH}}}}\\ ={\displaystyle \frac{\mathrm{2}}{\mathrm{3}}}\left[{\displaystyle \frac{\mathrm{1000}\left({}^{\mathrm{18}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}}/\mathrm{NO}-\mathrm{1}\right)\left(\mathrm{1}-f_{{\mathrm{NO}}_{\mathrm{2}}}\right)}{\left(\mathrm{1}-f_{{\mathrm{NO}}_{\mathrm{2}}}\right)+\left({}^{\mathrm{18}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}}/\mathrm{NO}\times f_{{\mathrm{NO}}_{\mathrm{2}}}\right)}}+\left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}-{\mathrm{NO}}_x\right)\right]+\\ {\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}\left[\left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}-{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)+\mathrm{1000}\left({}^{\mathrm{18}}{\mathit{\alpha }}_{\mathrm{OH}/{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}-\mathrm{1}\right)\right]\end{array},$$ and ${\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}$ can be determined as follows: $$\begin{array}{cc}{\displaystyle }& {\displaystyle }{\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow p{\mathrm{NO}}_{\mathrm{3}}^{-}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}={\mathit{\epsilon }}_{{\mathrm{O}}_{{\left({\mathrm{NO}}_x\leftrightarrow {\mathrm{HNO}}_{\mathrm{3}}\right)}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}={\displaystyle \frac{\mathrm{5}}{\mathrm{6}}}\left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}-{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)\\ & {\displaystyle }& {\displaystyle }+{\displaystyle \frac{\mathrm{1}}{\mathrm{6}}}\left({\mathit{\delta }}^{\mathrm{18}}\mathrm{O}-{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right),\end{array}$$ where ${}^{\mathrm{18}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}}$ and ${}^{\mathrm{18}}{\mathit{\alpha }}_{\mathrm{OH}/{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ represent the equilibrium O isotope fractionation factors between ${\mathrm{NO}}_{\mathrm{2}}$ and NO between and OH and ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$, respectively. The range of ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ can be approximated using an estimated tropospheric water vapor ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ range of $-\mathrm{25}$ ‰ to 0 ‰. The ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ values for ${\mathrm{NO}}_{\mathrm{2}}$ and ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ range from 90 ‰ to 122 ‰ (Zong et al., 2017).

${}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}}$, ${}^{\mathrm{15}}{\mathit{\alpha }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}/{\mathrm{NO}}_{\mathrm{2}}}$, ${}^{\mathrm{18}}{\mathit{\alpha }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}}$ and ${}^{\mathrm{18}}{\mathit{\alpha }}_{\mathrm{OH}/{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ in these equations are dependent on the temperature, which can be expressed as $$\begin{array}{cc}{\displaystyle }& {\displaystyle }\mathrm{1000}\left({}^m{\mathit{\alpha }}_{X/Y}-\mathrm{1}\right)={\displaystyle \frac{A}{T^{\mathrm{4}}}}\times {\mathrm{10}}^{\mathrm{10}}+{\displaystyle \frac{B}{T^{\mathrm{3}}}}\times {\mathrm{10}}^{\mathrm{8}}+{\displaystyle \frac{C}{T^{\mathrm{2}}}}\times {\mathrm{10}}^{\mathrm{6}}\\ & {\displaystyle }& {\displaystyle }+{\displaystyle \frac{D}{T}}\times {\mathrm{10}}^{\mathrm{4}},\end{array}$$ 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 ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ of ambient PM${}_{\mathrm{2.5}}$, a Monte Carlo simulation was performed to generate 10 000 feasible solutions. The error between predicted and measured ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ was less than 0.5 ‰. The range (maximum and minimum) of computed contribution ratios ($\mathit{\gamma }$) was then integrated in Eq. (1) to generate an estimate range for the nitrogen isotope effect ${\mathit{\epsilon }}_{\mathrm{N}}$ (using Eqs. 2–3). ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values can be calculated based on ${\mathit{\epsilon }}_{\mathrm{N}}$ and the estimated ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ range for atmospheric ${\mathrm{NO}}_x$ (see Sect. 2.4).

Bayesian isotope mixing model

Isotopic mixing models allow estimating the relative contribution of multiple sources (e.g., emission sources of ${\mathrm{NO}}_x$) within a mixed pool (e.g., ambient $p{\mathrm{NO}}_{\mathrm{3}}^{-}$). 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 ${\mathrm{NO}}_x$ 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 ($\mathrm{13.72}\pm \mathrm{4.57}$ ‰), transportation ($-\mathrm{3.71}\pm \mathrm{10.40}$ ‰), biomass burning ($\mathrm{1.04}\pm \mathrm{4.13}$ ‰) and biogenic emissions from soils ($-\mathrm{33.77}\pm \mathrm{12.16}$ ‰) were considered to be the most relevant contributors of ${\mathrm{NO}}_x$ (Table S2 and Sect. S2). The ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of atmospheric ${\mathrm{NO}}_x$ is unknown. However, it can be assumed that its range in the atmosphere is constrained by the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of the ${\mathrm{NO}}_x$ sources and the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ after equilibrium fractionation conditions have been reached. Following Zong et al. (2017), ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ 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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ values of the emission sources (mean and standard deviation) and the measured ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ of ambient PM${}_{\mathrm{2.5}}$ (Fig. S2).

Results

Sanjiang in northern China

The ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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${}_{\mathrm{2.5}}$ samples collected near the sites of biomass burning in Sanjiang vary between 4.0 and 20.5 $\mathrm{\mu }$g m${}^{-\mathrm{3}}$, 2 to 5 orders of magnitude higher than those measured during non-biomass-burning season (Cao et al., 2017, 2016). Levoglucosan is an anhydrosugar formed during pyrolysis of cellulose at temperatures above 300 ${}^{\circ }$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 ($R^{\mathrm{2}}=\mathrm{0.64}$; Fig. 2a), providing compelling evidence that particulate nitrate measured during our study period was predominately derived from biomass burning emissions.

(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-${\mathrm{K}}^{+}$ and ${\mathrm{Cl}}^{-}$ are indicative of a biomass-burning-dominated source. For sample ID information and exact sampling dates, refer to Table S3.

[Figure omitted. See PDF]

Nanjing in eastern China

The mass concentrations $\left({\mathrm{mean}}_{min}^{max}\pm \mathrm{1}\mathit{\sigma },n=\mathrm{43}\right)$ of PM${}_{\mathrm{2.5}}$ and $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ measured in Nanjing were ${\mathrm{122.1}}_{\mathrm{39.0}}^{\mathrm{227.8}}\pm \mathrm{47.9}$ and ${\mathrm{17.8}}_{\mathrm{4.0}}^{\mathrm{45.2}}\pm \mathrm{10.3}$ $\mathrm{\mu }$g m${}^{-\mathrm{3}}$, respectively. All PM${}_{\mathrm{2.5}}$ concentrations exceeded the Chinese Air Quality Standards for daily PM${}_{\mathrm{2.5}}$ (35 $\mathrm{\mu }$g m${}^{-\mathrm{3}}$), suggesting severe haze pollution during the sampling period. The corresponding ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values (raw data without correction) ranged between 5.39 ‰ and 17.99 ‰, indicating significant enrichment in ${}^{\mathrm{15}}\mathrm{N}$ relative to rural and coastal marine atmospheric ${\mathrm{NO}}_{\mathrm{3}}^{-}$ sources (Table S4). This may be due to the prominent contribution of fossil-fuel-related ${\mathrm{NO}}_x$ emissions with higher ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values in urban areas (Elliott et al., 2007; Park et al., 2018).

Discussion

Sanjiang campaign: theoretical calculation and field validation of N isotope fractionation during $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation

To be used as a quantitative tracer of biomass-combustion-generated 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-${\mathrm{K}}^{+}$ $=$ ${\mathrm{K}}^{+}$ $-$ $\mathrm{0.0355}\times {\mathrm{Na}}^{+}$) is considered as an independent/additional indicator of biomass burning (Fig. 2b). The association of elevated levels of levoglucosan with high nss-${\mathrm{K}}^{+}$ concentrations underscores that the two compounds derived from the same proximate sources and thus that aerosol levoglucosan 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 ${\mathrm{NO}}_{\mathrm{3}}^{-}$ compared to ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$ (a typical coal-related pollutant). This additionally points to biomass burning, and not coal-combustion, as the dominant $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ source in the study area, making SJ an ideal “quasi-single-source” environment for calibrating the N isotope effect during $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation.

Original ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values (${\mathit{\delta }}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{ini}}$) for $p{\mathrm{NO}}_{\mathrm{3}}^{-}$, calculated values for the N isotope fractionation (${\mathit{\epsilon }}_{\mathrm{N}}$) associated with the conversion of gaseous ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and corrected ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values (${\mathit{\delta }}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{corr}}$; ${}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{ini}}$ minus ${\mathit{\epsilon }}_{\mathrm{N}}$) of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ for each sample collected during the Sanjiang sampling campaign. The colored bands represent the variation range of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values for different ${\mathrm{NO}}_x$ sources based on reports from the literature (Table S2). See Table S3 for the information regarding sample ID.

[Figure omitted. See PDF]

Our ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values of biomass-burning-emitted ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fall within the range of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ values typically reported for emissions from coal combustion, whereas they are significantly higher than the well-established values for ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ emitted from the burning of various types of biomass (mean: $\mathrm{1.04}\pm \mathrm{4.13}$ ‰; range: $-\mathrm{7}$ to $+\mathrm{12}$ ‰) (Fibiger and Hastings, 2016). Turekian et al. (1998) conducted laboratory tests involving the burning of eucalyptus and African grasses, and determined that the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ (around 23 ‰) was 6.6 ‰ higher than the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ 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., ${\mathrm{NO}}_x$) have the same ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ as the biomass. Hence any discrepancy between the $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and the ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of the biomass can be attributed to the N isotope fractionation associated with the partial conversion of gaseous ${\mathrm{NO}}_x$ to aerosol ${\mathrm{NO}}_{\mathrm{3}}^{-}$. Based on the computational quantum chemistry (CQC) module calculations, the N isotope fractionation ${\mathit{\epsilon }}_{\mathrm{N}}\left({\mathrm{mean}}_{min}^{max}\pm \mathrm{1}\mathit{\sigma }\right)$ determined from the Sanjiang data was ${\mathrm{10.99}}_{\mathrm{10.30}}^{\mathrm{12.54}}\pm \mathrm{0.74}$ ‰. After correcting the primary ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values under the consideration of ${\mathit{\epsilon }}_{\mathrm{N}}$, the resulting mean ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ of ${\mathrm{1.17}}_{-\mathrm{1.89}}^{\mathrm{2.98}}\pm \mathrm{1.95}$ ‰ is very close to the N isotopic signature expected for biomass-burning-emitted ${\mathrm{NO}}_x$ ($\mathrm{1.04}\pm \mathrm{4.13}$ ‰) (Fig. 3) (Fibiger and Hastings, 2016). The much higher ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values in our study compared to reported ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ values for biomass burning can easily be reconciled when including N isotope fractionation during the conversion of ${\mathrm{NO}}_x$ to ${\mathrm{NO}}_{\mathrm{3}}^{-}$. Put another way, given that Sanjiang is an environment where we can essentially exclude ${\mathrm{NO}}_x$ sources other than biomass burning at the time of sampling, the data nicely validate our CQC-module-based approach to estimating ${\mathit{\epsilon }}_{\mathrm{N}}$.

Source apportionment of ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ concentrations derived from road traffic and coal combustion (Zhao et al., 2015). However, the raw ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values ($\mathrm{10.93}\pm \mathrm{3.32}$ ‰) fell well within the variation range of coal-emitted ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_x$ (Fig. 3). It is tempting to conclude that coal combustion is the main, or even sole, $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ source (given the equivalent ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values), yet this is very unlikely. The data rather confirm that significant isotope fractionation occurred during the conversion of ${\mathrm{NO}}_x$ to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and that, without consideration of the N isotope effect, traffic-related ${\mathrm{NO}}_x$ emissions will be markedly underestimated.

In the atmosphere, the oxygen atoms of ${\mathrm{NO}}_x$ rapidly exchanged with ${\mathrm{O}}_{\mathrm{3}}$ in the “$\mathrm{NO}$–${\mathrm{NO}}_{\mathrm{2}}$” cycle (see Reactions R1–R3) (Hastings et al., 2003), and the ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values are determined by its production pathways (Reactions R4–R7), rather than the sources of ${\mathrm{NO}}_x$ (Hastings et al., 2003). Thus, ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ can be used to gain information on the pathway of conversion of ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_{\mathrm{3}}^{-}$ derive from ${\mathrm{O}}_{\mathrm{3}}$ and one-third from $\mathrm{⚫}\mathrm{OH}$ in the $\mathrm{⚫}\mathrm{OH}$ generation pathway (Reaction R4) (Hastings et al., 2003); correspondingly, five-sixths of the oxygen atoms then derived from ${\mathrm{O}}_{\mathrm{3}}$ and one-sixth from $\mathrm{⚫}\mathrm{OH}$ in the “${\mathrm{O}}_{\mathrm{3}}$–${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$” pathway (Reactions R5–R7). The assumed range for ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{O}}_{\mathrm{3}}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ values were 90 ‰–122 ‰ and $-\mathrm{25}$ ‰–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 ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{O}}_{\mathrm{3}}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ values used. Nevertheless, the theoretical calculation of the average contribution ratio ($\mathit{\gamma }$) for nitrate formation in Nanjing via the reaction of ${\mathrm{NO}}_{\mathrm{2}}$ and $\mathrm{⚫}\mathrm{OH}$ 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 $\mathrm{⚫}\mathrm{OH}$ oxidation of ${\mathrm{NO}}_{\mathrm{2}}$ can be observed (Fig. S3), with much higher concentrations between 12:00 and 18:00. This indicates the importance of photochemically produced $\mathrm{⚫}\mathrm{OH}$ during daytime. Yet, throughout our sampling period in Nanjing, the average $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation by the heterogeneous hydrolysis of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ (12.6 $\mathrm{\mu }$g mm${}^{-\mathrm{3}}$) exceeded $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation by the reaction of ${\mathrm{NO}}_{\mathrm{2}}$ and $\mathrm{⚫}\mathrm{OH}$ (4.8 $\mathrm{\mu }$g mm${}^{-\mathrm{3}}$), even during daytime, consistent with recent observations during peak pollution periods in Beijing (Wang et al., 2017). Given the production rates of ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ in the atmosphere are governed by ambient ${\mathrm{O}}_{\mathrm{3}}$ concentrations, reducing atmospheric ${\mathrm{O}}_{\mathrm{3}}$ levels appears to be one of the most important measures to take for mitigating $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ pollution in China's urban atmospheres.

Comparison between the theoretical calculation and WRF-Chem simulation of the average contribution ratio ($\mathit{\gamma }$) for nitrate formation in Nanjing via the reaction of ${\mathrm{NO}}_{\mathrm{2}}$ and photochemically produced $\mathrm{⚫}\mathrm{OH}$.

[Figure omitted. See PDF]

(a) Time-series variation of coal combustion and road traffic contribution to the mass concentrations of ambient $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ in Nanjing, as estimated through MixSIR; (b) correlation analysis between the mass concentrations of coal-combustion-related $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{SO}}_{\mathrm{2}}$; (c) correlation analysis between the mass concentrations of road-traffic-related $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ and CO.

[Figure omitted. See PDF]

In Nanjing, dependent on the time-dependent, dominant $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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 ${\mathrm{NO}}_x$: 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 ${\mathrm{NO}}_x$ (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 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ values of $-{\mathrm{4.29}}_{-\mathrm{10.32}}^{\mathrm{0.42}}\pm \mathrm{3.66}$ ‰ are relatively close to the N isotopic signature of biomass-burning-emitted ${\mathrm{NO}}_x$ ($\mathrm{1.04}\pm \mathrm{4.13}$ ‰) compared to the other possible sources. Based on ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ alone, the isotope approach can be ambiguous if there are more than two sources. The N isotope signature of ${\mathrm{NO}}_x$ from biomass burning falls right in between the spectrum of plausible values, with highest ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ 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 ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ should have minimal impact or can be largely neglected (Zhao et al., 2015); (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 ${\mathrm{NO}}_x$ during the sampling period should also be minor. Indeed, Fig. S4 shows that the mass concentration of biomass-burning-related $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ is not correlated with the fraction of levoglucosan that contributes to OC, confirming a weak impact of biomass burning on the variation of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration during our study period.

Estimates of the relative importance of single ${\mathrm{NO}}_x$ sources (mean $\pm \mathrm{1}\mathit{\sigma }$) throughout China based on the original ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ values extracted from the literature (${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{0}$ ‰) and under consideration of significant N isotope fractionation during ${\mathrm{NO}}_x$ transformation (${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{5}$ ‰, 10 ‰, 15 ‰ or 20 ‰).

[Figure omitted. See PDF]

In a second, alternative and more realistic scenario, we excluded biomass burning and soil as a potential source of ${\mathrm{NO}}_x$ in MixSIR (see above). As illustrated in Fig. 5a, assuming that ${\mathrm{NO}}_x$ emissions in urban Nanjing during our study period originated solely from road traffic and coal combustion, their relative contribution to the mass concentration of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ is $\mathrm{12.5}\pm \mathrm{9.1}$ $\mathrm{\mu }$g m${}^{-\mathrm{3}}$ (or $\mathrm{68}\pm \mathrm{11}$ %) and $\mathrm{4.9}\pm \mathrm{2.5}$ $\mathrm{\mu }$g m${}^{-\mathrm{3}}$ (or $\mathrm{32}\pm \mathrm{11}$ %), respectively. These numbers agree well with a city-scale ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ emissions from coal-fired power plants in China were about 30 % higher than those from transportation. However, our isotope-based source apportionment of ${\mathrm{NO}}_x$ clearly shows that in 2014 the contribution from road traffic to ${\mathrm{NO}}_x$ 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., 2017, 2016b). Recent satellite-based studies have successfully analyzed the ${\mathrm{NO}}_x$ vertical column concentration ratios for megacities in eastern China and highlighted the importance of transportation-related ${\mathrm{NO}}_x$ emissions (Reuter et al., 2014; Gu et al., 2014; Duncan et al., 2016; Jin et al., 2017). Moreover, long-term measurements of the ratio of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ to non-sea-salt ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$ 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 $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations are highly correlated with their corresponding tracers (i.e., ${\mathrm{SO}}_{\mathrm{2}}$ 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 ${\mathrm{NO}}_x$ emissions from automotive/transportation sources in China based on bottom-up emission inventories may be too low.

Previous ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$-based estimates on ${\mathrm{NO}}_x$ sources

Stable nitrogen isotope ratios of nitrate have been used to identify nitrogen sources in various environments in China, often without large differences in ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ between rainwater and aerosol ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Kojima et al., 2011). In previous work, no consideration was given to potential N isotope fractionation during atmospheric $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation. Here, we reevaluated 700 data points of ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ in aerosol ($-\mathrm{0.77}\pm \mathrm{4.52}$ ‰; $n=\mathrm{308}$) and rainwater ($\mathrm{3.79}\pm \mathrm{6.14}$ ‰; $n=\mathrm{392}$) 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 ${\mathrm{NO}}_x$ source contribution estimates to the effect of N isotope fractionation), the Bayesian isotopic mixing model was applied (a) to the original ${\mathrm{NO}}_{\mathrm{3}}^{-}$ isotope data set and (b) to the corrected nitrate isotope data set, accounting for the N isotope fractionation during ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ 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, ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ sources in China in general (and coal-combustion-emitted ${\mathrm{NO}}_x$ in particular), it is imperative to determine the location-specific values for ${\mathit{\epsilon }}_{\mathrm{N}}$. Unfortunately, without ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ data on hand, or data on meteorological parameters that correspond to the 700 ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–${\mathrm{NO}}_{\mathrm{3}}^{-}$ values used in our meta-analysis, it is not possible to estimate the ${\mathit{\epsilon }}_{\mathrm{N}}$ values through the abovementioned CQC module. As a viable alternative, we adopted the approximate values for ${\mathit{\epsilon }}_{\mathrm{N}}$ as estimated in Sanjiang (10.99 ‰) and Nanjing ($\mathrm{15.33}\pm \mathrm{4.90}$ ‰). As indicated in Fig. 6, the estimates of the source partitioning are sensitive to the choice of ${\mathit{\epsilon }}_{\mathrm{N}}$. Whereas, with increasing ${\mathit{\epsilon }}_{\mathrm{N}}$, 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 ${\mathit{\epsilon }}_{\mathrm{N}}$, the average estimate of the fractional contribution of coal combustion decreased drastically from 43 % (${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{0}$ ‰) to 5 % (${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{20}$ ‰) (Fig. 6), while the contribution from biogenic soil to ${\mathrm{NO}}_x$ emissions increased in a complementary way. Given the lack of better constraints on ${\mathit{\epsilon }}_{\mathrm{N}}$ for the 13 sampling sites, it cannot be our goal here to provide a robust revised estimate on the partitioning of ${\mathrm{NO}}_x$ sources throughout China and its neighboring areas. But we have very good reasons to assume that disregard of N isotope fractionation during $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation in previous isotope-based source apportionment studies has likely led to overestimates of the relative contribution of coal combustion to total ${\mathrm{NO}}_x$ 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 ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ (${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{5}$ ‰), the approximate contribution from coal combustion to the ${\mathrm{NO}}_x$ 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., ${\mathit{\epsilon }}_{\mathrm{N}}=\mathrm{0}$ ‰) (Fig. 6).

Conclusion and outlook

Consistent with theoretical predictions, ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$–$p{\mathrm{NO}}_{\mathrm{3}}^{-}$ data from a field experiment where atmospheric $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation could be attributed reliably to ${\mathrm{NO}}_x$ solely from biomass burning revealed that the conversion of ${\mathrm{NO}}_x$ to $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ is associated with a significant net N isotope effect (${\mathit{\epsilon }}_{\mathrm{N}}$). It is imperative that future studies, making use of isotope mixing models to gain conclusive constraints on the source partitioning of atmospheric ${\mathrm{NO}}_x$, 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 ${\mathrm{NO}}_x$ chemistry. The O isotope signatures of $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ 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 ${\mathrm{NO}}_x$ source that may remain when just looking at ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ values alone. However, ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ in $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ will help in assessing the relative importance of the dominant $p{\mathrm{NO}}_{\mathrm{3}}^{-}$ formation pathway. Simultaneous ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ measurements of atmospheric nitrate thus allow reliable information on ${\mathit{\epsilon }}_{\mathrm{N}}$ and in turn on the relative importance of single ${\mathrm{NO}}_x$ sources. For example, for Nanjing, which can be considered representative for other large cities in China, dual-isotopic and chemical-tracer 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 ${\mathrm{NO}}_x$ sources on regional scales and for adapting suitable mitigation measures. Future assessments of ${\mathrm{NO}}_x$ emissions in China (and elsewhere) should involve simultaneous ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}$ and ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$ measurements of atmospheric nitrate and ${\mathrm{NO}}_x$ at high spatiotemporal resolution, allowing us to more quantitatively reevaluate former N-isotope-based ${\mathrm{NO}}_x$ source partitioning estimates.

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.

The Supplement related to this article is available online at https://doi.org/10.5194/acp-18-11647-2018-supplement.

YZ conceived the study. YZ, ML and YC designed the experimental strategy. YC, CT, XM, FC, SZ, ML and TK performed the geochemical and isotope measurements, analyzed the experimental data and constructed the model. YC and YZ proposed the hypotheses. XL and WZ assisted with the laboratory work. YC wrote the manuscript with ML and YZ; all other co-authors contributed to the data interpretation and writing.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Multiphase chemistry of secondary aerosol formation under severe haze”. It is not associated with a conference.

Acknowledgements

This study was supported by the National Key Research and Development Program of China (2017YFC0210101), the National Natural Science Foundation of China (grant nos. 91644103, 41705100 and 41575129), the Provincial Natural Science Foundation of Jiangsu (BK20170946), the University Science Research Project of Jiangsu Province (17KJB170011), the International Joint Laboratory on Climate and Environment Change (ILCEC) and the Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD) through NUIST and through University of Basel research funds.Edited by: Daniel Knopf Reviewed by: two anonymous referees