NO2 was sampled on an active (pumped) collection system using denuder tubes. This method is more efficient to collect NO2 than passive methods (Røyset, 1998), allowing for shorter collection times with a breakthrough of the absorption capacity below 1 % (Buttini et al., 1987; Williams and Grosjean, 1990). The sampled air was pumped through a ChemComb^® 3500 speciation cartridge (Thermo Scientific^®, USA). Initially used for the speciation of gases and aerosols, these advanced sampling platforms consist of a PM2.5 impactor inlet connected to a stainless-steel cylinder that contains two glass honeycomb denuders connected in series for gas collection and a Teflon stage filter pack for aerosols. To collect NO2, glass tubes were coated with an alkaline guaiacol solution. In basic medium, guaiacol (IUPAC name: 2-methoxyphenol) is known to react with NO2 to form stable NO2- ions (Nash, 1970), preserving the original NO2 isotopic signal due to the basic nature of the medium (pH = 14 after 10 mL extraction). Because NO or peroxyacetyl nitrate (PAN) are not collected by guaiacol, this methodology avoids potential interferences from these compounds in later analyses (Buttini et al., 1987). Although nitrous acid (HONO) can bind as NO2-, it is unlikely to adversely impact the results as its mixing ratio (i.e. mole fraction) is much lower than NO2 (by a factor of 10 to 20) even in very polluted cities (e.g. Harris et al., 1982; Michoud et al., 2014; Huang et al., 2017).

To evaluate the sampling system performance, a series of experiments were run with artificial gaseous NO2. Using a commercial gas-standard generator (KinTek FlexStream^®) feed with zero air, diluted NO2 (Metronics Dynacal^®) was sent through a ChemComb cartridge, while NOx mixing ratio was measured upstream and downstream of the cartridge. From 1 to 30 nmol mol-1 of NO2 (representative of rural to urban atmospheric conditions), mixing ratios coming out of the cartridge were never above the noise level of the NOx monitor (2.5 nmol mol-1). To estimate the denuder's trapping efficiency, we passed different mixing ratios of gaseous NO2 through the collection apparatus and measured the amount of NO2- collected on the two denuders both connected in series. The denuder efficiency E was then calculated according to the following equation (Buttini et al., 1987): 1E=1-ba×100%, with a and b representing the amount of NO2- collected on the first and the second denuder, respectively. From 0.3 to 1.3 µmol of generated NO2 (see Fig. 1), the mean E value was about (97 ± 3) %. The amount of NO2- measured on the second denuder was reproducible and equivalent to blanks, representing on average 3 % of the quantity measured on the first denuder. In light of these results, the denuder in the second position was not subjected to isotopic analysis and allowed for trapping efficiency control.

Simultaneous isotopic analyses of δ15N, δ18O, and δ17O were performed using a Finnigan^® MAT253 isotope ratio mass spectrometer (IRMS) following techniques described by Casciotti et al. (2002) and Kaiser et al. (2007). The azide method (McIlvin and Altabet, 2005) was used with ≈ 100 nmol of nitrites converted to N2O using a 50 : 50 by volume mixture of 2 M sodium azide and 100 % acetic acid. This chemical method has the advantage over the bacterial method to be free of nitrate interferences since HNO3 is certainly trapped with NO2 in the basic solution coating of the denuder tube. The principle of identical treatment (Brand, 1996) was strictly respected where the standards and samples possessed the same nitrite amount, water isotopes, total volume and matrix. Three international KNO2 salt standards – RSIL-N7373, RSIL-N10219, and RSIL-N23 with respective δ15N / δ18O values of -79.6/4.2 ‰, 2.8/88.5 ‰, and 3.7/11.4 ‰ – were used for normalization of the δ scale. Scale contraction factors were obtained with the linear regression between measured and known values of δ15N and δ18O. Although the three standards cover a wide range of isotopic composition in δ15N and δ18O, they do not have an isotopic anomaly in 17O. For the δ17O scale, MDF fractionation slope (0.52) is assumed for two of these laboratory-prepared nitrite standards (see Appendix A for more details). Accuracy of this analytical method on δ17O, δ18O, and δ15N measurements was estimated as the standard deviation (σ) of the residuals between our measurements of the RSIL standards and their expected values. Additionally, isotopic integrity from denuder's extraction to the analysis by IRMS has been investigated and showed no degradation over several weeks (see Appendix B), confirming that this method is suitable for isotopic analysis of NO2, as first demonstrated by Walters et al. (2018). The uncertainties applied to our measurements of δ15N, δ17O, and δ18O are reported as the propagation error of the measurement uncertainty and the uncertainty resulting from sample storage. Uncertainty on Δ17O is derived from the propagation error of the overall uncertainty on δ17O and δ18O. In our study, average uncertainties on δ15N, δ17O, δ18O, and Δ17O are estimated to be ±0.1 ‰, ±0.8 ‰, ±1.8 ‰, and ±0.3 ‰, respectively (1σ uncertainties).

Atmospheric NO2 was collected at the Université Grenoble Alpes campus site. Located in the eastern Grenoble urban area (690 000 inhabitants), the campus stands between a major transportation route and the Isère river. The city is located at the confluence of three valleys surrounded by mountain chains that influence the atmospheric dynamics and the local air quality. During winter, persistent temperature inversions combined with intense domestic heating can lead to severe PM10 pollution events (Largeron and Staquet, 2016) with daily-average mixing ratio above World Health Organization thresholds. In summer, emissions are mainly controlled by road traffic that can result in heightened ozone mixing ratios, especially during stagnant conditions.

Samplings were conducted on a platform 5 m above the ground surface. Ambient air was drawn through the cartridge with a Millipore vacuum pump at a flow rate of 10 L min-1 (room temperature and one atmospheric pressure) adjusted using a Cole-Palmer^® flowmeter (accuracy ±3 %). In order to capture the daily variability in NO2 isotopic composition, samples were collected during 24 h with 3 h sampling intervals during the day and 5 h sampling from midnight to 05:00 local time (LT)​​​​​​​. Ambient NO and NO2 mixing ratios were measured with a 2B Technologies^® NO monitor (model 410) paired with a NO2 converter (model 401).

Honeycomb denuders were cleaned and coated the day before sampling. After being generously rinsed (5 min under a stream of deionized water), the denuders were placed in a vacuum chamber (Thermo Scientific^® refrigerated vapour trap paired with a SpeedVac concentrator) and dried at 40 ∘C during 1 h. Then, denuder's internal walls were individually coated with 10 mL of a 95 : 5 by volume mixture of 2.5 M KOH (in methanol) and ultrapure guaiacol prepared daily. Denuders were then drawn off, dried in the vacuum chamber at 40 ∘C during 30 min to minimize blanks, hermetically sealed, and stored at ambient temperature in the dark until usage. The different components of the cartridge (impactor, filters, denuders) were cleaned, dried, and fitted together just before use. At the end of the sampling period, both denuders were removed from the ChemComb cartridge and rinsed with 10 mL of deionized water in order to leach trapped NO2 out. A volume of 1 mL of the eluent was rapidly used to determine the nitrite amount using the Griess–Saltzman reaction and UV–Vis spectrometry at 544 nm. Recovered eluent (≈ 7 mL by denuder) was poured into a labelled 15 mL Corning^® tube and stored in a freezer until isotopic analysis the following days.

Figure 2 shows the time evolution of the hourly NO2, NO, and O3 mixing ratios measured during the period covering two nights and 1 d (from 14 May 2019 21:00 LT to 16 May 2019 05:00 LT). Note that most of our NO measurements are found to be within the reported detection limit of the instrument except in the morning (see Table 1) and therefore have to be treated with a lot of caution. NO2 mixing ratios during the sampling period ((6.1 ± 4.2) nmol mol-1; mean ± 1 standard deviation) are in good agreement with the range of values measured at the local air quality site located a kilometre south of the sampling site (https://www.atmo-auvergnerhonealpes.fr/, last access: 18 August 2020).

During both nights, most of the NOx is in the form of NO2. After sunrise, there is a rapid interconversion between NO and NO2, driven by NO2 photolysis and reactions of NO with O3 and peroxy radicals (Jacob, 1999). NO2 levels are at a maximum on 15 May between 04:00 and 10:00 LT with a sharp peak of 21 nmol mol-1 at 08:00 LT. After the morning rise, NO2 decreases to reach a background mixing ratio of about (3.0 ± 0.5) nmol mol-1. This diurnal variation is common in urban/suburban sites characterized by a morning peak caused by important NOx emissions, mainly from road traffic (Mayer, 1999). As morning progresses, the boundary layer height increases rapidly, favouring fast dilution of NOx mixing ratios. Moreover, during the day, NO2 is converted to HNO3, notably by its reaction with OH radicals. Thus, NOx mixing ratio remains low during the day likely because of the combination of atmospheric dilution by vertical mixing and efficient chemical conversion by OH and organic radicals (Tie et al., 2007). In dense urban areas, a second NOx traffic emission peak can occur in late afternoon, but it is not observed at our sampling site for that specific day. This surface pollution peak is usually weaker than the morning peak due to an elevated boundary layer and a longer period of evening commuting. After sunset, NO2 mixing ratio increases gently and reaches a smooth peak with a maximum of 12 nmol mol-1 around 01:00 LT, also recorded at the local air quality site. This NO2 mixing ratio rise may be due to low NO emissions (converted to NO2 by reaction with O3) combined with a decreasing boundary layer height during the night which traps atmospheric species close to the surface (Tie et al., 2007; Villena et al., 2011).

Ozone also exhibits a diurnal variation typical of urban areas (Velasco et al., 2008). O3 peaks around 50 nmol mol-1 at the beginning of both nights and then declines continuously. Indeed, after sunset, O3 production ceases, and its mixing ratio drops due to its dry deposition, reactions with organics, and O3 titration by NO emitted from evening traffic, and industrial activities in the stable nocturnal boundary layer (Klein et al., 2019). O3 reaches a minimum (about 15 nmol mol-1) not at the end of the night but during the morning rush hour peak of NO. The Ox (= O3 + NO2) is a more conservative quantity than O3, because it is less affected by conversion of O3 into NO2 through NO titration which is important in urban environments (Kleinman et al., 2002). For instance, between 06:00 and 08:00 LT, O3 is strongly titrated by freshly emitted NO with its mixing ratio dropping to about 15 nmol mol-1, while Ox reaches a moderate minimum of 34 nmol mol-1. After this morning drop, O3 recovers rapidly to about 46 nmol mol-1 in the late morning, possibly caused by downward O3 flux associated with the formation of the daytime thick boundary layer (Jin and Demerjian, 1993; Klein et al., 2019). During the rest of the day, O3 and Ox keep increasing gently due to photochemical production and reach a close maximum at the end of the afternoon (Geng et al., 2008). After sunset, the important decline of both O3 and Ox highlights the physical losses, notably O3 deposition, and chemical loss of NOx, typical of urban areas.

We present the data for the multi-isotopic composition of seven atmospheric NO2 samples, while two additional samples were rejected as NO2- amounts were too low to perform a reliable analysis. Table 1 reports ambient mean mixing ratios of NO, NO2, and O3 for the isotopic sampling intervals and corresponding measured NO2 isotopic composition (δ15N(NO2), δ18O(NO2), and Δ17O(NO2)). Figure 3 depicts the time series of measured δ15N, δ18O, and Δ17O of atmospheric NO2. The temporal evolution of NO2 oxygen and nitrogen isotopic composition is interpreted in the following section.

The time evolution of δ18O of atmospheric NO2 (δ18O(NO2)) shown in Fig. 3 exhibits a substantial diurnal variation with a daytime mean of (93.4 ± 13.9) ‰ and a nighttime mean of (68.9 ± 9.5) ‰. A maximum value of 114.5 ‰ is observed in the morning (09:00–12:00 LT interval) and a minimum value of 62.2 ‰ for the late-night interval (00:00–05:00 LT). Using a similar sampling apparatus during summer in the urban/suburban site of West Lafayette, USA, Walters et al. (2018) reported daytime and nighttime mean δ18O(NO2) values of (86.5 ± 14.1) ‰ and (56.3 ± 7.1) ‰, respectively. Although our daytime values are higher than those of Walters et al. (2018), both datasets exhibit the same day–night contrast with a maximum during the day and a minimum at night. As expected from δ18O values, Δ17O(NO2) follows a similar diurnal variation with a maximum value of 39.2 ‰ for the 09:00–12:00 LT interval and a minimum value of 20.5 ‰ for the 00:00–05:00 LT interval. High Δ17O values are expected to reflect the importance of ozone in the oxidation of NO to NO2. Since daytime and nighttime chemistries are radically different, interpretations of our Δ17O measurements and their implications are discussed separately by day and night.

Measured δ15N(NO2) values range from -11.8 ‰ to -4.9 ‰ with no clear diurnal variation and values clustering around an overall mean of (-10.2 ± 2.2) ‰ (see Fig. 3). Using a similar method, Walters et al. (2018) collected atmospheric NO2 over 1 month in a urban/suburban location during the summer. They reported a mean δ15N value of (-11.4 ± 6.9) ‰, very close to our mean value but with a wider overall range (from -31.4 ‰ to +0.4 ‰). In another urban area but using passive samplers, Dahal and Hastings (2016) reported mean δ15N(NO2) values of (-8.3 ± 0.9) ‰ and (-6.4 ± 1.4) ‰ for summer and winter periods, respectively. All these values are within the δ15N range for NO emitted by industrial combustion and traffic sources which are reported to vary from -19.7 ‰ to -13.7 ‰ and from -9 ‰ to -2 ‰, respectively (Miller et al., 2017; Walters et al., 2015). Interestingly, all the δ15N values measured at our sampling site fall within a narrow range, from about -12 ‰ to -10 ‰, except for the sample collected between 06:00 and 09:00 LT which has a much higher value of -4.9 ‰. This singular value is well correlated with the morning NO traffic emission spike (see Fig. 2). However, once emitted into the atmosphere, NO can undergo isotopic fractionations that modify the nitrogen isotope distribution in NO2 relative to emitted NO (Freyer et al., 1993). In order to use δ15N(NO2) as a tracer of NOx sources, we need to quantify these nitrogen isotopic shifts to correct measured δ15N(NO2). Nitrogen isotopic fractionation, defined as Δ(NO2-NOx) = δ15N(NO2)-δ15N(NOx), is the result of a combination of three effects: (1) an equilibrium isotope effect (EIE) between NO and NO2, (2) a kinetic isotope effect (KIE) during NO oxidation to NO2, and (3) a photochemical isotope fractionation effect (PHIFE) during NO2 photolysis (other NO2 sinks are negligible during the day). The overall daytime nitrogen isotopic shift of NO2 relative to emitted NOx (Δday(NO2-NOx)) can be estimated using the steady-state isotopic mass balance for NO2. Li et al. (2020) derived an expression for Δ(NO2-NOx) by assuming that the conversion of NO to NO2 is solely driven by O3. This could therefore lead to uncertainties on the NO2 shift when other conversion pathways become significant with respect to the NO conversion by O3. A more general expression for Δ(NO2-NOx) can be derived by taking into account the conversion of NO to NO2 via other species, notably RO2 (see Eq. C11 in Appendix C). In our urban environment, we only consider the conversion of NO into NO2 via O3 and RO2 during the day. Assuming αKIE(NO+O3)≈αKIE(NO+RO2) (see derivation in Appendix C), Δday(NO2-NOx) can be expressed by 8ΔdayNO2-NOx=αLCIE∗Aday∗+αEIE-1Aday∗+1×1-fNO2, with αLCIE∗=αKIE(NO+O3)-αPHIFE and Aday∗=JNO2kNO+NO2[NO]=kNO+O3[O3]+kNO+RO2[RO2]kNO+NO2[NO2], where fNO2=[NO2]/[NOx], αLCIE∗ is the fractionation factor of combined KIE and PHIFE (LCIE represents the Leighton cycle isotope effect), and αEIE is the EIE fractionation factor. Aday∗ is defined as the ratio of the NO2 lifetime with respect to isotopic exchanges over the daytime NO2 chemistry lifetime. JNO2 is the NO2 photolysis rate, kNO+O3 is the rate constant of reaction NO + O3, kNO+RO2 is the rate constant of reaction NO + RO2, and kNO+NO2 is the rate constant of the isotopic exchange (Reaction CR1) (see Appendix D for rate constants data). Interestingly, we can combine Eqs. (8) and (6) and express Aday∗ as a function of oxygen isotopic variables discussed in the previous section: 9Aday∗=kNO+O3O3kNO+NO2NO2Δ17ONO+O3NO2Δ17OdayNO2. Since our NO measurements are not precise, and we do not have direct measurements of JNO2 or RO2, we use Eq. (9) to estimate the NO2 isotopic fractionation shift. Note that although Li et al. (2020) only consider the NO conversion via O3 in the analysis of their nitrogen isotopic data, they found an excellent agreement between their calculated values and field isotopic measurements at Jülich, Germany (Freyer et al., 1993). Nonetheless, the reason for this accordance remains unclear, as it could be attributable to an equivalent KIE of NO + O3 and NO + RO2 but also to the dominance of the NO oxidation via O3 over RO2.

At night, the isotopic fractionation shift Δnight(NO2-NOx) is driven by EIE, KIE, the N isotopic composition of NO emissions and fNO2, given that JNO2 is null (see derivation in Appendix C): 10ΔnightNO2-NOx≈Anight∗αKIE-1+δ15NNOemis1+δ15NNO2+αEIE-1Anight∗+11-fNO2, where δ15N(NOemis) is the N isotopic composition of NO emissions, and 11Anight∗=kNO+O3O3kNO+NO2NO2=E(NO)kNO+NO2NONO2, with E(NO) the NO emission flux. From laboratory experiments, Li et al. (2020) reported fractionation factors of 1.0289 ± 0.0019 and 0.990 ± 0.005 for αEIE and αLCIE∗, respectively. Using these experimental values and the ambient mixing ratios of ozone, NO, and NO2 measured at our sampling site, we estimate the time evolution of Δ(NO2-NOx) from Eqs. (8) and (9) for daytime. At night, [NO] ≪ [NO2]; hence, fNO2 tends towards 1 and Δnight(NO2-NOx)≈0 (Table 3 provides the calculated values). Δ(NO2-NOx) values are found to be negligible during the entire sampling period except between 06:00 and 09:00 LT with a mean Δ(NO2-NOx) value of 2.7 ‰ due to lower fNO2 and Aday∗ values. Overall, in our moderately polluted environment, nitrogen oxide isotope effects appear to induce very small nitrogen isotopic shift, reflecting the fact that NOx is overwhelmingly under the form of NO2 (mean fNO2 = 0.93). Our results are in good agreement with the Δ(NO2-NOx) range (between 1.3 and 2.5 ‰) calculated from isotopic measurements at West Lafayette, USA (Walters et al., 2018). Moreover, Li et al. (2020) calculated a mean Δ(NO2-NOx) of (1.3 ± 3.2) ‰ from isotopic measurements near San Diego, USA (NOx mixing ratios varied from 1 to 9 nmol mol-1).

Using estimated δ15N(NOx), we evaluate the relative contributions of the dominant NOx sources at our site using the Bayesian isotopic mixing model SIAR (Stable Isotope Analysis in R; Parnell et al., 2010). Initially developed for ecological studies (Inger et al., 2006; Samelius et al., 2007), isotopic mixing models have been recently used for atmospheric applications, notably to identify major NOx sources of aerosol nitrate from δ15N (Jin et al., 2021; Zong et al., 2017; Fan et al., 2019). Using as inputs not only isotopic measurements but also their uncertainties, the SIAR model can be used to calculate potential NOx source solutions as probability distributions. A recent emission inventory of NOx in the Grenoble urban area estimated that, in 2016, 52 % of emitted NOx could be attributed to transport, 26 % to industries, 20 % to the residential/tertiary sectors, and 2 % to agriculture (Topin et al., 2019). Looking at the type of energy consumed by each sector, we estimate that at this time of the year, our sampling site was mostly influenced by fossil-fuel combustion NOx sources, mainly gasoline/diesel and natural gas, and by biogenic NOx sources (soils emissions). As shown by previous studies, δ15N of NOx emitted by vehicle exhausts depends on the fuel type, the reduction emission technology, and the vehicle run time with values ranging from -21 ‰ to -2 ‰ (Walters et al., 2015). As 90 % of traffic-related NOx is emitted by diesel-powered engines in the Grenoble urban area (Atmo-Auvergne-Rhônes-Alpes, 2018), we use a value of (-4.7 ± 1.7) ‰, representative of the U.S. vehicle fleet (Miller et al., 2017) for which about 80 % of its traffic-NOx emissions originate from diesel vehicles (Dallmann et al., 2013). For δ15N of NOx emitted by natural gas combustion, we use a value of (-16.5 ± 1.7) ‰ which is the average isotopic signature of natural-gas-burning power plants and residential furnace exhausts (Walters et al., 2015). Despite the large range of δ15N values for biogenic NOx (from -59.8 % to -19.9 %) (Li and Wang, 2008; Yu and Elliott, 2017; Walters et al., 2015), these values are still very distinct from δ15N of fossil-fuel combustion NOx, making possible to roughly estimate the relative contributions of different NOx sources at our sampling site. We use a soil–NOx δ15N value of (-33.8 ± 12.2) ‰ (Zong et al., 2017), which is the average of values taken from several studies on NOx emitted by natural and fertilized soil (Felix and Elliott, 2014; Li and Wang, 2008). Over our sampling period, the SIAR model results indicate traffic as the dominant NOx emission source with a mean relative contribution of (57 ± 8) % (see Fig. 5). Natural gas combustion is found to be the second main NOx emission source ((36 ± 12) %) before soil emissions which account for only (7 ± 5) %. The limited nature of our measurement dataset (only 1 d of sampling) prevents us from drawing any general and robust conclusions on the relative contributions of NOx emissions at our site. Nonetheless, we note that the SIAR overall source apportionment is in close agreement with the Grenoble urban area emission inventory concerning traffic emissions (52 % in 2016), lending some support to the idea that δ15N of NO2 is a reliable tracer of NOx emission sources after correction for LCIE and EIE.