Filter samples from December 2016 to 2018 were obtained from the US EPA CASTNET program for several sites in the northeastern US, including (from west to east) Connecticut Hill, NY (CTH110; 42.40∘ N, -76.65∘ W; Elevation = 511 m); Abington, CT (ABT147; 41.84∘ N, -72.01∘ W; Elevation = 202 m); and Woodstock, NH (WST109; 43.94∘ N, -71.70∘ W; Elevation = 255 m) (Fig. 1). The CASTNET sites were characterized by their primary land use as forest for CTH110, urban/agricultural for ABT147, and forest for WST109, respectively (CASTNET Site Locations, 2023). CASTNET is a national monitoring program sponsored by the US EPA to assess spatiotemporal trends in pollutant concentrations and atmospheric deposition. The CASTNET monitoring locations have been sited to avoid the influence of major cities, highways, local activities, and point source pollution and are expected to be regionally representative (Clarke et al., 1997).

The CASTNET sampling protocols have been previously described (Baumgardner et al., 2002). The atmospheric samples consist of week-long integrated collections using a three-stage filter pack. The filter pack contains three types of filters in sequence: (1) a Teflon filter (Whatman membrane filter, 47 mm diameter, 1.0 µm pore size) for particulate collection, including pNO3; (2) a nylon filter (before January 2018: Pall Corporation Nylasorb, 47 mm diameter, 1.0 µm pore size; after January 2018: One Measurement Technology Laboratories, 47 mm diameter, 1.0 µm pore size) for acidic gas collections, including HNO3; and (3) two potassium carbonate (K2CO3) impregnated cellulose filters (Whatman 41 Ashless Circle filter) for SO2 collection. The filter pack sampling system is characterized as “open faced”, because a size-selective inlet is not used. The filter packs are prepared and shipped to the field weekly. The filter packs are exchanged at the sampling sites every Tuesday and shipped to the analytical chemistry laboratory for analysis. Blank filter packs are prepared quarterly to evaluate contamination. The filter pack samples are collected at 10 m, and the filter pack flow rate is maintained at 1.50 L min-1 at standard conditions. The filters were extracted and analyzed for concentrations following standardized protocols at the Wood Gainesville, FL, US laboratory. Briefly, the filters were extracted using 25 mL of ultra-high purity water (> 18.2 MΩ), and the Teflon and nylon filter extracts were measured using a micro membrane-suppressed ion chromatography to determine NO3-(aq) concentrations, which were utilized to calculate the concentration of pNO3 and HNO3 in the air (µg m-3) based on the volume of collected air. Following this analysis, the samples were stored in a laboratory at room temperature for up to 2 years until shipment to Brown University.

To determine the stability of the sample extracts during storage and shipment, the filter extracts were re-measured for the total concentrations of nitrate (NO3-(aq)) and nitrite (NO2-(aq)) utilizing standard colorimetric methods (i.e., US EPA Method 353.2) on an automated discrete UV-Vis Analyzer (SmartChem Westco Scientific Instruments, Inc.) once at Brown University. The detection limit was 0.1 and 0.3 µM for NO2-(aq) and NO3-(aq), respectively, and the pooled relative standard deviation of replicate quality control standards was better than 3 %. The nitrate concentrations reported by CASTNET were compared to our measured concentrations and gave a near 1:1 relationship for all sites and both filter types (nylon filter: y=(-0.08±0.03)+(0.99±0.01)x; r=0.994; p<0.01; Teflon filter: y=(0.09±0.03)+(1.04±0.09)x; r=0.997; p<0.01) indicating excellent NO3-(aq) stability in the filter extracts (Fig. 2). Additionally, the mean absolute difference and the mean percent difference between the re-measured and reported NO3-(aq) concentrations were (0.31 ± 0.36 µM; x‾ ± σ) and (10.4 ± 13.3 %), respectively (n=632). Equal volumes of 4-weekly collected filter extracts were combined into approximately monthly aggregates to provide sub-seasonal resolution of nitrogen isotope analysis for HNO3 and pNO3. Samples were combined into month aggregates to meet the typical mass requirements for isotope analysis, requiring 20 nmol for δ(15N) and δ(18O) and 50 nmol for Δ(17O) quantification. For samples where [NO2-] > 0.1 µM, NO2-(aq) was removed using a sulfamic acid treatment (Granger and Sigman, 2009), as it will cause interference when measuring the nitrogen and oxygen isotope ratios of the nitrate (see below). The samples were then frozen until subsequent isotopic analysis.

Nitrogen stable isotopic analysis was conducted for HNO3 and pNO3 from the monthly aggregated filter extracts using the well-established bacterial denitrifier method (Sigman et al., 2001; Casciotti et al., 2002). Briefly, samples were injected into vials containing Pseudomonas aureofaciens, which lacks the N2O reductase enzyme, such that NO3- (and NO2-) are quantitatively converted to nitrous oxide (N2O). The generated N2O was concentrated and purified using an automatic purge and trap system and introduced to a continuous flow isotope ratio mass spectrometer (CF-IRMS; Thermo Scientific Delta V) with a modified gas bench interface at Brown University. Measurement of N2O was conducted at m/z of 44, 45, and 46 to determine δ(15N), and unknowns were corrected relative to internationally recognized nitrate salt reference materials that included USGS34 (δ(15N) = -1.8 ‰), USGS35 (δ(15N) = 2.7 ‰), and IAEA-N3 (δ(15N) = 4.7 ‰) (Böhlke et al., 1993, 2003). We acknowledge that the δ(15N) range of the nitrate reference material is relatively narrow; however, the range of our calibrated unknowns was quite near these values (calibrated unknowns ranged from -10.6 ‰ to 5.8 ‰ and averaged -1.7 ± 3.7 ‰; n=158). Thus, while some of the unknowns will have a calibrated δ(15N) extrapolated from the reference materials, we do not anticipate this to impact our measurement accuracy and precision or the interpretation of the results. Isobaric influences from 17O contributions were corrected based on a separate analysis, in which N2O was thermally decomposed to O2 by passing through a gold tube heated to 770 ∘C. The generated O2 was introduced to a CF-IRMS (Thermo Scientific Delta V) and measured at m/z 32, 33, and 34 for Δ(17O) (defined as Δ(17O) = δ(17O) - 0.52×δ(18O)) determination (Kaiser et al., 2007). This correction resulted in a δ(15N) decrease typically near 1.5 ‰. All isotopic reference materials were diluted to similar concentrations as samples and run intermittently in each batch analysis. The overall standard deviations of isotopic reference materials were σ(δ(15N))=0.2 ‰ (n=13), 0.4 ‰ (n=13), and 0.2 ‰ (n=15) for USGS34, USGS35, and IAEA-N3, respectively.

Air mass back trajectories were computed using the HYSPLIT model and the North American Regional Reanalysis (NARR) 12 km dataset (Stein et al., 2015). The 72 h back trajectories were calculated at 50 m above ground level every other day for each site (CTH110, ABT147 and WST109) across the sample collection period from December 2016 to 2018. The trajectory data were collated with the reported CASTNET concentration data (pNO3, HNO3, and tNO3) at a weekly resolution to link concentration trends to the source regions for nitrate. Using the “openair” program package in R (Carslaw and Ropkins, 2012), geospatial statistical analysis that included back-trajectory clustering and the concentrated weighted trajectory (CWT) algorithm was conducted to determine patterns of transport and major contributing source regions for atmospheric nitrate. The CWT model is a statistical tool that utilizes the air mass residence time analysis to identify emission source regions (Hsu et al., 2003; Salamalikis et al., 2015; Cheng et al., 2013; Dimitriou et al., 2015). For each grid cell, CWT calculates the concentration of a pollutant as the following (Eq. 1): 1cij‾=1∑k=1Nτijk∑k=1Nckτijk, where i and j are the indices of grid, k is the index of trajectory, N is the total number of trajectories used in the analysis, ck is the pollutant concentration measured upon arrival of trajectory k, and tijk is the residence time of trajectory k in grid cell (i,j). A high value of cij¯means that air parcels that pass over the cell (i,j) would, on average, cause a high concentration at the receptor site (Carslaw and Ropkins, 2012).

Monthly anthropogenic NOx emission density estimates were extracted from a recent sector and fuel-based emission inventory to understand how precursor NOx emissions contribute to nitrate concentration and isotope trends (McDuffie et al., 2020). The monthly NOx emissions data were reported in gridded 0.5∘×0.5∘ units divided into 11 anthropogenic sectors: agriculture, energy production, industry, on-road transportation, non-road transportation, combustion-residential, combustion-commercial, combustion-other, shipping, solvents, and waste (note that solvents are not a source of NOx emissions). The combustion sector emissions were further broken down into fuel types (coal, solid biofuel, and liquid fuel), while non-combustion emissions were assigned to a single “process” fuel type. Monthly NOx emission density estimates by sector and fuel-type data were extracted from the nitrate source regions determined from the CWT analysis. The regions were defined using spatial polygons in “R”, which sets latitude and longitude coordinates to retrieve spatially encoded data. Monthly δ(15N, NOx) was modeled based on isotope mass balance using the fraction of NOx emissions by sector and fuel type and previously reported δ(15N, NOx) emission signatures following a previously described method (Eq. 2) (Walters et al., 2015a): 2δ(15N,NOx)=∑i=1nfiδi(15N,NOx), where δi is the emission signature of source and fi is the fraction contributing to the NOx emissions. The considered δ(15N, NOx) emission signatures included grouped agriculture and waste (Miller et al., 2018), on-road transportation (Miller et al., 2017), non-road transportation (Walters et al., 2015a), and shipping (Walters et al., 2015a). Energy production, industry, and combustion were grouped by fuel type as either combustion – coal & solid biofuel (Felix et al., 2012) or combustion – liquid fuel & process (Walters et al., 2015a). The emission inventory only considers anthropogenic NOx emissions such that natural emissions such as lightning and wildfires were not considered. Table 1 summarizes the δ(15N, NOx) emission signatures (Walters et al., 2015a; Miller et al., 2018, 2017; Felix et al., 2012).

The GEOS-Chem global model of atmospheric chemistry (http://www.geos-chem.org, last access: 22 September 2022) was utilized to predict NOx and O3 concentrations in the regions of the various CASTNET sites (Bey et al., 2001; Walker et al., 2012, 2019). The model was utilized to account for δ(15N) isotope fractionation that occurs during chemical reactions. We use version 13.2.1 (http://wiki.seas.harvard.edu/geos-chem/index.php/GEOS-Chem_13.2.1, last access: 22 September 2022) of the model driven by GEOS5-FP assimilated meteorology from the NASA Global Modeling and Assimilation Office (GMAO). A nested grid (0.25∘ latitude × 0.3125∘ longitude horizontal resolution; 25 km) simulation was conducted over the northeastern United States (97–60∘ W; 35–60∘ N) in 2017 and 2018. Boundary conditions were from global simulations performed at 4∘ latitude × 5∘ longitude horizontal resolution for the same years after a one-year initialization. Gas- and aerosol-phase chemistry was simulated using the default “fullchem” mechanism (Bates and Jacob, 2019; Wang et al., 2021). Inorganic gas and aerosol partitioning were conducted using version 2.2 of the ISORROPIA II thermodynamic equilibrium model (Fountoukis and Nenes, 2007). All default anthropogenic emissions were applied, which is primarily version 2.0 of the Community Emissions Data System (Hoesly et al., 2018) as previously implemented (McDuffie et al., 2020). Natural emissions respond to local meteorology and include biogenic volatile organic compounds from terrestrial plants and the ocean (Millet et al., 2010; Guenther et al., 2012; Hu et al., 2015; Breider et al., 2017), NOx from lightning and soil microbial activity (Murray et al., 2012; Hudman et al., 2012), mineral dust (Ridley et al., 2012), and sea salt (Jaeglé et al., 2011; Huang and Jaeglé, 2017). Biomass burning emissions were monthly means from version 4.1s of the Global Fire Emissions Database (GFED4.1s; van der Werf et al., 2017). Wet deposition for water-soluble aerosols is described by Liu et al. (2001) and by Amos et al. (2012) for gases. Dry deposition is based on the resistance-in-series scheme of Wesely and Lesht (1989).

The atmospheric nitrate concentrations (U.S. Environmental Protection Agency Clean Air Markets Division Clean Air Status and Trends Network, 2022) are shown in Fig. 1 and summarized in Table 2. The speciation of tNO3 concentration is important to evaluate due to HNO3 and pNO3 different atmospheric lifetime driven by deposition rates (Benedict et al., 2013). Due to a higher dry deposition rate, HNO3 has a shorter atmospheric lifetime of a few days (i.e., 1–3 d) relative to pNO3, which has a lifetime of several days (i.e., 5 to 15 d). Overall, the mean concentrations of the three examined northeastern US CASTNET sites were significantly different but showed similar seasonal trends. Lower nitrate concentrations at the Woodstock, NH, site compared to the other sites likely reflect the different amounts of NOx emissions and, thus, the amount of nitrate impacting the study sites. For example, the Woodstock, NH, site is relatively remote compared to the urban/agricultural characterization of Abington, CT, and Connecticut Hill, NY, which is directly downwind of the highly industrialized Ohio River valley and other midwestern cities. Across the sites, the annual concentrations of HNO3, pNO3, and tNO3 were significantly higher at Abington, CT, and Connecticut Hill, NY, than at Woodstock, NH (p<0.01). The concentrations were binned by season including winter (DJF), spring (MAM), summer (JJA), and autumn (SON), which indicated seasonal statistical differences at the considered CASTNET sites. The HNO3 concentrations were significantly greater during the winter for Woodstock, NH, than in other seasons (p<0.01). Additionally, HNO3 at Abington, CT, was significantly higher during summer than in autumn (p<0.01). There was no significant seasonal difference in HNO3 concentrations at Connecticut Hill, NY. At all three sites, the concentrations of pNO3 were greatest during the winter and lowest during the summer. These findings were consistent with previous reports of CASTNET samples in the northeastern and midwestern US collected from 2004 to 2005, in which pNO3 concentrations were highest in the winter and lowest in the summer and with little seasonal variation in HNO3 (Elliott et al., 2009). Thus, even as NOx emissions have dramatically decreased in the US by 38 % from 2005–2014 as evidenced from top-down global surface NOx observations (Miyazaki et al., 2017), the HNO3 and pNO3 seasonal trends in the northeast US have been retained.

Clustered air mass back trajectories were calculated for the CASTNET sites (Fig. 3). The annual clustered trajectories indicate that most air masses were associated with westerlies with prevailing winds from the continental US and Canada for all the considered CASTNET sites. The clustered trajectories also indicate the influence of marine/coastal air masses and winds from the northeast. The CWT analysis of tNO3 concentrations indicated that contributing source regions tended to be within approximately 1000 km of the CASTNET sites (Fig. 3). Like the cluster trajectory results, the CWT analysis indicated that the tNO3 source contributing regions tended to extend towards the west and northwest of the CASTNET sites with minimal contributions east of the sites. Similar source regions were identified for the various CASTNET sites, but there were slight spatial differences due to the location of the sites, which likely impacted the nitrate concentration trends observed at the sites. For example, the source regions contributing to CTH110 tended to extend further from the Midwest compared to the other sites, and a higher relative contribution from southeast Canada was identified for the WST109 site.

The measured atmospheric nitrate δ(15N) data are shown in Fig. 4 and summarized in Table 2. The δ(15N) data indicated significant spatial differences but with consistent seasonal patterns for δ(15N, HNO3), δ(15N, pNO3), and δ(15N, tNO3). The δ(15N) values were highest for Abington, CT, second highest for Connecticut Hill, NY, and lowest for Woodstock, NH. Across the sites, there was a consistent offset between δ(15N, HNO3) and δ(15N, pNO3), in which δ(15N, pNO3) tends to have higher values relative to δ(15N, HNO3) that averaged a (3.9 ± 1.8) ‰ (n=79) difference for simultaneously collected samples. This value was in close agreement with the theoretical isotope effect associated with N isotopic equilibrium between NO3- and HNO3, which has been calculated to be 3.2 ‰ at 298 K, favoring the preferential partitioning of 15N into NO3- (Walters and Michalski, 2015a).

Across all sites, δ(15N, HNO3), δ(15N, pNO3), and δ(15N, tNO3) indicated consistent temporal patterns, with the highest values observed during the winter and lowest values during the summer (Fig. 4). These findings were similar to previous δ(15N) measurements from HNO3, pNO3, and precipitation NO3- samples collected in the early 2000s in the midwestern and northeastern US, which also reported a significant spatiotemporal variation (Elliott et al., 2009, 2007). The CTH110 site was previously analyzed for its δ(15N) deltas in the early 2000s (Elliott et al., 2009). Overall, the range of measured δ(15N) at CTH110 was lower in 2017–2018 (δ(15N, HNO3)=-11.1 ‰ to -0.1 ‰; δ(15N, pNO3) = -6.8 ‰ to 4.4 ‰), compared to measurements conducted for 2004–2005 (δ(15N, HNO3) = -5 ‰ to 10 ‰; δ(15N, pNO3) = -1.0 ‰ to 12 ‰) (Elliott et al., 2009). This trend is consistent with an expected decrease in δ(15N) of atmospheric nitrate after implementing NOx reduction technologies on electricity generation units and their subsequent relative decrease in NOx emissions (Felix et al., 2012).

Previous spatiotemporal δ(15N) differences in atmospheric nitrate in the midwestern and northeastern US had been concluded to reflect the importance of precursor emission sources (Elliott et al., 2009, 2007). Specifically, stationary source NOx emissions associated with coal combustion with a high δ(15N, NOx) emission signature were suggested to drive higher δ(15N) values during winter and a longitudinal gradient across the midwestern and northeastern US (Elliott et al., 2009). To test this hypothesis on the current dataset, the monthly predicted NOx emission densities speciated by sector and fuel-specific sources based on the Community Emissions Data System (McDuffie et al., 2020) were extracted for spatial polygons that approximately corresponded to the identified tNO3 source contributing regions from the CWT analysis (Fig. 3). Across all sites, the predicted NOx emission densities (kg m-2 s-1) indicated similar seasonal variability, with a maximum observed during winter from higher residential, commercial, and other combustion emissions due to a significant heating demand (Fig. 5). A local maximum in NOx emission densities (kg m-2 s-1) was also observed during summer due to increased emissions related to electricity generation for cooling (Fig. 5). The absolute NOx emission densities were higher for CTH110 and ABT147 compared to WST109, which may explain the observed nitrate concentration trends with the lowest concentrations observed at WST109 (Fig. 1). Across the sites, the Community Emissions Data System predicts that there were similar annual contributing NOx emission sectors for the identified source regions contributing tNO3 to the study sites (CTH110, ABT147, WST109) that included energy (21.9 %, 22.5 %, 23.5 %), industry (14.4 %, 14.6 %, 14.1 %), non-road transport (17.3 %, 16.2 %, 15.0 %), combustion-residential, commercial, other (12.8 %, 14.2 %, 14.3 %), road (23.9 %, 23.2 %, 23.3 %), shipping (7.5 %, 7.5 %, 8.5 %), and agricultural/waste (2.1 %, 1.7 %, 1.5 %) (Fig. 5). Additionally, there was similar annual NOx emission density contributing fuel types across sites, including biofuel (2.6 %, 2.7 %, 2.7 %), coal (5.8 %, 5.2 %, 4.8 %), liquid-fuel (76.4 %, 75.0 %, 73.9 %), and process-based emissions (15.3 %, 17.2 %, 18.7 %) for the identified source regions contributing to tNO3 at CTH110, ABT147, and WST109, respectively (Fig. 5).

The monthly δ(15N, NOx) was calculated using the NOx emission estimates, assumed emission source values, and isotope mass balance (Fig. 6). Overall, this calculation indicated limited spatial variability with an annual δ(15N, NOx) average of (-11.7 ± 0.1) ‰, (-11.6 ± 0.1) ‰, and (-11.8 ± 0.8) ‰ for ABT147, CTH110, and WST109, respectively. We note that while there were significant differences in modeled NOx emission densities and observed nitrate concentrations at the study site, the relative contributions of NOx emissions contributing to the study sites were nearly identical, leading to similar modeled δ(15N, NOx) values. Thus, NOx emissions were not the main contributor to the observed spatial differences in δ(15N, HNO3, pNO3, tNO3). We note that for each of the monthly δ(15N, NOx) estimations, the propagated uncertainty based on the δ(15N, NOx) emission signature reported uncertainty was approximately ±3.4 ‰ and was not seasonally variable. There was limited seasonality in the modeled δ(15N, NOx) across all sites that was different by no more than 0.3 ‰ in the monthly mean values. The highest modeled mean δ(15N, NOx) values occurred during the summer due to increased emissions from the energy production sector, namely, an increase in coal and solid biofuel combustion, which has an elevated δ(15N, NOx) signature (Table 1) (Felix et al., 2012).

The modeled δ(15N, NOx) was compared with the measured monthly δ(15N, tNO3) to remove the potential δ(15N) phase fractionation between HNO3 and pNO3. Overall, the modeled δ(15N, NOx) was lower than the observed δ(15N, tNO3) values, and the lack of spatiotemporal variability in the modeled δ(15N, NOx) was in direct contrast to the δ(15N, tNO3) values (Fig. 6). This finding suggests that seasonal changes in NOx emission sectors by fuel type did not drive significant seasonal variability in δ(15N, NOx) or δ(15N, tNO3) across the considered CASTNET sites. Previous studies of atmospheric nitrate in the northeastern/midwestern US during the early 2000s found that stationary source NOx emissions, including power plants and industrial processes, were strongly positively correlated with δ(15N, NO3-) (Elliott et al., 2009, 2007), which is inconsistent with our results from a similar region from samples collected 10 years later. This inconsistency may suggest that the dramatic decrease in stationary combustion emissions, particularly from coal combustion, has led to decoupling between NOx emissions and δ(15N) of atmospheric nitrate.

The mismatch between the modeled δ(15N, NOx) and the observed δ(15N, tNO3) did not suggest that there were significant inaccuracies in the NOx emission inventories, such as under-constrained soil emissions and/or not accounting for natural sources of NOx such as lightning. Soil NOx emissions have a characteristic low δ(15N, NOx) emission signature (Miller et al., 2018; Yu and Elliott, 2017), such that underestimation of soil emissions could not explain the observed mismatch as the modeled δ(15N, NOx) was already lower than the observed δ(15N, tNO3). Lightning-generated NOx was also unlikely to explain the model mismatch with observations. Lightning NOx has a reported δ(15N) signature near 0 ‰ (Hoering, 1957), such that to match the modeled δ(15N, NOx) with the observed δ(15N, tNO3) would require a substantial amount of lightning-produced NOx. However, lightning NOx emissions are expected to be several times smaller than NOx emissions from anthropogenic sources (Murray, 2016). Thus, we next considered if the spatiotemporal δ(15N, tNO3) variability observed at the CASTNET sites during 2016–2018 can be explained by δ(15N) isotope fractionation associated with NOx oxidation.

NOx oxidation to atmospheric nitrate has been suggested to induce significant δ(15N) fractionation associated with NOx cycling and the reaction pathways leading to nitrate formation (Walters and Michalski, 2015; Freyer, 1991; Freyer et al., 1993; Walters et al., 2016; Walters and Michalski, 2016b; Fang et al., 2021; Li et al., 2020). We calculated the influence of δ(15N) fractionation associated with NOx cycling on δ(15N, NO2) derived from previous studies as the following (Eq. 3): 3δ(15N,NO2)≈δ(15N,NOx)+15ε(NO2/NO)×(1-f(NO2)), where δ(15N, NOx) represents the modeled emissions (Fig. 6), 15ε(NO2 / NO) is the isotope effect associated with NO conversion to NO2, and f(NO2) represents the amount fraction of NO2 in NOx (i.e., f(NO2) = [NO2] / [NOx]). The 15ε(NO2 / NO) value represents a combination of the NOx equilibrium isotope effect (EIE) and the Leighton cycle isotope effect (LCIE) (Freyer et al., 1993; Walters et al., 2016; Li et al., 2020). Briefly, the EIE between NO and NO2 has been shown to have an isotope effect of (28.9 ± 1.9) ‰ from an experimental investigation under ambient NOx conditions (Li et al., 2020). The effect favors higher δ(15N) values in NO2, which dominates δ(15N, NOx) fractionation during conditions of high NOx concentrations (Freyer et al., 1993; Walters et al., 2016; Li et al., 2020). The LCIE represents a combination of the kinetic isotope effect associated with NO oxidation, primarily driven by reaction with O3, and the isotope effect associated with NO2 photolysis (Walters et al., 2016; Li et al., 2020). The dominant factor in LCIE is likely the NO + O3 fractionation, as the NO2 photolysis isotope effect has been suggested to have a near-negligible fractionation (Fang et al., 2021). Indeed, laboratory investigation of the LCIE suggests an enrichment value of (-10 ± 5) ‰, which is in close agreement with the KIE from ab initio calculations of NO + O3 of -6.7 ‰ at 298 K (Walters and Michalski, 2016a). In contrast to the EIE, the LCIE dominates NOx δ(15N) fractionation during conditions of higher O3 concentrations relative to NOx concentrations (Li et al., 2020).

We have estimated the relative role of EIE and LCIE based on the following (Eq. 4): 415ε(NO2/NO)=fEIE15εEIE+1-fEIE15εLCIE. The fEIE represents the relative rate of NOx EIE to NO oxidation and is calculated as the following (Eq. 5): 5fEIE=k(NOx-EIE)[NO2]k(NO+O3)O3+k(NOx-EIE)[NO2], where k(NOx-EIE) is the reaction rate of NOx EIE with a reported value of 8.14×10-14 cm3 s-1 (Sharma et al., 1970), and k(NO+O3) is the NO + O3 reaction rate of 1.73×10-14 cm3 s-1 (Atkinson et al., 2004).

The value of fEIE was calculated using modeled NO, NO2, and O3 concentrations from GEOS-Chem integrated over the source regions that contributed tNO3 to the CASTNET sites. The modeled O3 and NOx concentrations indicated opposite seasonal trends for all considered source regions: O3 reached a maximum during summer due to increased photochemical activity, while NOx reached a maximum during winter due to lower photolysis frequencies and relatively higher NOx emissions, as expected (Fig. 7). The modeled f(NO2) closely followed the O3 seasonal profile (Fig. 7). The calculated fEIE also followed the NOx seasonal profile with peaks during the winter and ranged from 0.124 to 0.513 across the CASTNET sites (Fig. 7), which is the expected trend as the influence of EIE on δ(15N) fractionation is highest during conditions of higher NOx concentrations relative to O3 (Freyer et al., 1993; Walters et al., 2016; Li et al., 2020). The fEIE averaged 0.255 ± 0.108, 0.271 ± 0.115, and 0.218 ± 0.093 for ABT147, CTH110, and WST109, indicating that δ(15N) fractionation was largely driven by the NO + O3 oxidation rather than by NOx EIE due to the low modeled NOx concentration relative to O3. The calculated 15ε(NO2 / NO) had a similar seasonal profile as fEIE, with peaks during the winter compared with summer, and ranged from -5.2 ‰ to 10.0 ‰ across the CASTNET sites with an average of (0.5 ± 4.5) ‰, (-0.1 ± 4.2) ‰, and (-1.5 ± 3.6) ‰ for CTH110, ABT147, and WST109, respectively (Fig. 7).

The δ(15N, NO2) was then calculated using the monthly calculated 15ε(NO2 / NO), modeled f(NO2), and modeled δ(15N, NOx). Overall, the δ(15N, NO2) ranged from -12.4 ‰ to -10.3 ‰ across the CASTNET sites and averaged (-11.5 ± 0.5) ‰, (-11.7 ± 0.5) ‰, and (-12.0 ± 0.4) ‰ for CTH110, ABT147, and WST109, respectively (Fig. 7). These annual averages were nearly identical to the modeled δ(15N, NOx) values. There was slight seasonal variability in the calculated δ(15N, NO2), with slightly higher values during winter than in summer. However, neither the magnitude of the seasonal variability, which was no more than 1.6 ‰, nor the absolute value of the calculated δ(15N, NO2) agreed with the measured δ(15N, tNO3). Overall, this indicates that δ(15N) fractionation associated with NOx cycling played an insignificant role in explaining the spatiotemporal variabilities observed for δ(15N, tNO3) at the CASTNET sites.

Nitrogen isotope fractionation has also been suggested to occur during reactions leading to HNO3 and/or pNO3 formation (Walters and Michalski, 2015, 2016b; Fang et al., 2021). Assuming atmospheric nitrate formation represents an irreversible reaction in an open system with a constant supply of NOx emissions, we model the δ(15N, tNO3) as the following (Eq. 6): 6δ(15N,tNO3)=δ(15N,NO2)+15ε(tNO3/NO2). The 15ε(tNO3/NO2) corresponds to the enrichment factor associated with converting NO2 to tNO3. We acknowledge there could be potential differences in the formation pathway for the speciated phases of atmospheric nitrate (i.e., HNO3 and pNO3). However, we evaluated nitrate formation from the mass-weighted δ(15N, tNO3) to remove the potential δ(15N) phase fractionation between HNO3 and pNO3, which complicates evaluating the potential phase-dependent formation pathway. We calculated the 15ε(tNO3/NO2) as the difference between the measured δ(15N, tNO3) and the calculated δ(15N, NO2) (Fig. 8). Across all sites, 15εcalc(tNO3/NO2) ranged from 1.6 ‰ to 16.1 ‰, with an average of (8.7 ± 3.8) ‰, (10.9 ± 3.5) ‰, and (6.9 ± 2.9) ‰, for CTH110, ABT147, and WST109. Additionally, the 15εcalc(tNO3/NO2) indicated strong seasonality with higher values during the winter compared to the summer. The shift in the seasonal 15εcalc(tNO3/NO2) was likely attributed to a change in the dominant nitrate formation pathway from NO2 oxidation via hydroxyl radical during the summer to increased N2O5 hydrolysis during the winter, as previously suggested (Li et al., 2021) and in our companion study (Kim et al., 2023).

The two dominant polluted mid-latitude nitrate formation pathways include NO2 oxidation via hydroxyl radical (Reaction R1) and N2O5 hydrolysis (Reaction R2): R1NO2+OH+M⟶HNO3+MR2N2O5+H2O(surface)⟶2HNO3. These reactions have an isotope effect of -3 ‰ based on the reduced masses of the transition complex (Freyer, 1991) and 25.5 ‰ at 300 K based on EIE between NO2 and N2O5 (Walters and Michalski, 2016b) for Reactions (R1) and (R2), respectively, indicating that the range of the 15εcalc(tNO3/NO2) is between these end-member values. We estimated the relative role of Reactions (R1) and (R2) contributing to nitrate formation across the considered CASTNET sites based on the following (Eq. 7): 715εcalc(tNO3/NO2)=f(NO2+OH)×(15ε(NO2+OH)+(1-fNO2+OH)×(15εN2O5,T), assuming that Reactions (R1) and (R2) dominate the observed tNO3 formation, as expected for the polluted mid-latitudes (Alexander et al., 2020) (8): 8fNO2+OH+f(N2O5)=1, where 15εcalc(tNO3/NO2) is our calculated results (Fig. 8); f(NO2+OH) and f(N2O5) correspond to the fractional contribution of Reactions (R1) and (R2), respectively; 15ε(NO2+OH) = -3 ‰ (Freyer, 1991a); and 15ε(N2O5, T)/‰ = -0.163 ⋅T/K + 74.08 for a temperature range of 250 to 305 K (Walters and Michalski, 2016b). We utilized the temperature derived over the source regions contributing to the CASTNET sites from the GEOS-Chem simulations in our calculations, which indicated a range in the monthly temperature of 262.4 to 294.8 K, corresponding to a range in 15ε(N2O5, T): ‰ of 26.4 ‰ to 31.3 ‰. Overall, we estimated f(NO2+OH):f(N2O5) contributed 0.63 ± 0.11:0.37 ± 0.11, 0.56 ± 0.09:0.44 ± 0.09, and 0.69 ± 0.8:0.31 ± 0.08 to CTH110, ABT147, and WST109, respectively (Fig. 8). This calculation suggests that the observed spatial δ(15N) differences at the considered sites were driven by slight differences in nitrate formation and oxidation chemistry. For each of the considered sites, the temporal trends in the oxidation chemistry were similar.

The calculated f(NO2+OH) peaked during the summer, and f(N2O5) peaked during the winter, consistent with expected seasonal atmospheric nitrate formation and model results (Alexander et al., 2020). This seasonality in atmospheric nitrate formation is driven by photochemistry and temperature. The OH is formed via photolysis, so its abundance is greater during the summer, leading to a relative increase in the proportion of atmospheric nitrate formed via NO2+ OH homogeneous reactions. During the nighttime, higher order nitrogen oxides form and new pathways of atmospheric nitrate production become important. Under these conditions, NO2 is oxidized by O3 forming the nitrate (NO3) radical, which exists at thermal equilibrium with NO2 and N2O5, which can subsequently hydrolyze on wetted aerosol surfaces leading to atmospheric nitrate production. N2O5 is photolabile and thermally unstable, so N2O5 heterogeneous reactions on aerosol surfaces are typically most prevalent during the winter (Alexander et al., 2020).

We acknowledge that are uncertainties in our model regarding potential contributions from other nitrate formation pathways and the considered enrichment factors that have not been experimentally determined. Nevertheless, our results highlight that seasonal δ(15N, tNO3) values were driven by nitrate formation based on our current understanding of fractionation patterns.