The EPA trace pollutant emission model SMOKE (Sparse Matrix Operator Kernel Emissions) was used to simulate 14NOx and 15NOx emissions. 14NOx emissions were estimated using the SMOKE model based on the 2002 NEI (National Emission Inventory; United States Environmental Protection Agency, 2014), and 15N emissions were determined using these 14NOx emissions and the corresponding δ15N values of NOx sources from previous research (Table 1). Using the definition of δ15N (‰), 15NOx emitted by each SMOKE processing category (area, biogenic, mobile, and point) was calculated by 215NOxi=14NOxi×15RNOx(i), where 14NOx(i) denotes the NOx emissions for each category (i) obtained from NEI and SMOKE, and 15RNOxi is a 15N emission factor (15NOxi / 14NOxi) calculated by rearranging Eq. (1): 315RNOx(i)=δ15NOx(i)1000+1×0.0036, where δ15NOx(i) is the δ15N value of some NOx source (i= area, biogenic, mobile, and point).

Annual NOx emissions for 2002 were obtained from the NEI at the county level and were converted into hourly emissions on a 12 km × 12 km grid as previously published (Spak et al., 2007). The modeling domain includes latitudes between 37 and 45∘ N and longitudes between 98∘ W and 78∘ W, which fully covers the Midwestern US (Fig. 2, in yellow). SMOKE categorizes NOx emissions into four “processing categories”: biogenic, mobile, point, and area (Table 1). The choice of the 2002 version of NEI is, in part, arbitrary. However, to compare the model-predicted δ15N values with observations, it requires the emission inventory to be relevant to the same timeframe as the δ15N measurements of the NOy. The datasets we compare to the model (discussed below) span from 2002 to 2009; thus the 2002 inventory is more relevant than later inventories (2014 onward). The county-level annual 14NOx emission for the Midwestern US from NEI was converted to the dataset with hourly 14NOx emissions.

In order to investigate the role of mixing in the spatiotemporal distribution of δ15NOx values, CMAQ was used to simulate the meteorological transport effects (advection, eddy diffusion, etc.). In this “emission + transport” scenario, grid-specific δ15NOx values emitted are dispersed as NOx mixes across the regional scale. This dispersion will depend on grid emission strength and mixing vigor and is effectively treating NOx as a conservative tracer. The simulations used the 2002 National Emission Inventory (NEI), as well as 2002 and 2016 meteorological conditions respectively, to explore how meteorological conditions will impact the atmospheric δ15NOx. Simulations covering the full domain and extracted domain were conducted to explore and eliminate potential bias near the domain boundary.

We first examine the spatial heterogeneity of the NOx emission rate for a single time period to illustrate the overall pattern of NOx emission over the domain (Fig. 3). This is because the δ15NOx emission is determined by the fraction of each NOx source (Eq. 6), which in turn is a function of their emission rates. Since our NOx emissions are gridded by SMOKE using the NEI, they are, by definition, correct with respect to the NEI. However, a brief discussion of the salient geographic distribution of NOx emissions and comparisons with other studies is warranted for completeness and as a backdrop for the discussion of NOx fractions and resulting δ15N values. We have arbitrarily chosen to sum the NOx emissions during the April to June time period for this discussion (Fig. 3).

The April to June NOx emissions ranged from less than 0.01 t N d-1 to more than 15 t N d-1, with the seasonal grid average of 0.904 t N d-1. This average agrees well with estimates in previous studies for the United States, which were between 0.81 and 1.02 t N d-1 (Dignon and Hameed, 1989; Farrell et al., 1999; Selden et al., 1999; Xing et al., 2012). Within 75 % of the geographic domain, the NOx emissions are relatively low, ranging from between 0 and 0.5 t N d-1 (Fig. S3). Geographically, these grids are in rural areas some distance away from metropolitan areas and highways (Fig. 3). NOx emissions within about 20 % of the grids are relatively moderate, ranging between 0.5 and 2.0 t N d-1 (Fig. S3). Geographically, these grids are mainly located along major highways and areas with medium population densities (Fig. 3). Urban centers comprise about 5 % of the grids within the geographic domain, and these have high NOx emissions rates, ranging between 2.0 and 15.0 t N d-1 (Fig. S3). The metropolitan area's average is 5.03 t N d-1, which is nearly 14 times the average emission rate over the rest of the grids within the geographic domain (0.37 t N d-1) due to the high vehicle density associated with high population. The highest emission rates are located within large cities as well as the edge of the east coast metropolitan area (Fig. 3). Summing the NOx emissions among the grids that encompass these major midwestern cities yields city-level NOx emission rates that vary from 61.2 t N d-1 (Louisville, KY) to 634.1 t N d-1 (Chicago, IL). These city-level NOx emission rates (Table S4) agree well with estimates derived from the Ozone Monitoring Instrument (Lu et al., 2015). Grids containing power plants are significant NOx hotspots within the geographic domain. These account for less than 1 % of the grids, but the NOx emissions from a single grid that contains a power plant can be as high as 93.4 t N d-1. Geographically, the power plants are mainly located along the Ohio River valley, near other water bodies, and often close to metropolitan areas (Fig. 3). The NOx emission rates of the major power plants within the Midwest simulated by SMOKE (Table S5) match well with the measurement from the Continuous Emission Monitoring System (CEMS) (de Foy et al., 2015; Duncan et al., 2013; Kim et al., 2009). The geographic distribution of grid-level annual NOx emission density in our simulation also agrees with the county-level annual NOx emission density discussed in the 2002 NEI booklet (Fig. S4; United States Environmental Protection Agency, 2018b).

We next examine the spatial heterogeneity of the NOx source fractions (Fig. 4) for the same time period (April to June). The NOx fraction (f) is defined as the amount of NOx from a source category (s) normalized to total NOx (fs= NOx(source) / NOx(total)). The fraction for anthropogenic NOx emission is defined as the amount of NOx from a source category normalized to the sum of NOx emission from anthropogenic sources (fs= NOx(source) / (NOx(total)-NOx(biogenic))) Since the δ15NOx is determined by the NOx emission fractions within each grid, it is important to understand where in the domain these fractions differ and why. The area sources, which mainly consist of off-road vehicles, agriculture production, residential combustion, and industrial processes, which are individually too low in magnitude to report as point sources, are fairly uniform in their distribution across the domain.

The SMOKE simulation shows that the fs varies significantly across the domain. The average area NOx emission fraction (farea) was 0.271 for total NOx emission and 0.290 for anthropogenic NOx emission within the Midwest from April to June. The farea values show a clear spatial variation and range from 0.125 to 0.5 over about 75 % of the grids (Fig. S5). Geographically, the grids with relatively higher farea are in the rural area away from highways, where agriculture is the most common land use classification. In the states of Wisconsin and Missouri, the farea is slightly lower due to the higher fraction of NOx emission from biogenic sources (fbiog). In the states of Pennsylvania and Michigan, the farea is slightly lower due to the higher fraction of NOx emission from mobile sources (fmobile). In addition, the grids with farea greater than 0.75 are mainly located along the Mississippi River and Ohio River, due to wastewater discharge. The fbio shows a clear spatial variation and is highest in the western portion of the domain (Fig. 4). The fbio from April to June is less than 0.5 in more than 90 % of the grids within the geographic domain, with the average of 0.065 (Fig. S5). Geographically, the grids with relatively high fbio are located in the western regions of the Midwest, away from cities and highway where the density of agricultural acreage and natural vegetation is high. Furthermore, the lowest fbio values occur in the megacities and along the highways, which agrees well with the land use related to the biogenic emission. The April to June SMOKE simulation shows fmobile of 0.325 for total NOx emission and 0.347 for anthropogenic NOx emission. The fmobile shows a clear spatial variation, with relatively higher fmobile located in major metropolitan regions and along the highways, where vehicles have the highest density. The value of fmobile within the geographic domain distributes evenly on the histogram (Fig. S5). Based on the SMOKE simulation, the fraction of NOx emission from point sources (fpoint) is 0.339 for total NOx emission and 0.363 for anthropogenic NOx. The fpoint values are obviously highest in grids where the power plants are located, mainly along the Ohio River valley and near other water bodies close to metropolitan areas. The point sources occupy only 4 % of the domain grids, and about one-quarter of the power plants are not on the same grids as highways; thus these grids have a fpoint>0.9 NOx.

Using these NOx emission source fractions, the δ15NOx values were simulated, and the spatial heterogeneity of δ15NOx for a single time period is discussed. The “emission only” simulation of δ15NOx values (at 06:00 UTC on 26 July) ranged from -34.3 ‰ to 14.9 ‰ (Fig. 5a). The majority of the grids have δ15NOx values lower than -16.3 ‰, which is due to biogenic NOx emissions (-34.3‰) in sparsely populated areas where intensive agriculture dominates the land use (Fig. 5a). The δ15NOx values for grids containing big cities mainly ranged between -8.75 ‰ and -5 ‰ due to the higher fraction of NOx emission from on-road vehicles (-2.7‰). Similarly, the δ15NOx values for grids ranging between -8.75 ‰ and -5 ‰ resolve major highways. The highest value of δ15N occurs at the grids, where the coal-fired EGUs (+15‰) and hybrid-fired EGUs are the dominant NOx source (Fig. 5a).

The effect of atmospheric mixing on the δ15NOx spatial distribution was then taken into account by coupling the 15NOx emissions to the meteorology simulation. There are significant differences between δ15NOx values in the emission only (Fig. 5a) and the emission + transport (Fig. 5b) simulations. While emission only δ15N pattern shows biogenic NOx emissions dominating the spatial domain, anthropogenic emissions become dominant over most of the grids in the emission + transport simulations, especially for the grids located around major cities and power plants. In general, as isotopically heavier urban NOx disperses, the grid average increases from -20.2 ‰ under the emission only scenario to -11.5 ‰ under the emission + transport scenario. Similarly, the NOx emitted along major highways is transported to the surrounding grids, so that the atmospheric NOx at the grids around the major highways becomes isotopically heavier relative to the emission only scenario. We define Δδ15Ntransport as the δ15N difference between emission only and emission + transport scenarios. An example of the Δδ15Ntransport effect can be seen in grids encompassing a plume emanating from southern Illinois' Baldwin Energy Complex (marked with a transparent white box in Fig. 5b) that uses subbituminous coal and bituminous coal as its major energy source. The Δδ15Ntransport in the regions is altered as a function of distance away from the EGU. In this time snapshot (06:00 UTC on 26 July), the northeastwards-propagating plume of NOx emission from the EGU creates higher δ15NOx over 135 km away (Fig. 6).

We next examine the temporal heterogeneity of δ15NOx values over the domain for emission only and interpret them in terms of changes in NOx emission fractions as a function of time. The predicted δ15 NOx value for total emissions in the Midwest during each season shows a significant temporal variation (Fig. 7). The δ15NOx ranged from -35 ‰ to 15 ‰, with the annual average over the Midwest at -6.15 ‰. The maps for different seasons show the obvious changes in δ15N values over western regions of the Midwest, going from -15 ‰ to -5 ‰ in the spring to -35 ‰ to -15 ‰ in the summer. In order to qualitatively analyze the changes in δ15NOx among each season, the values over the grids (Fig. 7) were organized into histograms (Fig. S6). The grids with δ15NOx between -35 ‰ and -18 ‰ increase dramatically from less than 10 % during fall (October–December) and winter (January–March) to more than 20 % during spring (April–June) and summer (July–September). The grids with δ15NOx between -18 ‰ and -2 ‰ decrease from around 90 % during fall and winter to around 75 % during spring and summer. The significant temporal variation in the δ15NOx during different seasons can be quantitatively explained by changing fractions of NOx emission from the biogenic source in any grid (Fig. S7) using Eq. (6). Unlike other NOx emission sources, the fraction of NOx emission from biogenic sources changes significantly among each season within the geographic domain, especially over the rural areas (Fig. S7).

To qualitatively analyze the changes in the fraction of NOx emission from biogenic sources among each season, the distributions of the fractions among the same cutoffs as the maps in Fig. S7 were shown in the histograms (Fig. S8). In general, the distribution of the fraction shifts to higher values during spring (April–June) and summer (July–September), indicating the increase of biogenic emissions. During this period, the surface sunlight hours, temperature, and precipitation are relatively higher, and as a result, the canopy coverage of the plants becomes higher, which leads to the increase of the NOx emission from biogenic sources (Pierce, 2001; Vukovich and Pierce, 2002; Schwede et al., 2005; Pouliot and Pierce, 2009; United States Environmental Protection Agency, 2018a). Besides this, the fertilizer application during this period also increases soil NOx emissions (Li and Wang, 2008; Felix and Elliott, 2014). As a result, the distribution of δ15NOx shifts to lower values during these periods (Fig. 7). The percentage of the grids with the fraction of biogenic emission less than 0.125 decreases dramatically from more than 50 % during fall (October–December) and winter (January–March) to less than 35 % during spring (April–June) and summer (July–September). As the NOx emission from biogenic source becomes dominant, the percentage of the grids with δ15NOx between -35 ‰ and -18 ‰ increases, while the percentage of the grids with values between -18 ‰ and -2 ‰ decreases, which sufficiently explains the trends shown in Fig. 7.

The temporal variation in atmospheric δ15NOx is also controlled by the propagation of NOx emissions, which varies seasonally. The temporal heterogeneity of atmospheric δ15NOx under the emission + transport scenario is interpreted in terms of changes in the propagation of NOx emission as a function of time. The predicted seasonal average δ15NOx in the Midwest shows significant variations (Fig. 8). On an annual basis, the emission + transport average δ15NOx value was -6.10 ‰, which is similar to the emission only average range, but the range (-19.2 ‰ to 11.6‰) was narrower due to NOx transport and mixing. The maps for different seasons show the obvious changes in δ15N values over western regions of the Midwest, from -8.75 ‰ to -5 ‰ in fall and winter to -16.25 ‰ to -12.5 ‰ in spring and summer. The spatial heterogeneity of the δ15NOx under the emission + transport scenario (Fig. 8) was compared to that under the emission only scenario (Fig. 7). The difference was defined as Δδ15Ntransport (Fig. S9) and had values that ranged from -21.9 ‰ to 31.2 ‰, with an average of 4.9 ‰. The grids with Δδ15Ntransport between -5 ‰ and 0 ‰ are the urban areas and decrease slightly from about 11 % during fall (October–December) and winter (January–March) to 10 % during spring (April–June) and summer (July–September). The grids with Δδ15Ntransport between 0 ‰ and 5 ‰ are typically in the rural areas that are impacted by the urban NOx emissions and decrease dramatically from more than 50 % during fall and winter to less than 40 % during spring and summer. The grids with Δδ15Ntransport greater than 5 ‰ are in the rural areas obviously impacted by the urban NOx emission and increase dramatically from less than 40 % during fall and winter to more than 50 % during spring and summer. Therefore, the impacts from transport and mixing are more obvious during spring and summer (Fig. S10).

The planetary boundary layer (PBL) height is an effective indicator showing whether the pollutants are under synoptic conditions which are favorable for the dispersion, mixing, and transport after being emitted into the atmosphere (Oke, 2002; Shu et al., 2017; Liao et al., 2018; Miao et al., 2019). Comparing the distributions of Δδ15Ntransport values (Fig. S9) with the corresponding PBL height (Fig. S11) for each season, the effects of PBL height on the propagation of the air mass are clearly shown. NOx emitted by power plants is much higher than the emission rates at the surrounding grids and is a hotspot that impacts the δ15N values on the surrounding grids. As PBL increases, the emitted NOx from power plant mixes more effectively with the surrounding grid; thus there are higher δ15NOx values along the power plant plume transect. The PBL height changes significantly among each season within the geographic domain, especially over Minnesota, Wisconsin, and Iowa (Fig. S11). The PBL height over these areas increases from less than 250 m above the ground level to more than 625 m a.g.l., during spring and summer, which creates a more favorable synoptic condition for the dispersion, mixing, and transport of the pollutants after being emitted into the atmosphere. As a result, the difference in δ15N values shifts to higher values, showing the stronger effect of atmospheric processes during spring and summer. In order to qualitatively analyze how PBL height affects the δ15NOx along power plant plumes, the domain average PBL height for each month was plotted against δ15NOx (Fig. 9a). The δ15N values along the power plants' plumes and PBL heights over the domain have the same seasonal trend. Interestingly, the “turning point” of the δ15N values is about 1 month later than the turning point of the PBL heights. The scatter plot (Fig. 9b) shows a strong positive correlation (R2=0.85) between the domain average PBL height and average δ15N value along the power plants' plumes. The positive correlation between PBL height and propagation of air mass, indicated by the evolution of atmospheric δ15NOx in this study, agrees well with the corresponding measurement in megacities in China from previous studies (Shu et al., 2017; Liu et al., 2018; Liao et al., 2018).

The spatial heterogeneity of the δ15NOx using 2016 meteorology input dataset was compared to that using 2002 meteorology (Fig. S13). Overall, the simulated δ15NOx using 2002 meteorology has the similar geographic distribution and seasonal trend as the 2016 simulation. The difference was defined as Δδ15N2002–2016 (Fig. 10) and had values that ranged between -1.25 ‰ and +1.25 ‰ over most of the grids. However, in the western part of the domain, where the biogenic NOx emission is dominant, the more positive Δδ15N2002–2016 values (up to 5 ‰) occur during summer and fall. On the other hand, the more negative Δδ15N2002–2016 values (up to -5 ‰) occur along the power plant plume during the same period. The spatial heterogeneity of Δδ15N2002–2016 indicates how climate change alters the δ15NOx. If we have enough input datasets to generate and compare the seasonal/monthly δ15NOx over the past 20+ years, the impacts of anomalies in each meteorology variables could be explored. For the current dataset, a similar comparison between the δ15NOx and the corresponding PBL height was conducted for the simulation based on 2002 meteorology (Fig. S14) to show how PBL height changes the evolution of δ15NOx. Under the 2002 meteorology, lower PBL height during the winter caused surface δ15NOx values along the power plants' plumes to be lower relative to 2016 meteorology. On the other hand, due to the higher PBL height during spring and summer 2002, the δ15N values decreased through July before ending with relatively higher δ15N values in December. The scatter plot for the simulation based on 2002 meteorology (Fig. S14b) also shows a strong positive correlation between the domain average PBL height and average δ15N value along the power plants' plumes, with R2=0.78. The videos of atmospheric δ15NOx on an hourly basis throughout the years 2002 and 2016 are available on http://www.zenodo.org (last access: 8 December 2021) (10.5281/zenodo.4311986, Fang, 2020b).

Analysis of whether there was a difference between the extracted-domain simulation (Fig. 2) and full-domain simulation was conducted by defining Δδ15Nextracted-full and assessing the bias due to the motion of the air mass across the domain boundary (Fig. S17). The Δδ15Nextracted-full values ranged between -0.25 ‰ and +0.25 ‰ over most of the grids, showing that the difference between the extracted-domain simulation and full-domain simulation of δ15N values is usually trivial. However, near the southern border of the extracted domain, Δδ15Nextracted-full values are close to +0.75 ‰ (fall and winter) and close to +1.00 ‰ (spring and summer), suggesting the extracted domain may be required for accurate δ15NOx simulations

The emission + transport + enhanced NOx loss simulations significantly alter the δ15NOx relative to the “normal deposition” scenarios. Again, the enhanced NOx loss cases are removing NOx at rates similar to those by removal via its conversion into HNO3. Thus, the NOx deposited is ∼ δ15NO3- (assuming no photochemical isotope effects), and the δ15NOx is that in the residual NOx. The impact of enhanced NOx loss on the residual NOx was assessed using Δδ15Nhi-no, the difference between the δ15NOx values under the “enhanced NOx loss” and “no deposition” scenarios. The Δδ15Nhi-no range was ±4 ‰ and was especially obvious downwind of the locations with large emission rates, such as power plants or megacities (Fig. 11). This can be explained in a similar fashion to the no deposition scenarios (Fig. S18a), where the dispersion of the isotopically heavier NOx emission from big cities, major highways, and power plants elevated the δ15NOx values in rural areas, and the dispersion of the isotopically lighter biogenic NOx emission lowered the δ15NOx values in the surrounding grids located in the suburb of major cities (Fig. S18b). When enhanced NOx loss is used, the transport, mixing, and dispersion of local NOx emissions are restricted to a smaller geographical extent (Fig. S18b), leading to different δ15NOx values relative to no deposition. The temporal heterogeneity of Δδ15Nhi-no over the domain was examined and the impact of enhancing deposition rates of NOx on the δ15N of atmospheric NOx was explored on a seasonal basis (Fig. 12). The seasonal Δδ15Nhi-no values range from -3.67 ‰ to 5.34 ‰, with an average of 0.51 ‰. The overall pattern of the Δδ15Nhi-no values shows that due to deposition, the atmospheric NOx became isotopically lighter over the majority of the grids since EGU and vehicle NOx is not being transported as far. Conversely, in grids that contain or surround power plants and big cities, the δ15NOx increases because it is not as effectively mixing with low δ15NOx from nearby grids. The enhanced NOx loss simulation was used as a proxy to present the isotope effects associated with the “pseudo photochemical transformation” of NOx into NOy. The complete isotope effect of tropospheric photochemistry will be addressed in future work, which incorporates 15N into the chemical mechanism of CMAQ for the simulation.

The δ15NOx values of dry deposition (a proxy for δ15NO3-) simulated by CMAQ show similar monthly variations and seasonal trends to SMOKE (Fig. S22). The ranges of δ15NOx values within each month were narrower, compared to the simulation from SMOKE, with a minimum during February (-8.7 ‰ to -4.4 ‰) and a maximum during August (-11.8 ‰ to -4.2 ‰). The seasonal trend shows low δ15NOx values in deposition during summer, with the median around -7.4 ‰ and slightly higher values during winter (median around -6.0 ‰). Therefore, the CMAQ simulation inherits the monthly variations and seasonal trends from SMOKE, while the atmospheric NOx becomes isotopically heavier, after taking atmospheric mixing and transport into account. As mentioned above, most of the NADP sites are located away from big cities and power plants. Thus, the atmospheric mixing and transport led to the isotopically heavier atmospheric NOx.

In order to evaluate the SMOKE/CMAQ simulations of atmospheric δ15NOx, they were compared to two recent studies of δ15NOx. The first comparison was relative to rainwater measurements in West Lafayette, IN, from 9 July to 5 August 2016 (Walters et al., 2018). The measured δ15NOx values ranged from -33.8 ‰ to 0.2 ‰, with a median of -11.2 ± 8.02 ‰. Under the emission + transport + enhanced NOx loss scenario using 2016 meteorology, the simulated δ15NOx mean (-7.9 ± 2.19 ‰) was 3.3 ‰ less negative than the observations, and the range (-15.9 ‰ to -3.7 ‰) was about half that in the observations (Fig. 13, top, Table S7). The predicted δ15NOx was similar regardless of whether 2016 or 2002 meteorology was used but was closer to the measured values compared to the emission only simulations (Fig. 13, top). It is not surprising that the measurements are more negative than the observations because the model does not account for isotope fractionation during the conversion of NOx into NOy. Our previous work has shown that the photochemical isotope effect enriches NOy and depletes NOx (Fang et al., 2021; Walters and Michalski, 2015), and thus the lower measured δ15NOx relative to model is consistent with this isotopic depletion. Our model simulations were also compared to on-road vehicle plume measurement along Midwest highways from 8 to 18 August 2015 (Miller et al., 2017). The box plot also shows more accurate estimation of δ15N after considering the atmospheric mixing with the emission from surrounding grids (Fig. 13, bottom). Using the emission only scenario, the simulated δ15NOx mean was about 3 ‰ more negative than the observations. The predicted δ15NOx under the emission + transport + enhanced NOx loss scenario for these samples along Midwest highways was closer to the measured values, compared to the emission only simulations, regardless of whether 2016 or 2002 meteorology was used. The modeled values are quite close to the observations, suggesting that the photochemical isotope effect is small for these samples. This is not surprising given they were collected on major highways where NOx concentrations are high and the timescale between collection and emission is small, and thus only a small fraction of emitted NOx would have been converted to NOy, minimizing the photochemical isotope effect.

The 30-fold enhanced NOx loss (see methods) was used to simulate the δ15N value of NO3- deposition (δ15NO3-) that was then compared to observations (Fig. 14). As previously noted, rather than explicitly converting NOx into NOy via the chemical mechanism in CMAQ, which would require writing an isotope-enabled chemical scheme with appropriate rate constants, we amplified NOx deposition as a surrogate. This amplification reduced the NOx lifetime to about 1 d; thus by calculating the δ15NOx in the deposition fraction, as opposed to residual NOx in the atmosphere, we are approximating the δ15NO3- in deposition. The simulated δ15NO3- was compared to NO3- collected at NADP sites within Indiana, Illinois, and Ohio in the year 2002 (Table S4). The NEI 2002 and WRF2002 were used for the SMOKE emission model and CMAQ simulations, respectively. The value of deposition was calculated by δ15NO3-=ΣfNOxhδ15NOxh, where fNOxh is the hourly mole fraction of NOx isotopologue deposited (fNOxh= NOxh / NOxT), and δ15NOxh is the δ15N value of NOx in deposition. The total NOx deposited (NOxT) used to calculate fNOxh was the amount deposited 5 d prior to the sampling date since the NADP deposition collection integrates the week.

The δ15N values of NOx deposition simulated by CMAQ under the emission + transport + enhanced NOx loss scenario at each site were compared with the measurements of δ15N values of NO3 from prior studies (Mase, 2010; Riha, 2013). While the scatter plot shows a moderate positive correlation between observed and simulated δ15NO3-, the simulated value is consistently lighter than the sample δ15NO3- (Fig. 14, top). The magnitude of this negative bias varies among the NADP sites (Fig. S23) and is attributed to isotope fractionation during the conversion NOx into NOy, which enriches NO3- (Fang et al., 2021; Walters and Michalski, 2015). Globally, this enrichment has been estimated at 3.9 ± 1.8 ‰ (Song et al., 2021). But this enrichment is a function of NOx, volatile organic compounds (VOCs), and oxidant loading, as well as temperature and photolysis rate (Fang et al., 2021), and is not expected to be the same at each NADP site. After adjusting the simulated δ15N by raising the values by the average of the difference between sample δ15N and simulated δ15N for each site, the scatter plots of sample δ15N vs. simulated δ15N fit well into the 1 : 1 line (Fig. 14, bottom). The complete 15N-incorporated chemical mechanisms will be explored in a future study.