Important contributions of non-fossil fuel nitrogen oxides emissions

Since the industrial revolution, it has been assumed that fossil-fuel combustions dominate increasing nitrogen oxide (NOx) emissions. However, it remains uncertain to the actual contribution of the non-fossil fuel NOx to total NOx emissions. Natural N isotopes of NO3− in precipitation (δ15Nw-NO3−) have been widely employed for tracing atmospheric NOx sources. Here, we compiled global δ15Nw-NO3− observations to evaluate the relative importance of fossil and non-fossil fuel NOx emissions. We found that regional differences in human activities directly influenced spatial-temporal patterns of δ15Nw-NO3− variations. Further, isotope mass-balance and bottom-up calculations suggest that the non-fossil fuel NOx accounts for 55 ± 7% of total NOx emissions, reaching up to 21.6 ± 16.6Mt yr−1 in East Asia, 7.4 ± 5.5Mt yr−1 in Europe, and 21.8 ± 18.5Mt yr−1 in North America, respectively. These results reveal the importance of non-fossil fuel NOx emissions and provide direct evidence for making strategies on mitigating atmospheric NOx pollution. This study investigates in the importance of non-fossil fuel NOx emissions in the surface-earth-nitrogen cycle. The study shows how changes of regional human activities directly influence δ15N signatures of deposited NOx to terrestrial environments and that emissions have largely been underestimated.

O ver past decades, both concentrations and deposition fluxes of nitrogen oxides (NO x ), nitric acid (HNO 3 ), and nitrate (NO 3 − ) in the atmosphere have been remarkably elevated in many regions of the world [1][2][3][4] . This has caused negative effects on the environmental quality (e.g., haze, eutrophication), human health (e.g., respiratory and cardiovascular diseases, acute bronchitis), and the structure and functions of ecosystems (e.g., soil acidification, biodiversity losses) 5,6 . Gaseous NO x , the sum of N oxide (NO) and N dioxide (NO 2 ), is the precursor of atmospherically deposited NO 3 − 7,8 and mainly emitted from fossil fuel combustion (primarily via coal combustion and vehicle exhausts) and non-fossil fuel sources including biomass burning, microbial N cycles in soils and animal wastes 9 . Accurate differentiation of NO x emissions from fossil-fuel and non-fossil emission sectors is pivotal for regulatory action to mitigate emissions, budget NO 3 − deposition fluxes, and model ecological and climatic effects of atmospheric NO 3 − loading.
It is feasible to estimate fossil fuel NO x emissions according to known consumption amounts of fossil fuels and their NO x emission factors [10][11][12] . More often, fossil fuel NO x emissions in many countries have been recorded in national statistics yearbooks and emission inventories 2,[12][13][14][15] . Since the 1990s, fossil fuel NO x emissions have accounted for 95% of global NO x emissions 11 , 90% of NO x emissions in Europe 2 , 88% of NO x emissions in East Asia 10 , and 96% of NO x emissions in North America 14,15 . In contrast, the importance and amount of non-fossil fuel NO x emissions remain unclear due to the difficulties in obtaining their emission factors and amounts. Particularly, it is almost impossible to budget NO x emission amounts from diverse biomass burnings and microbial N cycles that occur in different solid-and liquidphase substrates [16][17][18] . In many cases, data of emission factors and estimates of emission budgets were rather incomplete and even unrecorded for non-fossil fuel NO x .
However, according to the simulation results of atmospheric chemical transport and terrestrial ecosystem models, biomass burning and soil emissions account for about 20% and 22% of global NO x emissions, respectively [19][20][21] . The combination of a bottom-up spatial model and top-down airborne observations of atmospheric NO x concentrations through satellite imagery pointed to a significant and overlooked NO x emission from cropland soils, which constitutes 20-51% of the total NO x budget at the regional scale 22 . Recently, natural stable N isotopes (expressed as δ 15 N, δ 15 N = ( 15 N/ 14 N) sample /( 15 N/ 14 N) standard −1, where atmospheric N 2 is used as the internationally recognized N isotopic standard) have been widely employed for tracking NO x emissions 7,23-25 . Isotopic investigations have demonstrated that NO x from biomass burning and microbial N cycle may account for more than 40% of NO 3 − in particulates and precipitation collected in urban sites of China 26,27 . In summary, we argue that the importance of non-fossil fuel NO x is still an open question.
NO is the most initial form of fossil fuel and non-fossil fuel NO x emissions, but NO is normally insoluble and will be rapidly oxidized to NO 2 in the atmosphere, forming the photochemical NO x cycle 28 . The mixing of fossil fuel and non-fossil fuel NO x emissions forms the initial NO x pool in the atmosphere (i-NO x ) ( Supplementary Fig. 1). In reality, it is extremely difficult if not impossible to directly measure the i-NO x pool due to instantaneous emissions and oxidations. However, the δ 15 N of the i-NO x (i.e., δ 15 N i-NOx ) is a straightforward parameter to integrate initial NO x emissions and thus to differentiate relative contributions between fossil and non-fossil fuel NO x emissions 26,27 . In the atmosphere, the i-NO x is partially oxidized to HNO 3 and particulate NO 3 − (p-NO 3 − ) ( Supplementary Fig. 1), during which N isotopic fractionations 29,30 lead to substantial δ 15 N differences between ambient NO x , HNO 3 , and p-NO 3 − . Because of the difficulty in constraining δ 15 N differences among these species, it remains a big challenge to evaluate i-NO x sources based on δ 15 N signatures of ambient NO x , HNO 3 , and p-NO 3 − . However, precipitation can scavenge both the ambient NO 2 and the oxidized NO 2 (i.e., HNO 3 and p-NO 3 − ) (Supplementary Fig. 1) 31 . Therefore, we can reconstruct the corresponding δ 15 N i-NOx values of the observed δ 15 N w-NO3− values ( Supplementary Figs. 1, 2). Assuming that the estimated δ 15 N i-NOx value represents and integrates the emission δ 15 N i-NOx value, we can differentiate relative contributions between fossil fuel and non-fossil fuel NO x emissions 7,24,32 .
Based on the above isotope theory, the δ 15 N i-NOx value can be estimated by the following equation (Eq. (1)): where C NO2 , C HNO3 , and C p-NO3− are concentrations of ambient NO 2 , HNO 3 , and p-NO 3 − in the atmosphere, respectively. f NO2 is the fraction of NO 2 in NO x . δ 15  To investigate the importance of non-fossil fuel NO x emissions to total NO x emissions, we compiled available δ 15 N values of NO 3 − in precipitation (denoted as δ 15 N w-NO3− hereafter) at urban and non-urban sites of East Asia, Europe, and North America (detailed in "Methods") ( Fig. 1). Both the concentrations and δ 15 N values of ambient NO x , HNO 3 , and p-NO 3 − were used to constrain the δ 15 N values of the initial mixture of fossil fuel and nonfossil fuel NO x in the atmosphere (denoted as δ 15 N i-NOx , detailed in "Methods") ( Supplementary Fig. 1). Then we evaluated the differences between δ 15 N w-NO3− and δ 15 N i-NOx values (denoted as 15  , we calculated relative contributions of dominant fossil fuel and non-fossil fuel NO x by using a statistical isotope mass-balance model.

Results and discussion
Spatial and temporal variations of δ 15 N w-NO3− values. In general, East Asia has significantly higher δ 15 N w-NO3− values (1.7 ± 5.4‰ at urban sites and 0.3 ± 3.1‰ at non-urban sites) than Europe (0.8 ± 2.6‰ and −1.5 ± 2.6‰, respectively) and North America (−0.5 ± 1.9‰ and −1.9 ± 2.1‰, respectively) ( Fig. 2). This result reflects more influences of the 15 N-enriched NO x from coal combustion (δ 15 N = 13.7 ± 3.9‰; Supplementary Fig. 3) in East Asia than in the other two study regions. Supportively, the amount of coal consumption in East Asia accounted for about 55% of the world's total amount during 1965-2015, even up to about 64% during 1990-2015 ( Supplementary Fig. 4a). Moreover, the NO x from coal combustion has influenced δ 15 N w-NO3− signatures of both urban and non-urban areas in East Asia, so that δ 15 N w-NO3− values did not differ between urban and non-urban sites (Fig. 2). The δ 15 N w-NO3− values are lower at non-urban sites than at urban sites in Europe and North America (Fig. 2), reflecting more influences of the 15 N-depleted NO x from microbial N cycle (δ 15 N = −30.2 ± 6.7‰; Supplementary Fig. 3) at non-urban sites of these two regions than that of East Asia.  However, relative contributions of non-fossil fuel NO x emissions average 49 ± 11% at urban sites and 69 ± 13% at non-urban sites for all three study regions ( Supplementary Fig. 9). By integrating urban and non-urban sites in each region, we found that relative contributions of non-fossil fuel NO x average 57 ± 13% in East Asia, 54 ± 13% in Europe, and 53 ± 13% in North America (Fig. 4a, Supplementary Fig. 9). Based on mean annual emission amounts of NO x from coal combustion and vehicle exhausts (Fig. 4b, Supplementary  Fig. 10) and their annual mean relative contributions to total NO x emissions (Fig. 4a), the mean annual NO x emissions are estimated (detailed in "Methods") at 37.9 ± 16.4Mt yr −1 in East Asia during 2000-2016, 13.7 ± 5.6Mt yr −1 in Europe during 2000-2017, and 41.1 ± 18.8Mt yr −1 in North America during 2000-2015, respectively (Fig. 4b). Then, non-fossil fuel NO x emission has been determined at 21.6 ± 16.6Mt yr −1 in East Asia, 7.4 ± 5.5Mt yr −1 in Europe, and 21.8 ± 18.5Mt yr −1 in North America, respectively (Fig. 4b). These values for regional NO x emissions are valuable because they have long been missing in budgeting NO x deposition and modeling effects of atmospheric NO x loading.
Although we have considered uncertainties, there are still a few factors that remain difficult to quantify in the current stage. First, not all NO x emission sources have been considered in δ 15 N observations, and other sources such as natural gases and oil fuel combustion might be important in a few sites. Second, data heterogeneities in time and space are also a source of uncertainty, as it is almost impossible to measure the parameters used in our calculations simultaneously. Furthermore, the SIAR model only provides possible distributions but not definitive solutions of relative contributions of multiple sources. Therefore, future efforts on constraining these uncertainties will improve natural isotope evidence on global NO x emissions.
Remarks. Our study provides direct isotope evidence on that the changes in regional human activities have distinct influences on δ 15 N signatures of deposited NO x to terrestrial environments.  The δ 15 N w-NO3− values exhibit significant spatiotemporal changes, which can be used to trace anthropogenic N inputs and help us understand decadal δ 15 N variations in materials of surface-earth systems, such as tree rings, sediments, and oceanic biota. Currently, environmental policies in many countries of the study regions mostly aim to mitigate more fossil fuel NO x emissions via technology promotion and energy structure adjustment. However, our study shows that non-fossil fuel NO x emission is equally as important as fossil fuel NO x emission, and it has long been underestimated. Accordingly, the control of nonfossil fuel NO x emissions should be equally considered in the mitigation of NO x pollution. Moreover, regional NO x emissions newly constrained in this study are useful for budgeting NO 3 − deposition fluxes and modeling ecological and climatic effects of atmospheric NO 3 − loading. There are totally 3483 individual δ 15 N w-NO3− data and 222 sampling sites when multiple observations in different sampling years at the same site were counted once only (Fig. 1). There are 56 urban sites, 158 non-urban sites, and eight arctic sites (Fig. 1), in which non-urban sites are mainly situated in rural, mountain, forest, and lake areas. Due to the sparsity of available data before 2000 ( Supplementary Fig. 11), we analyzed δ 15 N w-NO3− data at major urban and nonurban sites in East Asia, Europe, and North America during 2000-2017 to ensure a better site representation and to reduce the uncertainty caused by inconsistency in sampling time (Fig. 1). To describe spatial differences in δ 15 N w-NO3− values between urban and non-urban sites among three regions (totally 214 sites), only site-based mean values during the period of 2000-2017 (totally 169 sites) were used (detailed in Fig. 2). To describe temporal variations of δ 15 N w-NO3− values in urban and non-urban areas of each region, respectively (Fig. 3), we counted observation sites by different sampling years, given that δ 15 N w-NO3− observations at few sites have been conducted in different sampling years. In this way, there were a total of 206 sites during 2000-2017 (detailed in Fig. 3). In addition, 35%, 29%, and 36% of the δ 15 N w-NO3− observations were conducted in warmer, cooler, and the whole year, respectively. The seasonal effects of NO x emissions may not substantially influence the patterns of regional δ 15 N w-NO3− variations.

Methods
Differences between δ 15 N w-NO3− and δ 15 N i-NOx values. NO is normally insoluble in water, and w-NO 3 − is scavenged only from the ambient NO 2 and the oxidized NO x (i.e., HNO 3 and p-NO 3 − ) (Supplementary Fig. 1) 32,38,39 . Moreover, isotopic effects during the NO x cycles lead to differences between δ 15 N NOx and δ 15 N NO2 . Therefore, substantial differences exist between the δ 15 N w-NO3− and δ 15 N i-NOx values in the atmosphere (hereafter denoted as 15 Δ i-NOx→w-NO3− ). In this study, we calculated 15 Δ i-NOx→w-NO3− values by using the following equation (Eq. (2)): To obtain more accurate 15 Table 1.
Because data of f NO2 and δ 15 N NOx are very sparse globally, we used global mean values and considered their SD values into the uncertainty analysis by the Monte Carlo method. Furthermore, because of no significant difference between 15 Δ i-NOx→w-NO3− values obtained in Scenario 1 (2.1 ± 1.7‰) and Scenario 2 (5.7 ± 3.2‰) ( Supplementary Fig. 2), we used a mean value of them (3.9 ± 1.8‰; Supplementary  Fig. 2) in the calculations of source contributions (Eqs. (4) and (5)).
Contributions of dominant fossil fuel and non-fossil fuel NO x sources. Based on δ 15 N w-NO3− , 15 Δ i-NOx→w-NO3− , and δ 15 N values of NO x sources, we estimated relative contributions of dominant fossil fuel and non-fossil fuel NO x sources to total NO x emissions by using the isotope mass-balance method. We considered coal combustion (denoted as S1) and vehicle exhausts (S2) as dominant fossil fuel NO x sources, and biomass burning (S3), and microbial N cycles (S4) as dominant non-fossil fuel NO x sources. The major reasons include: (1) these four sources have been considered as dominant sources of total NO x emissions in studies of both emission inventory and deposition modeling 2,9,11,13-15,19-21 ; (2) they are also the dominant sources influencing δ 15 N variations of NO x and NO 3 − in the atmosphere; 26,27 (3) their mean δ 15 N values of NO x emission sources differ significantly (P < 0.05, Supplementary Fig. 3) and therefore can be used to differentiate their relative contributions. The S1-S4 are considered as dominant NO x sources at urban sites but S2 cannot be considered as a dominant NO x source at non-urban sites. First of all, studies of roadside NO x emissions have evidenced that vehicle exhausts contribute little to atmospheric NO x at non-urban sites due to limited amounts of long-range transport [40][41][42] . Statistical data also show 76%, 82%, and 78% of vehicles distributed in urban areas of East Asia, North America, and Europe, respectively while their urban areas account for only 1.7%, 1.4%, and 16.6% of total land area, respectively (Supplementary Tables 2, 3, Supplementary Fig. 12). Secondly, 76% and 91% of δ 15 N w-NO3− values at urban and non-urban sites fall in the δ 15 N range of NO x from vehicle exhausts (Supplementary Figs. 3, 13). Consequently, when the NO x from vehicle exhausts is considered into the calculations of relative contributions of different NO x sources at non-urban sites, its contributions at non-urban sites (25 ± 12%) are similar to urban sites (28 ± 8%), which is unlikely. Besides, because mutual NO x transportations always occur between urban and non-urban areas, δ 15 N values of NO 3 − in precipitation at a given urban or non-urban site integrate δ 15 N values of NO x from both local emissions and regional transportations. However, physical NO x transportation might have no substantial isotope effects, and thus likely will not influence the site-specific evaluations of fossil and nonfossil fuel NO x contributions.
The f S1 , f S2 , f S3 , and f S4 values were calculated by using a Bayesian isotope-mixing model (named Stable Isotope Analysis in R, SIAR). The SIAR model 43 uses a Bayesian framework to establish a logical prior distribution based on Dirichlet distribution 44 for estimating source contributions (f S1 -f S4 ). It has the potential to provide reliable estimations of source contributions because the isotope effect (i.e., 15 Δ i-NOx→w-NO3− values in this study), the variability in δ 15 N values of both sources (i.e., δ 15 N values of NO x from S1-S4 in this study), and the mixture (i.e., δ 15 N w-NO3− values in this study) 45,46 are considered. The SIAR model has been widely used to quantify the relative contributions of multiple NO x emission sources to p-NO 3 − and w-NO 3 −26,27,31,47 . In each run of the SIAR model, the mean ± SD of δ 15 N NOx values ( Supplementary  Fig. 3), the mean ± SD of 15 Δ w-NO3−→i-NOx values ( Supplementary Fig. 2), and replicate δ 15 N w-NO3− values at each urban or non-urban site in each sampling year (Fig. 3) were input into the model. In addition, the percentage data of each source (n = 10,000) output from each run of the SIAR model were used to calculate mean ± SD values of corresponding source contributions ( Supplementary Figs. 5-8).
We calculated the total contribution of each NO x source in each region (F; Eq. (6)) by using its annual mean relative contributions at urban and non-urban sites during 2000-2017 (n = 28, 9, 13 for urban sites and n = 47, 21, 88 for non-urban sites in East Asia, Europe, and North America, respectively) (f urban and f non-urban , respectively; Supplementary Fig. 9) and annual mean proportions of urban and non-urban populations in the total population of each region during 2000-2017 (P urban and P nonurban , respectively; Supplementary Fig. 14).
Then, we calculated annual mean relative contributions of dominant fossil fuel and non-fossil fuel NO x sources in each region (F fossil and F non-fossil , respectively) by using Eq. (7) and Eq. (8), respectively.
Finally, based on the annual mean amounts of fossil fuel NO x emissions (A fossil ) in  (Fig. 4b, Supplementary Fig. 10), the annual mean amounts of total NO x emissions (A total ) and non-fossil fuel NO x emissions (A nonfossil ) in each region during 2000-2017 were calculated by using Eq. (9) and Eq. (10), respectively: We estimated the SD values of calculated values in Eqs. (6)-(10) and finally propagated into the uncertainties of the A non-fossil values by using the Monte Carlo method.
Statistical analyses. The one-way analyses of variance (Fig. 2) and Pearson correlation analyses (Fig. 3) were performed by using the Origin 2016 statistical package (OriginLab Corporation, USA) and SPSS 16.0 statistical package (SPSS Inc., Chicago, IL). Because of regionally limiting observation sites and inherently high variability of δ 15 N w-NO3− , spatial differences are significant only at the level of P < 0.1 (Fig. 2). Mean values and standard deviation (SD) were reported.

Data availability
The data underlying the findings of this study are available in this article. Source data are provided with this paper.