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# Important contributions of non-fossil fuel nitrogen oxides emissions

## Abstract

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.

## Introduction

Over past decades, both concentrations and deposition fluxes of nitrogen oxides (NOx), nitric acid (HNO3), and nitrate (NO3) in the atmosphere have been remarkably elevated in many regions of the world1,2,3,4. 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 NOx, the sum of N oxide (NO) and N dioxide (NO2), is the precursor of atmospherically deposited NO37,8 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 wastes9. Accurate differentiation of NOx emissions from fossil-fuel and non-fossil emission sectors is pivotal for regulatory action to mitigate emissions, budget NO3 deposition fluxes, and model ecological and climatic effects of atmospheric NO3 loading.

It is feasible to estimate fossil fuel NOx emissions according to known consumption amounts of fossil fuels and their NOx emission factors10,11,12. More often, fossil fuel NOx emissions in many countries have been recorded in national statistics yearbooks and emission inventories2,12,13,14,15. Since the 1990s, fossil fuel NOx emissions have accounted for 95% of global NOx emissions11, 90% of NOx emissions in Europe2, 88% of NOx emissions in East Asia10, and 96% of NOx emissions in North America14,15. In contrast, the importance and amount of non-fossil fuel NOx emissions remain unclear due to the difficulties in obtaining their emission factors and amounts. Particularly, it is almost impossible to budget NOx emission amounts from diverse biomass burnings and microbial N cycles that occur in different solid- and liquid-phase substrates16,17,18. In many cases, data of emission factors and estimates of emission budgets were rather incomplete and even unrecorded for non-fossil fuel NOx.

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 NOx emissions, respectively19,20,21. The combination of a bottom-up spatial model and top-down airborne observations of atmospheric NOx concentrations through satellite imagery pointed to a significant and overlooked NOx emission from cropland soils, which constitutes 20–51% of the total NOx budget at the regional scale22. Recently, natural stable N isotopes (expressed as δ15N, δ15N = (15N/14N)sample/(15N/14N)standard −1, where atmospheric N2 is used as the internationally recognized N isotopic standard) have been widely employed for tracking NOx emissions7,23,24,25. Isotopic investigations have demonstrated that NOx from biomass burning and microbial N cycle may account for more than 40% of NO3 in particulates and precipitation collected in urban sites of China26,27. In summary, we argue that the importance of non-fossil fuel NOx is still an open question.

NO is the most initial form of fossil fuel and non-fossil fuel NOx emissions, but NO is normally insoluble and will be rapidly oxidized to NO2 in the atmosphere, forming the photochemical NOx cycle28. The mixing of fossil fuel and non-fossil fuel NOx emissions forms the initial NOx pool in the atmosphere (i-NOx) (Supplementary Fig. 1). In reality, it is extremely difficult if not impossible to directly measure the i-NOx pool due to instantaneous emissions and oxidations. However, the δ15N of the i-NOx (i.e., δ15Ni-NOx) is a straightforward parameter to integrate initial NOx emissions and thus to differentiate relative contributions between fossil and non-fossil fuel NOx emissions26,27. In the atmosphere, the i-NOx is partially oxidized to HNO3 and particulate NO3 (p-NO3) (Supplementary Fig. 1), during which N isotopic fractionations29,30 lead to substantial δ15N differences between ambient NOx, HNO3, and p-NO3. Because of the difficulty in constraining δ15N differences among these species, it remains a big challenge to evaluate i-NOx sources based on δ15N signatures of ambient NOx, HNO3, and p-NO3. However, precipitation can scavenge both the ambient NO2 and the oxidized NO2 (i.e., HNO3 and p-NO3) (Supplementary Fig. 1)31. Therefore, we can reconstruct the corresponding δ15Ni-NOx values of the observed δ15Nw-NO3− values (Supplementary Figs. 1, 2). Assuming that the estimated δ15Ni-NOx value represents and integrates the emission δ15Ni-NOx value, we can differentiate relative contributions between fossil fuel and non-fossil fuel NOx emissions7,24,32.

Based on the above isotope theory, the δ15Ni-NOx value can be estimated by the following equation (Eq. (1)):

$$\delta ^{15}{\mathrm{N}}_{{\mathrm{i}} - {\mathrm{NOx}}}\\ = (\delta ^{15}{\mathrm{N}}_{{\mathrm{NOx}}} \times {\mathrm{C}}_{{\mathrm{NO2}}}/f_{{\mathrm{NO2}}} + \delta ^{15}{\mathrm{N}}_{{\mathrm{HNO3}}} \times {\mathrm{C}}_{{\mathrm{HNO3}}} + \delta ^{15}N_{{\mathrm{p}} - {\mathrm{NO3}} - } \times {\mathrm{C}}_{{\mathrm{p}} - {\mathrm{NO3}} - }) /\\ \hskip 12pt({\mathrm{C}}_{{\mathrm{NO2}}}/f_{{\mathrm{NO2}}} + {\mathrm{C}}_{{\mathrm{HNO3}}} + {\mathrm{C}}_{{\mathrm{p}} - {\mathrm{NO3}} - }),$$
(1)

where CNO2, CHNO3, and Cp-NO3− are concentrations of ambient NO2, HNO3, and p-NO3 in the atmosphere, respectively. fNO2 is the fraction of NO2 in NOx. δ15NNOx, δ15NHNO3, and δ15Np-NO3− are δ15N values of NOx, HNO3, and p-NO3 in the atmosphere, respectively. The values used for CNO2, CHNO3, Cp-NO3−, fNO2, δ15NNOx, δ15NHNO3, and δ15Np-NO3− are listed in Supplementary Table 1. Due to the limited availability of fNO2 and δ15NNOx values, global mean values were used in our calculations (fNO2 = 64 ± 10%, and δ15NNOx = −7.7 ± 2.9‰) (Supplementary Table 1).

To investigate the importance of non-fossil fuel NOx emissions to total NOx emissions, we compiled available δ15 N values of NO3 in precipitation (denoted as δ15Nw-NO3− hereafter) at urban and non-urban sites of East Asia, Europe, and North America (detailed in “Methods”) (Fig. 1). Both the concentrations and δ15N values of ambient NOx, HNO3, and p-NO3 were used to constrain the δ15N values of the initial mixture of fossil fuel and non-fossil fuel NOx in the atmosphere (denoted as δ15Ni-NOx, detailed in “Methods”) (Supplementary Fig. 1). Then we evaluated the differences between δ15Nw-NO3− and δ15Ni-NOx values (denoted as 15i-NOx→w-NO3−, 15i-NOx→w-NO3− = δ15Nw-NO3− - δ15Ni-NOx, detailed in “Methods”). By combining the 15i-NOx→w-NO3− values (Supplementary Fig. 2), the observed δ15Nw-NO3− values, and δ15N values of dominant fossil fuel and non-fossil fuel NOx sources (Supplementary Figs. 3, 13), we calculated relative contributions of dominant fossil fuel and non-fossil fuel NOx by using a statistical isotope mass-balance model.

## Results and discussion

### Spatial and temporal variations of δ15Nw-NO3− values

In general, East Asia has significantly higher δ15Nw-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 15N-enriched NOx from coal combustion (δ15N = 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 NOx from coal combustion has influenced δ15Nw-NO3− signatures of both urban and non-urban areas in East Asia, so that δ15Nw-NO3− values did not differ between urban and non-urban sites (Fig. 2). The δ15Nw-NO3− values are lower at non-urban sites than at urban sites in Europe and North America (Fig. 2), reflecting more influences of the 15N-depleted NOx from microbial N cycle (δ15N = −30.2 ± 6.7‰; Supplementary Fig. 3) at non-urban sites of these two regions than that of East Asia.

The three study regions exhibit different temporal variations in δ15Nw-NO3− values (Fig. 3). In East Asia, δ15Nw-NO3− values increased at both urban and non-urban sites from 2000 to 2007 and then decreased very slowly (Fig. 3). This trend reflects the controlling strategies of NOx emissions from coal combustion in East Asia, particularly in China. During 2000–2007, the amount of coal consumption in China accounts for 89 ± 2% of the total amount in East Asia (Supplementary Fig. 4b). As a turning point, China started to implement mitigation measures for NOx from coal combustion in 2007, i.e., the policy of “replacing small generation units with large ones” for coal power plants33,34. Since 2008, a large-scale flue gas denitrification technology has been widely utilized in coal-fired power plants of China to reduce the NOx emission from industrial coal combustion33,35. Differently, δ15Nw-NO3− values in Europe decreased from 2002 to 2017 (Fig. 3) in response to a decrease in NOx emissions from the coal combustion because the coal consumption in Europe has reduced by 20% from 2002 to 2017 (Supplementary Fig. 4a). Although there was a significant decrease in the amount of coal combustion (by 34%) in North America during 2000–2017 (Supplementary Fig. 4a), corresponding δ15Nw-NO3− values were relatively consistent (Fig. 3). This pattern reflects the NOx emission reduction technology used in power plants because the technology can raise δ15N values of NOx emitted36.

### Importance of non-fossil fuel NOx emissions

Results from the Stable Isotope Analysis in R (the SIAR model; detailed in “Methods”) showed that variations in relative contributions of NOx from coal combustion are the main cause of different temporal patterns of regional δ15Nw-NO3− variations. (Supplementary Figs. 58). However, relative contributions of non-fossil fuel NOx 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 NOx 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 NOx from coal combustion and vehicle exhausts (Fig. 4b, Supplementary Fig. 10) and their annual mean relative contributions to total NOx emissions (Fig. 4a), the mean annual NOx 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 NOx 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 NOx emissions are valuable because they have long been missing in budgeting NOx deposition and modeling effects of atmospheric NOx loading.

Although we have considered uncertainties, there are still a few factors that remain difficult to quantify in the current stage. First, not all NOx emission sources have been considered in δ15N 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 NOx emissions.

### Remarks

Our study provides direct isotope evidence on that the changes in regional human activities have distinct influences on δ15N signatures of deposited NOx to terrestrial environments. The δ15Nw-NO3− values exhibit significant spatiotemporal changes, which can be used to trace anthropogenic N inputs and help us understand decadal δ15N 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 NOx emissions via technology promotion and energy structure adjustment. However, our study shows that non-fossil fuel NOx emission is equally as important as fossil fuel NOx emission, and it has long been underestimated. Accordingly, the control of non-fossil fuel NOx emissions should be equally considered in the mitigation of NOx pollution. Moreover, regional NOx emissions newly constrained in this study are useful for budgeting NO3 deposition fluxes and modeling ecological and climatic effects of atmospheric NO3 loading.

## Methods

### Global δ15Nw-NO3− observations

Publications of δ15Nw-NO3− studies were obtained through the databases of the Web of Science (http://isiknowledge.com), Google Scholar (http://scholar.google.com.hk), and Baidu Scholar (http://xueshu.baidu.com) by searching keywords of “nitrogen isotope”, “nitrate”, “rainfall”, and “precipitation”. By the end of December 2018, a total of 128 publications were available (Supplementary Text 1), spanning the sampling time of 1956–2017 (Supplementary Fig. 11). We extracted δ15Nw-NO3− values of individual precipitation samples by using the software of Web Plot Digitizer37.

There are totally 3483 individual δ15Nw-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 δ15Nw-NO3− data at major urban and non-urban 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 δ15Nw-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 δ15Nw-NO3− values in urban and non-urban areas of each region, respectively (Fig. 3), we counted observation sites by different sampling years, given that δ15Nw-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 δ15Nw-NO3− observations were conducted in warmer, cooler, and the whole year, respectively. The seasonal effects of NOx emissions may not substantially influence the patterns of regional δ15Nw-NO3− variations.

### Differences between δ15Nw-NO3− and δ15Ni-NOx values

NO is normally insoluble in water, and w-NO3 is scavenged only from the ambient NO2 and the oxidized NOx (i.e., HNO3 and p-NO3) (Supplementary Fig. 1)32,38,39. Moreover, isotopic effects during the NOx cycles lead to differences between δ15NNOx and δ15NNO2. Therefore, substantial differences exist between the δ15Nw-NO3− and δ15Ni-NOx values in the atmosphere (hereafter denoted as 15i-NOx→w-NO3−). In this study, we calculated 15i-NOx→w-NO3− values by using the following equation (Eq. (2)):

$${\,}^{15}{\Delta}_{{\mathrm{i}} - {\mathrm{NO}x} \to {\mathrm{w}} - {\mathrm{NO3}} - } = \delta ^{15}{\mathrm{N}}_{{\mathrm{w}} - {\mathrm{NO3}} - } - \delta ^{15}{\mathrm{N}}_{{\mathrm{i}} - {\mathrm{NO}x}}.$$
(2)

Combined Eq. (1) with Eq. (2), we get Eq. (3) to calculate the 15i-NOx→w-NO3− values.

$${\,}^{15}{\Delta}_{{\mathrm{i}} - {\mathrm{NO}x} \to {\mathrm{w}} - {\mathrm{NO3}}} = \delta ^{15}{\mathrm{N}}_{{\mathrm{w}} - {\mathrm{NO3}} - }\\ \quad- \left({\delta}^{15}{\mathrm{N}}_{{\mathrm{NO}x}} \times {\mathrm{C}}_{{\mathrm{NO2}}}/f_{{\mathrm{NO2}}} + \delta ^{15}{\mathrm{N}}_{{\mathrm{HNO3}}} \times {\mathrm{C}}_{{\mathrm{HNO3}}} + \delta ^{15}{\mathrm{N}}_{{\mathrm{p}} - {\mathrm{NO3}} - } \times {\mathrm{C}}_{{\mathrm{p}} - {\mathrm{NO3}}}\right)/\\ \quad \left({\mathrm{C}}_{{\mathrm{NO2}}}/f_{{\mathrm{NO2}}} + {\mathrm{C}}_{{\mathrm{HNO3}}} + {\mathrm{C}}_{{\mathrm{p}} - {\mathrm{NO3}} - }\right).$$
(3)

To obtain more accurate 15i-NOx→w-NO3− values, we estimated the 15i-NOx→w-NO3− values in two independent scenarios. In Scenario 1, mean values of global δ15NNOx and fNO2 values, simultaneously observed values of ambient CNO2, CHNO3, Cp-NO3−, δ15NHNO3, δ15Np-NO3−, and δ15Nw-NO3− were used for the calculation in Eq. (3). In Scenario 2, non-synchronously observed values of ambient fNO2, CNO2, CHNO3, Cp-NO3−, δ15NNOx, δ15NHNO3, δ15Np-NO3−, and δ15Nw-NO3− were used for the calculation in Eq. (3). The values and data sources of parameters used for estimating ambient 15i-NOx→w-NO3− values are included in Supplementary Table 1. Because data of fNO2 and δ15NNOx 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 15i-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 NOx sources

Based on δ15Nw-NO3−, 15i-NOx→w-NO3−, and δ15N values of NOx sources, we estimated relative contributions of dominant fossil fuel and non-fossil fuel NOx sources to total NOx emissions by using the isotope mass-balance method. We considered coal combustion (denoted as S1) and vehicle exhausts (S2) as dominant fossil fuel NOx sources, and biomass burning (S3), and microbial N cycles (S4) as dominant non-fossil fuel NOx sources. The major reasons include: (1) these four sources have been considered as dominant sources of total NOx emissions in studies of both emission inventory and deposition modeling2,9,11,13,14,15,19,20,21; (2) they are also the dominant sources influencing δ15N variations of NOx and NO3 in the atmosphere;26,27 (3) their mean δ15N values of NOx 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 NOx sources at urban sites but S2 cannot be considered as a dominant NOx source at non-urban sites. First of all, studies of roadside NOx emissions have evidenced that vehicle exhausts contribute little to atmospheric NOx at non-urban sites due to limited amounts of long-range transport40,41,42. 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 δ15Nw-NO3− values at urban and non-urban sites fall in the δ15N range of NOx from vehicle exhausts (Supplementary Figs. 3, 13). Consequently, when the NOx from vehicle exhausts is considered into the calculations of relative contributions of different NOx 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 NOx transportations always occur between urban and non-urban areas, δ15N values of NO3 in precipitation at a given urban or non-urban site integrate δ15N values of NOx from both local emissions and regional transportations. However, physical NOx transportation might have no substantial isotope effects, and thus likely will not influence the site-specific evaluations of fossil and non-fossil fuel NOx contributions.

According to isotope mass-balance theory, we calculated relative contributions of S1–S4 (fS1, fS2, fS3, and fS4, respectively) at urban sites by using Eq. (4):

$$\delta ^{15}{\mathrm{N}}_{{\mathrm{w}} - {\mathrm{NO3}} - } = (f_{{\mathrm{S1}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S1}}} + f_{{\mathrm{S2}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S2}}} + f_{{\mathrm{S3}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S3}}} + f_{{\mathrm{S4}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S4}}})\\ + {\,}^{15}{\Delta}_{{\mathrm{i}} - {\mathrm{NOX}} \to {\mathrm{w}} - {\mathrm{NO3}} - },$$
(4)

where we assumed that fS1 + fS2 + fS3 + fS4 = 1.

Then, we calculated their relative contributions at non-urban sites by Eq. (5):

$$\delta ^{15}{\mathrm{N}}_{{\mathrm{w}} - {\mathrm{NO3}} - } = {\,\,} (f_{{\mathrm{S1}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S1}}} + f_{{\mathrm{S3}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S3}}} + f_{{\mathrm{S4}}} \times \delta ^{15}{\mathrm{N}}_{{\mathrm{S4}}})\\ + {\,}^{15}{\Delta}_{{\mathrm{i}} - {\mathrm{NO}X} \to {\mathrm{w}} - {\mathrm{NO3}} - },$$
(5)

where we assumed that fS1 + fS3 + fS4 = 1. δ15NS1, δ15NS2, δ15NS3, and δ15NS4 represent δ15N values of NOx from coal combustion (S1), vehicle exhausts (S2), biomass burning (S3), and microbial N cycles (S4), respectively (Supplementary Fig. 3).

The fS1, fS2, fS3, and fS4 values were calculated by using a Bayesian isotope-mixing model (named Stable Isotope Analysis in R, SIAR). The SIAR model43 uses a Bayesian framework to establish a logical prior distribution based on Dirichlet distribution44 for estimating source contributions (fS1fS4). It has the potential to provide reliable estimations of source contributions because the isotope effect (i.e., 15i-NOx→w-NO3− values in this study), the variability in δ15N values of both sources (i.e., δ15N values of NOx from S1–S4 in this study), and the mixture (i.e., δ15Nw-NO3− values in this study)45,46 are considered. The SIAR model has been widely used to quantify the relative contributions of multiple NOx emission sources to p-NO3 and w-NO326,27,31,47. In each run of the SIAR model, the mean ± SD of δ15NNOx values (Supplementary Fig. 3), the mean ± SD of 15w-NO3−→i-NOx values (Supplementary Fig. 2), and replicate δ15Nw-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. 58).

We calculated the total contribution of each NOx 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) (furban and fnon-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 (Purban and Pnon-urban, respectively; Supplementary Fig. 14).

$${{F}} = f_{{\mathrm{urban}}} \times P_{{\mathrm{urban}}} \times f_{{\mathrm{non - urban}}} \times P_{{\mathrm{non - urban}}}.$$
(6)

Then, we calculated annual mean relative contributions of dominant fossil fuel and non-fossil fuel NOx sources in each region (Ffossil and Fnon-fossil, respectively) by using Eq. (7) and Eq. (8), respectively.

$$F_{{\mathrm{fossil}}} = F_{{\mathrm{S1}}} + F_{{\mathrm{S2}}},$$
(7)
$$F_{{\mathrm{non - fossil}}} = F_{{\mathrm{S3}}} + F_{{\mathrm{S4}}}.$$
(8)

Finally, based on the annual mean amounts of fossil fuel NOx emissions (Afossil) in East Asia during 2000–2010, in Europe during 2000–2015, and in North America during 2000–2016, respectively (Fig. 4b, Supplementary Fig. 10), the annual mean amounts of total NOx emissions (Atotal) and non-fossil fuel NOx emissions (Anon-fossil) in each region during 2000–2017 were calculated by using Eq. (9) and Eq. (10), respectively:

$${{A}}_{{\mathrm{total}}} = {{A}}_{{\mathrm{fossil}}}/F_{{\mathrm{fossil}}},$$
(9)
$${{A}}_{{\mathrm{non - fossil}}} = {{A}}_{{\mathrm{total}}} - {{A}}_{{\mathrm{fossil}}}.$$
(10)

We estimated the SD values of calculated values in Eqs. (6)–(10) and finally propagated into the uncertainties of the Anon-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 δ15Nw-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.

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## Acknowledgements

This study was supported by the State Key Project of Research and Development Plan (2017YFC0210101, 2016YFA0600802), the National Natural Science Foundation of China (Nos. 41730855, 41522301, 42073005), the Outstanding Youth Funds of Tianjin (No. 17JCJQJC45400), the Coordinated Research Project of IAEA (F32008), Shenzhen Science and Technology Program (KQTD20180413181724653), and the 11th Recruitment Program of Global Experts (the Thousand Talents Plan) for Young Professionals granted by the central budget of China. We would like to gratefully thank all researchers and coauthors who reported and kindly provided us precious data of concentrations and isotopes of atmospheric NOx, HNO3, and NO3.

## Author information

Authors

### Contributions

X.-Y.L. designed the research. W.S., X.-Y.L., C.-C.H. conducted the research (data collections and analyses). W.S. and X.-Y.L. co-wrote the paper, G.-Y.C., X.-J.L., W.W.W., G.M. and C.-Q.L. commented on the manuscript.

### Corresponding author

Correspondence to Xue-Yan Liu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks David Fowler, Shaoneng He, and Xuemei Wang for their contribution to the peer review of this work

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Song, W., Liu, XY., Hu, CC. et al. Important contributions of non-fossil fuel nitrogen oxides emissions. Nat Commun 12, 243 (2021). https://doi.org/10.1038/s41467-020-20356-0

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