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 (NO_x) emissions. However, it remains uncertain to the actual contribution of the non-fossil fuel NO_x to total NO_x emissions. Natural N isotopes of NO₃⁻ in precipitation (δ¹⁵N_w-NO3−) have been widely employed for tracing atmospheric NO_x sources. Here, we compiled global δ¹⁵N_w-NO3− observations to evaluate the relative importance of fossil and non-fossil fuel NO_x emissions. We found that regional differences in human activities directly influenced spatial-temporal patterns of δ¹⁵N_w-NO3− variations. Further, isotope mass-balance and bottom-up calculations suggest that the non-fossil fuel NO_x accounts for 55 ± 7% of total NO_x 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 NO_x emissions and provide direct evidence for making strategies on mitigating atmospheric NO_x pollution.

This study investigates in the importance of non-fossil fuel NO_x emissions in the surface-earth-nitrogen cycle. The study shows how changes of regional human activities directly influence δ¹⁵N signatures of deposited NO_x to terrestrial environments and that emissions have largely been underestimated.

Introduction

Over past decades, both concentrations and deposition fluxes of nitrogen oxides (NO_x), nitric acid (HNO₃), and nitrate (NO₃⁻) in the atmosphere have been remarkably elevated in many regions of the world^1–4. 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 (NO₂), is the precursor of atmospherically deposited NO₃^− 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 wastes⁹. Accurate differentiation of NO_x 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 NO_x emissions according to known consumption amounts of fossil fuels and their NO_x emission factors^10–12. More often, fossil fuel NO_x emissions in many countries have been recorded in national statistics yearbooks and emission inventories^2,12–15. Since the 1990s, fossil fuel NO_x emissions have accounted for 95% of global NO_x emissions¹¹, 90% of NO_x emissions in Europe², 88% of NO_x emissions in East Asia¹⁰, 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 liquid-phase substrates^16–18. 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^19–21. 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 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 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 NO₃⁻ 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 NO₂ in the atmosphere, forming the photochemical NO_x cycle²⁸. 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 δ¹⁵N of the i-NO_x (i.e., δ¹⁵N_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 HNO₃ and particulate NO₃⁻ (p-NO₃⁻) (Supplementary Fig. 1), during which N isotopic fractionations^29,30 lead to substantial δ¹⁵N differences between ambient NO_x, HNO₃, and p-NO₃⁻. Because of the difficulty in constraining δ¹⁵N differences among these species, it remains a big challenge to evaluate i-NO_x sources based on δ¹⁵N signatures of ambient NO_x, 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 δ¹⁵N_i-NOx values of the observed δ¹⁵N_w-NO3− values (Supplementary Figs. 1, 2). Assuming that the estimated δ¹⁵N_i-NOx value represents and integrates the emission δ¹⁵N_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 δ¹⁵N_i-NOx value can be estimated by the following equation (Eq. (1)):

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

where C_NO2, C_HNO3, and C_p-NO3− are concentrations of ambient NO₂, HNO₃, and p-NO₃⁻ in the atmosphere, respectively. f_NO2 is the fraction of NO₂ in NO_x. δ¹⁵N_NOx, δ¹⁵N_HNO3, and δ¹⁵N_p-NO3− are δ¹⁵N values of NO_x, HNO₃, and p-NO₃⁻ in the atmosphere, respectively. The values used for C_NO2, C_HNO3, C_p-NO3−, f_NO2, δ¹⁵N_NOx, δ¹⁵N_HNO3, and δ¹⁵N_p-NO3− are listed in Supplementary Table 1. Due to the limited availability of f_NO2 and δ¹⁵N_NOx values, global mean values were used in our calculations (f_NO2 = 64 ± 10%, and δ¹⁵N_NOx = −7.7 ± 2.9‰) (Supplementary Table 1).

To investigate the importance of non-fossil fuel NO_x emissions to total NO_x emissions, we compiled available δ¹⁵ N values of NO₃⁻ in precipitation (denoted as δ¹⁵N_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 δ¹⁵N values of ambient NO_x, HNO₃, and p-NO₃⁻ were used to constrain the δ¹⁵N values of the initial mixture of fossil fuel and non-fossil fuel NO_x in the atmosphere (denoted as δ¹⁵N_i-NOx, detailed in “Methods”) (Supplementary Fig. 1). Then we evaluated the differences between δ¹⁵N_w-NO3− and δ¹⁵N_i-NOx values (denoted as ¹⁵∆_{i-NOx→w-NO3−}, ¹⁵∆_{i-NOx→w-NO3−} = δ¹⁵N_w-NO3− - δ¹⁵N_i-NOx, detailed in “Methods”). By combining the ¹⁵∆_{i-NOx→w-NO3−} values (Supplementary Fig. 2), the observed δ¹⁵N_w-NO3− values, and δ¹⁵N values of dominant fossil fuel and non-fossil fuel NO_x sources (Supplementary Figs. 3, 13), we calculated relative contributions of dominant fossil fuel and non-fossil fuel NO_x by using a statistical isotope mass-balance model.

Fig. 1. Study sites with δ¹⁵N_w-NO3− observations.

Red, blue, and black dots represent urban sites (n = 56), non-urban sites (n = 158), and Arctic sites (n = 8), respectively.

Results and discussion

Spatial and temporal variations of δ¹⁵N_w-NO3− values

In general, East Asia has significantly higher δ¹⁵N_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 ¹⁵N-enriched NO_x 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 NO_x from coal combustion has influenced δ¹⁵N_w-NO3− signatures of both urban and non-urban areas in East Asia, so that δ¹⁵N_w-NO3− values did not differ between urban and non-urban sites (Fig. 2). The δ¹⁵N_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 ¹⁵N-depleted NO_x 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.

Fig. 2. δ¹⁵N_w-NO3− values at urban and non-urban sites of East Asia (n = 25 and n = 38, respectively), Europe (n = 8 and n = 15, respectively), and North America (n = 10 and n = 73, respectively).

Dots show mean values of replicate measurements at each site. The box encompasses the 25th−75th percentiles, whiskers, and line in each box are the SD and mean values, respectively. The symbol of * indicates differences between urban and non-urban sites. n.s.: not significant. Different letters indicate differences among East Asia, Europe, and North America. The significance level was set at P < 0.1.

The three study regions exhibit different temporal variations in δ¹⁵N_w-NO3− values (Fig. 3). In East Asia, δ¹⁵N_w-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 NO_x 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 NO_x from coal combustion in 2007, i.e., the policy of “replacing small generation units with large ones” for coal power plants^33,34. Since 2008, a large-scale flue gas denitrification technology has been widely utilized in coal-fired power plants of China to reduce the NO_x emission from industrial coal combustion^33,35. Differently, δ¹⁵N_w-NO3− values in Europe decreased from 2002 to 2017 (Fig. 3) in response to a decrease in NO_x 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 δ¹⁵N_w-NO3− values were relatively consistent (Fig. 3). This pattern reflects the NO_x emission reduction technology used in power plants because the technology can raise δ¹⁵N values of NO_x emitted³⁶.

Fig. 3. Variations of δ¹⁵N_w-NO3− values during 2000–2017.

a, b Urban and non-urban sites of East Asia. c, d Urban and non-urban sites of Europe. e, f Urban and non-urban sites of North America. Mean values of replicate measurements at each site in each year are shown. The gray lines are the 95% confidence intervals.

Importance of non-fossil fuel NO_x emissions

Results from the Stable Isotope Analysis in R (the SIAR model; detailed in “Methods”) showed that variations in relative contributions of NO_x from coal combustion are the main cause of different temporal patterns of regional δ¹⁵N_w-NO3− variations. (Supplementary Figs. 5–8). 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.

Fig. 4. Fossil and non-fossil fuel NO_x emissions in East Asia, Europe, and North America.

a Relative contributions. b Emission amounts. Mean ± SD values are shown.

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 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 NO_x emissions.

Remarks

Our study provides direct isotope evidence on that the changes in regional human activities have distinct influences on δ¹⁵N signatures of deposited NO_x to terrestrial environments. The δ¹⁵N_w-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 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 non-fossil 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 NO₃⁻ deposition fluxes and modeling ecological and climatic effects of atmospheric NO₃⁻ loading.

Methods

Global δ¹⁵N_w-NO3− observations

Publications of δ¹⁵N_w-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 δ¹⁵N_w-NO3− values of individual precipitation samples by using the software of Web Plot Digitizer³⁷.

There are totally 3483 individual δ¹⁵N_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 δ¹⁵N_w-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 δ¹⁵N_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 δ¹⁵N_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 δ¹⁵N_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 δ¹⁵N_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 δ¹⁵N_w-NO3− variations.

Differences between δ¹⁵N_w-NO3− and δ¹⁵N_i-NOx values

NO is normally insoluble in water, and w-NO₃⁻ is scavenged only from the ambient NO₂ and the oxidized NO_x (i.e., HNO₃ and p-NO₃⁻) (Supplementary Fig. 1)^32,38,39. Moreover, isotopic effects during the NO_x cycles lead to differences between δ¹⁵N_NOx and δ¹⁵N_NO2. Therefore, substantial differences exist between the δ¹⁵N_w-NO3− and δ¹⁵N_i-NOx values in the atmosphere (hereafter denoted as ¹⁵∆_{i-NOx→w-NO3−}). In this study, we calculated ¹⁵∆_{i-NOx→w-NO3−} values by using the following equation (Eq. (2)):

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

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

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

To obtain more accurate ¹⁵∆_{i-NOx→w-NO3−} values, we estimated the ¹⁵∆_{i-NOx→w-NO3}− values in two independent scenarios. In Scenario 1, mean values of global δ¹⁵N_NOx and f_NO2 values, simultaneously observed values of ambient C_NO2, C_HNO3, C_p-NO3−, δ¹⁵N_HNO3, δ¹⁵N_p-NO3−, and δ¹⁵N_w-NO3− were used for the calculation in Eq. (3). In Scenario 2, non-synchronously observed values of ambient f_NO2, C_NO2, C_HNO3, C_p-NO3−, δ¹⁵N_NOx, δ¹⁵N_HNO3, δ¹⁵N_p-NO3−, and δ¹⁵N_w-NO3− were used for the calculation in Eq. (3). The values and data sources of parameters used for estimating ambient ¹⁵∆_{i-NOx→w-NO3−} values are included in Supplementary Table 1. Because data of f_NO2 and δ¹⁵N_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∆_{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 δ¹⁵N_w-NO3−, ¹⁵∆_{i-NOx→w-NO3−}, and δ¹⁵N 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 δ¹⁵N variations of NO_x and NO₃⁻ in the atmosphere;^26,27 (3) their mean δ¹⁵N 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^40–42. 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 δ¹⁵N_w-NO3− values at urban and non-urban sites fall in the δ¹⁵N 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, δ¹⁵N values of NO₃⁻ in precipitation at a given urban or non-urban site integrate δ¹⁵N 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 non-fossil fuel NO_x contributions.

According to isotope mass-balance theory, we calculated relative contributions of S1–S4 (f_S1, f_S2, f_S3, and f_S4, respectively) at urban sites by using Eq. (4):

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

where we assumed that f_S1 + f_S2 + f_S3 + f_S4 = 1.

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

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

where we assumed that f_S1 + f_S3 + f_S4 = 1. δ¹⁵N_S1, δ¹⁵N_S2, δ¹⁵N_S3, and δ¹⁵N_S4 represent δ¹⁵N values of NO_x from coal combustion (S1), vehicle exhausts (S2), biomass burning (S3), and microbial N cycles (S4), respectively (Supplementary Fig. 3).

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 model⁴³ uses a Bayesian framework to establish a logical prior distribution based on Dirichlet distribution⁴⁴ 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∆_{i-NOx→w-NO3−} values in this study), the variability in δ¹⁵N values of both sources (i.e., δ¹⁵N values of NO_x from S1–S4 in this study), and the mixture (i.e., δ¹⁵N_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-NO₃⁻ and w-NO₃^{−26,27,31,47}. In each run of the SIAR model, the mean ± SD of δ¹⁵N_NOx values (Supplementary Fig. 3), the mean ± SD of ¹⁵∆ _{w-NO3−→i-NOx} values (Supplementary Fig. 2), and replicate δ¹⁵N_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_non-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 NO_x sources in each region (F_fossil and F_non-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 NO_x emissions (A_fossil) 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 NO_x emissions (A_total) and non-fossil fuel NO_x emissions (A_non-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 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 δ¹⁵N_w-NO3−, spatial differences are significant only at the level of P < 0.1 (Fig. 2). Mean values and standard deviation (SD) were reported.

Source data

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Author 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.

Data availability

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

Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary information is available for this paper at 10.1038/s41467-020-20356-0.