Ecology

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 15∆i-NOx→w-NO3−). In this study, we calculated 15∆i-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 15∆i-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 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 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 15∆i-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 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 NOx sources
Based on δ15Nw-NO3−, 15∆i-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  More

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