Closing Knowledge Gaps on Global Budget of Nitrogen Oxides (NO_x) by Quantifying Indirect Emissions From Anthropogenic...

Human activities emit nitrogen oxides (NO_x ≡ NO + NO₂; with source emissions approximated as nitric oxide (NO)), potent air pollutants and short-lived climate forcers, through direct and indirect pathways. Unlike direct releases, however, indirect NO_x emissions remain poorly understood and inadequately quantified. Here, by synthesizing available observations across global terrestrial ecosystems, we show that soil moisture and pH strongly affect the ratio of annual background NO to nitrous oxide (N₂O) emissions ( $R_{\mathrm{NO}/N_{2}O}$ ), with a critical threshold at 46% water-filled soil pore space. Combining soil moisture-stratified $R_{\mathrm{NO}/N_{2}O}$ modeled by machine learning with known indirect N₂O emission factors, global indirect NO_x emission factors ( ${\mathrm{EF}}_{4\left(N{O}_x\right)}$ ) are derived, yielding an aggregated median of 1.59% (95% confidence interval (CI): 0.45%-2.41%) and significantly higher (p < 0.01) disaggregated values of 1.77% (95% CI: 1.49%-2.61%) for wet climates ( ${\mathrm{EF}}_{4,\mathrm{WC}\left(N{O}_x\right)}$ ) than those of 0.89% (95% CI: 0.45%-1.28%) for dry climates ( ${\mathrm{EF}}_{4,\mathrm{DC}\left(N{O}_x\right)}$ ). We further estimate that the global indirect NO_x emissions resulting from atmospheric deposition of nitrogen released by all anthropogenic sources amounted to approximately 886 (95% CI: 314-1639) Gg N year^-1 (1 Gg = 10⁹ g) in 2015, with fertilization, animal husbandry, and other human activities contributing about 25%, 26%, and 49%, respectively. Crucially, without soil moisture stratification, the global indirect NO_x emissions would be underestimated by approximately 16% (p < 0.001), while the associated uncertainty would be about 1.5 times as large. Our novel $R_{\mathrm{NO}/N_{2}O}$ -based framework provides a robust approach for quantifying indirect NO_x emissions in regional, national and global inventories, thereby supporting targeted strategies to mitigate air pollution and climate change.