Fig. 3

N-Loss Index (NLI). a Global (yellow), tropical (magenta), and extratropical (cyan) NLIs. The thick line shows the baseline simulation. The thin lines show results forced by different inputs: dot (high BNF), dash-dot (low BNF), solid (Lu and Tian’s fertilizer⁴⁰), and dash (LULCC scenario without shifting cultivation¹⁵). Globally, the baseline simulation produces 128 TgN yr⁻¹ of BNF (medium) during 1991–2005 that is between 116 TgN yr⁻¹ (low) and 145 TgN yr⁻¹ (high) (Supplementary Table 1 and Supplementary Note 1). The low BNF is close to an estimate by Green and colleagues⁹ (112 TgN yr⁻¹) and the high BNF is close to an estimate by Galloway and colleagues¹ (139 TgN yr⁻¹). The NLIs were calculated after the results were 30-year moving averaged from 1750 to 2005. b, c Contemporary (1976–2005 average) NLIs for 159 major river basins (b) and their standard deviation across the different BNF settings, fertilizer inputs, and LULCC (c)