a Chord diagram depicting flows from the RIC (Table 4) version of the PIOT created with our method. b Chord diagram depicting flows from the PIOT prepared by Singh et al.

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Figure 5 provides a visualization of all PIOT flows in the two approaches, showing (Fig. 5a) the dominance of the flows between the economy and natural resources via raw materials and residuals in the process model approach, versus a dominant fertilizer production sector in the previous MFA-based approach (Fig. 5b). Since all flows represent N, this difference is due primarily to the fertilizer manufacturing sector. Residuals in Fig. 5a come primarily from the purge stream of air, since the yield of the Haber–Bosch process is low and recycle is needed. An interaction from the hog farming sector is also clearly visible in Fig. 5a, since N in manure is classified into residuals.Figure 5b shows a much larger production figure from the fertilizer manufacturing sector than Fig. 5a. An assumption was made in the PIOT by Singh et al. (2017) that all demands were met by local production, giving a total production of 895 thousand tons of N (see Additional file 1: Table A11). Here, our approach should be more accurate, giving a production of 194 thousand tons of N with the rest of the local demand met by imports (593 thousand tons of N).