In the BAU scenario, we assumed that PUE by country and crop type by 2050 would remain at the current level (the average of 2005-2014). In the MPA scenario, for each crop type, PUE by country lower than the MPA minimum level (median level of the 12 regions) would be improved to that level by 2050 and other PUE values would be kept the same. Similarly, in the HPA scenario, PUE by country and crop type lower than the HPA minimum level (75th percentile level of the 12 regions) would be improved to that level and other PUE values would be kept the same. Besides, we assumed that PUE by country and crop type by 2050 would not exceed one, considering that soil mining is unsustainable in the long run, and the PUE change between 2015 and 2050 would be linear. With these assumptions and designed scenarios, we projected PUE by country and crop type from 2015 to 2050.
We estimated future P yield based on FAO’s projection (FAO 2018). FAO projected crop production and harvested area change by region and crop type in 2030, 2035, and 2040 and 2050 in three scenarios (2018). We adopted the projection in FAO’s Business as Use scenario to project P in harvested crops. We assumed that the data’s change within those reported years would be linear, and P content by crop type will not change over time or by country.
With P yield and PUE by country and cop type by 2050, we then estimated P inputs (P demanded for crop production):
\begin{equation} P\ inputs=\frac{\text{P\ yield}}{\text{PUE}}\nonumber \\ \end{equation}
To calculate P fertilizer input by 2050, we need to know P fertilizer to total inputs ratio (total inputs include P in fertilizer and manure). As this ratio by country and crop type may change in the future, we designed three extreme cases to consider its uncertainties (Table 2): A) the least sustainable case, in which P fertilizer to total inputs (including fertilizer and manure) ratio would equal to 100% from 2014 to 2050 (meaning all P inputs would be from fertilizer) and total inputs would equal to the projected P inputs; B) the normal case, in which P fertilizer to total inputs (including fertilizer and manure) ratio would remain at the current level (the average of 2005-2014) from 2014 to 2050 and total inputs would equal to the projected P inputs; C) the most sustainable case, in which to P fertilizer to total inputs ratio would remain at the current level, but the total inputs would equal to the projected P inputs minus the total P residual accumulated in the soil since 1961, assuming that P residual would be used for crop production.
In total, we designed three scenarios (BAU, MPA, and HPA) to project PUE, P yield, P inputs, and P surplus by 2050, and nine scenarios (from 1A to 3C, Table 2) to project future P fertilizer and manure inputs. We designed these nine scenarios to study how much we can reduce P pollution and the demand for phosphate rock with different P management ambitions measured by PUE improvement and fertilizer to total inputs ratio.
3 Results
3.1 Historical Phosphorus Budget and PUE
On the global scale, P yield has increased by around two times from 1961 (5 kg P ha-1 yr-1) to 2014 (11 kg P ha-1 yr-1) (Fig. 2a), indicating increased agricultural productivity. At the same time, global PUE decreased since 1961 (54%), then began to grow in the 1980s (40%), and stabilized after entering the 21st century (Fig. 2a). Though the improved PUE indicates a smaller fraction of P inputs lost to soil and environment, P residual has accumulated from 1961 to 2014 (2 to 195 ha-1 yr-1, Fig. 2b), as a potential P source for future crop production.