Figure 1. Illustration of P flows and P budget terms used in this study. P inputs: blue arrows. P output (P yield): green arrow. P loss: red arrow.
Major P inputs to cropland include P fertilizer and P manure:
\begin{equation} P\ inputs=P\ fertilizer+P\ manure\nonumber \\ \end{equation}
To determine the amount of fertilizer applied to 150+ crop types and 200+ countries, we started with IFA fertilization data of 10+ crop type groups and 20+ country groups reported in 2006 2007, 2010, and 2014 and 2015 (IFA 2018) and the national fertilizer use data published by the Food and Agriculture Organization of the United Nations (FAO) (FAOSTAT 2020). Then, we projected fertilization rate by country and crop type from 1961 to 2014, assuming that the fraction of fertilizer applied to each crop type in each year is the same as that reported by IFA (1961-2006, same fraction as reported in IFA 2006 report; 2007, same fraction as reported in IFA 2007 report; 2008-2010, same fraction as reported in IFA 2010 report; 2011-2014, same fraction as reported in IFA 2014 report). For countries belonging to the same country group and crop types belong to the same crop type group, we assumed the same fertilization rate. For missing data between years, we did linear interpolation. The projected results were then further adjusted to increase accuracy, with other fertilizer use details mentioned by FAO (FAO 2002, FAOSTAT 2018) and in published studies (Smil 1999, Schroder et al. 2010, Lassaletta et al. 2014). In the previous work, P in fertilizer is expressed as the weight of P2O5, and we changed the unit to kg P. The content of P in animal excretion is also available in previous studies (Sheldrick et al. 2003, Andersen 2013, Chen and Graedel 2016, Chowdhury 2016, Liu et al. 2016, Bouwman et al. 2017). With that, we can estimate the total P in applied fertilizer and manure. More details of these calculations can be found in SI. On the global scale, our P inputs and output are similar with that found in the previous studies (Table S5 and S6).
With P fertilizer input data, we calculated P fertilizer demand to supply ratio and used it as the indicator of the P depletion challenge. P fertilizer demand is the total P demanded from fertilizer, and P supply is the total P provided by local phosphate rock reserves. This indicator suggests whether a country’s phosphate rock reserves along are sufficient for its food production. A ratio close to or higher than one (threshold: one) indicates the need to use more P from alternative sources or import more P to support future food production. Phosphate rock reserves data were collected from the United States Geological Survey (USGS) (2018).
The two pathways of P leaving the cropland system are (1) P in harvested crops (known as P output, or P yield to describe the P in harvested crops per unit land), including any part of the plants removed from the field, and (2) P loss through leaching, erosion, and runoff. Each crop’s P content was decided by taking the average of P content reported by FAO (2006), the United States Department of Agriculture (USDA 2013), AUSNUT (2013), Gourley et al. (2010), and Bouwman et al. (2017). The impacts of varying P content by crop type on P yield and PUE were examined with sensitivity tests (Text S6).
P surplus is also called P imbalance (MacDonald et al. 2011, Lun et al. 2018) or P budget (Bouwman et al. 2017). P surplus is the difference between P inputs and P output, and the sum of P loss and P residual:
\begin{equation} P\ surplus=P\ inputs-P\ output\nonumber \\ \end{equation}\begin{equation} P\ surplus=P\ loss+P\ residual\nonumber \\ \end{equation}
Here we used P surplus to measure P pollution and compared it with estimated planetary boundary, which in many studies marks the safe operating space for humanity (Rockström et al. 2009, Carpenter and Bennett 2011, Steffen et al. 2015). Based on Springmann et al.’s global P flow model (Springmann et al. 2018), we estimated the planetary boundary for global cropland P surplus is 4.5-9 Tg P yr-1 (i.e., 3.5-6.9 kg P ha-1yr-1, see Section TextS14 for the assumptions and methods used for deriving this planetary boundary).
P residual is the difference between the P surplus and P loss, indicating the amount of P available in the soil for future plant growth:
\begin{equation} P\ residual=P\ surplus-P\ loss\nonumber \\ \end{equation}
PUE, sometimes also called the recovery ratio, is defined as the ratio of P output (i.e., P in harvested crops or P yield) to P inputs:
\begin{equation} PUE=\frac{\text{P\ output}}{\text{P\ inputs}}\nonumber \\ \end{equation}
A PUE larger than one means the crop production is mining nutrients from the soil, while PUE smaller than one indicates extra P remained in the soil and/or lost. Our estimated PUE on the global scale is similar to the estimations in the earlier studies (Tables Sx).