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).