# Diagnosing Phosphorus Limitation in Subtropical Forests in China under Climate Warming
## 2 Materials and Methods
### Methods
#### 2.3.2 Diagnose of Additional P Demand  
The method used to diagnose the additional P demand in forest ecosystems based on NPP changes is mainly in reference to that of [PERSON] et al. (2017) [33]. Here, additional means the demand due to the increases of C storage since 1950. We assume that 100% of the plant uptake of P by NPP is equal to the P supply from all sources at 1950; that is, the additional P demand was zero at 1950. Then, the additional P demand (\(\Delta\)P\({}_{i,(t)}\)) in ecosystems related to NPP change is calculated as the total P demand minus changes in recycled P supply from leaf P resorption (\(\Delta\)P\({}_{RSB,\beta(t)}\)) and changes in the NPP uptake of mineralized P (\(\Delta\)P\({}_{MR,\beta(t)}\)):  
Figure 1: Spatial distribution of forest type in the study area and the location of field sampling sites.  
\[\Delta\text{P}_{i,(t)}=\sum_{j=1}^{3}\frac{\Delta NPP_{i,j,(t)}\times d_{i,j}}{r_{ i,j}}-\Delta P_{RSB,i(t)}-\Delta P_{MR,i(t)} \tag{1}\]  
where \(i\) and \(t\) represent forest type and year, respectively, and the numbers 1, 2 and 3 indexed by \(j\) represent the C pool for root, wood and leaf, respectively. The \(r_{i,j}\) is the C:P ratios in the corresponding C pool, and \(d_{i,j}\) is the fraction of NPP allocated to the C pool of leaf, wood and root, respectively.  
\(\Delta NPP_{i,j,(t)}\) is the difference of NPP between two years:  
\[\Delta NPP_{i,j,(t)}= NPP_{i,j,(t)}- NPP_{i,j,(t-1)} \tag{2}\]  
The changes of leaf P resorption available for the increment of NPP of the next year was assumed to be only associated with the leaf NPP change, which is given by:  
\[\Delta P_{RSB,i,(t)}=\frac{\sum_{j=1}^{3}\Delta NPP_{i,j,(t)}\times d_{i,3} \times RSB_{i}}{r_{i,3}} \tag{3}\]  
where \(RSB_{i}\) is the adsorption coefficient.  
The mineralization of P from SOM and litter is another source of inorganic P for NPP uptake, which is the difference between microbial immobilization and gross soil organic matter and litter mineralization. This flux (\(\Delta P_{MR,i(t)}\)) was inferred using two idealized scenarios. Scenario 1 (S\({}_{1}\)) assumes low mineralization, that is, only P in fallen leaves can be mineralized and support NPP in the following year, while P in wood and root components of litter is unavailable for vegetation to recycle. This is given by:  
\[\Delta P_{MR,i,S_{1}(t)}=\frac{\Delta NPP_{i,(t)}\times d_{i,3}\times(1-RSB_{i })}{r_{i,3}} \tag{4}\]  
Scenario 2 (S\({}_{2}\)) assumes high mineralization, that is, 90% of P in the wood and root litter is recycled in addition to all P in fallen leaves each year. This is given by:  
\[\Delta P_{MR,i,S_{2}t}=\frac{\Delta NPP_{i,(t)}\times d_{i,3}\times(1-RSB_{i}) }{r_{i,3}}+f\text{rac}\times\Delta NPP_{i,(t)}\times\left(\frac{d_{i,2}}{r_{i, 2}}+\frac{d_{i,1}}{r_{i,1}}\right) \tag{5}\]  
where frac is the fraction of P in litter reused in the ecosystems, which is set as 0.9.  
The accumulated additional P demand (AAPD) for a given period is given by:  
\[AAPD=\sum_{t1}^{t2}\Delta\text{P}_{i,(t)} \tag{6}\]  
where \(t_{1}\) and \(t_{2}\) represent the start and end year, respectively.  
The parameters used for diagnosing P limitation are listed in Table 1, in which \(r_{i,j}\) is obtained from literatures that reported the field measurements in subtropical forests in China. We used the fractions of C pools (leaves, wood and roots) to total vegetation C to represent NPP allocated to leaves, wood and roots, and \(d_{i,j}\) were obtained by averaging over 200 field observations in subtropical forests [22].