# Precipitation-Use Efficiency and Its Conversion with Climate Types in Mainland China
## 2 Materials and Methods
### Methods  
PUE was identified as the ratio of NPP to P [11]:  
\[PUE=\frac{NPP}{P} \tag{1}\]  
where NPP is the annual net primary productivity (unit: g\(\cdot\)m\({}^{-2}\)) and P is the annual precipitation (unit: mm). NPP is obtained through the Thornthwaite memorial model [64]:  
\[NPP=3000(1-e^{-0.0009695(ET_{a}-20)}) \tag{2}\]  
where ET\({}_{a}\) is the actual evapotranspiration. It can be obtained as Zhou and Zhang [65]. Although there are many methods to estimate ET\({}_{a}\), such as the water balance method, surface energy balance method, remote sensing analysis method, etc., they all have limitations, such as complicated parameters and difficulty to determine [66; 67]. [PERSON] and [PERSON]'s method fully reflects the limiting effect of energy and water on evapotranspiration, with its few parameters and clear physical significance making it high practicability. The method is as follows:  
\[ET_{a}=\frac{P\times R\times\left(P^{2}+R^{2}+P\times R\right)}{(P+R)\times(P^ {2}+R^{2})} \tag{3}\]  
Here, P is the annual precipitation, and R is the annual net radiation correction factor, which can be obtained by Equation (4):  
\[R=(ET_{0}\times P)^{0.5}\times(0.369+0.598\times(ET_{0}/P)^{0.5} \tag{4}\]  
where ET\({}_{0}\) is the potential evapotranspiration calculated using the FAO Penman-Monteith method. See [PERSON] et al. [68] for details.  
The sensitivity coefficient and the relative change were used to measure the contribution of environmental factors to the PUE change:  
\[Con_{X}=RC_{X}\times S_{X} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Stations** & **Latitude** & **Longitude** & **Observational Periods** & **Reference** \\ \hline
39 & **Yushu** & 44.85\({}^{\circ}\) N & 126.52\({}^{\circ}\) E & **2009** & [PERSON] et al. [57] \\
40 & **Sanjiang Plains** & 47.51\({}^{\circ}\) N & 133.51\({}^{\circ}\) E & **2017** & [PERSON] et al. [58] \\
41 & **Panjin** & 41.14\({}^{\circ}\) N & 121.90\({}^{\circ}\) E & **2005, 2006–2007** & [PERSON] et al. [59] \\
42 & **Dongtan** & 31.52\({}^{\circ}\) N & 121.96\({}^{\circ}\) E & **2005** & [PERSON] et al. [60] \\
43 & **Yunxiao** & 23.92\({}^{\circ}\) N & 117.42\({}^{\circ}\) E & **2009–2010** & [PERSON] [61] \\
44 & Gaoqiao & 21.57\({}^{\circ}\) N & 109.76\({}^{\circ}\) E & 2010 & [PERSON] et al. [62] \\ \hline \end{tabular}  
* Nos.1 to 16 are forest stations, 17 to 33 are grassland stations, 34 to 39 are cropland stations, and 40 to 44 are wetland stations. Periods in **bold** are the **Validation Data**. Haibei \({}^{\text{a}}\) and Haibei \({}^{\text{b}}\) are two sites in different geographical locations.  
\end{table}
Table 1: \(Cont.\)\[RC_{X}=\frac{58\times Trend_{X}}{|ave_{X}|}\times 100\% \tag{6}\]  
where \(Con_{X}\) is the contribution of a factor to the PUE change, \(RC_{X}\) is the relative change rate of the factor, \(Trend_{X}\) and \(ave_{X}\) are the change rate and average of the factor, respectively, and \(Sx\) is the sensitivity coefficient of the PUE with respect to environmental factor \(X\). \(Sx\) can be obtained as McCuen [69]:  
\[S_{x}=\lim_{\Delta X\to 0}\left(\frac{\Delta PUE/PUE}{\Delta X/X}\right)= \frac{\partial PUE}{\partial X}\times\frac{X}{PUE} \tag{7}\]