# Modeling the Impact of Atmospheric Warming on Staple Crop Growth in China in the 1960s and 2000s
## 2 Methods
### The Modeling Approach
\(\sigma\) is a coefficient. The effects of air temperature, soil moisture and atmospheric CO\({}_{2}\) concentration on photosynthesis are as follows:  
\[f(T_{i})=\left\{ \begin{array}{l}0\\ \left(\frac{T_{i}-T_{i}}{T_{0}-T_{L}}\right)^{(1+\gamma)}\times\left(\frac{T_{ UI}-T_{ji}}{T_{U}-T_{0}}\right)^{(1-\gamma)}\end{array} \right.\quad\text{for $T_{L}\leq T_{di}\leq T_{U}$} \tag{7}\]  
where \(T_{L}\), \(T_{U}\) and \(T_{O}\) are the base and maximum temperature limits, and optimum temperature (\({}^{\circ}\)C), respectively. \(T_{d}\) is the daytime air temperature (\({}^{\circ}\)C). \(\gamma\) is a coefficient that determines the shape of the temperature response curve of photosynthesis. Table 2 listed the three temperatures for crop photosynthetic growth measured: \(T_{L}\), \(T_{O}\), \(T_{U}\) and the range of \(T_{O}\) (within this range, \(f(T)\geq 0.95\), see Equation (7)). These temperature thresholds vary from crop to crop [35; 36]. When ambient temperatures are lower than the base temperature or higher than the maximum temperature, crop growth is inhibited, and when ambient temperatures fall within the optimum temperature range, crop photosynthetic efficiency is also optimistic, which was described in the Agro-C model [31]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Site** **(Province)**} & \multirow{2}{*}{**Logitude**} & \multirow{2}{*}{**Latitude**} & \multirow{2}{*}{**Attitude**} & \multirow{2}{*}{**Attitude**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**Total**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**pH**} & \multirow{2}{*}{**Crop**} & \multirow{2}{*}{**Area**} & \multirow{2}{*}{**Area**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**\%**} \\  & & & & & & & & & & & & & & **Emergence-Helding-Martiurb** \\ \hline \multirow{2}{*}{East China} & Changhua (Jiangsu) & 31\({}^{\circ}\)327 N & 120\({}^{\circ}\)447 E & 1.3 & \multirow{2}{*}{15.4} & \multirow{2}{*}{1095} & \multirow{2}{*}{2.33} & \multirow{2}{*}{6.90} & Rice & 1351 & 6/14 & 8/28 & 10/22 \\  & & & & & & & & & Winter & & 1339 & 10/28 & 4/15 & 5/29 \\ \multirow{2}{*}{South China} & Taoyuan (Huan) & 28\({}^{\circ}\)557 N & 111\({}^{\circ}\)277 E & 77.5 & \multirow{2}{*}{16.5} & \multirow{2}{*}{1353} & \multirow{2}{*}{1.31} & \multirow{2}{*}{5.44} & \multirow{2}{*}{rice} & \multirow{2}{*}{4062} & \multirow{2}{*}{7/14} & \multirow{2}{*}{9/2} & \multirow{2}{*}{10/10}  
\[f(W_{i})=\left\{ \begin{array}{l}0\\ \frac{W_{i}-W_{p}}{W_{l}-W_{p}}\\ 1\\ 0.5\times\left(1+\frac{W_{i}-1}{W_{n}-1}\right)\end{array} \right. \tag{8}\]  
where \(W_{p}\) is wilting moisture (cm\({}^{3}\) cm\({}^{-3}\)), and \(W_{l}\) and \(W_{u}\) are the lower and upper values of optimum soil moisture (cm\({}^{3}\) cm\({}^{-3}\)) for photosynthesis, respectively [31]. \[f(CO_{2})=1+B\ln\left(\frac{C_{y}}{C_{0}}\right) \tag{9}\]  
where \(B\) is 0.8 for C3 crops and 0.4 for C4 crops [31]; \(C_{y}\) is the CO\({}_{2}\) concentration for a given year and \(C_{0}\) is 340 umol mol\({}^{-1}\). The Agro-C model distinguishes crop-specific parameters for different crops. These parameters include the harvest index (HI), the fraction of photosyntheate matter partitioned to roots and leaves (PR and PL), specific leaf area (SLA), the irradiance extinction coefficient and the photosynthetic capacity per unit canopy leaf nitrogen (\(\alpha\)). In our previous study, the Agro-C model was used to simulate rice, wheat and maize. We mainly calibrated the three key parameters (SLA, PL and \(\alpha\)) of the Agro-C model, which are the most sensitive parameters. The parameters were calibrated with the crops' variety information. The calibrated parameters were shown in our previous published paper. For details, the reader is advised to refer to [PERSON] et al. (2017) [30].