## 3 Method
### Crop Growth Model
#### 3.1.2 Calibration of Crop Growth Model  
The CERES-Wheat model requires data on a range of parameters (containing at least four meteorological parameters, 18 soil parameters, nine management parameters and 33 crop parameters) for each cell in the grid to simulate the spatial distribution of crop yield [58]. Before using a crop model for a given region, the calibration should be firstly carried out, and the performance of the calibration should be evaluated to ensure that the model can accurately simulate the crop growth process by accounting for the variability of various local environmental parameters and the characteristics of the wheat [6]. Sensitivity analysis is an effective way to solve the above issues and to evaluate the uncertainty of the crop model quantitatively. This method investigates how the uncertainties of the model's estimates are related to its input parameters, so as to rank the parameters' influence on the uncertainty of the model's output and finding the key parameters. In this study, a global sensitivity analysis was performed using the extended Fourier amplitude sensitivity test method (EFAST) [69] to analyze the most sensitive parameters in the CERES-Wheat model, with the goal of identifying the most important parameters to be calibrated. Using Simlab software from Joint Research Centre, Ispra, Italy, eight crop initial condition parameters and seven cultivar parameters with sensitivity of the CERES-Wheat model to wheat yield were obtained (Table 3) and then calibrated. \begin{table}
\begin{tabular}{c l c c c} \hline \hline
**Parameters** & \multicolumn{2}{c}{**Descriptions**} & **Calibrated Values** & **Ranges** & **Units** \\ \hline \multicolumn{5}{c}{**Crop Initial Condition Parameters**} \\ \hline PDATE & Sowing date & 282 & 275–290 & day of year \\ \hline PPCP & Sowing population & 450 & 200–500 & plant/m\({}^{2}\) \\ \hline IDATE \& FDATE 1 & Irrigation and fertilization date 1 & 90 & 80–110 & day of year \\ \hline IDATE 2 & Irrigation date 2 & 130 & 111–140 & day of year \\ \hline IRVAL & Irrigation amount & 80 & 60–150 & mm \\ \hline FAMN & Nitrogen fertilizer at sowing & 120 & 0–300 & kg-ha\({}^{-1}\) \\ \hline FAMN1 & Nitrogen fertilizer at date 1 & 170 & 60–280 & kg-ha\({}^{-1}\) \\ \hline \multicolumn{5}{c}{Cultivar parameters} \\ \hline \multirow{3}{*}{P1V} & \multicolumn{2}{c}{Vernalization duration, which is the number} \\  & of days of optimum temperature necessary & 50 & 0–60 & days \\ \cline{1-1}  & for vernalization & & \\ \hline \multirow{3}{*}{P1D} & Photoperiod response, which is the percent & & \\  & reduction in photosynthesis for every 10 h & 55 & 0–200 & \% \\ \cline{1-1}  & reduction in the photoperiod & & \\ \hline \multirow{3}{*}{P5} & Grain-filling phase duration in growing & 559 & 100–1000 & \({}^{\circ}\)C... days \\ \cline{1-1}  & degree days & & \\ \hline G1 & Number of kernels per unit plant weight & 35 & 10–50 & number/g \\ \hline G2 & Standard kernel size & 40 & 10–80 & mg \\ \hline G3 & Standard filler weight & 1 & 1–8 & g \\ \hline \multirow{3}{*}{PHINT} & Photoperiod interval between leaf & \multirow{3}{*}{95} & 30–150 & \({}^{\circ}\)C... days \\ \cline{1-1}  & tip appearances & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter values used for calibration of the Crop Environment Resource Synthesis for Wheat (CERES-Wheat) model. To calibrate the crop model in an accurate simulation, forcing data (i.e., meteorological data, soil) and observations (i.e., flowering date, maturity date and yield ) during the winter wheat growing season at agricultural experimental stations were used, and an iterative process of adjusting the cultivar parameters (Table 3) was conducted until the best agreement between the modeled variables and observed parameters, such as the date of flowering, date of maturity, leaf area index, biomass and yield, was achieved and until the best-performing parameter values were generated.