## 2 Materials and Methods
### Data Input of AquaCrop Model and Analysis
#### 2.4.6 Model Evaluation  
Evaluation of model performance is essential for providing a quantitative estimate of its ability to reproduce an observed variable, to evaluate the impact of calibrating model parameters and to compare model results with previous research. Several statistical indicators are available to evaluate the performance of a model. Each has its own strengths and weaknesses, meaning that the use of an ensemble of different indicators is necessary to assess model performance sufficiently.  
The AquaCrop model results for both experimental groups were evaluated against the experimental data set from the 2013 rainy season using the calibrated model parameters. To evaluate the goodness of fit between the observed yield and simulated output, statistical indicators such as the coefficient of determination (R\({}^{2}\)), the Nash-Sutcliffe model efficiency coefficient (EF), [PERSON]'s index of agreement or compatibility (d), the root mean square error (RMSE) and the normalized root mean square error (NRMSE) were used to compare the simulated and measured values of the parameters [27; 67].  
R\({}^{2}\) shows the discrepancy between the simulated and measured values, signifying the proportion of the variance in the measured data described by the model. It ranges from 0 to 1, in which values close to 1 indicate a good agreement and values greater than 0.5 are considered acceptable. EF shows the efficiency of the model in simulations of the parameters. The index of the agreement is a measure of the relative error in the model estimates. It is a dimensionless number and ranges from minus infinity to 1, where 1 indicates a perfect match between the model and the observations. An EF of 0 means that the model predictions are as accurate as the average of the observed data. A negative EF occurs when the mean of the observations is a better prediction than the model [67].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Description**} & \multicolumn{3}{c}{**Value**} \\ \cline{2-4}  & **Group A** & **Group B** & **Units/Meaning** \\ \hline Soil surface covered by an individual seedling at 90\% & & & \\ emergence (cm\({}^{2}\)/plant) & 5 & 5 & \(\mathrm{CC_{o}}\) \\ \hline Number of plants per hectare & 2,000,000 & 2,000,000 & Plant/ha \\ Time from transplanting to recover & 1 & 1 & days \\ Maximum canopy cover (\(\mathrm{CC_{x}}\)) & 85.18 & 90.78 & \% \\ Time from transplanting to start of senescence & 107 & 98 & days \\ Time from transplanting to maturity, i.e., length of crop cycle & 110 & 105 & days \\ Time from sowing to flowering & 65 & 65 & days \\ Length of the flowering stage & 15 & 20 & days \\ Minimum effective rooting depth (\(\mathrm{Z_{n}}\)) & 0.30 & 0.30 & m \\ Maximum effective rooting depth (\(\mathrm{Z_{x}}\)) & 0.35 & 0.35 & m \\ Reference harvest index (\(\mathrm{HI_{o}}\)) & 36 & 43 & \% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cultivar-specific parameters input into the AquaCrop model.  
[PERSON]'s index of agreement (d) is a method used to measure the degree to which the observed data are approached by the predicted data. It ranges between 0 and 1, in which 0 indicates no agreement and 1 indicates perfect agreement. The root mean square error (RMSE) is the most widely used statistical indicator for measuring the average magnitude of the difference between predictions and observations. It ranges from 0 to positive infinity. The normalized root mean square error (NRMSE) is the normalized RMSE using the mean of the observed variable \(\overline{\text{O}}\). The NRMSE is expressed as a percentage and gives an indication of the relative difference between the model and the observations. A simulation can be considered excellent if the NRMSE is smaller than 10%, good if between 10% and 20%, fair if between 20% and 30% and poor if larger than 30% [67].