## 2 Materials and Methods
### AquaCrop Model
#### 2.3.3 Model Validation Criteria  
Root-Mean-Square Error (\(RMSE\)), Mean Absolute Error (\(MAE\)), Percent Measured Error (\(PME\)) and Index of Agreement (\(d\)) were used to validate the AquaCrop model. \(RMSE\)  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{1}{c}{**Parameter Description**} & \multicolumn{1}{c}{**Value**} \\ \cline{2-3}  & **Main Season (July to October)** & **Off Season (January to April)** \\ \hline Base temperature (\({}^{\circ}\)C) & 10 & 10 \\ Upper temperature (\({}^{\circ}\)C) & 30 & 30 \\ Initial canopy cover (\%) & 10 & 6.5 \\ Time from sowing to emergence (GDD) & 152 & 117 \\ Maximum canopy coverage (\%) & 95 & 90 \\ Time between sowing and flowering (GDD) & 1302 & 1135 \\ Duration of flowering stage (GDD) & 136 & 164 \\ Time between sowing and senescence & 1491 & 1273 \\ initiation (GDD) & 1891 & 1681 \\ Time between sowing and maturity (GDD) & 0.30 & 0.30 \\ Effective minimum root depth (m) & 0.60 & 0.55 \\ Normalized water productivity due to \(ET_{o}\) & 15 & 16 \\ and CO\({}_{2}\) (g m\({}^{-2}\)) & 44 & 38 \\ Harvest index (HI\({}_{o}\)) & 44 & 38 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calibrated parameters of the FAO-AquaCrop 6.0 model used in simulating rice yield for the off-season and main season.  
measures the difference between the model-predicted values and the observed values of a parameter. The individual differences, called residuals, are aggregated into a single measure of predictive power by the _RMSE_. It measures the magnitude of discrepancy between two sets of data and is a useful metric for comparing the accuracy of different models in the context of comparing prediction errors. _RMSE_ is expressed as:  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(O_{i}-S_{i}\right)^{2}}{n}} \tag{1}\]  
where \(Si\) is the simulated rice yield, \(O_{i}\) is the observed rice yield, and n is the number of observations.  
The mean absolute error (_MAE_) of a test sample is expressed by the weighted average of all absolute differences between the prediction and observations. Both _RMSE_ and _MAE_ express average model prediction error and can range from 0 to infinity; they are indifferent to the direction of errors. _MAE_ is expressed as:  
\[MAE= \frac{\left(S_{i}-O_{i}\right)}{O_{i}} \tag{2}\]  
Bias in prediction is indicated by a prediction error (_PE_) in terms of the total difference between the measured and simulated data points. It is determined by:  
\[PE=\frac{\sum_{i=1}^{n}\left(S_{i}-O_{i}\right)}{n} \tag{3}\]  
The index of agreement (_d_) is a standardised measure of model prediction error that varies from 0 to 1. This index represents the ratio of mean-square error and potential error. A value of 1 indicates perfect agreement, while a value of 0 denotes no agreement at all. Due to squared differences, the index of agreement is overly sensitive to extreme values in the observed and simulated means and variances. The index of agreement, \(d\), is expressed as:  
\[d= 1-\frac{\sum_{i=1}^{n}\left(O_{i}-S_{i}\right)^{2}}{\sum_{i=1}^{n}\left(S_ {i}-O/+/O_{i}-O/\right)^{2}} \tag{4}\]  
where \(\tilde{O}\) is the average rice yield.