## 3 Results and Discussions
### Model Training and Testing Evaluation  
In training of RNNs, several optimizers were tested including Stochastic gradient descent, Adam, Adagrad, and RMSprop. The performance of Adam remained better in comparison with other optimizers in terms of accuracy and model convergence. The better performance of the Adam optimizer is in agreement the findings of [PERSON] et al. (2016). No major effect of increasing the number of neurons on model R\({}^{2}\) and RMSE was observed in training of RNNs used in this study. Similarly, no major effect of different learning rates on model R\({}^{2}\) and RMSE was observed e.g., 10\({}^{-2}\), 10\({}^{-3}\), and 10\({}^{-4}\). Dropout effect was also tested by freezing the 10%, 20%, and 30% random neurons to reduce the overfitting effects in training of RNNs used in this study. However, because of data normalization of the datasets, the RNNs used in the study were successfully converged without over and under fitting with approximately equal training and testing accuracies. Similar results were found in a study by [PERSON] et al., (2016) as no major effect of dropout was observed with normalized data. Therefore, all the RNNs used in this study were trained without introducing dropout in LSTM layers. In training of LSTM models for the Saint Peter site, training and testing losses were recorded to be 0.042 and 0.0404, respectively. Approximately equal values of training and testing losses depict \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Site** & **Mean \(\pm\) SD** & **Minimum** & **Maximum** \\ \hline \multirow{6}{*}{Maximum Temperature (\(\lx@math@degree\)C)} & Harrington & \(10.5\pm 10.6\) & \(-17.7\) & 32.5 \\  & North Cape & \(9.2\pm 10.2\) & \(-17.6\) & 31.2 \\  & PEI & \(10.2\pm 10.5\) & \(-17.2\) & 31.8 \\  & Saint Peters & \(10.5\pm 10.4\) & \(-17.0\) & 32.0 \\  & Summerside & \(10.7\pm 10.8\) & \(-18.2\) & 33.7 \\ \hline \multirow{6}{*}{Reference Evapotranspiration (mm/day)} & Harrington & \(1.9\pm 1.5\) & 0.1 & 8.2 \\  & North Cape & \(1.8\pm 14.4\) & 0.0 & 7.9 \\  & PEI & \(1.9\pm 1.4\) & 0.1 & 7.8 \\  & Saint Peters & \(1.9\pm 1.5\) & 0.1 & 9.3 \\  & Summerside & \(2.0\pm 1.5\) & 0.1 & 7.3 \\ \hline \multirow{6}{*}{Rainfall (mm/day)} & Harrington & \(3.1\pm 7.0\) & 0.0 & 92.9 \\  & North Cape & \(3.1\pm 7.7\) & 0.0 & 147.5 \\ \cline{1-1}  & PEI & \(3.0\pm 6.0\) & 0.0 & 89.7 \\ \cline{1-1}  & Saint Peters & \(3.2\pm 7.1\) & 0.0 & 85.3 \\ \cline{1-1}  & Summerside & \(2.4\pm 6.1\) & 0.0 & 103.8 \\ \hline \multirow{6}{*}{Relative Humidity (\%)} & Harrington & \(78.1\pm 10.5\) & 37.6 & 99.4 \\ \cline{1-1}  & North Cape & \(80.7\pm 9.6\) & 49.3 & 100.0 \\ \cline{1-1}  & PEI & \(78.9\pm 9.5\) & 47.6 & 98.4 \\ \cline{1-1}  & Saint Peters & \(79.1\pm 10.0\) & 38.7 & 98.0 \\ \cline{1-1}  & Summerside & \(77.7\pm 10.2\) & 46.7 & 98.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics of input and output variables for year 2011 to 2017.  
the successful model convergence without overfitting. LSTM models training RMSE was recorded to be 0.497 mm/day and training R\({}^{2}\) was recorded to be 0.88. Similarly, the value of RMSE for testing the LSTM model was recorded to be 0.46 mm/day and testing R\({}^{2}\) was 0.91. No major differences were observed in training and testing set accuracies when modeled with bidirectional LSTM for the Saint Peters site (Table 4). It is evident that with both models, there were higher testing accuracies in comparison with training accuracies, maybe because in the training stage usually the ANNs try to adjust their weights. Another reason could be because of unequal data points for training and testing phases. The higher numbers of data points in the training stage (give number of data points) might have reduced the accuracy of RNNs during the training phase. For the Harrington site, slightly higher losses and lower accuracies were observed in comparison with the Saint Peters site (Table 3).