## 3 Results and Discussions
### Model Training and Testing Evaluation
In training of LSTM for the Harrington site, training and testing losses were recorded to be 0.0523 and 0.0555, respectively. Training and testing RMSE were 0.54 and 0.58, respectively, for LSTM models. The respective training and testing R\({}^{2}\) were 0.85 and 0.86, respectively. In training of bidirectional LSTM for the Harrington site, higher training and testing accuracies were recorded in comparison with LSTM. The testing accuracy of bidirectional LSTM was 5% higher in comparison with LSTM for the Harrington site. The advance architecture of bidirectional LSTM might help them to attain the higher accuracies in comparison with LSTM. Furthermore, the dataset of the Harrington sites showed slightly higher standard deviation in comparison with other sites selected for this study. The results suggested that the bidirectional LSTM can achieve higher accuracy with scatter data in comparison with LSTM. North Cape LSTM training and testing losses recorded to be 0.0337 and 0.0380, respectively; slightly lower than all other sites. The LSTM training and testing RMSE was recorded to be 0.35 and 0.39, respectively. The LSTM training and testing R\({}^{2}\) was recorded to be 0.93 and 0.92, respectively. No major differences were observed in losses and accuracies for the North Cape site when modeled with bidirectional LSTM. The two directional learning may achieve the higher accuracies in the time series forecasting problem. However, this study estimates the time steps of time series by inputting climatic variables only as there are no forecasting involved. Summerside LSTM training and testing losses were recorded to be 0.0550 and 0.0490, respectively. The LSTM training and testing RMSE was recorded to be 0.53 and 0.45, respectively. The LSTM training and testing R\({}^{2}\) was recorded to be 0.87 and 0.91, respectively. No major differences were observed in losses and accuracies for the Summerside site when modeled with bidirectional LSTM. For both RNN, higher testing accuracies were observed in comparison with training accuracies for Summerside. For the PEI data set, slightly lower LSTM training and testing losses were observed (Table 3). The LSTM training and testing R\({}^{2}\) were recorded to be 0.91 and 0.92 respectively. There were no major differences in losses and accuracies for PEI data set when modeled with bidirectional LSTM (Figure 5). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multirow{2}{*}{**Model**} & \multirow{2}{*}{\begin{tabular}{c} **Training** \\ **MAE** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Testing** \\ **MAE** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Training** \\ **RMSE** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Training** \\ **R\({}^{2}\)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Testing** \\ **RMSE** \\ \end{tabular} } \\ \hline \multirow{2}{*}{St Peters} & LSTM & 0.0420 & 0.0404 & 0.50 & 0.88 & 0.46 & 0.91 \\  & \({}^{1}\) B LSTM & 0.0419 & 0.0405 & 0.49 & 0.88 & 0.46 & 0.91 \\ \hline \multirow{2}{*}{Harrington} & LSTM & 0.0523 & 0.0555 & 0.54 & 0.85 & 0.58 & 0.86 \\  & B LSTM & 0.0461 & 0.0450 & 0.48 & 0.86 & 0.46 & 0.91 \\ \hline \multirow{2}{*}{North Cape} & LSTM & 0.0337 & 0.0380 & 0.35 & 0.93 & 0.39 & 0.92 \\  & B LSTM & 0.0340 & 0.0375 & 0.34 & 0.93 & 0.38 & 0.92 \\ \hline \multirow{2}{*}{Summerside} & LSTM & 0.0550 & 0.0490 & 0.53 & 0.87 & 0.45 & 0.91 \\  & B LSTM & 0.0563 & 0.0497 & 0.53 & 0.87 & 0.45 & 0.91 \\ \hline \multirow{2}{*}{PEI} & LSTM & 0.0417 & 0.0438 & 0.40 & 0.91 & 0.42 & 0.92 \\  & B LSTM & 0.0415 & 0.0437 & 0.40 & 0.91 & 0.42 & 0.92 \\ \hline \hline \end{tabular}  
\({}^{1}\) B LSTM; bidirectional LSTM.  
\end{table} 
Table 4: Training and testing evaluation of recurrent neural networks. Overall, no major effect was observed in the accuracy of LSTM and bidirectional LSTM for all sites. However, for Harrington and PEI data sets, the accuracy of bidirectional LSTM was slightly better.