## 3 Results and Discussion
At the end of 70 iterations, the set of hyperparameters with minimal validation loss was selected. These selected values are shown in Table 4. For simplicity, the decay and learning rates were modified to a power of 10. The model was trained on different datasets. Once the model was trained on all datasets (70% of each dataset). The other time, the model was trained on two datasets and tested on the third dataset. Each model was trained for a maximum number of 500 iterations (epoch = 500). Early stopping was used to avoid overfitting. Early stopping \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Learning Rate** & **Decay** & **Batch Size** & **Dropout Size** \\ \hline BLSTM & \(10^{-4}\) & \(10^{-5}\) & 124 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hyperparameters obtained from Bayesian optimization for each location. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model Architecture**} & \multirow{2}{*}{**Locations**} & \multicolumn{4}{c}{**Number of Nodes per Layer**} \\ \cline{3-5}  & & **64** & **128** & **256** & **512** \\ \hline \multirow{4}{*}{LSTM-2 layers} & Loc. 1 & 0.01713 & 0.01197 & 0.01135 & 0.01222 \\  & Loc. 2 & 0.01906 & 0.01591 & 0.01446 & 0.01466 \\  & Loc. 3 & 0.02064 & 0.02059 & 0.02065 & 0.02035 \\ \cline{2-5}  & Mean & 0.018943 & 0.016156 & 0.015486 & 0.015743 \\ \hline \multirow{4}{*}{LSTM-3 layers} & Loc. 1 & 0.01973 & 0.01221 & 0.01114 & 0.01128 \\  & Loc. 2 & 0.01923 & 0.01566 & 0.01463 & 0.01460 \\  & Loc. 3 & 0.02168 & 0.02089 & 0.02106 & 0.02134 \\ \cline{2-5}  & Mean & 0.020213 & 0.016253 & 0.01561 & 0.01574 \\ \hline \multirow{4}{*}{LSTM-4 layers} & Loc. 1 & 0.01911 & 0.01401 & 0.01317 & 0.01156 \\  & Loc. 2 & 0.02280 & 0.01623 & 0.01490 & 0.01490 \\  & Loc. 3 & 0.21685 & 0.15875 & 0.12353 & 0.11088 \\ \cline{2-5}  & Mean & 0.086253 & 0.0629 & 0.05053 & 0.045886 \\ \hline \multirow{4}{*}{BLSTM-1 layer} & Loc. 1 & 0.01527 & 0.01207 & 0.01104 & 0.0115 \\  & Loc. 2 & 0.01870 & 0.01715 & 0.01556 & 0.01522 \\  & Loc. 3 & 0.02001 & 0.02023 & 0.01949 & 0.01936 \\ \cline{2-5}  & Mean & 0.017993 & 0.016483 & 0.015363 & 0.01536 \\ \hline \multirow{4}{*}{BLSTM-2 layers} & Loc. 1 & 0.01574 & 0.01374 & 0.01268 & 0.01289 \\  & Loc. 2 & 0.01893 & 0.01689 & 0.01583 & 0.01583 \\ \cline{1-1}  & Loc. 3 & 0.02017 & 0.01959 & 0.01945 & 0.01982 \\ \cline{1-1} \cline{2-5}  & Mean & 0.01828 & 0.01674 & 0.015986 & 0.01618 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation MSE for different number of LSTM layers and LSTM nodes per layer. is a regularization strategy that determines how many epochs can be run before overfitting begins [31]. In our implementation, the validation error was monitored during training, and if it did not improve after a maximum of ten epochs, training was stopped. Figure 8 shows the \(R^{2}\) and RMSE during training on the training set and the validation set. The error improved after 200 epochs on the training set but did not improve again on the validation set. Tables 5 and 6 and Figure 9 show the evaluation of the model on the test set and the predicted value compared to the true values of the SWC and ETo, respectively. The results indicated that although the MSE (the variance of the error) at Loc. 2 was lower than the MSE at Loc. 3, the \(R^{2}\)- score (the variance explained by the model over the total variance) improved at Loc. 3. Therefore, it is not sufficient to use only one metric to evaluate a model. As Figure 9 and Table 5 show, the best accuracy in predicting ETo and SWC was achieved with the dataset of Loc. 2 and Loc. 3, respectively. ET was underestimated with the model in Loc. 2 and Loc. 3 but overestimated in Loc. 1. The results also show that as the depth of the soil increases, the accuracy of the model for predicting SWC increases. This could be due to the fact that the range and standard deviation of SWC decrease as the soil  
Figure 8: \(R^{2}\) and RMSE during training. The **left side** shows the \(R^{2}\)-score and the **right side** shows the RMSE.