## 3 Results and Discussion
### Training of the FTSW Prediction Model  
Figure 7 shows the \(R^{2}\)-score and RMSE during training of the BiLSTM model with input including the VPD (min) and irrigation amount and seven days of look-back. Early stopping [59] (an optimization strategy intended to lessen overfitting without sacrificing model accuracy) was used. The validation loss of the model was tracked during training, and if it did not improve after a certain number of iterations, the training was stopped. Figure 7 illustrates that the validation loss stopped improving at around Step 110, but the training loss continued to improve. The model with an output length of seven days required more time to complete the training compared to the model with an output length of one day. Figure 8 shows the \(R^{2}\)-score and RMSE during the training of these BiLSTM models with seven days of look-back and the output size. Figures 7 and 8 show that overfitting during training was more likely when the output size was greater than one and that the model overfit the training set without the early stopping optimization. \(R^{2}\)-score and a 5.85-7.31% decrease in the RMSE on the Colinas do Douro test set. Therefore, one of the important parameters affecting the BiLSTM model is the look-back of the model. Moreover, the performance of the BiLSTM model with the VPD (min) in its input features increased by 3-4% in the \(R^{2}\)-score compared to the model trained without these two variables as the input. To examine the effect of irrigation amount on the FTSW estimation, a model was trained to include irrigation as an input to the model. As shown in Table 5, the \(R^{2}\)-score increased in the range of 1%. Since the number of irrigations in the Colinas do Douro was low (between four and eight times in the period from 2018 to 2021), the influence of this variable on the performance of the model was also low. Figure 9 compares the observed value of the FTSW with the predicted values for the models with a look-back (input size) of seven days and an output length of one and seven days. The yellow line shows the best fit, and when the points in the scatter plot are closer to the line, better performance was obtained. As can be seen in Figure 4a,b, the points on the scatter plot for the model with the VPD as input were closer to the best-fit line than for the model with the VPD as the input, so better performance was obtained when the VPD was used as the input to the model. Table 6 shows the performance of the model trained with different look-backs and lengths of output. The model performed better when the look-back was extended, similar to the case where the output length was one, and the performance of the BiLSTM model with the VPD (min) in its input features was better than that of the BiLSTM without this feature. As shown in Tables 5 and 6, the model with an output length of one had a better performance compared to the models with an output size of three, five, and seven days. \begin{table}
\begin{tabular}{l c c c c c} \hline \multirow{2}{*}{**Input Variables**} & \multirow{2}{*}{**Look-Back** **(Days)**} & \multicolumn{4}{c}{**Colinas do Douro**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**Validation Set**} & \multicolumn{2}{c}{**Test Set**} \\ \cline{3-6}  & & \(R^{2}\)**-Score** & **RMSE (Normalized)** & \(R^{2}\)**-Score** & **RMSE** \\ \hline \multirow{3}{*}{Month, ETo, RH (avg), rainfall,} & 3 & 0.75 & 0.6 & 0.75 & 16.6 \\ \cline{2-6}  & 5 & 0.81 & 0.56 & 0.81 & 14.4 \\ \cline{2-6}  & 7 & 0.87 & 0.54 & 0.90 & 10.75 \\ \hline \multirow{3}{*}{Month, ETo, rainfall RH (avg), VPD (min)} & 3 & 0.77 & 0.50 & 0.79 & 15.39 \\ \cline{2-6}  & 5 & 0.83 & 0.53 & 0.85 & 12.78 \\ \cline{2-6}  & 7 & 0.92 & 0.41 & 0.93 & 8.98 \\ \hline \multirow{3}{*}{Month, ETo, rainfall, RH (avg), VPD (min), irr} & 3 & 0.75 & 0.51 & 0.79 & 15.34 \\ \cline{2-6}  & 5 & 0.87 & 0.46 & 0.86 & 12.53 \\ \cline{1-1} \cline{2-6}  & 7 & 0.96 & 0.31 & 0.94 & 8.03 \\ \hline \end{tabular}
\end{table} 
Table 5: The performance of the BiLSTM model to predict the FTSW one day ahead with different input variables.