## 7 Conclusions  
The data-driven model was used for forecasting the water surface elevation in a tidal river and applied to Hangang River, Korea, in this study. The LSTM was constructed using the TensorFlow, an open-source library of deep learning and hourly data, such as precipitation, outlet discharge and tidal level were used as the input dataset through a \(t\)-test analysis. In particular, the hybrid activation function was proposed to resolve a specific issue of the single activation function, which is that they tended to under-forecast the results at the conditions for high water surface elevations above EL. 3.9 m, the designated elevation for flood management in Hangang River. The parameters of LSTM were determined through the sensitivity analysis, in which the number of hidden layers was 10, the learning rate was 0.005, and there were 1000 iterations. Moreover, sequence length, which is the most important parameter that determines the temporal amount of learning information during the learning time, was simulated for various leading times. Finally, the forecasting results, compared with the observed data, show improvement in the prediction accuracy (Scenario I) and the enhancement of the application range of the leading time interval (Scenario II) with the hybrid activation function. First, for the application of the hybrid activation function, the optimal performance of the forecasting model was obtained when \(w_{1}\) = 0.6 and \(w_{2}\) = 0.4. The forecasting accuracy of all the data was presented to be 0.31 m in RMSE and 98.9% in NSE. However, in this case, the accuracy of the forecasting results was the same as the existing activation function, such as the hyperbolic tangent and ReLU. On the other hand, the RMSE was 0.32 m, NSE was 58.1%, and PE was 0.19 m at the conditions for high water surface elevation, which can cause flood damage at the riverside. These results show that the RMSE decreased by 0.22-0.25 m, PE also decreased by 0.11-0.21 m, and NSE increased up to 79.3%-97.0% compared with the existing single activation function. Therefore, the hybrid activation function proposed in this study was suitable for forecasting high-water levels above the specified elevation of Hangang River. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Activation Function** & **Accuracy \({}^{*}\)** & **Precision \({}^{*}\)** & **Recall \({}^{*}\)** \\ \hline Hyperbolic Tangent \({}^{**}\) & & & \\ (\(w_{1}\) = 0.0, \(w_{2}\) = 1.0) & & & \\ \hline Rectified Linear Unit \({}^{***}\) & & & \\ (\(w_{1}\) = 1.0, \(w_{2}\) = 0.0) & 0.99 & 0.90 & 0.76 \\ \hline Hybrid \({}^{***}\) & & & \\ (\(w_{1}\) = 0.6, \(w_{2}\) = 0.4) & 0.99 & 0.95 & 0.84 \\ \hline \hline \end{tabular} \({}^{*}\) Accuracy = (\(tf+m\))/(\(tf+tn+ff+fn\)); Precision = (\(tf\))/(\(tf+ff\)); Recall = (\(tf\))/(\(tf+fn\)); \({}^{**}\) Hyperbolic Tangent (\(tf\) = 19, \(tn\) = 8245, \(ff\) = 2, \(fn\) = 6); \({}^{***}\) Rectified Linear Unit (\(tf\) = 21, \(tn\) = 8244, \(ff\) = 3, \(fn\) = 4); \({}^{***}\) Hybrid (\(tf\) = 21, \(tn\) = 8246, \(ff\) = 1, \(fn\) = 4).  
\end{table} 
Table 13: The results of the classification evaluation according to the activation function. Secondly, the limitation of the application range of the leading time interval was obtained when the hybrid activation function was applied, which can be accurately forecasted at a high water surface elevation. We found a lower accuracy of forecasting at the longer leading time interval. The accuracy of forecasting was acceptable up to 3 h in terms of RMSE and NSE because the value of the partial autocorrelation coefficient about the water surface elevation at Hangang River was under the 95% confidence interval after the 3 h leading time interval. Therefore, it was considered that the correlation of the water surface elevation was significant up to 3 h in Hangang River. However, in the case of PE, the accurate forecasting was performed up to 6 h of leading time.