## 5 Model Setup
### Model Scenarios  
The optimal values derived for each parameter of LSTM through the sensitivity analysis were applied in this study. Prior to setting up the model scenarios, the input data used in this simulation were precipitation, outlet discharge of Paldang dam, water surface elevation of Hangang River, and tidal level of Incheon, as mentioned in the previous section, and all the data were obtained from the station at the study area. The collected input data is for 10 years. Moreover, two scenarios were set up to evaluate the performance of the flood forecasting model and to evaluate the performance of the hybrid activation function proposed in this study.  
In the first scenario, the weights of the hybrid activation function were set from the near hyperbolic tangent function (\(w_{1}=0.1\) and \(w_{2}=0.9\)) to the near rectified linear unit function (\(w_{1}=0.9\) and \(w_{2}=0.1\)) because, the hyperbolic tangent function has an under-forecasting problem due to vanishing gradient and the rectified linear unit function has an over-forecasting problem due to dying neuron. Therefore, we compensated for these problems by changing the weights and found the optimal value of weights for accurate forecasting. Moreover, the trend in frequency of utilization is moving from hyperbolic tangent function to rectified linear unit function in many researches [30]. Therefore, the forecasting accuracy of the hybrid activation function proposed in this study was checked and the change of the forecasting accuracy was compared by changing the weights (\(w_{1}\) and \(w_{2}\)) of the hybrid activation function. The second scenario involved checking the applicability of the maximum forecasting time when using the hybrid activation function and the change in the forecasting accuracy was compared by changing the leading time. The simulation cases were summarized in Table 6.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Uncertainty (m)** & **CPU Time (s)** \\ \hline \multirow{6}{*}{Hidden Layer} & 1 & 0.50 & 8 \\  & 3 & 0.48 & 8 \\  & 5 & 0.27 & 10 \\  & 10 * & 0.18 & 14 \\  & 20 & 0.23 & 24 \\ \hline \multirow{6}{*}{Learning Rate} & 0.005 * & 0.22 & 8 \\  & 0.01 & 0.50 & 8 \\  & 0.02 & 0.67 & 9 \\  & 0.05 & 0.40 & 9 \\  & 0.10 & 0.61 & 9 \\ \hline \multirow{6}{*}{Sequence Length} & 1 * & 0.25 & 8 \\  & 3 & 0.38 & 10 \\  & 6 & 0.65 & 19 \\  & 9 & 1.00 & 21 \\  & 12 & 1.25 & 28 \\  & 24 & 1.50 & 54 \\ \hline \multirow{6}{*}{Iterations} & 1 & 0.58 & 8 \\  & 10 & 0.45 & 8 \\ \cline{1-1}  & 100 & 0.50 & 8 \\ \cline{1-1}  & 1000 * & 0.11 & 22 \\ \cline{1-1}  & 10,000 & 0.10 & 158 \\ \hline \hline \end{tabular}  
*: Optimal value for flood forecasting model.  
\end{table}
Table 5: Sensitivity analysis for parameter.  
The 7 years of input data (from 2009 to 2015) were used as the training dataset and the 3 years of input data (from 2016 to 2018) were used for the test dataset in order to simulate the scenarios. In particular, 2016 was selected for model evaluation because the maximum water surface elevation occurred in 2016. Moreover, the observed water surface elevation corresponding to about 50 h from 5-7 July 2016 was compared. The maximum water surface elevation (EL. 5.61 m) occurred on 5 July 2016 at 10 p.m. In addition, the input data were normalized to improve the accuracy of the forecasting model and to improve the learning speed. The minmax normalization was used and rescaling (from 0 to 1) of the input data was applied to the simulation.