## 6 Results and Analysis
### Results from Scenario I  
The result of the improvement of the forecasting accuracy when using the hybrid activation function proposed in this study are summarized in Table 7. In addition, the forecasting result and the observed water surface elevation are presented in Figure 5 according to the change of weight (\(w_{1}\) and \(w_{2}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Scenario**} \\ \hline  & **1** & & **II** \\ \hline
**Case** & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) & **Case** & **Leading Time Interval** \\ \hline
1 & 0.1 & 0.9 & A & 1 h \\
2 & 0.2 & 0.8 & B & 3 h \\
3 & 0.3 & 0.7 & C & 6 h \\
4 & 0.4 & 0.6 & D & 9 h \\
5 & 0.5 & 0.5 & E & 12 h \\
6 & 0.6 & 0.4 & F & 15 h \\
7 & 0.7 & 0.3 & G & 18 h \\
8 & 0.8 & 0.2 & H & 21 h \\
9 & 0.9 & 0.1 & I & 24 h \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation cases for the application of the hybrid activation function. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **RMSE (m)** & **NSE (\%)** & **PE (m)** & **Remark** \\ \hline I-1 & 0.38 & 98.4 & 0.13 & No good \\ I-2 & 0.47 & 97.6 & 0.28 & No good \\ I-3 & 0.41 & 98.1 & 0.10 & No good \\ I-4 & 0.48 & 97.5 & 0.26 & No good \\ I-5 & 0.38 & 98.4 & 0.43 & No good \\ I-6 & 0.31 & 98.9 & 0.19 & Accept/Good \\ I-7 & 0.37 & 98.5 & 0.15 & Accept \\ I-8 & 0.43 & 97.9 & 0.11 & No good \\ I-9 & 0.41 & 98.2 & 0.20 & No good \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of accuracy for various weights in Scenario I (Period: 5–7 July 2016, about 50 h). The forecasting results were changed according to the weights (see Figure 6). And the forecasting results were well matched with the observed water surface elevation at \(w_{1}=0.6\) and \(w_{2}=0.4\). In terms of forecasting accuracy, the NSE was 98.9%, the RMSE was 0.31 m, and the PE was 0.19 m at \(w_{1}=0.6\) and \(w_{2}=0.4\), according to Table 7. The forecasting results have an uncertainty. Therefore, the confidence interval was examined by changing the weights (from \(w_{i}=0.1\) to \(w_{i}=0.9\) where, \(i=1\),2). Most of the forecasting results were under-forecasted and they were overfitted at high water surface elevations above the specified elevation (EL. 3.9 m) for flood management when compared with the observed data. The results of the confidence interval when using the hybrid activation function proposed in this study are summarized in Table 8.  
Figure 5: Results of the flood forecasting model in Scenario I. As shown in the I-6 case, the forecasting results of the hybrid activation function (\(w_{1}=0.6\) and \(w_{2}=0.4\)) obtained the smallest confidence interval and a better performance than the other cases. In addition, the forecasting results of the hyperbolic tangent function and the rectified linear unit \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **CI * (\%)** & **Accuracy ** (\%)** & **Standard Deviation (m)** & **Remark** \\ \hline I-1 & 99.0 & 29.0 & 0.12 & No good \\ I-2 & 95.0 & 18.0 & 0.11 & No good \\ I-3 & 95.0 & 25.0 & 0.10 & No good \\ I-4 & 90.0 & 32.0 & 0.11 & No good \\ I-5 & 80.0 & 40.0 & 0.10 & No good \\ I-6 & 80.0 & 61.0 & 0.10 & Accept/Good \\ I-7 & 80.0 & 46.0 & 0.11 & Accept \\ I-8 & 95.0 & 32.0 & 0.11 & No good \\ I-9 & 99.0 & 32.0 & 0.14 & No good \\ \hline \hline \end{tabular}  
* CI = Confidence Interval; ** accuracy = total number of correct forecasting/total number of observed data (at 80.0% CI).  
\end{table} 
Table 8: Summary of confidence intervals for various weights in Scenario I.  
Figure 6: Results of the flood forecasting model according to Scenario II ((**A**) = 1 h leading time; (**B**) = 3 h leading time; (**C**) = 6 h leading time; (**D**) = 9 h leading time; (**E**) = 12 h leading time; (**F**) = 15 h leading time; (**G**) = 18 h leading time; (**H**) = 21 h leading time; (**I**) = 24 h leading time).