## 6 Results and Analysis
### Results from Scenario II  
The maximum forecasting time for the hybrid activation function applying the results of Scenario I (\(w_{1}\)= 0.6 and \(w_{2}\)= 0.4) is summarized in Table 10. In addition, the forecasting results and the observed data were compared for about 50 h from 5 July 2016 as the leading time was changed (see Figure 6).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Activation Function** & **RMSE (m)** & **NSE (\%)** & **PE (m)** \\ \hline Hyperbolic Tangent (\(w_{1}\)= 0.0, \(w_{2}\)= 1.0) & 0.54 & \(-\)21.2 & 0.30 \\ \hline Rectified Linear Unit (\(w_{1}\)= 1.0, \(w_{2}\)= 0.0) & 0.57 & \(-\)38.9 & 0.40 \\ \hline Hybrid (\(w_{1}\)= 0.6, \(w_{2}\)= 0.4) & 0.32 & 58.1 & 0.19 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of the accuracy in various activation functions (above 3.9 m).  
As the leading time interval increased, the value of water surface elevation was shifted to delay the peak event and under-forecasted the values in the rising rim. The RMSE increased sharply after 3 h of leading time while the NSE decreased sharply after 3 h of leading time (see Figure 7). Therefore, the good forecasting of the water surface elevation was up to 3 h in terms of RMSE and NSE. When using the hybrid activation function, the RMSE decreased by 0.10 m to 0.25 m compared with the hyperbolic tangent function and the rectified linear function, and the NSE increased by 3.2% to 20.1% compared with the hyperbolic tangent function and the rectified linear function. Finally, the PE was 0.03 m to 0.41 m less than the hyperbolic tangent function and the rectified linear unit function, respectively. From the results of Scenario II (see Table 11), it can also be considered that the use of the hybrid activation function could partially solve the vanishing gradient and dying neuron problems through accurate forecasting results at a high water surface elevation. Moreover, it was considered that the leading time interval was two times longer than the single activation functions when using the hybrid activation function. However, when using the hybrid function, it was shown that the accuracy of the forecasting was poor after 3 h of leading time interval. The reason for this was that the value of partial the autocorrelation coefficient of the water surface elevation at Hangang River was under the 95% confidence interval after 3 h of leading time interval (the range of 95% confidence interval was \(-\)0.2 to 0.2 in the partial autocorrelation analysis). Therefore, it was shown that the correlation of the water surface elevation was significant up to 3 h in Hangang River (see the small figure in Figure 8). However, in the case of PE, accurate forecasting was performed up to 6 h of leading time. Thus, the leading time interval was acceptable up to 6 h because the accurate forecasting of the peak water surface elevation is also important in flood forecasting.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **RMSE (m)** & **NSE (\%)** & **PE (m)** & **Remark** \\ \hline II-(A) & 0.33 & 98.8 & 0.20 & Accept/Good \\ II-(B) & 0.31 & 98.9 & 0.19 & Accept/Good \\ II-(C) & 0.77 & 93.6 & 0.00 & Accept \\ II-(D) & 1.13 & 86.1 & 0.89 & Not Good \\ II-(E) & 1.31 & 81.2 & 1.69 & Not Good \\ II-(F) & 1.52 & 74.8 & 2.97 & Not Good \\ II-(G) & 1.93 & 59.3 & 2.98 & Not Good \\ II-(H) & 2.05 & 53.9 & 3.84 & Not Good \\ II-(I) & 2.33 & 40.8 & 4.25 & Not Good \\ \hline \hline \end{tabular}
\end{table}
Table 10: Summary of the accuracy for various leading times in Scenario II (Period: 5–7 July 2016 about 50 h, \(w_{1}=0.6\) & \(w_{2}=0.4\)).  
Figure 7: Overall results from Scenarios I and II. (**A**) Scenario I; (**B**) Scenario II.