## 3 Model Application in a Simulated River Network
### Impact of the Number of Measurement Stations and the Amount of Observed Data
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Measurement Station** & **Roughness** & **Water-Level** & **Water-Level** & **Water-Level** & **Water-Level** & **Water-Level** \\
**Station** & **RMSE** & **RMSE of Node 3** & **RMSE of Node 7** & **RMSE of Node 26** & **RMSE of** & **RMSE of** \\
**Number** & & & & & **Node 14** & **Node 24** \\ \hline
1 & 0.0018 & \(1.358\times 10^{5}\) & / & / & / & / \\
2 & 0.0012 & \(8.182\times 10^{6}\) & \(9.292\times 10^{6}\) & / & / & / \\
3 & 0.0011 & \(7.461\times 10^{6}\) & \(3.038\times 10^{6}\) & \(1.083\times 10^{5}\) & / & / \\
4 & 0.0010 & \(5.466\times 10^{6}\) & \(3.104\times 10^{6}\) & \(1.300\times 10^{5}\) & \(3.550\times 10^{6}\) & / \\
5 & 0.0008 & \(3.448\times 10^{6}\) & \(3.178\times 10^{6}\) & \(4.967\times 10^{6}\) & \(1.404\times 10^{6}\) & \(2.952\times 10^{6}\) \\ \hline \end{tabular}
\end{table} 
Table 1: RMSE values of roughness and water level at the measurement nodes. Figure 4: Impact of the number of measurement stations on roughness RMSE. Figure 5: Impact of the number of measurement stations on inversed roughness values at river segments 1 to 41. Table 2 shows that the roughness RMSE and water-level RMSE of the observational points generally decreased as the amount of observational data increased. The roughness RMSE decreased slightly, only 1.256%, when the observational data points increased from 10 to 20. A further increase in observational data caused a negligible decrease in roughness RMSE. This is also reflected by the spatial distribution of the inversed roughness at all 41 nodes (Figure 7). The radar map of 20 observational data overlapped with that of 30 observational data. However, the water-level RMSE significantly decreased when the observational data points increased from 20 to 30. For example, there was a 36.2% and 63.1% decrease in water-level RMSE at Nodes 3 and 26, respectively. This observation indicates that water-level forecasting is rather sensitive to variations in bed roughness. Care should be taken to invert the bed roughness at each node. Although the model calculation cost increased by 49% with observational data from 10 to 30, this calculation cost (less than 1 min) was still low given that a complex river network was used in this study. The personal computer used for analysis was a Windows 10 system equipped with a 3.2 GHz Intel Core i7-8700K processor and 16.0 GB DDR4 RAM. We obtained the optimized model with 3 measurement stations and 30 observ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Observational** & **Calculation** & **Roughness RMSE** & \multicolumn{3}{c}{**Water-Level RMSE**} \\ \cline{3-6}
**Data** & **Cost (s)** & & **Node 3 (m)** & **Node 7 (m)** & **Node 26 (m)** \\ \hline
10 & 26.9 & 0.00104467 & \(7.46\times 10^{6}\) & \(3.04\times 10^{6}\) & \(1.08\times 10^{5}\) \\
20 & 34.9 & 0.00103155 (\(\downarrow 1.256\%\)) & \(5.28\times 10^{6}\) (\(\downarrow 29.2\%\)) & \(3.23\times 10^{6}\) (\(\downarrow-6.3\%\)) & \(1.04\times 10^{5}\) (\(\downarrow 4.4\%\)) \\
30 & 40.2 & 0.00103153 (\(\downarrow 0.002\%\)) & \(3.37\times 10^{6}\) (\(\downarrow 36.2\%\)) & \(2.27\times 10^{6}\) (\(\downarrow 29.6\%\)) & \(3.82\times 10^{6}\) (\(\downarrow 63.1\%\)) \\ \hline \hline \end{tabular} Note: the \(\downarrow\) means the decreasing percentage.  
\end{table} 
Table 2: Roughness RMSE and water-level RMSE at Nodes 3, 7 and 26 with different observational data. Figure 6: Distribution of inversed values of roughness with three observational stations.