## 3 Results
### Validation of Existing Models M3 through M8  
For the validation of the six models proposed by [PERSON] [13], the measured results obtained by ADCP were used in the case of the depth (\(h\)), the river width (\(W\)), and the average velocity (\(V\)). The bed slope (\(S\)) was calculated by dividing the difference in the thalweg elevation at each point (measured using ADCP) by the river distance between successive points. These distances were calculated with the use of the Korea Reach File (KRF version 3.0 (Sejong, Korea)) provided by the Ministry of Environment for delineating stream network. For the median particle diameter of bed materials (\(d_{50}\)), basic reference data values for river management were used. Model validation was performed using 58 measurements, including the median particle diameter of bed materials among a total of 82 measurements. Among the 58 measured data, the Geumho (25 data) and Nam Rivers (14 data) yielded no data for median particle diameters of the bed materials before the confluence. The comparison was possible only in the case of the Hwang River (two data at upstream of confluence and 17 at downstream). Figure 8 shows the validation results of the models proposed by [PERSON] [13] using the explanatory variables. In the case of the models, relatively accurate prediction results were presented comparison with the measured results, except for M4. In particular, the measured results obtained from the Geumho and Nam Rivers have accurately predicted the characteristics, such as the value of the total sediment load, which was large in the vicinity of the Hwang River confluence, and the value of the total sediment load, which was smaller in regions before (rather than after) the Hwang River confluence. However, the predicted results of some models (M4 and M5) showed a low level of reliability (root-mean-square error (RMSE) > 3000 ton/km\({}^{2}\)-year). This is thought to be caused by the use of overly subdivided formulas compared with other models, thus leading to low predictability. In particular, the predicted total sediment load value of M4 was highly inaccurate even when compared with the results of M5. This is likely caused by the problem of determining submodels used for prediction (Figure 9). In the case of explanatory variables for 58 hydraulic factors used for model validation, the conditions are relatively similar owing to the location in the main stream of the Nakdong River. However, unlike other models, which used the water velocity with small coefficient of variations as the first classification criteria, M4 determined submodels based on the river width and water depth with relatively large variation. This led to a lack of consistency in the index values that corresponded to the explanatory variables of the subformulas developed based on inadequate explanatory variables, and thus resulted in inaccurate prediction results (Table 10). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Statistical Factor** & **Water Depth** & **Bed Slope** & **Width (\(W\))** & **Velocity** & **Median** \\  & **(\(h\))** & **(S)** & & **(\(V\))** & **Diameter (\(d_{50}\))** \\ \hline average & 5.50 & 0.001002 & 333.36 & 0.10 & 0.96 \\ \hline variance & 1.26 & 0.000001 & 4708.82 & 0.01 & 1.04 \\ \hline standarddeviation & 1.12 & 0.001208 & 68.62 & 0.08 & 1.02 \\ \hline coefficient of variation & 4.90 & 0.83 & 4.86 & 1.27 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Simple statistical analysis outcomes for explanatory variables for M3–M8. Figure 8: Predicted total sediment loads from models (**a**) M3, (**b**) M4, (**c**) M5, (**d**) M6, (**e**) M7, and (**f**) M8. The black circles represent total sediment load for Geumho River, red circles represent total sediment load for down stream of Hwang River confluence, blue circles represent total sediment load for upstream of Hwang River confluence, and the cyan circles represent total sediment load for Nam River. (In this figure, the measured total suspended sediment load is assumed to be the measured total sediment load).