## 2 Materials and Methods
### Existing Models Using Model Tree Technique of Data Mining
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Submodel**} & \multicolumn{4}{c}{**Conditions**} & \multicolumn{2}{c}{**Equations**} \\ \cline{3-6}  & & \(V\) **(m/s)** & \(H\) **(m)** & _d_\({}_{50}\) **(mm)** & & \\ \hline \multirow{4}{*}{M6} & E1 & \(\leq 0.51\) & - & - & - & \(2536.40\times S^{0.0079}\times W^{0.0091}\times V^{1.78}\times d_{50}^{-0.2791}\) \\ \cline{2-6}  & E2 & & \(\leq 0.76\) & - & \(165777.2\times S^{0.2737}\times W^{-0.1202}\times V^{2.4127}\times d_{50}^{-0. 01317}\) \\ \cline{2-6}  & E3 & \(0.51<V\leq\) & \multirow{2}{*}{\(\leq 236.51\)} & \(>0.76\) & - & \(2692.43\times S^{0.267}\times W^{0.5352}\times V^{3.5318}\times d_{50}^{-0.6276}\) \\ \cline{2-6}  & E4 & \(0.96\) & & \(\leq 0.42\) & - & \(391.86\times S^{0.0079}\times W^{0.5971}\times V^{1.5285}\times d_{50}^{-0. 30072}\) \\ \cline{2-6}  & E5 & & \(>236.51\) & \(>0.42\) & - & \(8.49\times 10^{-04}\times S^{0.0079}\times W^{0.2938}\times V^{0.5975}\times d_{50}^{-0. 30072}\) \\ \cline{2-6}  & E6 & \(0.96<V\leq\) & \multirow{2}{*}{\(\leq 0.79\)} & - & \(212266.96\times S^{0.3302}\times W^{0.0219}\times V^{2.5851}\times d_{50}^{-0. 4764}\) \\ \cline{2-6}  & E7 & \(1.2<V\leq\) & \multirow{2}{*}{\(\leq 278.38\)} & \multirow{2}{*}{\(\leq 0.79\)} & - & \(45922.02\times S^{0.5121}\times W^{0.0429}\times V^{3.018}\times d_{50}^{30 298}\) \\ \cline{2-6}  & E8 & \(1.95\) & & \(\leq 278.38\) & \(>0.79\) & - & \(9024.51\times S^{0.4256}\times W^{0.5475}\times V^{2.2057}\times d_{50}^{0. 30928}\) \\ \cline{2-6}  & E9 & & - & \(\leq 0.000358\) & \(68851\times S^{0.2539}\times W^{-0.247}\times V^{3.1039}\times d_{50}^{-0. 3761}\) \\ \cline{2-6}  & E10 & \(>1.95\) & & - & \(>0.000358\) & \(1690.37\times S^{-0.073}\times W^{0.0247}\times V^{3.1039}\times d_{50}^{-0. 3761}\) \\ \cline{2-6}  & E11 & & \(278.38<\) & \(\leq 311.69\) & \(\leq 0.66\) & - & \(32.78\times S^{0.0411}\times W^{1.3535}\times V^{2.6267}\times d_{50}^{1.2195}\) \\ \cline{2-6}  & E12 & \(>0.96\) & & \(>0.66\) & - & \(968.65\times S^{0.0735}\times W^{0.7367}\times V^{0.785}\times d_{50}^{-0. 0452}\) \\ \cline{2-6}  & E13 & & \(>311.69\) & \(>0.66\) & - & \(1351\times S^{0.3632}\times W^{1.1942}\times V^{0.4309}\times d_{50}^{-0. 0452}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Application conditions and determination coefficients of Model 5 (M5). In the model development process based on the use of the model tree, the minimum number of data points in the subsections of the model tree and the standard deviation reduction rate calculated after grouping for each variable must be specified. [PERSON] and [PERSON] [27] proposed that the subsections of the model tree can be established without being restricted by the minimum number of data and indicated that the minimum number of data for multiple regression analysis is four. Considering this and the utility of the formula, if a standard deviation \(\geq\)5% was not obtained after classification, the model development was terminated. Examination of all the submodels, which vary with respect to the conditions of the model (M1 and M2) proposed by [PERSON], the index values that corresponded to the explanatory variables exhibited consistency, and the correlations that considered the physical meaning of the applicable explanatory variables and SD values were identified. For example, with the developed model, it was argued that an increase in the mean annual precipitation will increase the sediment yield generated and transported. When the percentage of WW in the watershed increases, there will be increased chances of deposition of the transported sediment, thus properly reflecting the characteristics of the decrease in SD values.