# Assessment of Soft Computing Techniques for the Prediction of Suspended Sediment Loads in Rivers
## 4 Model Application and Results  
### Selection of Optimal Input Combinations Based on Gamma Test (GT)  
As the hydrological processes are inherently dynamic, the current response relies on the present and former responses in the hydrological system's record. Therefore, it is considered that the present-day SSL (\(S_{t}\)) response depends on the present day response of river water discharge (\(Q_{t}\)), and the previous one and the response of river water discharge that occurred the day before (\(Q_{t-1}\), \(Q_{t-2}\)) and SSL (\(S_{t-1}\), \(S_{t-2}\)). Thus, the present-day SSL (\(S_{t}\)) value would be a function of current and antecedent river water discharges and SSL values, as follows:  
\[S_{t}=f\left(Q_{t},Q_{t-1},Q_{t-2},S_{t-1},S_{t-2}\right)\]  
In this study, a total of five input variables (\(Q_{t}\), \(Q_{t-1}\), \(Q_{t-2}\), \(S_{t-1}\), and \(S_{t-2}\)) are considered for the modelling of SSL by analyzing the effects of various input combinations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Training Dataset**} & \multicolumn{2}{c}{**Testing Dataset**} & \multicolumn{2}{c}{**Whole Dataset**} \\ \cline{2-7}  & **Q (m3/s)** & **SSL (t/day)** & **\(Q\) (m3/s)** & **SSL (t/day)** & **\(Q\) (m3/s)** & **SSL (t/day)** \\ \hline Min & 84.70 & 11.73 & 74.20 & 7.99 & 74.20 & 7.99 \\ \hline Max & 2860.40 & 50,779.32 & 1260.00 & 15,794.78 & 2860.40 & 50,779.32 \\ \hline Mean & 329.37 & 936.99 & 231.76 & 336.23 & 303.46 & 777.50 \\ \hline S\({}_{\text{d}}\) & 255.03 & 2317.28 & 144.62 & 694.24 & 234.91 & 2035.29 \\ \hline CV (\%) & 77.43 & 247.31 & 62.40 & 206.48 & 77.41 & 261.77 \\ \hline \(\text{C}_{\text{xx}}\) & 2.94 & 9.84 & 2.09 & 8.87 & 3.08 & 10.96 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical analysis of the Pirna gauging station datasets.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Training Dataset**} & \multicolumn{2}{c}{**Testing Dataset**} & \multicolumn{2}{c}{**Whole Dataset**} \\ \cline{2-7}  & **Q (m3/s)** & **SSL (t/day)** & **\(Q\) (m3/s)** & **SSL (t/day)** & **\(Q\) (m3/s)** & **SSL (t/day)** \\ \hline Min & 179.00 & 40.56 & 133.00 & 38.88 & 133.00 & 38.88 \\ \hline Max & 5010.00 & 27,806.98 & 4450.00 & 15,977.09 & 5010.00 & 27,806.98 \\ \hline Mean & 565.96 & 1378.78 & 387.70 & 638.98 & 522.78 & 1199.59 \\ \hline S\({}_{\text{d}}\) & 419.78 & 1654.76 & 264.86 & 786.14 & 395.41 & 1524.81 \\ \hline CV (\%) & 74.17 & 120.02 & 68.32 & 123.03 & 75.64 & 127.11 \\ \hline C\({}_{\text{xx}}\) & 2.81 & 4.57 & 6.03 & 7.59 & 3.14 & 4.91 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical analysis of the Magdeburg-Strombrücke gauging station datasets.  
Based on these five input variables, a total of \(2^{m}-1\) (i.e., 31) input combinations can be used to model SSL. Thus, to find the best possible input combinations for both stations, the Gamma test (GT) was performed to determine the optimal combinations. For both gauging stations, the best 5 out of 31 possible input combinations were selected based on minimum Gamma statistic (\(\Gamma\)), and _V-Ratio_ value criterion, as presented in Tables 3 and 4.