# Assessment of Soft Computing Techniques for the Prediction of Suspended Sediment Loads in Rivers
## 4 Model Application and Results
### The Suspended Sediment Load (SSL) Estimation through Local Linear Regression Models  
The LLR models were trained to predict the SSL for both Pirna and Magdeburg-Strombrucke gauging stations by optimizing the number of nearest neighbours (NN) and a threshold value. The number of nearest neighbours is an important parameter to train the LLR model and it depends on the data length. [PERSON] [62] recommended that if the data length is relatively shorter, then the appropriate number of NN is in the range of 10-20, but, for the larger input data length, the number of NN should be increased to obtain a more precise solution. The threshold value in LLR is applied to filter the local eigenvectors and its default value is around \(10^{-6}\). By setting it to a low value or zero, all the eigenvectors in the local model are included while, by increasing the value, more eigenvectors are filtered out. In this study, the optimal value of NN for all five best-input combinations of each gauging station was selected by applying the increasing near neighbors test, which gave the least value and a nearly smooth line of Gamma statistic and standard error. For instance, the value of the NN for combination 1 of the Pirna station LLR model was taken as equal to 22, where Gamma statistics and the standard error value is minimal and the line is smooth, as presented in Figure 9. Furthermore, the optimal threshold value was found to be 0.01 using the hit and trial method. Subsequently, different LLR models were developed to compute the SSL for all the best combinations of each station in the river, and the results for both stations are presented in Table 6. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Comb.**} & \multicolumn{2}{c}{**R**} & \multicolumn{2}{c}{**R2**} & \multicolumn{2}{c}{**RMSE (\(\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{\boldsymbol{ \boldsymbol{ }}}}}}}}}}}}}\)} \\ \cline{3-10}  & & **Training** & **Testing** & **Training** & **Testing** & **Training** & **Testing** & **Training** & **Testing** \\ \hline \multirow{6}{*}{Pirna gauging station} & 1 & 0.95 & 0.94 & 0.90 & 0.89 & 742.54 & 235.60 & \(-\)1.73 & 8.78 \\ \cline{2-10}  & 2 & 0.94 & 0.94 & 0.89 & 0.87 & 768.31 & 250.59 & \(-\)1.37 & 9.12 \\ \cline{2-10}  & 3 & 0.94 & 0.94 & 0.89 & 0.89 & 760.26 & 232.65 & \(-\)1.71 & 5.56 \\ \cline{2-10}  & 4 & 0.92 & 0.87 & 0.84 & 0.76 & 916.14 & 347.15 & \(-\)2.28 & 13.49 \\ \cline{2-10}  & 5 & 0.94 & 0.94 & 0.89 & 0.88 & 784.60 & 249.09 & \(-\)1.45 & 11.61 \\ \hline \multirow{6}{*}{Magdeburg-Strombrucke gauging station} & 1 & 0.92 & 0.89 & 0.85 & 0.79 & 644.52 & 363.81 & \(-\)1.26 & 2.12 \\ \cline{2-10}  & 2 & 0.92 & 0.88 & 0.85 & 0.78 & 637.28 & 372.30 & \(-\)1.20 & 2.06 \\ \cline{1-1} \cline{2-10}  & 3 & 0.92 & 0.90 & 0.85 & 0.81 & 650.44 & 345.32 & \(-\)1.31 & 2.41 \\ \cline{1-1} \cline{2-10}  & 4 & 0.92 & 0.90 & 0.85 & 0.82 & 651.34 & 339.23 & \(-\)0.72 & 3.17 \\ \cline{1-1} \cline{2-10}  & 5 & 0.92 & 0.89 & 0.85 & 0.80 & 648.03 & 353.32 & \(-\)1.53 & 2.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The performance evaluation of the different LLR models. Figure 9: Selection of NN value for combination 1 of the Pirna Station. To estimate the LLR model efficiency, several statistical parameters were calculated as presented in Table 6 and overall results at the Pirna station revealed that an input of combination 1 gave a relatively high accuracy and, similarly, for the Magdeburg-Strombrucke station LLR model with input, combination 4 provided the best performance criteria. It could be seen in Table 6 that the values of \(R\), \(R^{2}\), _RMSE_ and _PBIAS_ for the testing of the LLR model (Combination 1 and NN 20) of the Pirna and Magdeburg-Strombrucke stations (Combination 4 and NN 22) were 0.94, 0.89, 235.6 (t/day), 8.78%, and 0.90, 0.82, 339.23 (t/day), 3.17%, respectively.