## 3 Results and Discussion
### Results of Soft Computing Based Models  
Figures 4-6 provide agreement plots between observed and predicted relative energy dissipation (%) of spillway by RF, M5P, and stochastic M5P based models for training and testing stages, respectively. Predicted values from RF, M5P, and stochastic M5P based models closely follow the observed values. It is clear that the predictions of RF are less scattered than those of the M5P. However, the stochastic M5P provided better predictions compared to RF. Results of test data set from Table 4 indicates that the performance of the stochastic M5P approach is the best among the implemented approaches. The stochastic M5P based model with correlation coefficient of 0.9993 and RMSE of 0.8246% presents reliable results in comparison to the RF-based model with a correlation coefficient of 0.9992 and RMSE of 0.9093%. Additionally, the M5P based model with correlation coefficient of 0.9958 and RMSE of 2.054% has poor results in comparison to stochastic M5P and RF-based models. Comparison of M5P and stochastic M5P based models reveals that the latter model considerably improved the first model (traditional M5P); an increase in CC by 0.35% and decrease in RMSE by 60% (Table 4). Figure 4: Agreement plot of observed and predicted relative energy dissipation by the random forest (RF) model using training and testing data sets, respectively. Figure 3: Agreement plot of observed and predicted relative energy dissipation by the Equation (14) based model using training and testing data sets, respectively. The brief statistical properties of the observed and predicted values using regression and soft computing-based models are summarized in Table 5. The statistics of predictions by the RF and stochastic M5P are very close to those of the observations. Using the results of single-factor ANOVA presented in Table 6, it can be seen that used regression and soft computing-based models results have an insignificant difference in comparison to actual values. For the comparison of regression and soft computing-based models, an agreement, performance, and relative error plot are shown in Figure 7 using the testing data set. It can be inferred from this figure that the predicted values provided by the stochastic M5P based model lies very closer to the line of perfect agreement and predicted relative energy dissipation (%) of the spillway was found to follow the same patterns of actual relative energy dissipation (%) of the spillway with minimum relative error. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Approaches**} & \multicolumn{4}{c}{**Training Data Set**} & \multicolumn{4}{c}{**Testing Data Set**} \\ \cline{2-9}  & **CC** & **RMSE** & **MAE** & **SI** & **CC** & **RMSE** & **MAE** & **SI** \\ \hline
**MSP** & 0.9965 & 1.853 & 1.048 & 0.0321 & 0.9958 & 2.054 & 1.071 & 0.0358 \\
**Stochastic MSP** & 0.9996 & 0.6142 & 0.3803 & 0.0106 & 0.9993 & 0.8246 & 0.4278 & 0.0144 \\
**RF** & 0.9997 & 0.5019 & 0.3673 & 0.0087 & 0.9992 & 0.9093 & 0.5054 & 0.0159 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance assessment measures for soft computing-based models using training and testing data sets. Figure 5: Agreement plot of observed and predicted relative energy dissipation by the M5P model using training and testing data sets, respectively. Figure 6: Agreement plot of observed and predicted relative energy dissipation by the stochastic M5P model using training and testing data sets, respectively. Figure 7: Performance of various regression and soft computing-based models during the testing stage. For the assessment of the obtained outcomes, box plots (Figure 8) were drawn, in which overall error distribution was presented. Accordingly, the negative and positive error values correspond to the over and under estimation behavior of the models, respectively.