## 3 Application Results
### Application Results of Standalone Models  
In this study, a standalone well-designed OPELM algorithm and CHAID models were utilized by conducting the MATLAB and Statistica software, respectively. As demonstrated in Figure 5, in  
Figure 4: The autocorrelation function (ACF) and partial autocorrelation function (PACF) for the streamflow variable at Dizaj and Tapik stations.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stream (Station)** & \
\begin{tabular}{c} **Skewness before** \\ **Normalization** \\ \end{tabular} & **Normalization** &
\begin{tabular}{c} **Skewness after** \\ **Normalization** \\ \end{tabular} \\ \hline Baranduzchai (Dizaj) & 2.05542 & \(Q_{t}\ =\ \ln(Q_{0}\ +\ 0.714)\) & \(-0.000187245\) \\ Nazluchai (Tapik) & 2.821872 & \(Q_{t}\ =\ \ln(Q_{0}\ +\ 0.268)\) & \(0.000861473\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Skewness and normalization equations for the studied streams.  
order to assess the performance of standalone models, the results of streamflow by using both OPELM and CHAID models are compared with their historical and observed data for both Dizaj (the blue one) and Tapik (the red one) stations. In Dizaj and Tapik stations, the CHAID model showed better prediction performance by relying on the determination of the coefficient metric at the validation stage, while, in the comparison between two stations, the OPELM model performed better at Dizaj station. Overall, in the evaluation of these two standalone models for monthly streamflow prediction, it is interesting to conclude that the CHAID model as a DDM model appeared to be a better model in both candidate stations.  
Table 4 brings the comparison standalone OPELM and CHAID models, which are developed for streamflow prediction at two selected stations (Dizaj and Tapik) in terms of five different indices, namely R, RMSE, NSE, MAE, and RSD. According to this table, in the calibration stage, Dizaj-OPELM had the highest R (R = 0.92). It was followed by Dizaj-CHAID and Tapik-OPELM (R = 0.91) and Tapik-CHAID (R = 0.90). In the case of root mean square errors, Dizaj-OPELM had the lowest error (RMSE = 3.378 m\({}^{3}\)/s), and Tapik-CHAID had the highest error (RMSE = 7.816 m\({}^{3}\)/s) while Tapik-OPELM (RMSE = 7.428 m\({}^{3}\)/s) and Dizaj-CHAID (RMSE = 3.655 m\({}^{3}\)/s) were located between these two values. As NSE, Dizaj-OPELM had the highest value (NSE = 0.84). It was followed by Dizaj-CHAID (NSE = 0.82), Tapik-OPELM (NSE = 0.81) and Tapik-CHAID (NSE = 0.79). By considering MAE, Dizaj-OPELM had the lowest error (MAE = 1.854 m\({}^{3}\)/s). It was followed by Dizaj-CHAID (MAE = 2.144 m\({}^{3}\)/s), Tapik-OPELM (MAE = 3.374 m\({}^{3}\)/s), and Tapik-CHAID (MAE = 3.697 m\({}^{3}\)/s). In the case of the ratio of RMSE to the standard deviation, Tapik-CHAID had the highest RSD value (RSD = 0.451). It was followed by Tapik-OPELM (RSD = 0.429), Dizaj-CHAID (RSD = 0.419), and Dizaj-OPELM (RSD = 0.387). The higher R and NSE values present a better-predicted model. In the comparison of two other parameters of RMSE and MAE, this table reveals that the calculated MAE values are about half of the RMSE values; the reason is that the RMSE evaluation metric gives special importance to large errors. For the validation stage dataset, CHAID had an R = 0.94, RMSE = 1.571 (m\({}^{3}\)/s), NSE = 0.91, MAE = 1.863 (m\({}^{3}\)/s) and RSD = 0.328 was considered as better model in Dizaj station and CHAID with an R = 0.89, RMSE = 4.329 (m\({}^{3}\)/s), NSE = 0.77, MAE = 2.253 (m\({}^{3}\)/s) and RSD = 0.473 was considered as the selected model in Tapik station.  
Figure 5: Scatter plots between the observed and the predicted value of streamflow for OPELM and CHAID models at Dizaj (blue color) and Tapik (red color) stations.