## 3 Application Results
### Results for the Integration of OPELM, CHAID and ARCH Models  
The ARCH model is combined with the best-resulted models OPELM and CHAID. The results of this part can be divided into two categories of ARCH-OPELM and ARCH-CHAID combinations. Figure 6 looks at two combined models of ARCH-OPELM and ARCH-CHAID at both stations of Dizaj and Tapik. Focusing on calibration and validation stages in both stations, Figure 6 shows excellent similarities between observed and modeled data in both calibration and validation stages at two stations of (a) Dizaj, (b) Tapik. In general, it reveals that ARCH-CHAID has more significant results of the determination coefficient in comparison to ARCH-OPELM combined models. In the right above, this figure represents scatterplots of both ARCH-OPELM and ARCH-CHAID models with their regression lines and correlation of determination (R\({}^{2}\)). The regression equation, which is based on modeled and observed values of streamflow is obtained from \(y\) (\(G_{m}\)) = aG\({}_{0}\) + b. In which G\({}_{0}\) stands for observed streamflow datasets, and \(G_{m}\) stands for the modeled streamflow datasets. Based on a, b, and R\({}^{2}\) values, the best models could be selected. The results were a = 1.123, b = 2.8305, and R\({}^{2}\) = 0.8166 (for ARCH-OPELM), also a = 0.9616, b = 1.9938, and R\({}^{2}\) = 0.9201 (for ARCH-CHAID); in Dizaj station, the ARCH-CHAID model was selected as a better model. Also in Tapik station, the outcomes were a = 1.1633, b = 3.6354, and R\({}^{2}\) = 0.797 (for ARCH-OPELM), also a = 0.9163, b = 3.5381 and R\({}^{2}\) = 0.885 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Statistical Error Indices**} \\ \cline{3-6}  & & **R** & **RMSE (m\({}^{3}\)/s)** & **NSE** & **MAE (m\({}^{3}\)/s)** & **RSD** \\ \hline \multicolumn{6}{l}{_Total available data in calibration stage_} \\ \hline Dizaj & Dizaj-OPELM & 0.92 & 3.378 & 0.84 & 1.854 & 0.387 \\ \cline{2-6}  & Dizaj-CHAID & 0.91 & 3.655 & 0.82 & 2.144 & 0.419 \\ \hline Tapik & Tapik-OPELM & 0.91 & 7.428 & 0.81 & 3.374 & 0.429 \\ \cline{2-6}  & Tapik-CHAID & 0.90 & 7.816 & 0.79 & 3.697 & 0.451 \\ \hline \multicolumn{6}{l}{_Total available data in validation stage_} \\ \hline Dizaj & Dizaj-OPELM & 0.89 & 2.568 & 0.78 & 1.544 & 0.463 \\ \cline{2-6}  & Dizaj-CHAID & 0.94 & 1.571 & 0.91 & 0.863 & 0.328 \\ \hline Tapik & Tapik-OPELM & 0.86 & 5.185 & 0.67 & 2.663 & 0.566 \\ \cline{2-6}  & Tapik-CHAID & 0.89 & 4.329 & 0.77 & 2.253 & 0.473 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance results of standalone OPELM and CHAID models for Dizaj and Tapik stations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stream (Station)** & **Distribution** & **Log-Likelihood** & **ARCH Model** \\ \hline Baranduzchai (Dizaj) & Gaussian & \(-\)361.7161 & \(\sigma_{t}^{2}\ =\ 1.88E-08*\epsilon_{t-1}^{2}\ +\ 0.4417033\) \\ \hline Nazluchai (Tapik) & Gaussian & \(-\)375.2455 & \(\sigma_{t}^{2}\ =\ 4.94E-08*\epsilon_{t-1}^{2}\ +\ 0.4602025\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ARCH model estimation using Gaussian distribution for Dizaj and Tapik stations. (for ARCH-CHAID) were obtained. The ARCH-CHAID model was selected in Tapik station based on the above-mentioned results. In another way of comparing the performances of the hybrid models, Table 6 summarizes the performance evaluation metrics outcomes of hybrid ARCH-OPELM and ARCH-CHAID models for Dizaj and Tapik stations. In the calibration stage, Dizaj-ARCH-OPELM had the highest R-value of 0.94. It was followed by Tapik-ARCH-CHAID (R = 0.93), Dizaj-ARCH-CHAID and Tapik-ARCH-OPELM (R = 0.92). Dizaj-ARCH-OPELM had the lowest error (RMSE = 2.168 m\({}^{3}\)/s). It was followed by Dizaj-ARCH-CHAID (RMSE = 2.395 m\({}^{3}\)/s), Tapik-ARCH-CHAID (RMSE = 5.678 m\({}^{3}\)/s) and Tapik-ARCH-OPELM (RMSE = 6.896 m\({}^{3}\)/s). In the case of the NSE coefficient, Tapik-ARCH-CHAID had the highest value (NSE = 0.85).