## 3 Application Results
### Discussion  
On the one hand, as expressed earlier, streamflow and other hydrological variables have a nonlinear behavior, so that in modeling experts should consider both deterministic (algebraic) and stochastic parts of this parameter in order to make a proper decision for water resources management purposes [48]. According to the above study results, the stochastic part of streamflow has extremely improved the performance of the sole-models, i.e., OPELM and CHAID, in terms of prediction. ARCH was introduced as a nonlinear parametric time-series approach that describes the behavior of the conditional variance of the data. In this regard, integration of ARCH with the fast and efficient ELM and CHAID models led to the newly developed ARCH-OPELM/CHAID models, which effectively 'learns' those two parts in emulating monthly streamflow. On the other hand, one of the challenging issues is that the models can predict river flow accurately by chance or perform well only in some ranges of input and output variables [65]. To respond to this circumstance, the current research considers two rivers in ULB with different characteristics of input and output variables in order to assess the applicability of the predictive models. It should be highlighted that this study tried to give some applications and models to ease the monthly time-scale forecasting of streamflow since the available data are very poor in quality and hard to achieve, especially in developing countries like Iran. By the previous results, the better-predicting capability of ARCH-OPELM/CHAID in the monthly-time forecasting horizon is clear from the predictor metrics and the diagnostic plots at both the study sites. To evaluate the improvement achieved by the proposed models on the other two compared models of OPELM and CHAID, the performance promotion is fully exhibited in Table 4, where the five performance metrics values are revealed. Remarkable performance improvement can be observed for all indices. The average promotion ratio of indices RMSE, MAE, and RSD of both two horizons are evident in confirming the improvements, in which the ARCH-ELM models for Dizaj and Tapik could decrease prediction error by 17% and 38%, respectively. This percentage for ARCH-ELM reaches about 41% (Dizaj) and 29% (Tapik) for validation stage. According to the scatter plots, standalone OPELM and CHAID models show an under-predicted performance in the calibration stage for both Dizaj and Tapik stations, although this drawback improved by considering the stochastic process of streamflow integrating with ARCH time-series model. In the validation stage, the ARCH-OPELM based on histogram could predict river flow values as well as the ARCH-CHAID model. Thus the classification CHAID modeling method used in the study is confirmed as being a very useful tool to investigate the methods for forecasting streamflow on a monthly scale. Figure 7: Taylor plots indicating the correlation coefficient and standard deviation in the validation stage based on the standalone OPELM and CHAID, vs. the hybrid ARCH-OPELM and ARCH-CHAID models for predicting monthly streamflow at two candidate study stations. The hybrid models were found to improve the streamflow prediction across the evaluation criteria for two stations of Dizaj and Tapik on two main streamflow of Nazluchai and Baranduzchai in ULB. The whole study revealed that the hybrid ARCH-DDMs could increase the performance of sole DDMs up to 10%. As the perspective for real applications, it should be noted that providing a reliable model to forecast river flow could be instrumental for water resources planning and management [5]. Hydrological forecasting plays an essential role in the investigation of physical mechanisms and the causes underlying changes therein. The results of forecasting can also be used for agricultural irrigation management, water resources management, flood warning, and the design and management of hydraulic structures [66].