*4.3. Predicted Monthly Streamflow of MLR, ANN, and C-Vine Models*

Figure 7 shows a comparison of the predicted and observed streamflow acquired by the MLR, ANN, and CVQR models. For the MLR model, the results indicate that the values of R<sup>2</sup> , NSE, and RMSE are 0.73, 0.72, and 16.16 in the calibration period and 0.73, 0.66, and 16.72 in the validation period. For the MLR model (Figure 7a), the predicted value is slightly underestimated in the case of high flow observation values (1980–1986), and vice versa, the predicted value is slightly overestimated during 2004–2009. Due to the inherent characteristics of the algorithm, the predicted values even become negative at some low-flow records (e.g., 1999 and 2000).

The ANN model performs better than the MLR model in the calibration period (Figure 7b). The ANN model obtains an R<sup>2</sup> of 0.75, an NSE of 0.73, and an RMSE of 15.57 in the calibration period. Similar to the results of the MLR model, the ANN model, with values of R<sup>2</sup> at 0.72, NSE at 0.69, and RMSE at 16.53, performs worse in the validation period than that in the calibration period. Moreover, as presented in Figure 7b, the ANN model also underestimates some streamflow during the high flow periods (e.g., 1963–1964) but overestimates more records during 2004–2009.

As presented in Figure 7c, the predicted monthly streamflow using the CVQR model could satisfy the observed values well. In the calibration period, the values of R<sup>2</sup> , NSE, and RMSE obtained by the CVQR model are 0.73, 0.70, and 16.75, respectively. In the validation period, the values are 0.74, 0.71, and 16.13, which shows that the performance of CVQR model in the validation period is similar to that in the calibration period. The CVQR model underestimates some high flow values (e.g., during 1980–1986). Generally, compared with MLR and ANN models, the CVQR model performs best in the calibration period for monthly streamflow prediction. The CVQR model can effectively capture both linear and nonlinear dependence of these input variables (e.g., temperature, precipitation, and streamflow). Additionally, the CVQR model based on the multivariate copula functions

els.

could effectively reveal the correlation structures between predictor–response variables, which provides a potent and adaptable tool to model the dependence of such complex and jointly correlated variables. functions could effectively reveal the correlation structures between predictor–response variables, which provides a potent and adaptable tool to model the dependence of such complex and jointly correlated variables.

As presented in Figure 7c, the predicted monthly streamflow using the CVQR model could satisfy the observed values well. In the calibration period, the values of R2, NSE, and RMSE obtained by the CVQR model are 0.73, 0.70, and 16.75, respectively. In the validation period, the values are 0.74, 0.71, and 16.13, which shows that the performance of CVQR model in the validation period is similar to that in the calibration period. The CVQR model underestimates some high flow values (e.g., during 1980–1986). Generally, compared with MLR and ANN models, the CVQR model performs best in the calibration period for monthly streamflow prediction. The CVQR model can effectively capture both linear and nonlinear dependence of these input variables (e.g., temperature, precipitation, and streamflow). Additionally, the CVQR model based on the multivariate copula

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 18 of 24

**Figure 7.** Comparison of predicted and observed monthly streamflow using the MLR (**a**), ANN (**b**), and CVQR (**c**) mod-**Figure 7.** Comparison of predicted and observed monthly streamflow using the MLR (**a**), ANN (**b**), and CVQR (**c**) models.

Table 5 illustrates the general resulting statistics from the ANN, MLR, and CVQR models for forecasting during the calibration and validation periods. For the results of R2, NSE, and RMSE, these results indicate that the ANN model performs best in the calibration period compared to the MLR and CVQR models while the proposed CVQR achieves the best results among the validation period compared to other models. However, the results show that ANN and CVQR performed best in terms of 90% confidence interval Table 5 illustrates the general resulting statistics from the ANN, MLR, and CVQR models for forecasting during the calibration and validation periods. For the results of R<sup>2</sup> , NSE, and RMSE, these results indicate that the ANN model performs best in the calibration period compared to the MLR and CVQR models while the proposed CVQR achieves the best results among the validation period compared to other models. However, the results show that ANN and CVQR performed best in terms of 90% confidence interval prediction (CR90 and DI) while MLR performed worst. The result, on the other hand, shows that MLR is not effective in quantifying nonlinear relationships among hydrological variables. In general, the results show that CVQR performs best in the calibration period for monthly streamflow prediction compared to ANN and MLR models. Moreover, the CVQR and ANN models can reflect the complex nonlinear relationships between the hydrological and meteorological factors. Therefore, in order to understand the prediction performance of CVQR in the tail correlations, the comparison of regression predictions between the CVQR and ANN models at different quantiles are explored in the next section.


**Table 5.** Summary statistics of streamflow forecasting during the validation period through different models.
