As shown in Table 8, all developed ensemble techniques have shown very good performance in both the calibration and validation phases in terms of their NSE, R2, RSR and RMSE values according to Moriasi et al. (2007, 2015). Similar to the single models, the linear ensemble techniques (WAE and SAE) showed unsatisfactory performance in terms of the PBIAS value. The linear ensemble technique improved the performance of the HEC-HMS model by 9.65 and 12.1% and the HBV model by 8.8 and 8.5% in the calibration and validation phases, respectively, based on the NSE value. The SAE technique improved the performances of individual models except for the SWAT model. According to Nourani et al. (2021a, 2021b), this could be because arithmetic averaging yields a higher value than the minimum value and lower than the highest values in the dataset. The results of the ensemble technique (Table 9) show that the difference in performance between the linear ensemble models (SAE and WAE) is not large on most statistical performance, but the WAE technique was slightly better than SAE. This could be due to the weighting of the inputs of this technique according to their relative importance. The WAE technique improved the HEC-HMS, SWAT and HBV models by increasing the NSE values by 15.75, 2.4 and 12%, respectively, in the validation phase.

Table 9

RMSE values (m3/s) of the ensemble technique in each segment of the hydrograph

Hydrograph phaseRange (m3/s)SAEWAENNE
Very low flow 1.188–1.559 0.279 0.278 0.643 
Low flow 1.641–2.415 1.163 1.152 0.538 
Medium flow 2.526–18.788 6.712 6.69 2.371 
High flow 19.244–60.032 9.866 9.839 6.515 
Very high flow 61.048–110.624 6.44 6.585 8.43 
Hydrograph phaseRange (m3/s)SAEWAENNE
Very low flow 1.188–1.559 0.279 0.278 0.643 
Low flow 1.641–2.415 1.163 1.152 0.538 
Medium flow 2.526–18.788 6.712 6.69 2.371 
High flow 19.244–60.032 9.866 9.839 6.515 
Very high flow 61.048–110.624 6.44 6.585 8.43 

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