To improve the single physically based model's prediction efficiency, three ensemble techniques were developed using the results of the SWAT, HEC-HMS and HBV models as inputs. The results of nonlinear and linear ensemble techniques for runoff simulation are shown in Table 8. The SAE value was obtained by simply taking the arithmetic average of the physically based models’ outputs. In the WAE technique, on the other hand, ensemble modeling was performed by assigning weights for every single model's output based on its NSE value in the validation phase. Thus, in the WAE technique, the weights assigned for the SWAT, HBV and HEC-HMS models were 0.3575, 0.3251 and 0.314, respectively. The weights of WAE were obtained using NSE values of the single model in the validation phase.

Table 8

Results of the proposed ensemble techniques for rainfall-runoff modeling

Goodness of fitSAE
WAE
NNE
CalibrationValidationCalibrationValidationCalibrationValidation
NSE 0.829 0.792 0.846 0.818 0.924 0.896 
R2 0.918 0.877 0.919 0.878 0.925 0.904 
MAE (m3/s) 5.807 6.008 4.204 5.985 3.244 3.726 
RSR 0.398 0.426 0.3766 0.4225 0.2717 0.3216 
RMSE (m3/s) 7.97 8.53 7.54 8.46 5.44 6.44 
PBIAS (%) −22 −34 −17.9 −33.9 −3.94 −9.1 
Goodness of fitSAE
WAE
NNE
CalibrationValidationCalibrationValidationCalibrationValidation
NSE 0.829 0.792 0.846 0.818 0.924 0.896 
R2 0.918 0.877 0.919 0.878 0.925 0.904 
MAE (m3/s) 5.807 6.008 4.204 5.985 3.244 3.726 
RSR 0.398 0.426 0.3766 0.4225 0.2717 0.3216 
RMSE (m3/s) 7.97 8.53 7.54 8.46 5.44 6.44 
PBIAS (%) −22 −34 −17.9 −33.9 −3.94 −9.1 

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