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In Table 4, the best hydrological and optimal SSQ variables for the new 4P-NVPMLMM model as well as two four- and five-parameter models are compared. The optimal SSQ value is calculated to be 9453.2 using the first model, while in the five-parameter model, where the parameter m is modified with five flow levels, the optimal SSQ value is obtained 31394.99. The variable parameter method has reduced the objective function value by 70%. For the 4P-NVPMLMM model, the corresponding hydrological parameters are K = … and m = ... and the corresponding dimensionless parameters are r1 = ... and r2 = ...
As shown in this figure, the routed outflows very well fit the observed outflow hydrograph using the new 4P-NVPMLMM method and the PSO-GA algorithm.
According to Table 5, for all four examples, the values of SAD, ETP, and MARE are decreased in the new 4P_NVPMLMM method compared to the other methods. Furthermore, the VarexQ value is increased in the new 4P-NVPMLMM method in comparison with the other methods. In Wilson (1974), River Wye, and Viessman and Lewis (2003), the ETP value is reduced; however, in the Karoon River, this value is higher than the other two methods.
Finally, it has been concluded that for all four examples, the value of the objective function is reduced by the new 4P-NVPMLMM method. This model can be applied to the problems that require more precision.
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Thanks a lot in advance