The performance of the employed kernel-depend methods was compared with those of the traditional models based on dimensional analysis. To achieve this aim, the formulas of Shahrokhnia & Javan (2003, 2005, 2006), and Zahedani et al. (2012) were used as depicted in Table 10. The results illustrated in Figure 13 and Table 11 reflect that the employed kernel-depend methods give superior performance than the selected dimensionless formulas.
Table 10

A select set of dimensionless formulas for predicting discharge coefficients

Flow conditionNameFormula
Submerged Shahrokhnia & Javan (2006)   
Shahrokhnia & Javan (2005)   
Zahedani et al. (2012)   
Free Shahrokhnia & Javan (2003)   
Zahedani et al. (2012)   
Flow conditionNameFormula
Submerged Shahrokhnia & Javan (2006)   
Shahrokhnia & Javan (2005)   
Zahedani et al. (2012)   
Free Shahrokhnia & Javan (2003)   
Zahedani et al. (2012)   
Table 11

Global statistical indices of the traditional models

Flow conditionNamePerformance criteria
RSIBIASRMSE
Submerged Shahrokhnia & Javan (2006)  −0.102 0.618 0.086736 0.485 
Shahrokhnia & Javan (2005)  −0.001 0.890 0.587679 0.699 
Zahedani et al. (2012)  −0.027 0.575 −0.248229 0.452 
Free Shahrokhnia & Javan (2003)  0.582 2.68 2.06514 2.081 
Zahedani et al. (2012)  0.491 0.209 −0.059289 0.161 
Flow conditionNamePerformance criteria
RSIBIASRMSE
Submerged Shahrokhnia & Javan (2006)  −0.102 0.618 0.086736 0.485 
Shahrokhnia & Javan (2005)  −0.001 0.890 0.587679 0.699 
Zahedani et al. (2012)  −0.027 0.575 −0.248229 0.452 
Free Shahrokhnia & Javan (2003)  0.582 2.68 2.06514 2.081 
Zahedani et al. (2012)  0.491 0.209 −0.059289 0.161 
Figure 13

The obtained results of dimensionless formulas.

Figure 13

The obtained results of dimensionless formulas.

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