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Figure 4 illustrates the observed and simulated daily streamflow in calibration and verification periods. The NSE for calibration and verification are both above 0.6, which indicates a decent fit; the coefficients of R2 for the two phases are both above 0.6, which indicates a good coincidence between simulated flow and the observed values. The value of DV (%) is below 10 for verification phase and slightly above 10 for calibration, indicating a low level of system error. The results also demonstrate that the simulated peak flow are underestimated during both calibration and verification periods. It might be attributed to the potential observation errors and complexities of hydrological processes. To improve the accuracy of streamflow forecasting system, four parameters, including PF, maximum capacity for fast store (MF), RF, and RS, are investigated through the type-2 fuzzy analysis technique with four α-cut levels (i.e. 0, 0.25, 0.5, and 0.75). Table 2 presents the values of the four parameters under different α-cut levels, which are expressed as dual intervals.
Table 2

Values of fuzzy parameters under different membership grades

α-cut levelPF (−)MF (mm)RF (d)RS (d)
α = 0 [[8.0, 9.5], [13.5, 15.0]] [[10.0, 80.0], [260.0, 330.0]] [[1.0, 9.0], [31.0, 39.0]] [[100, 180], [420, 500]] 
α = 0.25 [[8.8, 10.0], [13.0, 14.1]] [[50.0, 102.5], [237.5, 290.0]] [[5.8, 11.8], [28.3, 34.3]] [[150, 210], [390, 450]] 
α = 0.50 [[9.8, 10.5], [12.5, 13.3]] [[90.0, 125.0], [215.0, 250.0]] [[10.5, 14.5], [25.5, 29.5]] [[200, 240], [360, 400]] 
α = 0.75 [[10.6, 11.0], [12.0, 12.4]] [[130.0,147.5], [192.5, 210.0]] [[15.3, 17.3], [22.8, 24.8]] [[250, 270], [330, 350]] 
α-cut levelPF (−)MF (mm)RF (d)RS (d)
α = 0 [[8.0, 9.5], [13.5, 15.0]] [[10.0, 80.0], [260.0, 330.0]] [[1.0, 9.0], [31.0, 39.0]] [[100, 180], [420, 500]] 
α = 0.25 [[8.8, 10.0], [13.0, 14.1]] [[50.0, 102.5], [237.5, 290.0]] [[5.8, 11.8], [28.3, 34.3]] [[150, 210], [390, 450]] 
α = 0.50 [[9.8, 10.5], [12.5, 13.3]] [[90.0, 125.0], [215.0, 250.0]] [[10.5, 14.5], [25.5, 29.5]] [[200, 240], [360, 400]] 
α = 0.75 [[10.6, 11.0], [12.0, 12.4]] [[130.0,147.5], [192.5, 210.0]] [[15.3, 17.3], [22.8, 24.8]] [[250, 270], [330, 350]] 

PF, precipitation factor; MF, maximum capacity for fast store; RF, retention constant for fast store; RS, retention constant for slow store.

Figure 4

Observed and simulated daily streamflow.

Figure 4

Observed and simulated daily streamflow.

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