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Table 3 presents the model performance at daily level under different α-cut levels. Since varied α-cut levels correspond to different values of the parameters, any changes in α-cut levels would yield different model performance. The values of the parameters would have significant influence on the output values of NSE, DV (%), and R2. For example, for the parameter of RF, the value of NSE would vary from 0.49 to 0.82 under α = 0; the interval would decrease to [0.74, 0.77] when the α-cut level increases to 0.75. The results demonstrate that the uncertainties projected in the parameters and initial conditions would significantly impact the simulated outputs; neglecting uncertainties in hydrological simulation would easily lead to a lack of information regarding system performance.

Table 3

Daily time series hydrological simulation results under different membership grades

ParametersValuesα = 0
α = 0.25
α = 0.50
α = 0.75
NSEDV (%)R2NSEDV (%)R2NSEDV (%)R2NSEDV (%)R2
PF  0.59 14.76 0.71 0.67 11.27 0.74 0.76 4.53 0.77 0.76 4.53 0.77 
 0.71 8.89 0.75 0.74 6.47 0.76 0.76 4.74 0.77 0.76 3.52 0.77 
 0.72 –6.94 0.81 0.74 –4.85 0.80 0.75 –2.96 0.80 0.76 3.52 0.77 
 0.60 –12.89 0.82 0.67 –9.39 0.81 0.73 –6.14 0.81 0.76 –2.40 0.79 
MF  0.49 –4.51 0.72 0.64 –6.38 0.74 0.61 1.21 0.68 0.75 0.21 0.77 
 0.63 –1.00 0.70 0.63 0.80 0.68 0.75 0.31 0.77 0.74 0.49 0.77 
 0.80 0.90 0.82 0.78 3.31 0.80 0.76 2.93 0.77 0.77 2.41 0.78 
 0.82 –0.56 0.83 0.81 0.87 0.82 0.80 1.58 0.81 0.77 2.24 0.78 
RF  0.51 –7.85 0.72 0.79 0.52 0.80 0.79 1.04 0.79 0.76 1.91 0.77 
 0.76 3.03 0.77 0.80 –1.21 0.81 0.75 0.42 0.78 0.75 1.95 0.77 
 0.73 0.69 0.76 0.76 0.41 0.79 0.76 1.42 0.78 0.75 0.43 0.77 
 0.65 1.35 0.72 0.66 1.93 0.71 0.75 0.54 0.77 0.75 0.38 0.77 
RS  0.67 –15.45 0.79 0.75 –0.18 0.76 0.68 11.85 0.77 0.68 11.40 0.77 
 0.73 6.78 0.77 0.65 13.31 0.77 0.65 13.35 0.77 0.77 3.02 0.78 
 0.72 2.34 0.77 0.70 8.08 0.77 0.73 7.10 0.78 0.73 5.69 0.77 
 0.60 14.93 0.77 0.73 1.71 0.78 0.69 8.03 0.78 0.73 6.96 0.78 
ParametersValuesα = 0
α = 0.25
α = 0.50
α = 0.75
NSEDV (%)R2NSEDV (%)R2NSEDV (%)R2NSEDV (%)R2
PF  0.59 14.76 0.71 0.67 11.27 0.74 0.76 4.53 0.77 0.76 4.53 0.77 
 0.71 8.89 0.75 0.74 6.47 0.76 0.76 4.74 0.77 0.76 3.52 0.77 
 0.72 –6.94 0.81 0.74 –4.85 0.80 0.75 –2.96 0.80 0.76 3.52 0.77 
 0.60 –12.89 0.82 0.67 –9.39 0.81 0.73 –6.14 0.81 0.76 –2.40 0.79 
MF  0.49 –4.51 0.72 0.64 –6.38 0.74 0.61 1.21 0.68 0.75 0.21 0.77 
 0.63 –1.00 0.70 0.63 0.80 0.68 0.75 0.31 0.77 0.74 0.49 0.77 
 0.80 0.90 0.82 0.78 3.31 0.80 0.76 2.93 0.77 0.77 2.41 0.78 
 0.82 –0.56 0.83 0.81 0.87 0.82 0.80 1.58 0.81 0.77 2.24 0.78 
RF  0.51 –7.85 0.72 0.79 0.52 0.80 0.79 1.04 0.79 0.76 1.91 0.77 
 0.76 3.03 0.77 0.80 –1.21 0.81 0.75 0.42 0.78 0.75 1.95 0.77 
 0.73 0.69 0.76 0.76 0.41 0.79 0.76 1.42 0.78 0.75 0.43 0.77 
 0.65 1.35 0.72 0.66 1.93 0.71 0.75 0.54 0.77 0.75 0.38 0.77 
RS  0.67 –15.45 0.79 0.75 –0.18 0.76 0.68 11.85 0.77 0.68 11.40 0.77 
 0.73 6.78 0.77 0.65 13.31 0.77 0.65 13.35 0.77 0.77 3.02 0.78 
 0.72 2.34 0.77 0.70 8.08 0.77 0.73 7.10 0.78 0.73 5.69 0.77 
 0.60 14.93 0.77 0.73 1.71 0.78 0.69 8.03 0.78 0.73 6.96 0.78 

NSE, Nash–Sutcliffe efficiencies; DV, deviation of volume; R2, determination coefficient.

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