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The hypothesis will be rejected if the errors are similar even though the number of sub-annual calibration groups (n) increases. This is because given that the hypothesis is true, the model becomes more complicated (i.e., one model with m × n parameters) when the number of groups n increases, which results in less error due to overfitting (Figure 11). The calibration has been performed on an annual, biannual, seasonal, bimonthly and monthly time scale based on SCS. The model performances are presented in Table 3. The RMSE values are similar among different time scales which mean that the sub-annual calibration scheme does not improve the model performance. Therefore, the hypothesis should be rejected. The reason for no improvements in the complicated model is that the model structures are still the same although the sub-annual calibration has been performed in different time scales. Hence, the sub-annually (n groups) calibrated model (m parameters) is not equivalent to a single model with m × n parameters.
Table 3

RMSE of different calibration period

Calibration periodAnnualBiannualSeasonalBimonthlyMonthly
RMSE (m3/s) 4.24 4.23 4.31 4.40 4.33 
Calibration periodAnnualBiannualSeasonalBimonthlyMonthly
RMSE (m3/s) 4.24 4.23 4.31 4.40 4.33 
Figure 11

Schematic of overfitting issue when the number of groups increases: (a) a model with one parameter; (b) a model with two parameters; (c) a model with four parameters.

Figure 11

Schematic of overfitting issue when the number of groups increases: (a) a model with one parameter; (b) a model with two parameters; (c) a model with four parameters.

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