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In this study, 10 years of daily data (precipitation, temperature, and streamflow) were used for model calibration, and another 10 years of daily data were used for model validation, as presented in Table 2. The first year of the calibration and validation periods were used to warm up the hydrological model and the other 9 years were used for simulation. The observed daily precipitation and temperature were taken from the gridded observations of the Hutchinson et al. (2009) data set, which was obtained by interpolating station data to a 10-km grid using a thin plate smoothing spline surface fitting method. All the grid points within the watershed were averaged to obtain a single precipitation and temperature time series for each basin. The daily discharge at the watershed outlet was obtained from Hydro-Québec. HSAMI, with all 23 free parameters, was independently calibrated and validated 1,000 times within the same parametric space, but with different random seeds. A large number of calibrations were used to obtain a robust distribution for each parameter to quantify the parameter equifinality. The median of NSE and TRMSE for these 1,000 calibrations showed good performances of HSAMI for both watersheds. The results for the CDD watershed were consistently better than those of the COW watershed. This is because the input data quality of the former is considered better than that of the latter, due to there being more weather stations, and because the daily time step used in this study was less suited to the smaller watershed. In addition, snowmelt-dominated basins are also usually easier to model, because the winter streamflow is not sensitive to the precipitation input. Since TRMSE is discharge dependent, its values are smaller for the COW watershed, even though HSAMI was better optimized for the CDD watershed based on NSE values.

Table 2

Median, maximum (Max) and minimum (Min) values of the NSE and transformed root mean squared error (TRMSE) for 1,000 calibrations and validations of HSAMI with all 23 free parameters for two watersheds. Optimum NSE and TRMSE values are 1 and 0, respectively

NSE
TRMSE
WatershedSourcePeriodMedianMinMaxMedianMinMax
CDD Calibration 1979–1988 0.89 0.87 0.90 1.52 1.49 2.42 
 Validation 1989–1998 0.88 0.79 0.90 1.78 1.70 2.75 
COW Calibration 1990–1999 0.75 0.63 0.76 0.65 0.64 0.98 
 Validation 2000–2009 0.72 0.59 0.74 0.78 0.75 1.11 
NSE
TRMSE
WatershedSourcePeriodMedianMinMaxMedianMinMax
CDD Calibration 1979–1988 0.89 0.87 0.90 1.52 1.49 2.42 
 Validation 1989–1998 0.88 0.79 0.90 1.78 1.70 2.75 
COW Calibration 1990–1999 0.75 0.63 0.76 0.65 0.64 0.98 
 Validation 2000–2009 0.72 0.59 0.74 0.78 0.75 1.11 

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