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HSAMI is a 23-parameter, lumped, conceptual, rainfall–runoff model developed by Hydro-Québec, and which has been used to forecast natural inflows for over 20 years (Fortin 2000). HSAMI is used by Hydro-Québec for daily forecasting of natural inflows on nearly 100 watersheds with drainage areas ranging from 160 to 69,195 km2. HSAMI was also used in several flow forecasting and climate change impact studies (e.g., Minville et al. 2008, 2009; Chen et al. 2011a, 2011b, 2012; Poulin et al. 2011; Arsenault et al. 2013). Of HSAMI's 23 parameters, two account for evapotranspiration, six for snow accumulation/melting, ten for vertical water movement, and five for horizontal water movement (see Table 1). Vertical flows are simulated with four interconnected linear reservoirs (snow on the ground, surface water, unsaturated and saturated zones). Horizontal flows are routed through two unit hydrographs and one linear reservoir. In addition, the model takes into account snow accumulation, snowmelt, soil freezing/thawing, and evapotranspiration. Model calibration was done automatically using the covariance matrix adaptation evolution strategy (CMAES) (Hansen & Ostermeier 1996, 2001), following the conclusions of Arsenault et al. (2014).

Table 1

HSAMI 23 free parameters

Sub-modelIDAcronymPhysical meaningUnitParameter range
Evapo-transpiration P1 FAETP Factor multiplying potential evapotranspiration (PET) for the estimation of summer real evapotranspiration (RET) – [0.6 3] 
P2 POUR Factor multiplying PET for estimating the RET in winter – [0 0.3] 
Snowmelt P3 FKM Snow melting rate during daytime. ΔT in Celsius is calculated as the difference between Tmax and parameter of Tmax threshold for snowmelt (TB) cm/Δ°C/day [0.05 0.4] 
P4 FKYN Snow melting rate during night-time. ΔT in Celsius is calculated as the difference between parameter TB and Tmin cm/Δ°C/day [0.05 0.5] 
P5 TB Tmax threshold for snowmelt °C [−6 7] 
P6 TBN Tmin threshold for accelerated snowmelt °C [−6 6] 
P7 TACAL Reference temperature for calculating the heat supplied by the rain to the snow cover °C [−6 4] 
P8 CC Empirical parameter used to connect the state variables describing snow cover and cumulated snowmelt to the proportion of the basin covered by snow – [0.8 5] 
Surface runoff P9 CGEL Empirical parameter used to connect the state variables describing soil freezing and thawing to the proportion of snowmelt water flowing on the surface – [0.8 15] 
P10 CIMAX 24-hour rainfall amount needed to generate 50% runoff with completely dry soil cm [10 45] 
P11 CSAP 24-hour rainfall amount needed to generate 50% runoff with completely saturated soil cm [1 8] 
Vertical water movement P12 RMIN Water amount in the unsaturated zone that cannot drain by gravity cm [0 7] 
P13 RMAX Maximum water amount that can be contained in the unsaturated soil zone cm [3 25] 
P14 SAPMAX Maximum water amount that can be contained in the aquifer before generating surface runoff cm [4 30] 
P15 Proportion of surface water flowing through the intermediate hydrograph instead of moving through the soil column – [0.15 0.7] 
P16 Proportion of soil water that is directed to the intermediate hydrograph when the unsaturated zone overflows – [0.3 1] 
P17 PER Emptying rate of the unsaturated zone to the groundwater reservoir 24h−1 [0.09 0.07] 
P18 Emptying rate of the groundwater reservoir (base flow) 24h−1 [0.006 0.018] 
Horizontal water movement P19 ALP Emptying rate of the intermediate reservoir, through the intermediate hydrograph 24h−1 [0.6 1.2] 
P20 TPOINT Time to peak for the surface unit hydrograph day [0.3 5] 
P21 BETA Shape parameter of the surface hydrograph (using a gamma distribution function) – [0.4 5] 
P22 BET/GAMMA Time to peak for the intermediate unit hydrograph day [1.5 13] 
P23 GAMMA Shape parameter of the intermediate hydrograph (using a gamma distribution function) – [0.15 1.5] 
Sub-modelIDAcronymPhysical meaningUnitParameter range
Evapo-transpiration P1 FAETP Factor multiplying potential evapotranspiration (PET) for the estimation of summer real evapotranspiration (RET) – [0.6 3] 
P2 POUR Factor multiplying PET for estimating the RET in winter – [0 0.3] 
Snowmelt P3 FKM Snow melting rate during daytime. ΔT in Celsius is calculated as the difference between Tmax and parameter of Tmax threshold for snowmelt (TB) cm/Δ°C/day [0.05 0.4] 
P4 FKYN Snow melting rate during night-time. ΔT in Celsius is calculated as the difference between parameter TB and Tmin cm/Δ°C/day [0.05 0.5] 
P5 TB Tmax threshold for snowmelt °C [−6 7] 
P6 TBN Tmin threshold for accelerated snowmelt °C [−6 6] 
P7 TACAL Reference temperature for calculating the heat supplied by the rain to the snow cover °C [−6 4] 
P8 CC Empirical parameter used to connect the state variables describing snow cover and cumulated snowmelt to the proportion of the basin covered by snow – [0.8 5] 
Surface runoff P9 CGEL Empirical parameter used to connect the state variables describing soil freezing and thawing to the proportion of snowmelt water flowing on the surface – [0.8 15] 
P10 CIMAX 24-hour rainfall amount needed to generate 50% runoff with completely dry soil cm [10 45] 
P11 CSAP 24-hour rainfall amount needed to generate 50% runoff with completely saturated soil cm [1 8] 
Vertical water movement P12 RMIN Water amount in the unsaturated zone that cannot drain by gravity cm [0 7] 
P13 RMAX Maximum water amount that can be contained in the unsaturated soil zone cm [3 25] 
P14 SAPMAX Maximum water amount that can be contained in the aquifer before generating surface runoff cm [4 30] 
P15 Proportion of surface water flowing through the intermediate hydrograph instead of moving through the soil column – [0.15 0.7] 
P16 Proportion of soil water that is directed to the intermediate hydrograph when the unsaturated zone overflows – [0.3 1] 
P17 PER Emptying rate of the unsaturated zone to the groundwater reservoir 24h−1 [0.09 0.07] 
P18 Emptying rate of the groundwater reservoir (base flow) 24h−1 [0.006 0.018] 
Horizontal water movement P19 ALP Emptying rate of the intermediate reservoir, through the intermediate hydrograph 24h−1 [0.6 1.2] 
P20 TPOINT Time to peak for the surface unit hydrograph day [0.3 5] 
P21 BETA Shape parameter of the surface hydrograph (using a gamma distribution function) – [0.4 5] 
P22 BET/GAMMA Time to peak for the intermediate unit hydrograph day [1.5 13] 
P23 GAMMA Shape parameter of the intermediate hydrograph (using a gamma distribution function) – [0.15 1.5] 

Tmax, maximum temperature; Tmin, minimum temperature.

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