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 km^{2}. 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

Sub-model . | ID . | Acronym . | Physical meaning . | Unit . | Parameter 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 T_{max} and parameter of T_{max} 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 T_{min} | cm/Δ°C/day | [0.05 0.5] | |

P5 | TB | T_{max} threshold for snowmelt | °C | [−6 7] | |

P6 | TBN | T_{min} 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 | D | Proportion of surface water flowing through the intermediate hydrograph instead of moving through the soil column | – | [0.15 0.7] | |

P16 | X | 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 | Y | 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-model . | ID . | Acronym . | Physical meaning . | Unit . | Parameter 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 T_{max} and parameter of T_{max} 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 T_{min} | cm/Δ°C/day | [0.05 0.5] | |

P5 | TB | T_{max} threshold for snowmelt | °C | [−6 7] | |

P6 | TBN | T_{min} 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 | D | Proportion of surface water flowing through the intermediate hydrograph instead of moving through the soil column | – | [0.15 0.7] | |

P16 | X | 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 | Y | 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] |

T_{max}, maximum temperature; T_{min}, minimum temperature.

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