The first model used in this paper is the conceptual rainfall–runoff model IHACRES (Jakeman & Hornberger 1993) which has eight parameters. This model has been widely applied to a variety of catchments for hydrological analysis and climate impact studies (Jakeman *et al*. 1993; Littlewood 1999; Letcher *et al*. 2001; Kim & Lee 2014). The model is composed of a non-linear module and a linear module, as shown in Figure 2, and model parameters are listed in Table 1. A non-linear module converts rainfall to effective rainfall which is calculated from the following equations:where *r*_{k} is the observed rainfall, *C* is the mass balance, *l* is the soil moisture index threshold and *p* is the power on soil moisture, respectively. The soil moisture is calculated from:where is the drying rate given by:where is the drying rate at reference temperature, *f* is the temperature modulation, is the reference temperature, and is the observed temperature. A linear module assumes that there is a linear relationship between the effective rainfall and flow. Two components in this module, quick flow and slow flow, can be connected in parallel or in series. In this study, two parallel storages in the linear module are used because they reflect the catchment conditions, and the streamflow at time step *k* is defined by the following equations:where and are quick flow and slow flow, respectively, and and *β* are recession rate and peak response, respectively. The relative volumes of quick flow and slow flow can be calculated from:Therefore, one parameter is determined if the other three parameters are known among the four linear module parameters (*α*_{q}, α_{s}, β_{q}, β_{s}).

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Table 1

Module . | Parameter . | Description . | Range . |
---|---|---|---|

Non-linear | c | Mass balance | 0 to 0.04 |

τ _{w} | Reference drying rate | 0 to 50 | |

f | Temperature modulation of drying rate | 0 to 4 | |

l | Soil moisture index threshold | 0 to 50 | |

p | Power on soil moisture | 0 to 3 | |

Linear | α _{q}, α_{s} | Quick and slow flow recession rate | −1 to 0 |

β _{q}, β_{s} | Fractions of effective rainfall for peak response | − 1 to 0 |

Module . | Parameter . | Description . | Range . |
---|---|---|---|

Non-linear | c | Mass balance | 0 to 0.04 |

τ _{w} | Reference drying rate | 0 to 50 | |

f | Temperature modulation of drying rate | 0 to 4 | |

l | Soil moisture index threshold | 0 to 50 | |

p | Power on soil moisture | 0 to 3 | |

Linear | α _{q}, α_{s} | Quick and slow flow recession rate | −1 to 0 |

β _{q}, β_{s} | Fractions of effective rainfall for peak response | − 1 to 0 |

Figure 2

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