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Original Articles

Balance between calibration objectives in a conceptual hydrological model

Equilibre entre objectifs de calage dans un modèle hydrologique conceptuel

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Pages 1017-1032 | Received 07 Oct 2009, Accepted 09 Jun 2010, Published online: 20 Aug 2010

Figures & data

Fig. 1 Location and schematization of the Meuse basin upstream of Borgharen in HBV-15 with numbers referring to sub-basin names. 1: Meuse source–Meuse St Mihiel; 2: Chiers; 3: Meuse St Mihiel–Meuse Stenay; 4: Meuse Stenay–Meuse Chooz; 5: Semois; 6: Viroin; 7: Meuse Chooz–Meuse Namur; 8: Lesse; 9: Sambre; 10: Ourthe; 11: Amblève; 12: Vesdre; 13: Mehaigne; 14: Meuse Namur–Meuse Borgharen; 15: Jeker.

Fig. 1 Location and schematization of the Meuse basin upstream of Borgharen in HBV-15 with numbers referring to sub-basin names. 1: Meuse source–Meuse St Mihiel; 2: Chiers; 3: Meuse St Mihiel–Meuse Stenay; 4: Meuse Stenay–Meuse Chooz; 5: Semois; 6: Viroin; 7: Meuse Chooz–Meuse Namur; 8: Lesse; 9: Sambre; 10: Ourthe; 11: Amblève; 12: Vesdre; 13: Mehaigne; 14: Meuse Namur–Meuse Borgharen; 15: Jeker.

Table 1  Characteristics of nine sub-basins

Table 2  Model parameters and their minimum and maximum values used in the Monte Carlo simulation

Fig. 2 Combined rank measure as a function of scaled parameter value for: (a) identifiable parameter and (b) non-identifiable parameter. The points within the squares are used in the calculation of the identifiability of a parameter.

Fig. 2 Combined rank measure as a function of scaled parameter value for: (a) identifiable parameter and (b) non-identifiable parameter. The points within the squares are used in the calculation of the identifiability of a parameter.

Table 3  Single-objective function values from calibration for maximum value of combined rank measure (comb.) and for maximum value of each single-objective function (optimum) and maximum value of combined rank measure (R*) for nine sub-basins

Fig. 3 Contribution of calibration parameters to total identifiability for balance between calibration objectives with maximum total parameter identifiability for nine sub-basins. Dotted lines indicate total parameter identifiability for λRVE = λNS =λRMERV = λRMAEL = 0.

Fig. 3 Contribution of calibration parameters to total identifiability for balance between calibration objectives with maximum total parameter identifiability for nine sub-basins. Dotted lines indicate total parameter identifiability for λRVE = λNS =λRMERV = λRMAEL = 0.

Fig. 4 Balance between four objectives expressed as scaled rank number for maximum identifiability of each of three parameters for nine sub-basins.

Fig. 4 Balance between four objectives expressed as scaled rank number for maximum identifiability of each of three parameters for nine sub-basins.

Fig. 5 Total parameter identifiability (PI) as a function of balance between four objectives expressed as constants added to scaled rank numbers (λRVE, λNS, λRMERV, λRMAEL) for the Amblève sub-basin.

Fig. 5 Total parameter identifiability (PI) as a function of balance between four objectives expressed as constants added to scaled rank numbers (λRVE, λNS, λRMERV, λRMAEL) for the Amblève sub-basin.

Table 4  Single-objective function values for calibration for maximum value of combined rank measure (cal.) and validation (val.) and related ME value (for equal importance of the SOFs) and maximum ME value (varying the importance of SOFs) for nine sub-basins

Fig. 6 Model validation (ME) as a function of balance between four objectives expressed as constants added to scaled rank numbers (λRVE, λNS, λRMERV, λRMAEL) for the Amblève sub-basin.

Fig. 6 Model validation (ME) as a function of balance between four objectives expressed as constants added to scaled rank numbers (λRVE, λNS, λRMERV, λRMAEL) for the Amblève sub-basin.

Fig. 7 Balance between four objectives expressed as scaled rank number for maximum values of three measures (combined rank measure, parameter identifiability and model validation) for nine sub-basins.

Fig. 7 Balance between four objectives expressed as scaled rank number for maximum values of three measures (combined rank measure, parameter identifiability and model validation) for nine sub-basins.

Fig. 8 Balance between four objectives expressed as scaled rank number for maximum values of three measures (combined rank measure, parameter identifiability and model validation) for Chiers and Ourthe sub-basins in the validation period.

Fig. 8 Balance between four objectives expressed as scaled rank number for maximum values of three measures (combined rank measure, parameter identifiability and model validation) for Chiers and Ourthe sub-basins in the validation period.

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