Sensitivity analysis of conceptual model calibration to initialisation bias. Application to karst spring discharge models

In this paper the perturbation approach is used to investigate the analytical properties of the sensitivity to the initial conditions on the calibration and simulation results of two karst spring discharge reservoir models. The propagation of uncertainty in the initial conditions is shown to depend on both model structure and the values assumed by state variables at the beginning of simulation. Depending on model structure, nonlinearity may either hasten or delay the dissipation of the initialisation bias. In particular, threshold-based transfer functions are shown to generate Dirac sensitivity patterns. When associated with long-term memory reservoir and fast discharge models, they may generate a substantial initialisation bias even after very long periods of inactivity. As a practical consequence, the commonly-used one year warm-up period may not be sufficient to dissipate the initialisation bias. Calibration results may be impacted significantly. A careful examination of the initialisation bias behaviour should be part of “good modelling practice“. In particular, the use of elaborate procedures for locating the global optimum of the objective function used for parameter optimization can only be justified in so far as the initialisation bias has been efficiently eliminated. This study advocates the use of local sensitivity analysis as a low-computational cost tool to identify the main characteristics of the bias behaviour, even for conceptual models with strongly non-linear transfer functions.