One decade of multi-objective calibration approaches in hydrological modelling: a review

One decade after the first publications on multi-objective calibration of hydrological models, we summarize the experience gained so far by underlining the key perspectives offered by such approaches to improve parameter identification. After reviewing the fundamentals of vector optimization theory and the algorithmic issues, we link the multi-criteria calibration approach with the concepts of uncertainty and equifinality. Specifically, the multi-criteria framework enables recognition and handling of errors and uncertainties, and detection of prominent behavioural solutions with acceptable trade-offs. Particularly in models of complex parameterization, a multi-objective approach becomes essential for improving the identifiability of parameters and augmenting the information contained in calibration by means of both multi-response measurements and empirical metrics (soft data), which account for the hydrological expertise. Based on the literature review, we also provide alternative techniques for dealing with conflicting and non-commeasurable criteria, and hybrid strategies to utilize the information gained towards identifying promising compromise solutions that ensure consistent and reliable calibrations.