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We present a probability based theoretical scheme for building process‐based models of uncertain hydrological systems, thereby unifying hydrological modeling and uncertainty assessment. Uncertainty for the model output is assessed by estimating the related probability distribution via simulation, thus shifting from one to many applications of the selected hydrological model. Each simulation is performed after stochastically perturbing input data, parameters and model output, this latter by adding random outcomes from the population of the model error, whose probability distribution is conditioned on input data and model parameters. Within this view randomness, and therefore uncertainty, is treated as an inherent property of hydrological systems. We discuss the related assumptions as well as the open research questions. The theoretical framework is illustrated by presenting real‐world and synthetic applications. The relevant contribution of this study is related to proposing a statistically consistent simulation framework for uncertainty estimation which does not require model likelihood computation and simplification of the model structure. The results show that uncertainty is satisfactorily estimated although the impact of the assumptions could be significant in conditions of data scarcity.

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 multiobjective 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.Key words multi-objective evolutionary algorithms; multiple responses; uncertainty; equifinality; hybrid calibration; soft data Une décennie d'approches de calage multi-objectifs en modélisation hydrologique: une revue Résumé Une décennie après les premières publications sur le calage multi-objectifs des modèles hydrologiques, nous résumons l'expérience acquise jusqu'ici en soulignant les perspectives clefs offertes par de telles approches pour améliorer l'identification des paramètres. Après la revue des éléments fondamentaux de la théorie de l'optimisation de vecteurs et des problèmes algorithmiques, nous relions l'approche de calage multi-critères avec les concepts d'incertitude et d'équifinalité. Spécifiquement, le cadre multi-critères permet de reconnaître et de gérer des erreurs et des incertitudes, et d'identifier les principales solutions comportementales selon des compromis acceptables. En particulier pour des modèles ayant un paramétrage complexe, une approche multi-objectifs devient essentielle pour améliorer l'identification des paramètres et augmenter l'information contenue dans le calage au moyen de mesures à réponses multiples et de métriques empiriques (données "molles"), qui tiennent compte de l'expertise hydrologique. Sur la base d'une revue de la littérature, nous fournissons également des techniques alternatives pour gérer les critères contradictoires et incommensurables, et des stratégies hybrides pour utiliser l'information obtenue durant l'identification de compromis prometteurs qui assurent des calages cohérents et fiables.