Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation / Indices pour évaluer les bornes de prévision de modèles hydrologiques et mise en œuvre pour une estimation d'incertitude par vraisemblance généralisée

Abstract

To reflect the uncertainties of a hydrological model in simulating and forecasting observed discharges according to rainfall inputs, the estimated result for each time step should not be just a point estimate (a single numerical value), but should be expressed as a prediction interval, i.e. a band defined by the prediction bounds of a particular confidence level α. How best to assess the quality of the prediction bounds thus becomes very important for understanding the modelling uncertainty in a comprehensive and objective way. This paper focuses on seven indices for characterizing the prediction bounds from different perspectives. For the three case-study catchments presented, these indices are calculated for the prediction bounds generated by the generalized likelihood uncertainty estimation (GLUE) method for various threshold values. In addition, the relationships among these indices are investigated, particularly that of the containing ratio (CR) to the other indices. In this context, three main findings are obtained for the prediction bounds estimated by GLUE. Firstly, both the average band-width and the average relative band-width are seen to have very strong linear correlations with the CR index. Secondly, a high CR value, a narrow band-width, and a high degree of symmetry with respect to the observed hydrograph, all of which are clearly desirable properties of the prediction bounds estimated by the uncertainty assessment methods, cannot all be achieved simultaneously. Thirdly, for the prediction bounds considered, the higher CR values and the higher degrees of symmetry with respect to the observed hydrograph are found to be associated with both the larger band-widths and the larger deviation amplitudes. It is recommended that a set of different indices, such as those considered in this study, be employed for assessing and comparing the prediction bounds in a more comprehensive and objective way. Indices pour évaluer les bornes de prévision de modèles hydrologiques et mise en oeuvre pour une estimation d'incertitude par vraisemblance généraliséeRésumé Afin de refléter les incertitudes d'un modèle hydrologique lors de la simulation et de la prévision de débits à partir de données de pluie, le résultat estimé à chaque pas de temps ne devrait pas être juste un point (une unique valeur numérique), mais devrait être exprimé sous la forme d'un intervalle de prévision, c'est-à-dire une bande définie par des bornes de prévision associées à un niveau de confiance particulier α. Estimer au mieux la qualité des bornes de prévision devient ainsi très important pour comprendre l'incertitude de modél-isation dans un sens complet et objectif. Cet article s'intéresse à sept indices pour caractériser les bornes de prévision, selon différentes perspectives. Pour les trois bassins versants présentés, ces indices sont calculés pour les bornes de prévision générées par la méthode GLUE, pour plusieurs valeurs de seuillage. De plus, les relations entre ces indices sont étudiées, en particulier entre le rapport de recouvrement (R...

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