Comment on "Hydrological forecasting uncertainty assessment:Incoherence of the GLUE methodology" by Pietro Mantovan and Ezio Todini

This comment is a response to the criticisms of the GLUE methodology by [Mantovan, P., Todini, E., 2006. Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, J. Hydrology, 2006]. In this comment it is shown that the formal Bayesian identification of models is a special case of GLUE that can be used where the modeller is prepared to make very strong assumptions about the nature of the modelling errors. For the hypothetical study of Mantovan and Todini, exact assumptions were assumed known for the formal Bayesian identification, but were then ignored in the application of GLUE to the same data. We show that a more reasonable application of GLUE to this problem using similar prior knowledge shows that gives equally coherent results to the formal Bayes identification. In real applications, subject to input and model structural error it is suggested that the coherency condition of MT06 cannot hold at the single observation level and that the choice of a formal Bayesian likelihood function may then be incoherent. In these (more interesting) cases, GLUE can be coherent in the application of likelihood measures based on blocks of data, but different choices of measures and blocks effectively represent different beliefs about the information content of data in real applications with input and model structural errors