Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology

Abstract

The aim of the paper is to demonstrate the incoherence, in terms of Bayesian inference, of the generalized likelihood uncertainty estimation (GLUE) approach, introduced by Beven and Binley in 1992. This results into a reduced capacity of the technique to extract information, in other words to “learn”, from observations. The paper also discusses the implications of this reduced learning capacity for parameter estimation and hydrological forecasting uncertainty assessment, which has led to the definition of the “equifinality” principle. The notions of coherence for learning and prediction processes as well as the value of a statistical experiment are introduced. These concepts are useful in showing that the GLUE methodology defines a statistical inference process, which is inconsistent and incoherent.