Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations

Several methods have been recently proposed for quantifying the uncertainty of hydrological models. These techniques are based upon different hypotheses, are diverse in nature, and produce outputs that can significantly differ in some cases. One of the favored methods for uncertainty assessment in rainfall-runoff modeling is the generalized likelihood uncertainty estimation (GLUE). However, some fundamental questions related to its application remain unresolved. One such question is that GLUE relies on some explicit and implicit assumptions, and it is not fully clear how these may affect the uncertainty estimation when referring to large samples of data. The purpose of this study is to address this issue by assessing how GLUE performs in detecting uncertainty in the simulation of long series of synthetic river flows. The study aims to (1) discuss the hypotheses underlying GLUE and derive indications about their effects on the uncertainty estimation, and (2) compare the GLUE prediction limits with a large sample of data that is to be simulated in the presence of known sources of uncertainty. The analysis shows that the prediction limits provided by GLUE do not necessarily include a percentage close to their confidence level of the observed data. In fact, in all the experiments, GLUE underestimates the total uncertainty of the simulation provided by the hydrological model.