Daily streamflow prediction with uncertainty in ephemeral catchments using the GLUE methodology

The Generalised Likelihood Uncertainty Estimation (GLUE) approach is presented here as a tool for estimating the predictive uncertainty of a rainfall-runoff model. The GLUE methodology allows to recognise the possible equifinality of different parameter sets and assesses the likelihood of a parameters set being acceptable simulator when model predictions are compared to observed field data. The results of the GLUE methodology depend greatly on the choice of the likelihood measure and on the choice of the threshold which determines if a parameters set is behavioural or not. Moreover the sampling size has a strong influence on the uncertainty assessment of the response of a rainfall-runoff model. This is one of the most controversial and criticized aspect of the GLUE methodology, because it seems that this procedure does not learn from observations. Following these premises, this paper investigated first on the effect of different likelihood measures on the uncertainty analysis in the rainfall-runoff modelling of a mediterranean catchment. Performance of individual parameter sets has been assessed using three likelihood measures with a shaping factor. The acceptability threshold influence on the uncertainty analysis has been also evaluated. Finally it can be demonstrated how, using the GLUE, the predictive uncertainty grows with the streamflow variance while remains almost the same with the sampling size. In order to overcome these inconsistencies, a new simple likelihood measure, which explicitly takes into account the sample variance and extension, is here proposed.