Appraisal of the Generalized Likelihood Uncertainty Estimation (GLUE) Method

Recent research documents that the widely accepted Generalized Likelihood Uncertainty Estimation (GLUE) method for describing forecasting errors and the impact of parameter uncertainty in rainfall/runoff watershed and other environmental simulation models fails to achieve the intended purpose. In particular, GLUE generally fails to produce credible regions for the uncertainty in model predictions, and the difference between predictions and future observations that agree with accepted and correct methods of uncertainty analysis. This paper documents problems with GLUE using a simple linear rainfall/runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are available. Beven and others have suggested that the choice of the likelihood function used in a GLUE computation is subjective and may be selected to reflect the goals of the modeler. If an arbitrary likelihood function is adopted that does not reasonably reflect the sampling distribution of the model errors, then GLUE generates arbitrary results without statistical validity that should not be used in scientific work. We show how the GLUE methodology when properly implemented with a statistically valid likelihood function can provide credible regions for model predictions (not just averages) which will agree with widely accepted and statistically valid analyses.