An empirical method to improve the prediction limits of the GLUE methodology in rainfall–runoff modeling

The generalized likelihood uncertainty estimation (GLUE) method is one of the most widely used methods for investigating the uncertainties in the water resources and environmental modeling. However, some researches have found that the percentage of the observations falling within the prediction limits provided by the GLUE is much lower than the given certainty level used to produce these prediction limits in many cases. One possible reason contributing to such a low enveloping efficiency is the fact that, as the GLUE method indiscriminatingly accepts the simulation output of the hydrological model as its input, the errors in the simulation output of the hydrological model will be directly reflected in the prediction limits provided by the GLUE method. So, it is suggested in this paper to modify the original GLUE methodology by applying a new procedure designed to at least partially correct the simulation/prediction of the hydrological model prior to the derivation of the prediction limits at each time step, in an attempt to improve the efficiency of the GLUE prediction limits in enveloping the real-world observations. To test this simple concept, both the original GLUE and the suggested modified GLUE methods have been employed to produce the prediction limits of runoff on two different catchments. In terms of the containing ratio, i.e. the percentage of the observed data bracketed by the respective runoff prediction limits, the modified GLUE method has shown substantial improvements over the original method, in both the calibration and the verification periods.