Bayesian Estimation of Uncertainty in Runoff Prediction and the Value of Data: An Application of the GLUE Approach

Abstract

This paper addresses the problem of evaluating the predictive uncertainty of TOPMODEL using the Bayesian Generalised Likelihood Uncertainty Estimation (GLUE) methodology in an application to the small Ringelbach research catchment in the Vosges, France. The wide range of parameter sets giving acceptable simulations is demonstrated, and uncertainty bands are presented based on different likelihood measures. It is shown how the distributions of predicted discharges are non‐Gaussian and vary in shape through time and with discharge. Updating of the likelihood weights using Bayes equation is demonstrated after each year of record and it is shown how the additional data can be evaluated in terms of the way they constrain the uncertainty bands.