Hydrologists shift their focus from seeking optimization strategies for identifying a single best model to trying to reduce the uncertainties in the predictions of the models. This is due to not only that there usually does not exist a single best combination of parameters to optimize the behavior of a model, but also that hydrologists realize that consistency is more important than optimality. Many hydrological models are used to analyze current systems, forecast into future under the scenarios of climate and land use changes and, therefore assist sustainable management of water resources. It is key for the policy makers to be aware of the uncertainties associated with the models. Research to date has focused mainly on quantifying parameter and data uncertainties, however model structure error can be the most significant component of the overall predictive uncertainty. This paper demonstrated a case study of applying Bayesian inference to determine the uncertainties associated with model structure as well as data and parameters. Compared to many ad hoc methods, Bayesian has the advantages of easy interpretation, being consistent and having learning ability. The hydrological model we studied is GR4J -- a daily lumped rainfall- runoff model with four parameters. We revised the model to include snow component. We applied this model to two control watersheds in Coweeta Basin in southwestern North Carolina. The results are two folds: the posterior means of the four parameters and streamflow corresponded well to the field measurements; the posterior distribution presented an easy and direct estimation of credible intervals of the simulated streamflow. Since the hydrological model we used is not spatial explicit, posterior distribution of simulated soil moisture content could provide a hint about model structure uncertainties related with not accounting for spatial variances.
