In recent years, increasing computational power has been used to weight competing hydrological models in a Bayesian framework to improve predictive power. This may suggest that for a given measure of association with the observed data, one hydrological model is superior to another. However, careful analyses of the residuals of the model fit are required to propose further improvements to the model. In this paper we consider an alternative method of analyzing the shortcomings in a hydrological model. The hydrological model parameters are treated as varying in time. Simulation using a particle filter algorithm then reveals the parameter distribution needed at each time to reproduce the observed data. The resulting parameter, and the corresponding model state, distributions can be analyzed to propose improvements to the hydrological model. A demonstrative example is presented using rainfall-runoff data from the Leaf River, United States. This indicates that even when explicitly representing the uncertainty of the observed rainfall and discharge series, the technique shows shortcomings in the model structure.