Urban runoff modelling uncertainty: Comparison among Bayesian and pseudo-Bayesian methods

Urban stormwater quality modelling plays a central role in evaluation of the quality of the receiving water body. However, the complexity of the physical processes that must be simulated and the limited amount of data available for calibration may lead to high uncertainty in the model results. This study was conducted to assess modelling uncertainty associated with catchment surface pollution evaluation. Eight models were compared based on the results of a case study in which there was limited data available for calibration. Uncertainty analysis was then conducted using three different methods: the Bayesian Monte Carlo method, the GLUE pseudo-Bayesian method and the GLUE method revised by means of a formal distribution of residuals between the model and measured data (GLUE_f). The uncertainty assessment of the models enabled evaluation of the advantages and limitations of the three methodologies adopted. The models were then tested using the quantity–quality data gathered for the Fossolo catchment in Bologna, Italy. The results revealed that all of the models evaluated here provided good calibration results, even if the model reliability (in terms of related uncertainty) varied, which suggests the adoption of a specific modelling approach with respect to the others. Additionally, a comparison of uncertainty analysis approaches showed that, regarding the models evaluated here, the classical Bayesian method is more effective at discriminating models according to their uncertainty, but the GLUE approach performs similarly when it is based on the same founding assumptions as the Bayesian method.