Bayesian approach for uncertainty quantification in water quality modelling: The influence of prior distribution

Mathematical models are of common use in urban drainage, and they are increasingly being applied to support decisions about design and alternative management strategies. In this context, uncertainty analysis is of undoubted necessity in urban drainage modelling. However, despite the crucial role played by uncertainty quantification, several methodological aspects need to be clarified and deserve further investigation, especially in water quality modelling. One of them is related to the \u201ca priori\u201d hypotheses involved in the uncertainty analysis. Such hypotheses are usually condensed in \u201ca priori\u201d distributions assessing the most likely values for model parameters. This paper explores Bayesian uncertainty estimation methods investigating the influence of the choice of these prior distributions. The research aims at gaining insights in the selection of the prior distribution and the effect the user-defined choice has on the reliability of the uncertainty analysis results. To accomplish this, an urban stormwater quality model developed in previous studies has been employed. The model has been applied to the Fossolo catchment (Italy), for which both quantity and quality data were available. The results show that a uniform distribution should be applied whenever no information is available for specific parameters describing the case study. The use of weak information (mostly coming from literature or other model applications) should be avoided because it can lead to wrong estimations of uncertainty in modelling results. Model parameter related hypotheses would be better dropped in these cases