Bayesian approach for the calibration of models: application to an urban stormwater pollution model

In environmental modelling, estimating the confidence level in conceptual model parameters is necessary but difficult. Having a realistic estimation of the uncertainties related to the parameters is necessary i) to assess the possible origin of the calibration difficulties (correlation between model parameters for instance), and ii) to evaluate the prediction confidence limits of the calibrated model. In this paper, an application of the Metropolis algorithm, a general Monte Carlo Markov chain sampling method, for the calibration of a four-parameter lumped urban stormwater quality model is presented. Unlike traditional optimisation approaches, the Metropolis algorithm identifies not only a "best parameter set", but a probability distribution of parameters according to measured data. The studied model includes classical formulations for the pollutant accumulation during dry weather period and their washoff during a rainfall event. Results indicate mathematical shortcomings in the pollutant accumulation formulation used.