We address the analysis and proper representation of posterior dependence among parameters obtained from model calibration. A simple water quality model for the Elbe River (Germany) is referred to as an example. The joint posterior distribution of six model parameters is estimated by Markov Chain Monte Carlo sampling based on a quadratic likelihood function. The estimated distribution shows to which extent model parameters are controlled by observations, highlighting issues that cannot be settled unless more information becomes available. In our example, some vagueness occurs due to problems in distinguishing between the effects of either growth limitation by lack of silica or a temperature dependent algal loss rate. Knowing such indefiniteness of the model structure is crucial when the model is to be used in support of management options. Bayesian network technology can be employed to convey this information in a transparent way.