In solving real-world river water-quality problems, mathematical models at present are used very little at the decisional level. The reason for this is, in our opinion, the existence of unresolved difficulties associated with the collection of the data required for model calibration. Surprisingly, the literature does not contain a consistent description of criteria supporting the design of data gathering campaigns explicitly dedicated to model calibration. In particular little attention is paid to the role that dispersion plays in this context. It is known that plug flow models can be more easily calibrated than dispersion models when the data gathering campaign is suitably organized. But when can a plug flow model substitute a dispersion model?.This paper derives a theoretically sound criterion to reply to this fundamental question.