Temporal moments routing in streams and rivers with transient storage

Closed-form expressions for the temporal moments of concentration–time distributions in streams and rivers with transient storage (TS) have been derived. In addition to the mathematical relationships known already for the case of an instantaneous slug release, further and more general results were obtained for stream reaches with arbitrary inflow pollutographs. Thus, the temporal moments of the concentration-versus-time distribution at the lower end of a reach can be linked to the respective moments at the upper end and the transport and mixing parameters of the so-called TS or Dead Zone Model. Therefore, starting from the site of a release (or some arbitrary cross-section within the zone of validity of the TS model), the first to fourth temporal moments of concentration–time distributions can be routed in flow direction along a cascade of stream reaches. The moment-routing equations presented are expected to be useful in the interpretation of measured field data (including estimation of the transport and mixing parameters) as well as for simulation purposes and as an easily used tool to check the accuracy of numerical codes.