In the one-dimensional 'Rhine Alarm Model' differences between the actual travel time of a pollution cloud, originating from an instantaneous release of an accidental spill, and the travel time, based on the flow velocity is represented by a lag coefficient. In the model this lag coefficient is defined by the relative difference between these two travel times. This paper presents the results of a study on the influence of tributaries and suppressed flow by weirs on the lag coefficient in general and on the influence of the River Aare and the suppressed flow by water power stations on this coefficient in the Upper-Rhine River between Lake of Constance and Basel especially. Also the influence of incompletely transversal mixing in the vicinity of the point of release at a river bank as a special case of a polluted tributary is discussed. In the study analytical and numerical approaches were applied. For the numerical approach a two-dimensional transport model of the "Versuchsanstalt fUr Wasserbau (VAW)" (Hydraulic Research Institute) of the ETH-Ziirich (Federal University of Technology of Zurich) was used. The main conclusion is that the behaviour of the lag coefficient along the Upper-Rhine River is strongly influenced by sudden increases of the flow velocity at power stations, due to the differences in waterdepth upstream and downstream of the station, and at the Aare-Rhine confluence, due to the large discharge ratio of these river branches. The outcome of these flow-velocity discontinuities is a relatively large negative value of the lag coefficient upstream of the discontinuity and a relatively large positive value downstream. This is because upstream of the discontinuity the transport velocity of the centroid of the pollution cloud is already influenced by the larger flow velocity downstream of the discontinuity as soon as the front of the cloud has passed the discontinuity. Downstream of the discontinuity the transport velocity of the centroid is still influenced by the smaller flow velocity upstream of the discontinuity as long as the tail of the cloud remains upstream of the discontinuity. Case studies on the Upper-Rhine River between Lake of Constance and Basel show good fits of the calibrated values of the lag coefficient in the Rhine Alarm Model with the results of the two-dimensional transport model.