We investigate the coupling of river network structure and hydraulic geometry thereby relaxing the assumption of spatially invariant celerities and hydrodynamic dispersion coefficients. The presence of spatially varying celerities induces a dispersion effect, referred to as kinematic dispersion, on the network travel time distribution. Its contribution to the total dispersion is comparable to that due to the heterogeneity of path lengths, that is, geomorphologic dispersion, and significantly larger than the hydrodynamic dispersion. If this contribution is ignored, the hydrograph shows a higher peak flow, a shorter time to peak, and shorter duration.