Kinematic dispersion effects of hillslope velocities

When the flow parameters, such as celerity and hydrodynamic coefficient, are allowed to vary spatially within a basin, three mechanisms, namely, geomorphologic, kinematic, and hydrodynamic dispersion, contribute to the variance of the instantaneous response function. The relative contributions of the three dispersion mechanisms as a function of scale, or Strahler order of the basin, were studied earlier by Saco and Kumar [2002a, 2002b]. In this study we investigate the main mechanisms that are responsible for the variance when we take into account the hillslope dynamics. We use an approach similar to that derived by Saco and Kumar [2002a, 2002b], but for width functions, to compute the relative contributions of geomorphologic and kinematic dispersion due to hillslope celerities. We find that the kinematic dispersion due to hillslopes does not tend to reinforce the effect of geomorphologic dispersion; rather, it tends to counteract it. This means that the effect of hillslopes tends to "decrease" the variance induced by the geomorphology of the network. For hillslope celerities that are very small compared with channel celerities, the travel times in the hillslopes begin to be of the same order of magnitude as those in the network. If the celerity continues to decrease, all the variance is induced by the travel times at the hillslopes and the impact of geomorphologic dispersion becomes negligible.