The physical framework of the dependence between channel flow hydrographs and drainage network morphometry

Abstract The physical basis of the linkage between magnitude and timing of channel flow hydrographs and drainage network morphometry is reviewed. Small Hortonian and structurally Hortonian networks are analysed using numerical runoff simulation. For Hortonian networks the variability of the geometry of individual channels and subcatchments within each Strahler order has generally little effect upon the overall character of the hydrograph in channels of higher order. If the network is also structurally Hortonian, the analysis of the simultaneous formation, travel, and concentration of the hydrographs in all channels of the network can be simplified to a sequence of one representative hydrograph per channel order. This approach is used in this study. Three major runoff processes control the flow hydrograph characteristics: the overland flow process which determines the water supply to the drainage network; the channel flow process which translates the hydrograph in space and time; and the drainage network process which concentrates and magnifies the flow at the junctions of the drainage network. Functional relations for the hydrograph peak, timing, and flow velocity are presented. For a given uniform rainfall and infiltration rate, the peak of the channel flow hydrograph is shown to increase geometrically with channel order, and its magnitude is directly related to the bifurcation ratio. The travel time of the peak also increases geometrically with channel order, and it is directly related to the channel length ratio over velocity ratio. The flow velocity of the peak changes in a downstream direction as a function of the bifurcation and slope ratio. It was also found that for negligible channel storage the channel flow and drainage network processes do not contribute significantly to the observed nonlinear response of a watershed to precipitation.