The direct runoff hydrograph of a basin is a result of complex interaction between precipitation and runoff generation processes, and hillslope and channel dynamics. Both network and hydraulic geometry interact to shape the runoff process at the shorter time scales, while the runoff variability shapes the hydraulic geometry at the longer time scale. Flow transport equations with various degrees of approximation have been combined with the systematic organization of the planar network geometry, as characterized through the Horton's ratios, width function and self-similar trees. Theoretical formulations that combine channel flow dynamics with the network and hydraulic geometry open up the possibility of addressing the long standing problem of "prediction in ungaged basins" for hydrograph prediction by taking advantage of the signatures of the streamflow variability as evidenced through the existing characteristics of planar network topology and (bankfull) hydraulic geometry.