Nonlinear Instantaneous Unit-Hydrograph Theory

The proposed equation for instantaneous unit hydrographs (IUHs) contains three physically-significant parameters: K₁, the overland storage-discharge factor; K₂, the channel storage-discharge factor; T, the time of concentration; and a functional parameter, w(τ), called the concentration-time diagram. Analysis of hyetographs and hydrographs for various storms over six drainage basins indicates a definite relationship between the parameters T and K₂, and the instantaneous equivalent rainfall excess, R_e. Nonlinearities in the instantaneous unit hydrographs derived from surface-runoff hydrographs caused by different storms over the same drainage basin are accounted for by the parameters of the IUH equation. Procedures for the analysis of data to establish relations between the parameters and R_e, and the use of established relations to derive a surface-runoff hydrograph from a given effective hyetograph are explained and supplemented by examples.