Simple Parametric Instantaneous Unit Hydrograph

Abstract

A new, simple, parametric instantaneous unit hydrograph (IUH) with conceptual and physical justification is proposed. The new IUH has only two parameters, one of which is the time base of the unit hydrograph, an obvious physically conceivable parameter. The new mathematical form of the IUH has the properties of a statistical frequency distribution, which qualifies it for a new statistical distribution, although this distribution is not addressed in statistical books. The use of the new IUH simplifies the computations involved in obtaining the runoff from a complex rainfall event, and the calculations can even be performed on a handheld calculator or an Excel worksheet. The applicability of the proposed IUH is illustrated by using several sets of published multistorm data, wherein an optimization method is used for estimating the representative parameters of the new IUH from a single representative rainfall-runoff event obtained by processing all multistorm events. The performance criteria used in this paper give equal weight to small and large peak storm events. The new IUH with the proposed method performs better than the more computationally complex IUHs or UHs. It outperforms the least squares and linear programming approaches by prior investigators for identifying the UH based on the normalized standard error of estimate. The new IUH and proposed method are useful to field engineers and practitioners with enhanced practical utility. The new bounded statistical distribution, developed as a by-product, may find applications in other branches of applied science, economics, and engineering.