Nonlinear transformation of unit hydrograph

Unit hydrograph (UH) and its numerous derivatives have been popular for estimation of flood hydrographs. Two major assumptions still overshadow UH applications. One is the linearity and the other is time invariance. In theory, only peak discharge of an equilibrium hydrograph follows linear proportionality to excess rainfall intensity. In trying to relax the linearity constraint, this paper aims to propose a nonlinear way of transforming a given UH to other general hydrographs. The transformation or mapping technique relies on a simple rainfall ratio raised to a power less than unity. The case of nonlinear transformation is illustrated for a number of watershed geometries with either known kinematic wave analytic solutions or observed data. The nonlinear UH approach also relaxes the assumption of constant time base of the UH. The proposed nonlinear UH transformation may thus be viewed as a major step in closing the gap between physically based and traditional UH-based surface runoff simulation approaches.