The meaning of oscillations in unit hydrograph S-curves

ABSTRACT

The Duhamel superposition integral is used to obtain some exact solutions for unit hydrograph applications. These equations and numerical examples are used to show that oscillations will occur in an S-curve when the time step is less than the excess rainfall duration if the measured hydrograph differs from a hydrograph that would be obtained by solving a linear differential equation with time-independent coefficients. The implications of this result with regard to the calculation of the instantaneous unit hydrograph (IUH) are discussed.