We postulate that the spatial variability in flow velocity in a basin, arising from the systematic downstream variation of celerity, may explain the observed nonlinear rainfall-runoff relationships. This is based on the argument that different rainfall excess rates will produce different velocity fields in a basin due to the nonlinear relation between velocity and flow. In particular, we show that if the mean velocity V varies with flow Q as V $propto$ Qm, then the time to peak tp and the peak f(tp) of the network instantaneous response function (IRF) vary as tp $propto$ ie-m and f(tp) $propto$ ie+m, where ie is the rainfall excess rate.