Hydraulic geometry and the nonlinearity of the network instantaneous response

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 ∝ Q ^m, then the time to peak t_p and the peak f(t_p) of the network instantaneous response function (IRF) vary as t_p ∝ i_e^-m and f(t_p) ∝ i_e ^+m, where i_e is the rainfall excess rate.