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 Vproportional toQ(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) proportional to i(e)(-m) and f(t(p)) proportional to i(e)(+m), where i(e) is the rainfall excess rate.