Hydraulic geometry and the nonlinearity of the network instantaneous response

Abstract

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 tp and the peak f(tp) of the network instantaneous response function (IRF) vary as tp ∝ ie-m and f(tp) ∝ ie+m, where ie is the rainfall excess rate.