Asymptotic Rayleigh instantaneous unit hydrograph

The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude,N, tends asymptotically, asN grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor,, where is a mean link wave travel time.