Unit hydrograph approximations assuming linear flow through topologically random channel networks

Abstract

The instantaneous unit Hydrograph (IUH) of a drainage basin is derived in terms of fundamental basin characteristics ( Z , α, β), where α parameterizes the link (channel segment) length distribution, and β is a vector of hydraulic parameters, Z is one of three basin topological properties, N , ( N , D ), or ( N , M ), where N is magnitude (number of first‐order streams), D is diameter (mainstream length), and M is order. The IUH is derived based on assumptions that the links are independent and identically distributed random variables and that the network is a member of a topologically random population. Linear routing schemes, including translation, diffusion, and general linear routing are used, and constant drainage density is assumed. By using ( N , α, β) as the fundamental basin characteristics, asymptotic (for large N ) considerations lead to a Weibull probability density function for the IUH, with time to peak given by t p = (2 N ) ½ α * /β * where α * is mean link length, and β * is a scalar hydraulic parameter (usually average celerity). This asymptotic IUH is identical for all linear routing schemes.