Unit hydrograph approximations assuming linear flow through topologically random channel networks

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 tp = (2N)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.