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Unit hydrograph approximations assuming linear flow through topologically random channel networks
Author(s) -
Troutman Brent M.,
Karlinger Michael R.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i005p00743
Subject(s) - mathematics , scalar (mathematics) , routing (electronic design automation) , independent and identically distributed random variables , hydrograph , random variable , probability density function , geometry , mathematical analysis , topology (electrical circuits) , statistics , combinatorics , drainage basin , computer science , geography , computer network , cartography
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.