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The Profile of a Random Stream
Author(s) -
Dacey Michael F.
Publication year - 1968
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/wr004i003p00651
Subject(s) - elevation (ballistics) , equidistant , constant (computer programming) , mathematics , random variable , geometry , statistics , hydrology (agriculture) , geodesy , geology , computer science , geotechnical engineering , programming language
A probabilistic formulation is given for the profile of a stream. The elevation of a stream is considered at successive points j , j = 1, 2, · · ·, that have equidistant spacing along the stream. The basic assumptions of the model are (1) between the j th and ( j + l)th points stream elevation remains constant or drops by a unit of elevation, and (2) the probability p of decrease between the j th and ( j + l)th points is independent of j . Two formulations of the model are examined by assuming that p is constant throughout the stream length, and that p is a random variable. The model is analyzed for these two cases, and results include the frequency functions, means, and variances of length of stream from its origin to ‘sea‐level’ and for elevation of stream at each point j .