Shreve's probabilistic‐topologic model for drainage network topology is herein extended and generalized to allow for the presence of lakes. Drainage network topology is represented by an integer string directly analogous to the binary strings used for channel networks without lakes. Validity constraints on integer strings are presented, along with combinatorial results and methods for generating ‘topologically random’ networks. The hypothesis that network element degree and type is independent of position within the integer string leads to good predictions of the relative frequencies of various classes of small subnetworks within a 596‐link network in northern Ontario. For the special case of networks without lakes the model is equivalent to Shreve's.
Water Resources Research – Wiley
Published: Apr 1, 1982
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