Journal of Conference Abstracts

Basin Morphology Inferred from a Generalization of Hack's Law

Peter S. Dodds (dodds@mit.edu), Romualdo Pastor-Satorras (romu@segovia.mit.edu) & Daniel H. Rothman (dan@segovia.mit.edu)

Rm 54-627 MIT, 77 Massachusetts Avenue, Cambridge, 02139, U.S.A.

A conjectured form for an extended, statistical version of Hack's law is critically examined. A simple lattice simulation of river networks is employed to study the form of the conditional probability distribution relating maximal stream length to drainage area. Hack's law is seen to be the mean value of this distribution which is succinctly described by one scaling function and one exponent. Further, finite size scaling effects are seen to bring about a marked deviation from Hack's law above a critical value of drainage area. This is argued to be due to the constraints on the possible morphology of drainage basins imposed by the overall scale of the landscape. Finally, Hack scaling functions extracted from two real landscapes are presented and discussed.