In the fifty-two
years since Robert Horton's 1945 pioneering quantitative description of
channel network planform, no conclusive findings have been presented that
permit the inference of geomorphological processes from any measures of
network planform. All measures of network planform studied exhibit limited
geographic variability across widely different environments. Horton (1945),
Langbein et al. (1947), Schumm (1956), Hack (1957), Melton (1958), and
Gray (1961) established various "laws" of network planform, that is, statistical
relationships between different variables which have limited variability.
A wide variety of models which have been proposed to simulate the growth
of channel networks in time over a landsurface are generally also in agreement
with the above planform laws.
An explanation
is proposed for the generality of the channel network planform laws. Channel
networks must be space filling, that is, they must extend over the landscape
to drain every hillslope, leaving no large undrained areas, and with no
crossing of channels, often achieving a roughly uniform drainage density
in a given environment. It is show that the space-filling constraint can
reduce the sensitivity of planform variables to different network growth
models, and it is proposed that this constraint may determine the planform
laws.
The "Q model"
of network growth of Van Pelt and Verwer (1985) is used to generate samples
of networks. Sensitivity to the model parameter Q is markedly reduced when
the networks generated are required to be space filling. For a wide variety
of Q values, the space-filling networks are in approximate agreement with
the various channel network planform laws. It is proposed that the space-
filling constraint may be an important determinant of the empirical laws
of network planform. Additional constraints, including
of energy efficiency, were not studied but may further reduce the variability
of planform laws.
Inference of
model parameter Q from network topology is succesful only in networks not
subject to spatial constraints. In space-filling networks, for a wide range
of Q values, the maximal-likelihood Q parameter value is generally in the
vicinity of 1/2, which yields topological randomness. It is proposed that
space filling originates the appearance of randomness in channel network
topology, and may cause difficulties to geomorphological inference from
network planform.
This dissertation received the 1997 Lorenz G. Straub Award
Supervisory Committee:
Dr. Stephen J. Burges, Chairman
Dr. David R. Montgomery, Graduate School Rep.
Dr. James W. Kirchner
Dr. Dennis P. Lettenmaier
Dr. Catherine M. Petroff
Dr. Ronald E. Nece