River network scaling: optimality and anisotropy

River networks are one of the many branching patterns in nature that exhibit power laws. The origin of these power laws is debated. Explanations of river network scaling have ranged from topological inevitability to growth mechanisms and from dynamics to optimality principles. The main contenders are dynamics and optimality, and the latter is controversial. The first part of my research is concerned with optimality theories of river networks. I distinguish between local and global optimality constraints. Under local constraints, optimality of an overall network is a byproduct of local optimality. Local optimality can be produced by dynamics, and is not controversial when this is the case. Under global constraints, optimality of an overall network is the result of direct optimization. Global constraint optimality is the truly controversial variety. I show that the success of global constraint theories is likely due to the optimization algorithm employed rather than to the optimality constraint itself. There exists a hierarchy of possible global constraints, some of which yield realistic river scaling while others do not, but no justification has been provided for why one constraint should be favored rather than another. Global constraint optimality lacks a mechanism and conflicts with erosion dynamics. Since these results indicate that optimality does not offer a satisfactory explanation of river network scaling, I turn to a degenerate network model, in which all steady-state networks have the same efficiency and thus questions of optimality are irrelevant. Simulations of this model show that scaling depends on initial conditions. Perturbations over time would also affect the scaling of this model. Based on these results, I argue that initial conditions and perturbations, together with dynamics, provide a more promising direction than optimality for understanding network scaling. The second part of my research is concerned with the dependence of river network scaling on initial conditions. I focus on the effect of landscape slope in initial conditions, which is a type of anisotropy since it provides a preferential direction for flow. Simulated river networks exhibit scaling deviations and crossover behavior as a result of slope. I also measure the scaling of twelve natural river networks with a parallel pattern, which reflects the influence of slope. Some of these natural networks exhibit scaling deviations and crossover behavior, confirming the simulation results. This provides an explanation for exponent drift and for correlations between scaling and basin shape that have been observed in natural networks. More importantly, it confirms the importance of initial conditions in explaining river network scaling. Future research on river network scaling should focus on factors such as geometry, sources of anisotropy and noise, and perturbations, not on optimality.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Poore, Geoffrey M.

Contributors dc:contributor

• Kieffer, Susan W.
• Stack, John D.
• Hubler, Alfred W.
• Nathan, Alan M.

• networks
• pattern formation
• landscape evolution
• parallel drainage
• thermodynamics
• power laws
• fluvial geomorphology

Statement dc:rights

• Copyright 2010 Geoffrey M. Poore

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16811

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16811