University of Illinois Urbana-Champaign

River network scaling: optimality and anisotropy

Poore, Geoffrey M.

Content Files
2_Poore_Geoffrey.pdf

Permalink

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

Description

Title
River network scaling: optimality and anisotropy
Author(s)
Poore, Geoffrey M.
Issue Date
2010-08-20T17:58:26Z
Director of Research (if dissertation) or Advisor (if thesis)
Kieffer, Susan W.
Doctoral Committee Chair(s)
Stack, John D.
Committee Member(s)
  • Kieffer, Susan W.
  • Hubler, Alfred W.
  • Nathan, Alan M.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2010-08-20T17:58:26Z
Keyword(s)
  • networks
  • pattern formation
  • landscape evolution
  • parallel drainage
  • thermodynamics
  • power laws
  • fluvial geomorphology
Abstract
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.
Graduation Semester
2010-08
Permalink
http://hdl.handle.net/2142/16811
Copyright and License Information
Copyright 2010 Geoffrey M. Poore

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois