Complexity, Emergence, and Self-Similar Organization in River Networks
Paik, Kyungrock
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Permalink
https://hdl.handle.net/2142/83293
Description
Title
Complexity, Emergence, and Self-Similar Organization in River Networks
Author(s)
Paik, Kyungrock
Issue Date
2006
Doctoral Committee Chair(s)
Kumar, Praveen
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Language
eng
Abstract
Hydrologic predictions lie at the core of a variety of environmental studies. Often these predictions need the specification of geomorphologic properties. However, geomorphologic properties themselves change in response to hydrologic variability. Therefore, for the long term prediction we need a better understanding of the interplay between hydrologic variability and landscape formation. This may be achieved by investigating the dynamics behind the observed signatures that emerge as the result of hydro-geomorphologic interactions. In this research, I investigate the driving mechanisms that give rise to key signatures such as the power functional relationship between the direct runoff and the rainfall excess rates and the self-similar organization in river networks. I also investigate the connectivity structure of binary trees which enables ubiquitous characteristics, such as self-similar topology, observed in river networks as well as other diverse tree networks. To understand these phenomena, I investigate the role and interaction of variabilities of hydrologic, geologic, and geomorphologic characteristics at different space and time scales. With this premise, I examine from a broader perspective river networks as general complex networks that are characterized by the high clustering of nodes and the small characteristic path lengths. The original contributions of this research can be stated as the following key discoveries: (1) The nonlinearity in network instantaneous response to different rainfall excess rates is driven by the nonlinear at-a-station hydraulic geometry relationships. (2) Inherent randomness is a sufficient condition for the generation of a tree topological organization in dissipative systems under the evolutionary dynamics, which is driven by a flow gradient and subject to proximity constraint, that is, the matter and energy can traverse only through a continuum. (3) Statistical self-similar topology is an inevitable consequence of any full binary tree with few exceptions. However, geometric self-similarity is dependent on the definition of geometric parameters such as the distance. (4) The degree of the hierarchical density, identified as exponents of size distribution, shows great variability over an infinite number of theoretical trees. Attempts to group trees in distinct classes based on their size distribution should be cautious.
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