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Title:Overcoming unrealistic behavior of landscape evolution models attributed to the stream power incision model: Scale invariance and ultra-sensitivity to initial conditions
Author(s):Kwang, Jeffrey S.
Director of Research:Parker, Gary
Doctoral Committee Chair(s):Parker, Gary
Doctoral Committee Member(s):Anders, Alison; Garcia, Marcelo; Paola, Chris
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):landscape evolution models, initial conditions, stream power incision model, bedrock streams, numerical models, experimental models, geomorphology, fluvial geomorphology
Abstract:Landscape evolution models (LEMs) have been used as tools for geomorphologist to explain and understand mountain formation and landform development. Initially these models were conceptual ideas of how geomorphic processes create the landscapes we see today. Now, we predominantly use numerical models of landscape evolution to investigate how large-scale landforms behave over long timescales. These models are typically reduced in complexity, where many processes are parameterized. While most studies focus on geologic timescales, some researchers have begun to use these types of models at engineering timescales. There is a large amount of uncertainty associated with these predictions due to the uncertainty in the parameters as well as the governing physical processes. Here, we take an in-depth look at current landscape evolution models to understand their fundamental behavior, and we identify key issues and propose possible remedies. This dissertation is made up of three chapters: Chapter 2 explores the steady-state behavior of the most-commonly used bedrock incision model used in LEMs; Chapter 3 compares the sensitivity of numerical LEMs and physical experiments to their initial conditions; and Chapter 4 explores a recently published sub-model that can remedy unrealistic behavior in current LEMs. The abstracts for each chapter are shown below. Chapter 2: LEMs often utilize the stream power incision model to simulate river incision: E=KAmSn, where E = vertical incision rate, K = erodibility constant, A = upstream drainage area, S = channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m/n = 0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only at small scales) is neglected, the choice m/n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10 km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000 km2 domain. Chapter 3: Numerical LEMs are dependent on their initial conditions (ICs). Commonly, LEMs use a horizontal surface with randomized perturbations as their IC and tend toward a steady-state under constant forcing. The initial and steady-state topography are inherently linked, but they bear no obvious resemblance to each other. Here, we reveal a connection by adding a shallow sinusoidal channel to the IC. This channel transforms into a deep canyon at steady-state. Hence, the general behavior of LEMs is to indefinitely preserve topological features from their initial topography. Here we test whether experimental landscapes exhibit a similar behavior. In our experiments, we use the same sinusoidal signal, but find that it is ultimately erased. We believe that the culprit reorganizing processes are lateral channel migration and spatiotemporal variability in incision. Our results imply that LEMs are missing fundamental mechanisms, and that long-term topological preservation of initial conditions in erosional environments is unlikely. Chapter 4: LEMs have been shown to preserve topographic and topologic signals from initial conditions over long periods, a phenomenon which Kwang and Parker (2019) named ultra-sensitivity. In contrast, the general behavior of physical experiments of landscape evolution is to erase and reorganize drainage networks. Kwang and Parker (2019) propose that this discrepancy between the experiments and numerical simulations are due to missing key physical processes in LEMs. One such process is lateral incision of bedrock channels. Recently, Langston and Tucker (2018) developed a lateral incision sub-model for use in landscape evolution models. Here, we implement this sub-model to show that LEMs do not preserve information from initial conditions when subjected to lateral incision. In addition, we show that the long-term behavior of LEMs with lateral incision approaches a highly dynamic steady-state where channels constantly migrate, and drainage networks reorganize frequently.
Issue Date:2019-06-25
Rights Information:Copyright 2019 Jeffrey S. Kwang
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08

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