Topographic Asymmetry and Climate Controls
on Landscape Evolution
ARCHNES
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
by
SEP 2 8 2015
Paul William Richardson
LIBRARIES
B.S., University of Washington (2009)
Submitte I in partial fulfillment of the requirements for the degree of Doctor
of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
Paul Richardson, MMXV. All rights reserved.
The author hereby grants to MIT permission to reproduce and distribute
publicly paper and electronic copies of this thesis document in whole or in
part in any medium now known or hereafter created.
Author........
Signature redacted
Massachusetts Institute of Technology
August 31, 2015
Certified by....
Signature
redacted
....
....................
J. Taylor Perron
Associate Professor, Massachusetts Institute of Technology
Thesis Supervisor
Acre ted bi
p
....
Signature redacted
....
....
...
....
...
Robert van der ilst
Department Head and Schlumberger Professor of Earth Sciences
Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology
2
Topographic Asymmetry and Climate Controls
on Landscape Evolution
by
Paul William Richardson
Submitted to the Massachusetts Institute of Technology on August
31, 2015, in partial fulfillment of the requirements for the degree
of Doctor of Philosophy
Abstract
Landscapes are expected to evolve differently under the influence of different climate
conditions. However, the relationship between landscape evolution and climate is not
well understood. I investigate the relationship between landscape evolution and climate
by using natural experiments in which climate varies with slope aspect (geographic
orientation) and causes differences in landscape form, such as steeper equator- or polefacing slopes. In order to understand which mechanisms are responsible for the
development of this topographic asymmetry, I adapted a numerical landscape evolution
model to include different asymmetry-forming mechanisms such as aspect-induced
variations in soil creep intensity, regolith strength, and runoff, and also lateral channel
migration. Numerical experiments reveal topographic signatures associated with each of
these mechanisms that can be compared with field sites that exhibit asymmetry. I used
these numerical model results, along with estimates of field-saturated hydraulic
conductivity, soil strength, evidence of stream capture and channel beheadings, and
erosion rates determined from cosmogenic radionuclides to determine which asymmetryforming mechanisms are likely responsible for the topographic asymmetry at Gabilan
Mesa, a landscape in the central California Coast Ranges. I find that aspect-dependent
differences in runoff are most likely responsible for the bulk of the asymmetry at Gabilan
Mesa, but lateral channel migration has contributed to the asymmetry in some locations.
To further investigate climate's influence on landscape evolution, I compiled new and
previously published estimates of slope-dependent soil transport efficiency across a range
of climates. I find that soil transport efficiency increases with mean annual precipitation
and the aridity index, a measure that describes water availability for plants. I also find
that soil transport efficiency varies with lithology and that different measurement
techniques can bias estimates of the soil transport coefficient.
Thesis Supervisor: J. Taylor Perron
Title: Associate Professor of Geology
3
Table of Contents
A cknow ledgem ents................................................................................
5
C hapter 1. Introduction..............................................................................
7
Chapter 2. Modeling the formation of topographic asymmetry by lateral channel
migration and aspect-dependent erosional processes...........................................11
Chapter 3. Unraveling the mysteries of an asymmetric landscape.........................67
Chapter 4. The influence of climate on hillslope sediment transport efficiency..........113
C hapter 5. C onclusion ............................................................................
Referen ces...........................................................................................14
A p p en dix ............................................................................................
4
139
5
159
Acknowledgements
First and foremost, I would like to acknowledge Lisa Richardson, who has been
supportive throughout this process and has found much time to pursue new hobbies and
interest while I completed my thesis. Secondly, I would like to thank my family and
friends who encouraged me to persevere when results did not come as quickly as one
might like.
There are also a number of other people that I owe significant gratitude to
including my thesis advisor Taylor Perron and my thesis committee members: David
McGee, Dara Entekhabi, Noah Snyder, and Jim Kirchner. They all supplied valuable
input. I would also like to thank Scott Miller who offered me considerable help with the
topographic asymmetry analysis and very useful feedback throughout my graduate
studies. I thank Naomi Schurr for helping compile some of the data and for making some
of the topographic measurements in Chapter 4. I would also like to thank those who
helped me in the field or helped prepare equipment for the field including David de Jong,
Michael Sori, and Peter Polivka.
Furthermore, I would also like to thank all of the funding agencies that supported
this work, including the National Defense Science and Engineering Graduate Fellowship
through the Department of Defense. I would also like to thank the Geological Society of
America for funding some of my travel and research, and the National Science
Foundation for a grant to Taylor Perron that provided some of the funding for this
research.
5
A man's interest in a single bluebird is worth more than a complete
but dry list of the fauna andflora of a town.
-Henry David Thoreau
6
Chapter 1. Introduction
Despite many studies addressing how landscapes respond to differences in climate
[e.g., Riebe et al., 2004; Perron et al., 2008; Dixon et al., 2009; Moon et al., 2011; Owen
et al., 2011; Champagnacet al., 2012; Ferrieret al., 2013b], many questions still remain
about how climate influences landscape evolution. In particular, questions remain about
how hillslope form, erosion rates, and sediment transport efficiency vary under different
climate conditions. Some geomorphologists have successfully quantified relationships
between precipitation and erosion rates at specific sites [Moon et al., 2011; Ferrieret al.,
2013a], but a general relationship between these factors and climate does not exist
[Portengaand Bierman, 2011]. The difficulty in quantifying the relationship between
climate and erosion is likely due in part to differences in rock type, tectonic processes,
vegetation, and the degree of chemical versus physical weathering at different sites. One
way to make progress on this question is by studying natural experiments in which
climate varies, but other factors remain constant.
An ideal natural experiment for studying the effects of small climatic variations has
been carried out in many landscapes. Variations in insolation, the amount of sunlight that
strikes a surface, can generate microclimates - small variations in temperature, soil
7
moisture, humidity, wind and other measurable climate factors - on slopes that face
different directions [e.g., Branson and Shown, 1990; Yetemen et al., 2010; Anderson et
al., 2012]. These differences in microclimate can lead to the development of topographic
asymmetry, and several mechanisms - including aspect-induced variations in soil creep
intensity, regolith strength, and runoff, and also lateral channel migration - have been
proposed to explain the asymmetry [e.g., Melton, 1960; Kane, 1970; Dohrenwend, 1978;
Yetemen et al., 2010; West et al., 2013; McGuire et al., 2014]. Topographic asymmetry is
the phenomenon that slopes with different aspect exhibit different topographic
characteristics, such as the occurrence of north-facing slopes that are steeper than southfacing slopes. The specific mechanisms that control topographic asymmetry are not well
understood, but two leading hypotheses have emerged to explain the occurrence of
topographic asymmetry in semi-arid landscapes when lithological or structural
explanations cannot be invoked [Kane, 1970; Dohrenwend, 1978]. One hypothesis relies
on aspect-dependent differences in erosion such as differences in regolith strength, soil
creep rates, or runoff. According to the other hypothesis, aspect-dependent differences
are not enough, and the occurrence of lateral channel migration, possibly driven by
differences in sediment flux rates on opposing slopes due to the microclimates, leads to
oversteepening of the undercut slope. However, the long-term topographic consequences
of the different mechanisms have not been fully explored, and identifying which
mechanism or mechanisms are responsible for the topographic asymmetry in a given
landscape remains a challenge.
In Chapter 2, I present a set of landscape evolution modeling experiments that test
how landscapes respond to microclimatic differences and other possible
8
asymmetry-forming mechanisms. I explore the relationship between different
topographic characteristics that develop asymmetry and erosion rate patterns to determine
if unique signatures exist that may help pinpoint which asymmetry-forming mechanisms
are occurring in real landscapes. In Chapter 3, I use these predictions to help determine
which asymmetry-forming mechanisms are most responsible for the topographic
asymmetry at Gabilan Mesa, a landscape in the central California Coast Ranges that
exhibits very high topographic asymmetry. At Gabilan Mesa, significant differences in
hillslope morphology are well-documented and correlate with modern differences in
aspect-controlled microclimates and vegetation. I use a combination of techniques
including terrain analysis, measurements of field-saturated hydraulic conductivity and
soil shear strength, numerical modeling, and erosion rate measurements to test which
asymmetry-forming mechanisms are responsible for the topographic asymmetry at
Gabilan Mesa.
Another outstanding question about climate and landscape evolution is how
hillslope sediment transport efficiency varies with climate conditions. Fernandes and
Dietrich [1997] suggested that the long response time of hillslopes to perturbations in
topography or soil transport makes it unlikely that hillslopes were capable of reaching an
equilibrium shape during the Quaternary, and that hillslopes may have constantly
modified their form as climate fluctuated between glacial and interglacial periods.
Numerous studies point toward climate and vegetation influencing sediment transport
[e.g., Fernandesand Dietrich, 1997; Roering, 2004; Hughes et al., 2009; Hurst et al.,
2013a; McGuire et al., 2014; West et al., 2014]. However, how climate influences
sediment transport efficiency is not well understood, but is fundamental in influencing
9
global sediment flux rates. Hillslope sediment flux rates, which are dominantly controlled
by hillslope gradient and disturbance mechanisms that influence the sediment transport
efficiency [McKean et al., 1993; Roering et al., 2002], are not easily predicted without
specific measurements for a particular landscape. This information generally requires
field measurements [e.g., Almond et al., 2008; Jungers et al., 2009], estimates of erosion
rates [Perronet al., 2012; Hurst et al., 2013a], or knowledge of the age and initial
topography of hillslopes [e.g., Colman and Watson, 1983; McGuire et al., 2014]. In
Chapter 4, I compile previously published estimates of hillslope soil transport efficiency,
add a new set of estimates using laser altimetry and erosion rates estimated from
cosmogenic nuclides, and analyze the combined dataset to determine how hillslope soil
transport efficiency varies with climate and other factors.
10
Chapter 2. Modeling the formation of topographic
asymmetry by lateral channel migration and aspectdependent erosional processes
11
Abstract
Some landscapes exhibit the intriguing characteristic that slopes facing a certain direction
are systematically steeper than slopes facing other directions, even where there is no bias
introduced by bedrock structure. This topographic asymmetry, which is particularly
common in semi-arid regions, has inspired a variety of explanations, but most rely in
some way on the presence of different microclimates on opposing slopes. In the simplest
scenario, the microclimatic differences lead to differences in erosion rates on opposing
slopes and topographic asymmetry develops. In contrast, some geomorphologists have
argued that lateral channel migration and the corresponding steepening of undercut slopes
are the dominant cause of topographic asymmetry in some landscapes, but this hypothesis
has received less attention. To examine these two proposed origins of asymmetric
topography, I adapted a numerical landscape evolution model to include lateral channel
migration as well as aspect-induced variations in soil creep intensity, regolith strength,
and runoff. I compared the characteristics of asymmetric ridges and valleys along with
the spatial and temporal patterns of erosion rates produced by each mechanism and found
that the model with lateral channel migration produces a unique ridgetop Laplacian and
erosion rate signature relative to the other models. This result provides a way to test if
lateral channel migration is the dominant cause of topographic asymmetry in a given
landscape. To further investigate the dynamics of lateral channel migration, I developed a
simple model of hillslope profile evolution in which sediment fluxes from opposing
slopes control lateral channel migration rate and direction by deflecting the channel. I
find that topographic asymmetry in this system can be self-sustaining and that the degree
of asymmetry depends on two non-dimensional numbers that express the relative
magnitudes of river incision and soil creep and the relative rates of lateral base level
migration and river channel response.
12
2.1. Introduction
2.1.1. Motivation
An outstanding problem in the study of Earth's surface is determining how climate
influences erosion rates and the long-term evolution of landscapes. Currently, there is no
clear consensus on the relationship between erosion rates and climate variables such as
precipitation and temperature [von Blanckenburg, 2006], although some
geomorphologists have successfully quantified relationships between precipitation and
erosion rates at specific sites [Moon et al., 2011; Ferrieret al., 2013a; 2013b]. The
difficulty in quantifying the relationship between climate and erosion is likely due in part
to differences in rock type, tectonic processes, vegetation, and the degree of chemical
versus physical weathering at different sites. One way to make progress on this question
is by studying natural experiments in which climate varies, but other factors remain
constant.
An ideal natural experiment for studying the effects of small climatic variations has
been carried out in many landscapes. Variations in insolation, the amount of sunlight that
strikes a surface, can generate microclimates - small variations in temperature, soil
moisture, humidity, wind and other measurable climate factors - on slopes that face
different directions [e.g., Branson and Shown, 1990; Yetemen et al., 2010; Anderson et
al., 2012]. These differences in the microclimates may lead to the development of
topographic asymmetry, which is the phenomenon that slopes of different aspect exhibit
different topographic characteristics (Figure 2.1). Several mechanisms, including lateral
channel migration and aspect-induced variations in soil creep intensity, regolith strength,
and runoff, have been proposed to explain the asymmetry [e.g., Melton, 1960; Kane,
13
1970; Dohrenwend, 1978; Yetemen et al., 2010; West et al., 2013; McGuire et al., 2014].
However, the long-term topographic consequences of the different mechanisms have not
been fully explored, and identifying which mechanism or mechanisms are responsible for
the topographic asymmetry remains a challenge at many sites.
W4
Figure 2.1. Aerial photograph of Gabilan Mesa, CA. The landscape exhibits a high
degree of topographic asymmetry, and there are large differences in microclimates and
vegetation on slopes with opposing aspects. Oak trees are primarily present on northfacing slopes and rarely grow on south-facing slopes.
2.1.2. Hypothesized origins of asymmetric topography
The systematic occurrence of steeper pole-facing slopes and gentler equator-facing
slopes is documented in a variety of landscapes around the world [Bass, 1929; French,
1971; Dohrenwend, 1978; Churchill, 1982; Cerda et al., 1995; Wende, 1995; Siegmund
and Kevin, 2000; Burnett et al., 2008; Poulos et al., 2012]. The opposite scenariosteeper equator-facing slopes and gentler pole-facing slopes-has also been observed to
14
occur, but has been reported less often [Gilbert, 1884; Davis, 1895; Fuller, 1914; Glock,
1932; Churchill, 1982; Burnett et al., 2008; Poulos et al., 2012].
Numerous explanations have been proposed for the systematic presence of
asymmetric hillslopes, and the debate over their origin dates back almost to the beginning
of the formal study of Earth surface processes. Many early observers attributed
asymmetric hillslopes to the Coriolis effect summarized in Baer's Law, which they
believed caused preferential erosion of the right stream bank in the northern hemisphere
[Gilbert, 1884; Davis, 1895; Fuller, 1914; Einstein, 1926; Glock, 1932]. Later workers
found that the steepest valley slopes were not always along the right stream bank, and
instead found that the steepest slopes were more often the pole-facing slopes [Reed, 1927;
Bass, 1929; Fairchild,1932; Emery, 1947]. Asymmetry has also been attributed to
differences in eolian deposition and erosion or evapotranspiration driven by regional
prevailing winds [Reed, 1927; Bass, 1929; Fairchild, 1932; Emery, 1947], but wind is
unlikely to be the main cause of asymmetry because the direction of the prevailing winds
does not always match the direction of asymmetry [Powell, 1874; Emery, 1947;
Dohrenwend, 1978].
In some regions, topographic asymmetry can be attributed to regional stratigraphic
dips or other aspects of bedrock structure or lithology [Powell, 1874; Bass, 1929; Emery,
1947; Melton, 1960; Dohrenwend, 1978], but in areas without such effects, other
explanations are necessary. In the absence of tectonic and bedrock structural controls,
topographic asymmetry has been attributed to microclimates [Hack and Goodlett, 1960;
Dohrenwend, 1978; Istanbulluoglu et al., 2008; Yetemen et al., 2010; Anderson et al.,
2012; Poulos et al., 2012].
15
/
The observed correlation between topographic asymmetry and slope aspect-polefacing slopes, which receive less sunlight, are generally steeper-implies that insolation
influences the physical and chemical processes that shape landscapes [Poulos et al.,
2012]. Recently, geomorphologists have focused on the role of aspect-dependent
differences in hillslope
b)
Aspect-dependent
erosional efficiency
a)
Lateral channel
migration
Ridgeline migrates
towards the equator
Pole
Ridgeline migrates
towards the pole
4-
-
q,
I
/
I
/
I
I
%
/
/
/
/
/
..
/
~
I
%
/
IN.
/
/
/
*~
I,
/j
/
-.
/
/
I
/
/ /
/
/
I
.,
I
-
qN
~I%*~
/
/
-
--
I
I
/
I
I
N.
N.
/
/
I
/
Baselevel migrates
towards the equator
/
Figure 2.2. Diagrams showing evolution of asymmetry for two hypothesized asymmetryforming mechanisms. The aspect-dependent erosional efficiency scenario is diagramed in
(a) and the lateral channel migration scenario is diagramed in (b). The diagrams show the
time evolution of a simplified hillslope profile for hillslopes that develop steeper polefacing slopes. The solid brown lines show the initial and final hillslope profiles, and the
dashed red lines show intermediate profiles. In (b), the lengths of the red arrows represent
the relative magnitudes of sediment flux from opposing slopes (q,) and the brown blocks
represent the relative magnitudes of sediment transported to the main channel.
16
processes that may lead to differences in the efficiency of erosion processes between
pole-facing and equator-facing slopes (Figure 2.2). If soil transport or channel incision is
more efficient on one side of the divide, the divide will be displaced toward the less
efficient side until the difference in slopes compensates for the difference in efficiency.
Possible mechanisms causing such a difference in erosional efficiency include (1)
reduced runoff, and therefore slower channel incision, on more vegetated slopes [Hack
and Goodlett, 1960; Kane, 1970; Wende, 1995; Istanbulluogluet al., 2008; Yetemen et
al., 2010] due to either more rapid infiltration [Emery, 1947; Hack and Goodlett, 1960;
Kane, 1970] or increased evapotranspiration; (2) higher regolith strength, and therefore
slower channel incision, on more vegetated slopes [Emery, 1947; Ollier and Thomasson,
1957; Yetemen et al., 2015] [Emery, 1947; Ollier and Thomasson, 1957]; or (3)
asymmetry in soil creep rates due to differences in bioturbation rates [Perronand
Hamon, 2012; West et al., 2013; McGuire et al., 2014], frost-generated crack growth
[Anderson et al., 2012], or solifluction [Ollier and Thomasson, 1957].
Another hypothesis is that asymmetric aggradation of sediments in a valley bottom
forces a river flowing through the valley to migrate away from the side of the valley that
experiences faster aggradation, leading to undercutting of the opposite bank and
steepening of the adjacent hillslope [Bass, 1929; Melton, 1960; Dohrenwend, 1978]
(Figure 2.2). In the northern hemisphere, once the initial undercutting of the north-facing
slope occurs, the increased length of the south-facing slope should increase the sediment
flux to the north bank of the channel. This may lead to a positive feedback where lateral
channel migration is maintained by the difference in sediment flux and aggradation due
to the different slope lengths [Wende, 1995]. However, if undercutting persists and the
17
whole ridgeline migrates, erosion rates must remain asymmetric. One possible reason
why an initial difference in aggradation may occur is because of the presence of different
microclimates. For a site in the central California Coast Ranges, Dohrenwend [1978]
suggested that microclimatic differences initially led to a slightly higher erosion rate on
south-facing slopes. He suggested that this difference in erosion rates caused higher
aggradation on the north bank of channels and southward lateral channel migration, but
that the higher erosion rate alone on the south-facing slope was not enough for the
development of the topographic asymmetry. Dohrenwend [1978] posited that
microclimate-driven lateral channel migration is the dominant mechanism responsible for
the high degree of topographic asymmetry witnessed at his study site in the central
California Coast Ranges. Furthermore, he concluded that microclimate-driven lateral
channel migration is a general process that leads to the development of topographic
asymmetry in other semi-arid environments. After investigating asymmetric topography
in the Laramie Range, WY, Melton [1960] suggested that most cases of microclimateinduced asymmetry are attributable to lateral channel migration. Wende [1995]
concluded that the asymmetric valleys of the Tertiary Hills of Lower Bavaria, Germany
were not necessarily formed by microclimates as had been previously suggested for that
region. Instead, Wende suggested that the asymmetry might be due to other factors such
as non-microclimate-driven lateral channel migration or the initial development of the
drainage network.
McGuire and coworkers [2014] explored the topographic consequences of different
asymmetry-forming mechanisms on cinder cones in the western United States, which
generally have gentler south-facing slopes. They found that the asymmetry was likely due
18
to more efficient colluvial transport on the south-facing slopes. Cinder cones offer a
unique opportunity to examine the role of aspect-dependent erosional processes where
base level effects such as lateral channel migration can easily be ignored. However, base
level effects cannot easily be ruled out in many landscapes. Other geomorphologists have
also incorporated aspect-dependent erosional processes into landscape evolution models
for sites where base level effects are more challenging to rule out [Anderson et al., 2012;
Yetemen et al., 2015]. In these cases, they were not able to include the potential effects of
lateral channel migration. Microclimates clearly influence erosional processes in some
landscapes, but the degree to which lateral channel migration influences the development
of topographic asymmetry is not well understood.
2.1.2. Implications for landscape evolution
If differences in sediment transport efficiency on opposing slopes are enough to
explain the development of topographic asymmetry, then relatively small differences in
climate-differences that currently exist on opposing slopes in some regions-can lead to
significant differences in hillslope evolution and form. This is especially true for
landscapes where the climatic conditions are at a tipping point and a small change in
climate can substantially impact the type of vegetation that is capable of growing.
Landscapes may undergo considerable drainage network reorganization if lateral
channel migration occurs. Valleys and hillslopes are expected to migrate across the
landscape if lateral channel migration is occurring, since opposing slopes experience
different erosion rates. Where migration rates vary, drainage capture may occur instead of
continuous migration of neighboring valleys. Dohrenwend [1978] identified multiple
19
sites of drainage capture in the central California Coat Ranges and suggested that they
were due to continuous microclimate-driven lateral channel migration. Whether or not
lateral channel migration can occur is likely dependent on additional factors in addition to
the presence of microclimates. If lateral channel migration is the dominant mechanism
controlling topographic asymmetry then hillslope erosional processes may be less
sensitive to microclimates, and therefore changes in climate.
Different asymmetric landscapes may be influenced by different asymmetryforming mechanisms. If so, some asymmetric landscapes may be undergoing drainage
reorganization associated with topographic asymmetry whereas others are not.
Understanding whether or not differences in erosional efficiency or sediment transport
efficiency are significant enough to explain observed topographic asymmetry or if lateral
channel migration is required to explain asymmetry at specific sites is critical for
understanding how sensitive erosional processes are to changes in climate.
2.1.3. Purpose and outline
The purpose of this study is to explore the topographic characteristics of
asymmetric landscapes formed by different mechanisms to determine if topographic
signatures can be used to distinguish the mechanisms from one another. In section 2.2, I
modify a landscape evolution model to incorporate a range of possible asymmetryforming mechanisms, including lateral channel migration, aspect-dependent soil creep,
aspect-dependent regolith strength and aspect-dependent runoff. In section 2.3, I carry out
a series of model experiments in which I use numerical models to create hillslopes with
varying degrees of asymmetry. In section 2.4, I investigate the results of a one-
20
dimensional hillslope model with lateral channel migration in which the topographic
asymmetry is driven by differences in sediment flux on opposing slopes instead of having
a fixed lateral channel migration rate. In section 2.5, I discuss the results and implications
of the numerical modeling experiments. Based on the results from the experiments, I
propose two tests to determine if lateral channel migration is responsible for the
formation of asymmetric topography and explain how these tests could be applied to
high-resolution topographic data and erosion rate estimates determined from cosmogenic
radionuclides (CRNs).
2.2. Model
2.2.1. Model description
I adapt a numerical landscape evolution model (LEM) to incorporate hypothesized
mechanisms for generating topographic asymmetry. I do not attempt to explicitly include
hydrology, vegetation, or energetics into the model or parameterize the model for a
specific landscape.
I modify a commonly used landscape evolution governing equation,
DV 2 z+ E
az
at
A' Vz s
2
DV z - K(A' Vz -9)+ E
A"n Vz" >6,
(2.1)
where z is elevation, D is soil transport efficiency, K is the fluvial incision coefficient and
depends on bedrock lithology, precipitation, and channel morphology in addition to other
21
factors [Perronet al., 2008], A is the cumulative drainage area, 0, is the fluvial incision
threshold, and E is the uplift rate or boundary lowering rate [Howard, 1994; Perron et
al., 2008]. DV2 z describes soil creep for the scenario in which soil flux is linearly
for the to the hillslope gradient. K(A" Vz
proportional
-Q,) describes channel incision
-
scenario in which the channel incision rate is proportional to stream power [Seidl et al.,
1994] or shear stress [Howard and Kerby, 1983]. Stream discharge is approximated by A
and they are related by a power law [Knighton, 1998].
I use the Peclet number (Pe) to describe the magnitude of fluvial incision relative to
soil creep,
K
Pe= -
where
t("+I-"
0 t, 2
- 6LC)(2.2)
is relief and [ is slope length. Pe has been used to capture the competition
between soil creep and channel incision in small catchments in soil-mantled landscapes
[Perronet al., 2009; 2012]. For a particular landscape, many of the parameters in
equation (2.1) are often considered constant [Howard, 1994; Tucker and Bras, 1998;
Roering et al., 1999; Perronet al., 2009; 2012] while f and ( depend on the scale of the
hillslope feature being analyzed. K, D, 0, m, and n can vary significantly among
landscapes with different rock types, tectonic settings or climates [Perronet al., 2012].
Pe ~ 100 is representative of a hillslope with small 1 "-order valleys [Perronet al., 2012].
Pe ~ 250 is representative of the transition from Ist-order to 2"d-order valleys and
hillslopes with Pe ~ 1000 usually have well developed 2"d-order valleys.
22
I adapted the Tadpole model developed by Perron and coworkers [2008, 2009,
2012] to include aspect-dependent erosional mechanisms and lateral channel migration.
Tadpole is a numerical finite-difference LEM capable of modeling landscapes dominated
by fluvial incision and soil creep. Tadpole solves equation (2.1) on a rectangular grid of
N, x Ny points with grid spacing of Ax in the x-direction and Ay in the y-direction. I set
Ax = Ay for all of the experiments. For all of the experiments, the grid represents a ridge
bounded by two straight channels that correspond to the y-boundaries, such that NxAx
represents the slope width along the bounding channels and NAy12 is the length of the
slope on either side of the divide. The y-boundary conditions are periodic while the xboundary conditions are fixed for all of the model runs.
Perron and coworkers [2009, 2012] set 0, = 0 m for most of their model
experiments because they were interested in how the competition between soil creep and
channel incision controls landscape form, although Perron and coworkers [2009] did
explore some of the effects on valley spacing when 0, > 0 m. I explore the topographic
consequences for both O = 0 m and for 0, > 0 m.
2.2.2 Models with aspect-dependent processes
I incorporate aspect dependence into the LEM by incorporating a weighting
function into the governing equation that modifies the efficiencies of processes, including
soil creep, regolith strength, and runoff, according to the degree to which the slope is
facing the sun.
23
2.2.2.1 Weighting function for aspect-dependent processes
To incorporate the effects of insolation into a landscape evolution model,
parameters in the model associated with insolation-dependent processes were weighted
according to
#-
the vertical angle between the surface normal and the sun. The sun
altitude angle can be parameterized for a specific latitude. cos(#) is a good proxy for the
direct solar radiation that reaches a hillslope (Figure 2.3). I parameterized the model with
a sun altitude angle of 700, which minimizes the variance between cos(#) and annually
averaged solar radiation for a landscape at a latitude of 36'. This is the latitude of the
landscape in Figure 1, where both lateral channel migration and erosional efficiencies
have been suggested as asymmetry-forming mechanisms [Kane, 1970; Dohrenwend,
1978].
I developed a simple weighting function that is suitable for modifying the
magnitudes of individual terms in equation (2.1). The form of the weighting function is
16 cos(#b)
osG
c+
)
1
CO
cos(#)
cos(#,,dg,)
(2.3)
=
1-1
cos()
cos(#-dge
where
/ridge
N
cos() <cos(#,,d,,)
d
is the slope-normal vector of the ridgeline (always 90' from horizontal) and 6
is the magnitude of the weighting function (Figure 2.4). If 6 > 0, w is higher on the polefacing slope. If 6 < 0, o is higher on the equator-facing slope. Increasing the magnitude
of 6 causes larger differences in co on opposing slopes.
24
350
I
I
I
I
I
I
300-
A
250
200300
150 -2
-
'Z
P250
200
C 100
150
50-
0500 m
0
0
0.1
0.2
0.3
0.5
cos(#)
0.4
0.6
0.7
N
100
0.8
0.9
1
Figure 2.3. Mean annual solar radiation for daylight hours against cos(O) for the portion
of Gabilan Mesa, CA, shown in the inset. For clarity, only 10% of data (selected
randomly) are plotted. Inset is a shaded relief map overlaid with a color map of mean
solar radiation (W m 2 ) for daylight hours.
I chose the form of the weighting function so that w = 1 at the ridgeline. I chose a
weighting function that is similar to that of Petroff and coworkers [2012], but I modified
its form so that w is always greater than zero. Petroff and coworkers explored a limited
range of weighting magnitudes, so they did not encounter o < 0. If w is not normalized
relative to the ridgeline, then as 5 increases, the coefficient describing the aspectdependent mechanism increases or decreases on both slopes, but at different rates. I
formulated equation (2.3) so that as 5 increases, a increases on one slope while
decreasing on the other slope instead of increasing or decreasing on both slopes at
25
different rates. Defining the weighting function in this manner also avoids dramatic
variations in average erosion rate as 6 varies.
a)
|
b)
Pole
1.5
10
10
0
0.2
0.6
0.4
0.8
0.5
1
cos((,))
Figure 2.4. (a) Example of the weighting function, w, for aspect-dependent process rate
coefficients. cos(#)= 1 occurs when the slope-normal vector points directly at the sun.
Red line shows o for 6 = 10 and the blue line shows o for 6 = -10. The dashed line is at
o always equals 1. (b) Perspective view of a landscape produced with the
LEM showing value of w for 6 = 10. Horizontal tick interval is 100 m; vertical tick
interval is 50 m.
0ridge where
For sites near the equator, differences in solar radiation are minimal on pole-facing
and equator-facing slopes. At very high latitudes, sun angles are low and differences in
solar radiation on opposing slopes are large. However, this does not imply that high
latitudes exhibit the largest sensitivity in microclimates. Often semi-arid environments
found at mid-latitudes exhibit the most striking aspect-dependent differences in
vegetation. This is because semi-arid landscapes are often near a tipping point where
pole-facing slopes have adequate soil moisture that is available for vegetation while
equator-facing slopes have limited soil moisture available to vegetation [Branson and
Shown, 1990; Kutiel, 1992; Istanbulluoglu et al., 2008].
26
2.2.2.2 Aspect-dependent infiltration and runoff
Infiltration and runoff are not calculated directly in the model. Instead, I weighted
A, which effectively changes the predicted stream discharge at each point in the
landscape. For idealized scenarios, such as during a storm when evapotranspiration is
insignificant, runoff is simply the difference between precipitation and infiltration.
Normally, discharge is determined by calculating the upslope contributing area and
assuming that all parts of that area contribute an equal flux of water. For the aspectdependent runoff LEM, instead of each upslope cell having a value of 1, the cell is
weighted according to co and the weighted grid cells are then summed in the typical
manner. I introduced aspect-dependence to the relationship between volume discharge
(Q,) and A so that
Q,
= okA" and both k and a are determined empirically [Leopold and
Maddock, 1953; Knighton, 1998]. If volume discharge is conserved and precipitation is
spatially uniform, which is a reasonable assumption at the hillslope scale, a =1 and the
governing equation can be written as
az
DV 2 z+E
(wA)" Vz
at
DV 2 z - K((wA)" Vz
-6) + E (wA)" Vz
s
(2.4)
In order to introduce aspect dependence to the fluvial incision term, McGuire and
coworkers [2014] weighted K. However, weighting A instead of K allows the non-local
effects of aspect-dependent infiltration, or runoff in this case, to be integrated across the
drainage basin.
27
2.2.2.3 Aspect-dependent regolith strength
In semi-arid landscapes, incision occurs in ephemeral channels during large storm
events that are capable of removing transportable material and vegetation from the
channel [Tucker et al., 2006]. In between storm events, I assume bedrock material in the
channels is converted to regolith. In this case, regolith refers to weathered material above
the bedrock, including soil, and exists on both the hillslopes and in the channel. Regolith
strength is partially reflected in the value of Oc [ProsserandDietrich, 1995], but may also
influence D and K. I assume that Oc is comparable on both the hillslope and in the
channel. Differences in vegetation type and density due to different microclimates on
opposing slopes may cause regolith strength to vary with aspect [Yetemen et al., 2015].
For the aspect-dependent regolith strength experiments, I focus on modifying Oe in
equation (2.1). Oc is weighted by w and the governing equation is
az
at
DV 2 z+ E
A"' Vz
w6
-=
2
>
Vz
A"'
E
DV z - K(A' Vz -wO)+
(2.5)
(2
2.2.2.4 Aspect-dependent soil creep
To model the effect of aspect-dependent soil creep, I modified the LEM to include
aspect-dependent D. When D varies in space and time according to w, D becomes D(O),
and the diffusion term in the governing equation becomes V - D(w) Vz
.
I investigate the
simplest case: D(w) = coD. The form of the modified governing equation is
28
az
at
V -wDVz+ E
A" Vz
-=
V -o)DVz
-K(A"' 1Vz1 -0
C)+E
sO
Vz(2.6)
A"' jVzj
> OC
Since o changes relatively slowly as the landscape evolves, D(w) can be incorporated
into the existing numerical scheme and solved with the Crank-Nicolson method in a
similar fashion as if D were constant.
2.2.3 Lateral channel migration
Like most previously published LEMs, my model does not explicitly include
channels [Howard, 1994; Tucker and Bras, 2000; Moon et al., 2015; Yetemen et al.,
2015]. This is in part due to the difficulty of coupling channel bank evolution with
hillslope processes, the lack of adequate process laws for the evolution of channel crosssections, and the difficulty of representing relatively narrow channels in grids that span
entire landscapes. These issues make it similarly challenging to incorporate lateral
channel migration into a LEM. Instead of attempting to model the migration of discrete
channels across a landscape, I consider the y boundaries of the model grid to represent
straight channels with a fixed spacing equal to NyAy bounding a single hillslope (e.g.,
Figure 2.4) and perform the simulation in the reference frame of these migrating
, to the governing equation so
channels. I introduce a lateral channel migration term, y
ay
that
29
V-DVz+E-y
A"' Vz " s
ay
where y (L T-') is the lateral channel migration rate. The lateral channel migration term is
an advection term that shifts the model topography in the positive y-direction, which
mimics the effect of channels undercutting slopes that face in the positive y-direction and
migrating away from slopes that face in the negative y-direction. The addition of this
term leads to competition between the lateral channel migration term, which tends to
make these opposing slopes more asymmetric, and the fluvial incision term, which tends
to even out the opposing slopes. I describe this competition with a dimensionless value
that I refer to as the Migration number,
M = Y(2.8)
C
where C= KA" Vz
fl-I
, the
wave celerity of the fluvial incision term [Whipple and
Tucker, 1999].
2.2.4 Model experiments
I investigate the degree of topographic asymmetry that develops for the different
LEMs by executing a series of model runs with different parameters. For the aspectdependent efficiency runs, I vary Pe and the weighting parameter 6. For the LEM with
lateral channel migration, I vary Pe and the lateral channel migration rate y. By varying
the asymmetry-forming mechanism and Pe, I am able to explore the degree of
30
topographic asymmetry that develops for different regions of parameter space, as well as
the other topographic and erosional characteristics of the asymmetric landscapes
produced by each mechanism.
2.2.4.1. Aspect-dependent efficiency runs
In order to explore how topographic asymmetry develops due to differences in
aspect-dependent efficiency mechanisms, I run a series of models in which I vary 6 and
Pe for the aspect-dependent runoff LEM, aspect-dependent regolith strength LEM, and
the aspect-dependent soil creep LEM. I produce hillslopes with different Pe by varying t
(by changing N,) in equation (2.2) and estimate the required Pe using equation (2.3). As
asymmetry develops, different values of Pe develop on opposing slopes due to
differences in f and co. Since ( is not known a priori, I estimate the parameter value for
0, = 0 m to produce the required Pe. If O is low and ( is reasonable, the difference in the
actual Pe is small. I calculate the actual Pe a posteriori,once ( is known, for all of the
model analyses.
I run each model for 10 Myr, with a time step that guaranteed kinematic waves
travel no more than Ax or Ay during one time step using the parameters listed in Table
1.1. I solve the advection term using an explicit, forward-time, upwind differencing
technique and use the Crank-Nicolson method, which is unconditionally stable, to solve
the diffusion term. The stability condition is modified for each aspect-dependent
efficiency model to guarantee that no part of the landscape is unstable. All of the modeled
hillslopes are oriented so that the side of the ridge that faces in the negative y direction
abuts the equator-facing slope and the upper boundary abuts the pole-facing slope.
31
Table 2.1. Tadpole Model Parameters (unless otherwise noted)
Parameter (units)
Value
K(m- 2 m yr-1)
ix10-4
D (m2 yr-)
0.02
n
0.5
1
Oe (m 2 m
E (m yr-')
1 e-4
Ax, Ay (in)
5
N, Ny
200, 100
Sun angle
700
Pe
100-1000
6*
-500-500
50-1500
7** (m Myr~')
*aspect-dependent efficiency models
**lateral channel migration models
2.2.4.2. Lateral channel migration runs
To explore how topographic asymmetry develops due to lateral channel migration, I
run a series of models where I vary y and Pe. Similar to the aspect-dependent efficiency
models, I produce models with different Pe by varying f (by changing Ny) in equation
(2.2). For this set of model experiments, y is fixed for each model run. I calculate M by
using y from the respective run and estimate C using the half-width of the hillslope and
Hack's law, which relates slope length to drainage area by A = kat h where ka and h are
empirically derived, to estimate a representative A. For Hack's law, I use h and ka from
Table 2.2. In my experiments, n =1, so C is independent of Vz
.
I ran each model for 10
Myr, which guaranteed that the model reached a steady form, and with a time step that
32
guaranteed stability for the advection term and did not exceed 1000 yr. The model
parameters are summarized in Table 2.1.
2.2.4.3 Definition and measurements of asymmetry
Geomorphologists have described topographic asymmetry in many different ways.
When multiple hillslopes or valleys exhibit topographic asymmetry in a landscape,
multiple terms have been used, including valley asymmetry [Bass, 1929; Emery, 1947;
Dohrenwend, 1978], hillslope asymmetry [Poulos et al., 2012], slope asymmetry
[Kreslavsky and Head, 2003] and topographic asymmetry [McGuire et al., 2014] to
describe the same characteristics. A review of the literature reveals that valley asymmetry
is the most popular term, likely because most geomorphologists historically witnessed
asymmetry in-person from the bottom of valleys instead of along ridgelines. The
weakness of these terms is that they do not describe a specific characteristic that exhibits
asymmetry and are defined differently by each author. I choose to refer to the asymmetry
as topographic asymmetry as it is sufficiently vague as to not point to a single
characteristic or mechanism while also being descriptive enough to characterize the
phenomenon. I define topographic asymmetry to include all topographic characteristics
that exhibit aspect-dependent asymmetry. To describe the asymmetry of a single
characteristic, I define specific metrics.
Emery [1947] developed a simple method for reporting the magnitude of
topographic asymmetry for opposing slopes. He calculated a single value, referred to as
an asymmetry index, which is the ratio of the north-facing hillslope gradient to the southfacing hillslope gradient. Poulos and coworkers [2012] defined a slightly modified
33
asymmetry index (IN-s) as the logarithm of the ratio of the mean gradient of north-facing
pixels to the mean gradient of south-facing pixels within a window. This measure is well
suited to measuring the topographic asymmetry of large regions, but often does not
reflect the significant differences in slope length that occur across a valley. This is
because the longer slope can be more deeply incised and therefore comparably steep to
the opposing slope on average, even though significant differences in slope lengths exist.
I define an asymmetry metric, the bulk slope asymmetry (BSA), that is similar to
the slope gradient asymmetry metric used by Emery [1947]:
BSA&
1
0lo 2
(2.9)
Pt/
SO
where S is the hillslope relief divided by the horizontal slope length, pf refers to polefacing slopes and efrefers to equator-facing slopes. I chose to quantify bulk slope
asymmetry in this manner because the measurement effectively compares opposing slope
lengths normalized by the relief of the hillslope and therefore reflects the visual
impression of asymmetry witnessed by an observer of a landscape.
I also define an additional metric of asymmetry, the erosion rate asymmetry
(ERA), that is used to compare the difference in erosion rate on opposing slopes:
ERAN_, = log 2
34
E
r
Eef
(2.10)
where E is the erosion rate. If soil creep dominates the morphology near the ridgeline,
V 2 zR , the ridgetop Laplacian, is related to the ridgeline erosion rate by D [Perronet al.,
2009], the soil transport coefficient, so that
(2.11)
E = -DV 2 z
I developed an additional asymmetry metric that can serve as a proxy for ERApfef and
may be useful if estimates of erosion rates on opposing asymmetric slopes are not
available, but suitable topographic data does exist. I define ridgetop Laplacian asymmetry
(RLA) as
RLA_%
=
log2
V z
(2.12)
V_1 RC2
where V2 zR is the ridgetop Laplacian. If a landscape is eroding at steady state, V 2 zR is
expected to be constant where soil creep dominates and channel incision does not occur.
However, if the erosion rate is not constant across the hillslope, differences in
exist. To estimate
V2Z
V 2ZR
may
, I plot V2z against A"' Vz " where A is drainage area and m and
n are semi-empirical exponents that can be parameterized for a particular landscape
[Perronet al., 2012]. I bin V 2 z into 10 bins spaced logarithmically in A' Vz n, calculate
the median in each bin, and assign
V2 ZR
as the most negative of these median values. In
35
this case, V 2 zR is a proxy measurement of the fastest erosion rate on the soil creepdominated portion of the hillslope.
2.3.2 Model Results
2.3.2.1 Aspect-dependent efficiency results
In this section, I present the results for each of the aspect-dependent efficiency
model runs with 0, = 1 m and show how topographic asymmetry varies for different
values of 5 and Pe. For most of the model results, I present results in terms of o instead
of 6. For all of the aspect-dependent efficiency models, I compare the topographic
asymmetry that develops against the ratio of the mean o on equator-facing slopes, Wef,
with the mean w on pole-facing slopes, opf. I do this because 0 is a function of 6 and the
hillslope morphology, particularly relief, and best accounts for the magnitude of the
asymmetric forcing.
For the aspect-dependent runoff LEM, pole-facing slopes become steeper and
equator-facing slopes become gentler when (o is higher on the equator-facing slope
relative to the pole-facing slope (Figure 2.5). This occurs because the magnitude of
channel incision increases on the equator-facing slope relative to the pole-facing slope.
The opposite occurs when a) is lower on the equator-facing slope relative to the polefacing slope (Figure 2.5).
36
Pole
a) 0.06
0.04
l>
BSAfCef
S
10
0
*
0
S
I
0
0
0
0
0
0
Sa
S
0
0
0
S
10-
S
S
0
0
Pol
I-
200
0
10
0
100
AO.5IzI (M)
10
I -1
b) 0.06[
0
S
~ 0.04
-3
0
p
0.02 F
3
10 2
600
400
800
1000
Pe
P
0.02
0
10 1
10 0
AO,5IzI
10
(M)
Figure 2.5. Model results for the aspect-dependent runoff LEM showing BSApfet in color.
I exclude results for 6 = 500 and 6 = -500 because they produce IBSApte I> 3. Profiles to the
right of the scale bar show schematic examples of hillslope profiles with BSApfr = 2.
Model results of the ridgetop Laplacian signature are shown in (a) and (b) for models
with BSApfeI z 2 and BSApfe/ z -2. In (a) and (b), lower values of A 045 Vz are near the ridge
while higher values are in the valley. Dark grey points are from the equator-facing slope and
light grey points are from the pole-facing slope. White circles are the binned medians.
The solid line is fit through the binned medians for the pole-facing data and the dashed
line is fit through the binned medians of the equator-facing data. Insets are perspective
views of the final model landscapes. Horizontal tick interval is 100 m; vertical tick
interval is 10 m.
For regions of the hillslope where A 0 5. VzI <~1 m, there are no measurable
differences in V 2 z on equator-facing and pole-facing slopes (Figure 2.5a and 2.5b). At
steady state, RLApfef and ERApej both approximate zero for the aspect-dependent runoff
model runs.
37
Pole
a) 0.06
:0
0 .04
BSApfef
104
102
Pole
S
0
0
S
S
0
S
0
100
0
0
0
0
0
0
0
S
ea
S
0
10
0.02
3
r
S
12
ob
eb
I
0
0
600
400
800
100
10- 1
AO 5IVzI
0
10
(M)
S
0
S
2 0I O
b) 0.06
-3
200
0
0
0
S
0
0
0.04
-
1000
Pe
Ii
0.02 [
0
10
100
10
A0
|IVz
(m)
Figure 2.6. Model results for the aspect-dependent fluvial incision threshold LEM
showing BSAp1eLin color. Profiles to the right of the scale bar show schematic examples of
hillslope profiles with BSApfe[ = 2. Model results of the ridgetop Laplacian signature are
shown in (a) and (b) for models with BSApfe,~ 2 and BSApfe 1 ~-2. In (a) and (b), dark grey
points are from the equator-facing slope and light grey points are from the pole-facing
slope. White circles are the binned medians. The solid line is fit through the binned
medians for the pole-facing data and the dashed line is fit through the binned medians of
the equator-facing data. Inset is of shaded relief map. Horizontal tick interval is 100 m;
vertical tick interval is 10 m.
Unlike the aspect-dependent runoff model, higher values of 0 on the equator-facing
slope lead to a decrease in slope length of the equator-facing slope for the aspectdependent regolith strength LEM (Figure 2.6). This occurs because an increase in 060
leads to less channel incision. Slopes that experience a decrease in ow6 due to the
05
weighting function have V 2z that are less negative at low values of A . Vz relative to the
slope where w6e increases due to the weighting function (Figure 2.6a and Figure 2.6b).
38
Even though some differences in the behavior of V2z exist on opposing slopes, no RLApfef
was discernable for any of the aspect-dependent regolith strength model runs using my
current V2 zR measuring technique because neither slope produced more locations with
negative V 2 z. In addition, ERApjefalso did not vary significantly from zero when steady
state was reached.
Unlike the aspect-dependent runoff and regolith LEMs, an increase in Pe for the
aspect-dependent soil creep LEM does not necessarily lead to a consistent style, or even
sign, of topographic asymmetry (Figure 2.7). For Pe ~ 250, BSApjej does not develop for
small differences in o (Figure 2.7a). This is likely due to the increase in erosion rate on
the interfluves balancing the increase in channel filling. As Pe increases, the importance
of channel incision as an erosional mechanism also increases. If soil creep efficiency on
one slope is increased by the weighting function then it can partially fill the channels and
limit the effectiveness of channel incision, causing the slope that experiences higher soil
creep efficiency to become shorter (Figure 2.7d and 2.7e). If soil creep efficiency
continues to increase to the point that the channels are entirely filled, then the slope that
experiences higher soil creep efficiency can become longer relative to the opposing slope
(Figure 2.7c and 2.7f). Because D is effectively changing on each slope for the aspectdependent soil creep model, V 2zR cannot serve as a proxy for the erosion rate like it does
for the other LEMs. This leads to asymmetry developing in V 2zR even though there is no
difference in the erosion rate on opposing slopes (Figure 2.7b). The aspect-dependent soil
creep LEM did not produce landscapes that appear realistic and often have large RLApjej
(>3). This is because for large BSApfef to develop, the longer slope must have
39
BSAPf f
a)
102
1.5
0
d
c)
0.5
100
-0.5
2
*
0
-1.5
-
10-
200
400
Pe
600
800
1000
d)
RLAf e
b)
102
I
0
00
10
0
e)
8
e)
20
*
10-
0
-5
200
A
600
400
800
1000
Pe
Figure 2.7. (a) Model results for the aspectdependent soil creep LEM showing BSApfef
in color. Examples of the model results are
shown in 1-4. (b) Model results for the
aspect-dependent soil creep LEM showing
RLAp-ef. Perspective views of model
topography for (c) 6 = 500 and BSAp-eJ
= 0.9, (d) 6 = 50 and BSApfef
= -0.4, (e) 5 = -25 and BSAp-ef= 0.3, and (f) 6
= -500 and BSApjef= -1.1. Horizontal tick
interval is 100 m; vertical tick interval is 10
m.
40
much high soil creep efficiency and no channel incision while the opposing slope was
heavily dissected (Figure 2.7c and 2.7f).
None of the aspect-dependent LEMs produced significant erosion rate asymmetry
when the model runs reached a steady form. However, while topographic asymmetry was
developing and the ridgeline was being actively offset, erosion rate asymmetry did exist.
This occurred because the lengthening slope erodes more slowly as it becomes longer and
shallower, and conversely, the shortening slope erodes more rapidly as it becomes shorter
and steeper. Eventually, equilibrium is reached, topographic asymmetry is maintained,
and the erosion rates on equator- and pole-facing slopes are equal.
For some of the highly asymmetric scenarios, I observed low-order valleys nested
in the main tributaries on the longer slope that continue to migrate even though the main
ridgeline has stopped migrating. The internal migration is driven by differences in w that
occur on equator- and pole-facing slopes in the nested valleys. These discrepancies in wo
that occur in small valleys are visible in Figure 2.4b. These variations in w do cause some
local variations in erosion rate, but do not significantly affect the mean erosion rate of the
whole equator- or pole-facing slope.
2.3.2.2 Lateral channel migration results
For the lateral channel migration LEM, significant differences in slope length
develop on the equator-facing and pole-facing slope and depend on M (the ratio of the
lateral channel migration rate to wave celerity of the fluvial incision term) and Pe. Model
runs with wider hillslopes, and therefore higher Pe, developed higher topographic
41
BSAIkf
a) 0.15,
3
I
0.05
0
*
-0.05
Ii
I
I
I
Id
U
0
I
d)
-2
0
200
400
Pe
800
600
Pole
0.06 F
-1
-0.1
-0.15
Pole
12
0. 1
-0.04
1000
0.02
RLAjfeO
b) 015
2
S
I
0
0.5
10-
0.1
0.05
100
AO 5IVz (m)
10
05
e)
-
-0.05
0.06 r
-1.5
-
-2
0
200
600
400
800
0.04
1000
Pe
L>0.02
ERA Pftf
c) 0.I5r
0. I
4
0
0.05
II
0
-0.05
-V
3
I
I
I
S
I
I
I
0
10-1
4
AO
5
10
(
-0.15
101
1VzI (in)
-3
-0.1
-4
-0.15
0
200
600
400
800
1000
Pe
Figure 2.8. Model results for hillslopes produced with the lateral channel migration LEM
indicating (a) BSApe, (b) RLA,., and (c) ERAptejwith color map. Profiles to the right of
the scale bar show schematic examples of hillslope profiles with BSAp, = 2. Model
results of the ridgetop Laplacian signature are shown in (d) and (e) for models with BSAp,
-2. In (d) and (e), dark grey points are from the equator-facing slope
~ 2 and B
and light grey points are from the pole-facing slope. White circles are the binned
medians. The solid line is fit through the binned medians for the pole-facing data and the
dashed line is fit through the binned medians of the equator-facing data. Inset is of shaded
relief map. Horizontal tick interval is 100 m; vertical tick interval is 10 m.
42
asymmetry for the same M (Figure 2.8). The undercut slope developed more negative
V 2 z than the aggrading slope and a dip in the binned V 2 z can be observed near Aohvzl ~
1 m where the most negative values of V2 z occur (Figure 2.8d and Figure 2.8e). The
erosion rate near the ridge is not uniform.
The spine of the divide erodes at the same rate as E, but varies on the rest of the
hillslope. On the undercut slope, the erosion rate increases with distance from the divide
and is highest along the steepest pitch of the creep-dominated zone. On the aggrading
slope, the erosion rate is lower than E. The sustained difference in erosion rates on the
undercut and aggrading slope causes sustained migration of the hillslope. Even though
sustained differences in erosion rate occur, the hillslope does reach a steady form where
the ridgeline and the channel migrate at the same rate and maintain an asymmetric
profile.
2.3.2.3 Model predictions and comparisons
All of the models that I tested are capable of producing topographic asymmetry. For
the aspect-dependent LEMs, the spatial pattern of erosion rates followed a similar history
as each model evolved from an initial condition to a steady state. Initially, the slope with
the higher erosional potential eroded faster, causing the divide to migrate towards the
slower eroding slope until steady state was reached. In stark contrast, the lateral channel
migration LEM predicts that differences in erosion rate are maintained on opposing
slopes and that the hillslope reaches a steady form that continually migrates. Both the
lateral channel migration LEM and the aspect-dependent soil creep LEM are capable of
producing hillslopes with nonzero RLApf..ef(Figure 2.9b). For the lateral channel migration
43
LEM, this occurred because of differences in the erosion rate on equator- and pole-facing
because of
slopes. For the aspect-dependent soil creep LEM, nonzero RLApfefoccurred
differences in D on equator- and pole-facing slopes and not because of differences in the
erosion rate. However, in cases for which the aspect-dependent soil creep LEM produced
hillslopes with high BSApf-e, other characteristics of the topography were unrealistic, such
as steep, heavily dissected slopes opposing shallow, completely undissected slopes
(Figure 2.7c and 2.7d). The lateral channel migration LEM was the only model that
produced asymmetric erosion rates (nonzero ERApfg) (Figure 2.9a). In addition, the
lateral channel migration LEM was the only model that produced RLAp-ej significantly
different from zero and high BSApf-ef while also producing realistic topographic
characteristics.
a) 3
SOcreep
2
1
b)
** ,* ,*
3 -00
CP 0
*
A runoff
* regolith strength
* lateral channel
migration
S
Ck*
,.~00
a
o6
0
0
0
*
*
**,
-3
*
***
00
0 0
3
0
*
-2
-2
-2
-1
0
1
2
-3
3
-2
-l
0
1
2
BSApfef
BSAp.ej
soil
Figure 2.9. Asymmetry signatures for hillslopes produced with the aspect-dependent
creep LEM, the aspect-dependent runoff LEM, the aspect-dependent regolith strength
(a)
LEM, and the lateral channel migration LEM. O, = 1 m for all of the model runs.
Erosion rate asymmetry against bulk slope asymmetry. (b) Ridgetop Laplacian
asymmetry against bulk slope asymmetry. Refer to legend in (a) for symbol definitions.
44
3
2.3.2.4 Effect of fluvial incision threshold
The RLApfef and ERApfef signaturesare valuable for distinguishing the results of the
aspect-dependent LEMs from the results of the lateral channel migration LEM. Since
QC
determines where fluvial incision occurs on the landscape and can influence the
morphology near the ridgeline, RLApf< may be sensitive to different values of OC. To
determine how
QC
effects the asymmetry signatures, I duplicated the modeling
experiments for the aspect-dependent runoff LEM, aspect-dependent soil creep LEM, and
the lateral channel migration LEM, but set 0, = 0 m instead of 6c = 1 m (Figure 2.10). I
excluded the aspect-dependent regolith strength LEM since it requires Oc > 0 m for
topographic asymmetry to develop.
0 creep
A Runoff
2 - * lateral channel
migration
1
o0
00
0
0
0
0
0
~00
-1 -e
o
-2-
0 0
-3
0
-2
-1
0
0
1
2
3
BSApfef
Figure 2.10. Asymmetry signatures for hillslopes produced with the aspect-dependent soil
creep LEM, the aspect-dependent runoff LEM, the aspect-dependent regolith strength
LEM, and the lateral channel migration LEM. 0, = 0 m for all of the model runs.
I also performed an additional set of lateral channel migration LEM runs with 0, = 2
m and explore how 0, may influence RLA~pf and ERA~pf- (Figure 2.11). I did not explore
45
scenarios for the aspect-dependent runoff LEM or the aspect-dependent regolith strength
LEM for O, > 1 m because the relationship between BSApjej and RLApfef is unlikely to
differ significantly from the OC = 1 m scenario. This is because as
QC
increases, the
creep-dominated zone near the ridgeline should grow larger and lead to a larger zone of
uniform V2 zR if the other parameters remain constant. I only expect the RLApfef
measurements to change when the soil creep-dominated zone is small, which occurs for
lower values of 0. , not higher.
The results for the aspect-dependent soil creep LEM are similar to the results when
= I m as they both exhibit significant differences in V2 zR between equator- and polefacing slopes when the hillslope is asymmetric (Figure 2.9b and 2.10). The differences in
V 2ZR
are significantly less pronounced on the equator- and pole-facing slopes for the
lateral channel migration runs for Oc = 0 m. This occurs because the entire hillslope,
including the ridgeline, experiences fluvial incision when Oe = 0 m, and this mutes the
highest magnitude V2 z that would develop if soil creep alone were responsible for
responding to the higher erosion rate on the ridges of the undercut slope. For high
BSApfef, the aspect-dependent runoff LEM did produce small differences in V2 zR for 6hc
1 m (Figure 2.10). This occurred because the higher magnitude of fluvial incision on the
lengthening slope influenced V 2 z
,,
not because there was a difference in erosion rates.
46
a)
3-
*
Om
1000
AOL=Im
2
*
b)
O=0m
A= I M
900
*0,=2m=2m
700
600
300
2000
-3-
0
-3
2
BSANteI
-2
0
3
BSApfef
Figure 2.11. Effect of fluvial incision threshold on characteristics of asymmetric
topography. (a) Plot of ERApf_, against BSApg for hillslopes produced with the lateral
channel migration LEM for different values of 0c. (b) RLApp,/against BSA p/e/ for hillslopes
produced with the lateral channel migration LEMs for different values of 0'. Color
indicates Pe and is the same color scale as (a).
For the lateral channel migration LEM, runs with lower Pe or higher 0, produce a
steeper trend between ERApfef and BSApf-ef and also RLApfej and BSApfef (Figure 2.11).
This may occur for two reasons. First, channels near the ridgeline are less effective at
migrating the ridgeline away from the undercut slope for model runs with higher O. If the
ridgeline is not able to migrate as efficiently, higher BSApf.ef will develop as the slope is
undercut. Second, as 0, increases or Pe decreases, bigger differences in V 2z R exist
because the creep-dominated portion of the ridgeline becomes larger. The most
significant differences in erosion rate occur on the steeper portions of the hillslope away
from the ridgeline. Model runs with higher values of 0, or lower values of Pe have
expanded creep-dominated zones that include steeper portions of the landscape.
47
2.4 1 -D model of lateral channel migration
In the previous model experiments, I explored the behavior of a 2-D LEM that
included lateral channel migration that occurred at a constant rate. Given the hypothesis
that lateral channel migration is driven by asymmetric sediment fluxes to channels from
adjacent hillslopes, it is possible that there are feedbacks between lateral channel
migration and the asymmetric erosion rates it produces. In this section I use a 1 -D
(profile) model to explore how topographic asymmetry develops when lateral channel
migration varies with time and is set by the difference in the sediment flux on equatorand pole-facing slopes. In one set of experiments, I modify the lateral channel migration
rule so that the migration rate is determined by the difference in sediment flux from
opposing slopes instead of occurring at a fixed rate and explore the influence of initial
conditions on asymmetry. In a second set of experiments, I investigate how model
parameters D, K, y, and slope length influence asymmetry.
2.4.1 1-D lateral channel migration model framework
The 1 -D model consists of a topographic profile of a ridge bounded on either end by
a migrating channel, analogous to a transect in the y-direction of the 2-D model. The
profile is subject to both fluvial channel incision and soil creep. The lateral channel
migration rate is modified so that
y=K
(EIL -EL)
48
(12)
where Kcm (L) is the lateral migration constant, E is the mean erosion rate for the slope
denoted by the subscript, and L is the horizontal slope length from the main divide to the
channel. The sediment flux at each boundary is calculated by summing the eroded
volume per unit width on equator- and pole-facing slopes at each time step and dividing
by the length of the time step. The area that is advected across the grid boundaries is also
considered in the flux calculation so that mass is conserved across the domain. In this
scenario, a model with perfectly symmetrical initial topography and erosion rates will
never develop asymmetry, so the model needs to be seeded by an additional asymmetryforming mechanism or by the appropriate initial conditions in order for a discrepancy in
sediment flux to occur and asymmetry to develop.
2.4.2 Model experiments
I ran a series of 1 -D models to determine if models with the new lateral channel
migration rule can initiate and sustain lateral channel migration in response to an initial
background slope or asymmetry. I also explored how M, K, D, L, and y influence
asymmetry.
For these experiments, I ran each model with the parameters listed in Table 2.2 until
a steady form was reached. I chose a ridge half-width of 500 m such that Pe = 250, which
corresponds approximately to the transition from l't-order to 2"d-order valleys [Perron et
al., 2008].
49
Table 2.2. l-D Model Parameters*
Parameter
Value
K (mi-2"' yr-t)
1x10 -5
D (m2 yr-1)
0.01
h**
1.67
ka** (m2-h)
6.69
m
0.5
n
I
E (m yr-)
2x10-
L (m)
1000
Ax (m)
2
*Unless otherwise noted
**Hack [1957]
2.4.2.1 Model experiments to explore the influence of initial conditions
I ran two experiments to explore how either initial hillslope asymmetry or a
background slope may influence the development of asymmetry. In the first experiment, I
varied the initial BSApfef from -3 to 3 in increments of 0.25 and Kc, from 2.5x 10-3 to
4x 10-3 m- 1 in increments of 1 x 104 m-1 to explore the final degree of BSApfef that
develops. The initial form of the topography was of a hillslope with linear slopes and
initial relief of 0.05L. In the second experiment, I varied the background slope by seeding
the model runs with a tilted initial surface. I varied the background slope from -0.015 to
.
0.015 in increments of 0.002 and Ke, from 0 to 4x10-3 m-1 in increments of 2x10-4 m~ 1
For each of these runs, I measured the final BSApef and compared it with the background
slope.
50
2.4.2.2 Model experiments to explore the influence of M, K, and y on
asymmetry.
I ran two series of experiments. For both of these experiments, I use a fixed lateral
channel migration rate, but the results should be consistent regardless of which lateral
channel migration rule is used. For the first set of experiments, I varied L, D, or K and y. I
varied L, D, and K so that Pe ranges from 50 to 500. I used equation (2.8) and varied y for
each of the model runs with a different L, D or K so that M ranges from 0 to 0.15 in
increments of 0.01. For the second experiment, I varied y to determine how BSApjej
responds to different values of y and K for Pe = 250. In order to maintain Pe = 250, I
varied D according to equation (2.8). I ran models with three different values of K:
M-1
.
Ix10-5, 5x10-5, and 10x10
2.4.3 1-D model results
2.4.3.1 Influence of initial conditions
For models with Ki, > 2.8x 10-3 m~ 1, topographic asymmetry always developed
when some initial asymmetry was present (Figure 2.12). The degree of asymmetry that
develops is almost entirely dependent on Kcm and not the initial degree of asymmetry
(Figure 2.12a). The time required to reach a steady-state form varied significantly for the
different model runs. I define the time to reach steady-form as the time required for the
model to reach a state for which the maximum change in the elevation at any point is less
than 1 x 10-9 m y-1. It was necessary to require such a slow rate because model runs with
low initial BSApfef and low Kcm develop asymmetry extremely slowly. If the definition is
less strict, the hillslope will not reach the final degree of topographic asymmetry that
51
BSA5fef
a)
3
2
3.
44 Pole
I
0
-1
-3
2.5
-3
Initial
2
1
0
-I
-2
3
BSAp-ef
BSAfef
b)
A
3
3.5
3
M
2.5
6
0
.1
1.5
-1
-2
0.5
-3
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Background slope (dz/dx)
Figure 2.12. (a) Phase diagram of Klm against initial BSA ,lfor the 1-D aggradationdriven lateral channel migration model. Pe = 250 for all models. Profiles to the right of
the scale bar show examples of hillslope profiles. Each grid cell represents an individual
model solution. (b) Phase diagram of Kicm against background slope gradient for the 1 -D
aggradation-driven lateral channel migration model. Pe = 250 for all models. Profiles to
the right of the scale bar show examples of hillslope profiles. Each grid cell represents an
individual model solution.
would otherwise develop if the model ran longer. I verified that this definition worked by
running the model for significantly longer and verifying that the form did not change
significantly. The model with Kcm = 2.8x 10-3 m~ 1 and initial BSApfef= 0.25 required 173.4
52
Myr to reach a steady form while the model with the same Kem and initial BSApfef= 0.75
only required 9.9 Myr. The model with Kem = 4x 10- m- and initial BSApff = 0.25
required 8.3 Myr to reach a steady-state form while the model with the same Kic, and
initial BSApfg= 3 only required 2.4 Myr. Models with high Klem and initial BSApfef that is
similar to the final BSApjej reached a steady form the fastest.
If a background slope is initially present, asymmetry develops, but is relatively
small (Figure 2.12b). This is because the slopes must develop different gradients and
slope lengths on each side of the divide to maintain a uniform erosion rate. When Kicm > 0
mI, higher asymmetry develops and the difference in slope lengths due to the
background slope causes a difference in sediment flux on the equator- and pole-facing
slopes that drives lateral channel migration.
2.4.3.2 Exploring the influence of M, K, and y on asymmetry
For the first set of experiments (Figure 2.13a) in which I changed L, D, or K and y,
the model results for a given value of M, the Migration number, produced comparable
results for BSApff. The degree of BSApfef that develops is determined by the rate at which
the bounding channel migrates and the rate at which the hillslope can respond to the
migration. As asymmetry develops, the undercut slope becomes steeper and shorter while
the aggrading slope becomes longer and gentler. Even though the undercut slope
steepens, it is not capable of matching the sediment flux of the aggrading slope. Even
though the sediment fluxes in the model are not balanced on opposing slopes, the
hillslopes do reach a steady form. The rate at which the slope can respond to
53
Pe
-JU
a)
450
400
350
2-
-300
250
200
150
100
0.15
0.1
0.05
0
M
b) 6 *
K=lx
5
- yrI
K=5x10-5 yrI
K
K = I0xI0-5 yr 1
5 -
-
4
-
2
T
100
200
300
400
500
600
700
800
900
1000
y (m Myr-1)
Figure 2.13. (a) Plot of BSA,/,against M for the 1-D fixed-rate lateral channel migration
model. For these results, K and y were varied to produce models with different Pe and M.
M. Model
1
However, changing D or L also produce the same trend between BSA ,/against
results with BSApjIe < 3.5 are included in the figure. (b) Plot of BSApe against y for the 1D fixed-rate lateral channel migration model. I varied y for three different values of K to
explore the dependence of BSAple 1 on K.
54
over-steepening is a function of D and C (= KA" Vz
). This is why both Pe, which
includes D and some components of C, and M, which includes C and y, must both be
considered to predict BSApf-ef (Figure 2.13a). As D and C increase, the rate at which the
hillslope can respond to undercutting increases and the ridgeline is able to migrate faster,
leading to a decrease in BSApjej. For the fixed-y modeling scenario, M is known a priori.
For the aggradation-driven scenario, y, and therefore M, are emergent values.
For the second set of model experiments (Figure 2.13b), model runs with lower
values of K developed higher BSAp.f I include the results in Figure 2.13b to show the
strong control that K has on BSApjej and to show how BSApgf develops for different
values of y. Asymmetry plateaus in the case of K= 1 x 10 m-' because the oversteepened
slope becomes a cliff and cannot be further steepened. This degree of asymmetry is
unrealistic and the inclusion of non-linear soil creep would limit the BSApfef that develops
in these scenarios. Whether or not y is reasonable depends significantly on C.
2.5. Discussion
2.5.1 Controls on topographic asymmetry
The degree of topographic asymmetry that develops depends on many factors. For
the aspect-dependent efficiency LEMs, these factors are summarized by two
dimensionless values that emerge from equation (2.1) and subsequent modifications: Pe
and co, / of (Figure 2.5, 2.6, and 2.7). Changes in Pe can represent changes in slope
length (n ), soil transport efficiency (D), or rock strength and fluvial incision efficiency
(K). wo / w, represents the magnitude of the asymmetry-forming mechanism. If
55
a/ / WP, is comparable across a landscape, differences in basin area and orientation may
explain much of the variability in topographic asymmetry witnessed for a single
landscape.
The aspect-dependent soil creep LEM produced hillslopes with both signs of BSApf
ef for
positive values of 6 and negative values of 6 (Figure 2.7). If the governing equation
is modified so that soil creep does not occur in the channels, I expect that the sign of
BSApfef would not change as Pe is increased. I use the existing form of equation (2.1)
because it has been validated for some landscapes [Perronet al., 2009; 2012]. The
aspect-dependent soil creep LEM predicts that slopes experiencing the same
microclimatic effects may develop different signs of BSApf-ef depending on Pe, which
correlates with f for a particular landscape. McGuire and coworkers' [2014] numerical
modeling experiments of asymmetric cinder cones in the American West suggests that
the asymmetry at their field sites develop due to higher soil creep rates on south-facing
slopes. Our results match their findings when Pe <~400. However, our results suggest
that this result is not universal and that cinder cones experiencing the same microclimatic
conditions may develop the opposite sign of asymmetry if their slopes are longer and Pe
>
~400 (Figure 2.7a). When Pe > 400, the sign of asymmetry that develops depends on
the magnitude of co,, / op/.
For the lateral channel migration LEM, the degree of asymmetry that develops can
also be summarized by two dimensionless factors: Pe and M (Figure 2.8). For the
aggradation-driven lateral channel migration scenario, M is an emergent property
determined by the efficiency of lateral channel migration (represented by Ken), C, and
Pe. M emerges due to the equilibrium that is reached when the difference in sediment
56
flux on equator- and pole-facing slopes is at a maximum and an increase in y no longer
leads to a further increase in the difference in sediment fluxes. For both the
aggradation-driven and fixed-rate lateral channel migration models, M and Pe are
dimensionless numbers that can be used to predict the final BSA pj.. that develops (Figure
2.8 and Figure 2.13a). It should be possible to estimate the value of y required to produce
a particular value of BSApjej if Pe and C are known from high-resolution topographic data
[Perronet al., 2012].
2.5.2 Model and weighting function
One limitation of incorporating a weighting function into a LEM to characterize
aspect-dependent differences is the challenge of reproducing the correct spatial scale of
microclimates. There is likely a minimum scale for which microclimates can effectively
cause differences in erosional processes. Xu and coworkers [2004] examined the
correlation coefficients between landscape characteristics (e.g., elevation, gradient) and
microclimate proxies (e.g., air temperature, soil temperature, and soil moisture) at
different length scales along a transect in the southeastern Missouri Ozarks and found
that landscape characteristics measured at scales below 100 meters do not correlate well
with microclimate proxies while landscape characteristics measured at scales between
100-500 meters exhibit some correlation. Landscape characteristics measured at scales
above 500 meters generally correlated the best with microclimate proxies. These scales
are on par with the scale of many hillslopes. Of the three aspect-dependent LEMs that I
test, the aspect-dependent runoff LEM best captures the spatial scale of microclimates
since co is integrated over the upstream drainage area at each point on the landscape. For
57
all of the aspect-dependent LEMs, o is determined locally and the calculation does not
take into account the surrounding microclimatic environment. For example, locations in
low-order valleys on equator-facing and pole-facing slopes may have identical
# even
though the microclimatic conditions for the equator-facing and pole-facing slopes are
quite different. This may lead to an over or under estimation of w depending on the
surrounding microclimate conditions.
In this study, I did not investigate the topographic signatures of multiple
asymmetry-forming mechanisms acting simultaneously even though there is some
evidence that multiple mechanisms may act in unison to cause topographic asymmetry.
Hack and Goodlett [1960] suggested that differences in both soil creep rates and runoff
led to the development of topographic asymmetry at their field site near the headwaters of
the Shenandoah River, VA. Other geomorphologists have also suggested that multiple
asymmetry-forming mechanisms may act in conjunction to cause asymmetry [Walker,
1948; Churchill, 1981; Siegmund andKevin, 2000]. It would be possible to combine
multiple asymmetry-forming mechanisms in the LEM, but this was beyond the scope of
this study.
I modeled soil creep with a linear sediment flux law, which is a good descriptor for
soil creep in many soil-mantled landscapes [Hanks et al., 1984b; McKean et al., 1993;
Rosenbloom and Anderson, 1994]. However, as hillslopes approach a critical gradient
(~0.6), non-linear sediment flux is a better approximation of soil creep [Roering et al.,
1999]. For the 2-d LEM, I was careful to produce models that did not have
gradients > 0.6. In regards to topographic asymmetry, the sediment flux law likely
58
influences the degree of BSApfejthat develops when steep gradients exist. A non-linear
sediment flux law for soil creep may be necessary for future modeling scenarios.
I limited my investigation to the evolution of a hillslope divide and the
corresponding slopes on either side of the divide. I focused on hillslope signatures due to
the difficulty of incorporating lateral channel migration into a larger scale LEM. This
causes the divide and the valley to be strongly coupled. In real landscapes, neighboring
valleys do not necessarily migrate at the same rate, which may lead to differences in the
rate of ridgeline and channel migration. Larger scale topographic signatures of lateral
channel migration may develop due to differences in ridgeline and valley migration rates,
boundary conditions or drainage geometry. I was not able to investigate these signatures
due to the limitations of incorporating lateral channel migration into a LEM which could
allow multiple channels to migrate.
2.5.3 Self-sustained lateral channel migration and microclimates
In my 1 -D model, a range of solutions exists for which hillslopes maintain a
constant form and migrate at a constant rate while maintaining differences in sediment
flux rates. The extent to which this actually occurs in nature likely depends on local
conditions such as drainage geometry and the regularity of basin size, because basins
with different sizes will develop different lateral channel migration rates for the same
efficiency of undercutting (represented by Kcm). Smith and Bretherton [1972] developed
a simple geometric model to explore the stability and form of aggradation-driven lateral
channel migration, but in their experiments, the hillslope did not reach a steady form.
This likely occurred because they did not consider the feedback between multiple
59
migrating ridgelines and valleys or allow for the migration of an entire ridgeline. They
only considered the feedbacks between an aggrading slope and the opposing undercut
slope, which led to a scenario where the undercut slope was neither able to balance the
sediment flux on the aggrading slope nor migrate away from the aggrading slope. If they
had allowed the entire undercut slope, including the ridgeline, to migrate, their hillslope
model should also have been able to reach a steady form.
My 1 -D lateral channel migration model runs with initial topographic asymmetry or
background slope developed topographic asymmetry due to the differences in slope
lengths and the corresponding difference in sediment flux. This suggests that the presence
of microclimatic variability may not be necessary for topographic asymmetry to develop.
However, for some of these scenarios, it is important to consider the amount of time
required to reach a steady form. Some of the model runs that started with low initial
topographic asymmetry required over 100 Myr to reach a steady form, and the
asymmetry develops slowly throughout the model run. It is unrealistic that any natural
landscape will reach a steady form or develop much asymmetry at all if so much time is
required. The time required for the model runs with higher values of Kc, were much
more realistic, but still could require on the order of 10 Myr to reach a steady form.
2.5.6 Application to field sites
The lateral channel migration models predict a unique relationship between BSApfj.
and ERApfef (Figure 2.9a). Cosmogenic radionuclide-derived erosion rates could be used
to test if lateral channel migration is occurring in landscapes with topographic
60
asymmetry. The lateral channel migration LEM clearly predicts that sustained differences
should exist, with the undercut slope eroding faster than the aggrading slope.
The lateral channel migration LEM also predicts a unique relationship between
BSApjefand RLApfef that can often be distinguished from the results of the other LEMs
(Figure 2.9b). This asymmetric signature could also be used to test whether or not lateral
channel migration is occurring at a field site and if the degree of lateral channel migration
is sufficient to explain the degree of topographic asymmetry that is present.
For the lateral channel migration LEM, model runs with higher values of 6, are
more easily distinguished from the aspect-dependent runoff and aspect-dependent
regolith strength results than model runs with low
at a field site is low, it may
QC. If QC
be difficult to use the RLApfef against BSApfef signature to identify lateral channel
migration because the degree of RLApfef that develops may be insufficient. The aspectdependent soil creep LEM also produces hillslopes with high values of RLAp.ej, but the
slope between BSAp.ef and RLApfpej is much steeper than the slope for all of the lateral
channel migration LEM scenarios that I explored. In addition, the aspect-dependent soil
creep LEM produced unrealistic topographic characteristics for models with high RLApfef
and only moderate BSApe{. If an additional asymmetry signature was used, for example
one that would measure asymmetry in drainage density, it should be easy to distinguish
the topographic characteristics produced by the aspect-dependent soil creep LEM and the
lateral channel migration LEM.
My 1 -D hillslope modeling results suggest that initial differences in slope length
alone are capable of producing topographic asymmetry, but the fact that the sign of
asymmetry is latitude-dependent implies that microclimates do play an important role in
61
controlling the sign of asymmetry [Parsons, 1988; Poulos et al., 2012]. Our results
corroborate the work of Wende [1995] that it may be important to consider the role of
tilting or initial basin geometry in the formation of asymmetric landscapes if lateral
channel migration is responsible for development of topographic asymmetry. Landscapes
that exhibit high asymmetry, such as Gabilan Mesa, CA, commonly form in poorlyconsolidated, gently dipping sediments [Dohrenwend, 1978]. In some cases, tilting alone
may be enough to cause topographic asymmetry to develop [Garciaand Mahan, 2012].
Dohrenwend [1978] postulated that rock strength is an important factor influencing
the degree of topographic asymmetry that develops in landscapes where LCM causes the
asymmetry. In particular, lateral channel migration would occur less efficiently and at a
slower rate in valleys with hard bedrock. Rock hardness likely influences Kcn, and softer
rocks are better described by high values of Kicm and more efficient lateral channel
migration for a particular difference in sediment flux on opposing slopes. Channels with
strong bedrock are less prone to migrate laterally [Montgomery, 2004; Limaye and Lamb,
2014]. In landscapes with weaker rocks, lateral channel migration may occur more easily,
which would be reflected in a higher Kcm in the aggradation-driven hillslope model. All
else being equal, models with higher K1,, have higher values of M and develop higher
BSApfef. The aspect-dependent LEMs should not exhibit the same sensitivity to bedrock
channel strength. No study has been carried out to investigate the occurrence and degree
of asymmetry in landscapes with different bedrock strength. The dynamics between Kem
and K for different rock strengths may be critical for determining if more or less
topographic asymmetry develops for weaker rocks. If landscapes with stronger bedrock
develop less asymmetry, this may be evidence that lateral channel migration is occurring
62
at many sites, as it is the only asymmetry-causing mechanism that is sensitive to rock
strength.
If aggradation-driven lateral channel migration is a major cause of topographic
asymmetry and only differences in sediment fluxes are necessary to cause the asymmetry,
it is reasonable to ask why topographic asymmetry does not develop in all landscapes.
The simplest reason is that the conditions necessary for lateral channel migration are
probably not present in all landscapes. Dohrenwend [1978] suggested that some basins at
Gabilan Mesa developed little or no asymmetry because their channel gradients were
sufficiently high that significant aggradation did not occur, and thus there was
insufficient sediment to deflect channels. An updated explanation would rely on stream
power or shear stress instead of channel gradient as a predictor of the channel sediment
transport capacity. In addition, some valleys may experience insufficient sediment flux
from the hillslopes to develop significant aggradation-driven asymmetry, independent of
the channel's transport capacity.
My 1 -D modeling experiments (Figure 2.12a) provide an additional explanation for
why asymmetry may not develop. Even though the models reach almost identical BSApfef
independent of the initial BSApfef, the time required for the model profile to reach a
steady form can be exceedingly long because the asymmetry develops slowly. The
models that started from conditions of low initial BSApfef and had low values of Kc,
developed topographic asymmetry very slowly and can require > 100 Myr to reach a
steady form. If this accurately reflects the time required for landscapes to develop
pronounced asymmetry, it is understandable why asymmetry is not more widespread.
63
2.6. Conclusion
I incorporated microclimate-dependent erosional mechanisms and lateral channel
migration into a landscape evolution model to investigate the origins of asymmetric
topography. The model with lateral channel migration predicts a unique topographic
signature that the ridgetop Laplacian of the undercut slope should be higher than the
ridgetop Laplacian on the south-facing slope. This topographic signature is distinguished
easily from the other models for many scenarios. The lateral channel migration model
also predicts that the steeper slope in asymmetric landscapes will be eroding at a
significantly higher rate than the opposing, shallower slope while the other models do
not. The aspect-dependent runoff model and aspect-dependent regolith strength model
produce comparable signatures between bulk slope asymmetry and ridgetop Laplacian
asymmetry. The aspect-dependent soil creep model produces topography with relatively
high ridgetop Laplacian asymmetry and low bulk slope asymmetry and is not capable of
producing topography with high values of the P6clet number, which describes the
competition between channel incision and soil creep, with realistic topographic
characteristics. The aspect-dependent soil creep model also predicts that different signs of
bulk slope asymmetry develop for different values of Pe. Multiple mechanisms may act
in real landscapes, making it difficult to decipher which mechanism is responsible for
causing the topographic asymmetry. Results from a 1 -D model with aggradation-driven
lateral channel migration suggest that topographic asymmetry may develop or be
sustained in landscapes without variability in microclimates.
64
2.6. Acknowledgements
I would like to thank Scott Miller for useful discussions that helped direct some of
the modeling efforts. I would also like to acknowledge the Department of Defense for
funding through a National Defense Science and Engineering Graduate Fellowship.
65
66
Chapter 3. Unraveling the mysteries of an asymmetric
landscape
67
Abstract
North-facing slopes in semi-arid regions of the northern hemisphere are commonly
steeper than south-facing slopes. The most common modern explanations for this
topographic asymmetry ultimately invoke aspect-related microclimate. However, the
specific mechanisms that generate the asymmetry are not well understood. I investigated
the potential causes of topographic asymmetry at Gabilan Mesa, CA, a site that
experiences large differences in microclimates and has highly asymmetric landforms with
north-facing slopes that are considerably steeper than south-facing slopes. Two different
hypotheses have been suggested to explain the asymmetry at Gabilan Mesa. For one
hypothesis, different microclimates on opposing slopes are responsible for causing
differences in erosional efficiency, which directly leads to the topographic asymmetry.
For the other hypothesis, differences in microclimates alone are not enough to cause the
asymmetry to develop. Instead, lateral channel migration, driven by differences in
sediment flux on the opposing slopes, and the corresponding undercutting causes the
topographic asymmetry. I also considered the role of initial tilting of the mesa in causing
the asymmetry. I carry out numerical modeling experiments, complete terrain analysis,
and make field measurements to test these different hypotheses. I considered two aspectdependent efficiency mechanisms: aspect-dependent runoff and aspect-dependent
regolith strength. If aspect-dependent runoff causes the asymmetry, runoff should be
higher on south-facing slopes. I estimated field-saturated hydraulic conductivity at two
different sites with varying degrees of asymmetry and found that field-saturated hydraulic
conductivity is considerably higher on south-facing slopes in a highly asymmetric basin.
This is consistent with the expectation if aspect-dependent runoff is responsible for the
asymmetry. If aspect-dependent regolith strength causes the asymmetry, the north-facing
slopes should have higher soil shear strength. I measured soil shear strength on northfacing and south-facing slopes and found that soil shear strength was significantly higher
on the south-facing slope, which is inconsistent with aspect-dependent regolith causing
the topographic asymmetry. If lateral channel migration is responsible for the asymmetry,
associated stream captures and channel beheadings may occur. I identified the locations
of several stream captures and channel beheadings, but did not identify them in most of
the asymmetric valleys. I also tested erosion rate and topographic predictions made by the
numerical landscape evolution models that incorporate the different asymmetry-forming
mechanisms against cosmogenic radionuclide-derived erosion rates and topographic
characteristics at Gabilan Mesa. The aspect-dependent runoff model and the aspectdependent regolith model best reproduce the signature between erosion rate asymmetry
and topographic asymmetry when compared to the lateral channel migration model.
When considered with the field measurements of soil strength and field-saturated
hydraulic conductivity, aspect-dependent runoff is the most likely mechanism responsible
for the bulk of the topographic asymmetry at Gabilan Mesa. However, it is not possible to
rule out the role of tilting in influencing the initial development of asymmetry in some
basins. Furthermore, the erosion rate analysis and the physical evidence suggests that
lateral channel migration is occurring at some locations, but taken in conjunction with the
numerical modeling predictions and erosion rates, lateral channel migration is most likely
only intensifying topographic asymmetry locally and not fundamentally responsible for
its development.
68
3.1. Introduction
3.1.1 Motivation
Although much effort has been made to understand the role of climate in
landscape evolution, many fundamental questions remain [Molnar, 2004; Molnar et al.,
2006]. Some studies have found a relationship between erosion rate and precipitation rate
and show that erosion rate increases with increased precipitation rate [Moon et al., 2011;
Ferrieret al., 2013a]. However, even the relationship between something as fundamental
as precipitation and erosion rate is not easily predicted in many landscapes, with some
geomorphologists arguing that erosion rates may increase with aridity due to differences
in the frequency and magnitude of storms [Molnar, 2001; Molnar et al., 2006] or a
decrease in cohesive vegetative groundcover [Bull, 1997]. One way of addressing how
landscapes evolve under different climates is by studying how landscapes respond to
differences in microclimates, which can vary on hillslopes that face different directions
with respect to the sun. Understanding how microclimatic variability at the hillslope scale
influences landscape evolution offers a unique opportunity to isolate climatic variability
from other variables that influence landscape evolution, such as lithology and tectonic
uplift. Some landscapes that exhibit microclimatic differences also exhibit significant
differences in topographic characteristics that appear to also vary with aspect. Some
geomorphologists have suggested that the different microclimates are directly responsible
for the differing topographic characteristics [e.g., [Emery, 1947; Melton, 1960;
Dohrenwend, 1978; Churchill, 1982; Burnett et al., 2008; McGuire et al., 2014]. I seek to
address some of the potential mechanisms that may be sensitive to the differences in
microclimate and responsible for the development of topographic asymmetry.
69
Understanding how landscapes respond to different microclimates should help illuminate
the relationship between larger-scale climates and landscape evolution.
3.1.2 Background
Numerous studies have been carried out to address how microclimates may
influence the development of asymmetric topography, in which characteristics such as
slope gradient differ on hillslopes with different aspects (Figure 3.1). The occurrence of
steeper pole-facing slopes and gentler equator-facing slopes has been documented for
different landscapes around the world [Bass, 1929; French, 1971; Dohrenwend, 1978;
Churchill, 1982; Cerdli et al., 1995; Wende, 1995; Siegmund and Kevin, 2000; Burnett et
al., 2008; Poulos et al., 2012]. In regions where the topographic asymmetry cannot be
attributed to regional stratigraphic dips or other aspects of bedrock structure or lithology,
geomorphologists have often relied on the presence of microclimates to explain the
topographic asymmetry [Hack and Goodlett, 1960; Dohrenwend, 1978; Istanbulluogluet
al., 2008; Yetemen et al., 2010; Anderson et al., 2012; Poulos et al., 2012].
Two leading hypotheses have emerged to explain the occurrence of
microclimatically induced topographic asymmetry. One hypothesis states that small
differences in microclimate cause differences in the efficiency of erosional processes on
slopes with different aspects. The more efficiently eroding slope erodes faster until the
resulting slope asymmetry compensates for the difference in erosional efficiency.
Possible mechanisms causing such a difference in erosional efficiency include: (1)
70
Figure 3.1. Image of Gabilan Mesa, CA (36.917' N, 120.760' W). Striking topographic
asymmetry and large differences in vegetation on opposing slopes are plainly visible.
North-facing slopes have steeper gradients and denser vegetation than south-facing
slopes. Image courtesy of Google Earth.
reduced runoff, and therefore slower channel incision, on more vegetated slopes [Hack
and Goodlett, 1960; Kane, 1970; Wende, 1995; Istanbulluoglu et al., 2008; Yetemen et
al., 2010] due to either more rapid infiltration [Emery, 1947; Hack and Goodlett, 1960;
Kane, 1970] or increased evapotranspiration; (2) stronger regolith, and therefore slower
channel incision, on more vegetated slopes[Emery, 1947; Ollier and Thomasson, 1957;
Yetemen et al., 2015] or (3) asymmetry in soil creep rates due to differences in
bioturbation rates [Perronand Hamon, 2012; West et al., 2013; McGuire et al., 2014],
frost-generated crack growth [Anderson et al., 2012], or solifluction [Ollier and
Thomasson, 1957].
According to the hypothesis that depends on lateral channel migration, the
difference in erosional efficiency is not sufficient to create the observed topographic
asymmetry. Instead, sediment aggradation at the foot of the more quickly eroding slope
71
forces lateral channel migration and undercutting of the opposing slope [Bass, 1929;
Melton, 1960; Dohrenwend, 1978], which steepens the undercut slope and reduces the
gradient of the opposing slope. Melton [1960] investigated asymmetric topography in the
Laramie Range, WY and suggested that most cases of microclimate-induced asymmetry
are attributable to lateral channel migration. Dohrenwend [1978] also came to a similar
conclusion for a landscape with a high degree of topographic asymmetry in a semi-arid
region of California. Wende [1995] examined asymmetric valleys of the Tertiary Hills of
Lower Bavaria, Germany and, contrary to former conclusions, suggested that
microclimates may not be required for their formation. Instead, Wende suggested that
factors not relating to microclimates such as lateral channel migration that was driven by
asymmetry in initial development of the drainage network may be responsible. In Chapter
2, I showed that lateral channel migration may be a self-sustaining process and does not
necessarily require the presence of microclimates if an asymmetry in sediment flux to
opposite banks of a channel occurs for other reasons such as differing slope lengths
across a valley.
There are conflicting hypotheses about the origins of topographic asymmetry, with
some geomorphologists appealing to lateral channel migration, which may or may not be
driven by microclimatic differences, and others suggesting that differences in erosional
efficiency on opposing hillslopes experiencing different microclimates is enough to cause
the asymmetry. Understanding which mechanism is dominantly responsible requires a
detailed examination of a field site where either mechanism may be active. In the
following section, I describe such a field site.
72
3.1.3 Study site: Gabilan Mesa, California
3.1.3.1 Site Description
Gabilan Mesa is a ~2500 km 2 rectangular region in central California that is
bordered to the southwest by the Salinas River and to the northeast by the San Andreas
Fault (Figure 3.2). The area is considered a mesa because of the elevated, roughly planar
surface defined by concordant ridge tops that stretch from the Salinas River towards the
San Andreas Fault. Evidence of landslides is uncommon [Perronet al., 2009]. Portions
of Gabilan Mesa remain undissected; these relict surfaces are most common in the
northern portion of the mesa while the southern portion of the mesa is generally dissected
into ridge-and-valley topography characterized by sharply concave-up valleys and
smooth, concave-down hilltops. Many first- and second-order valleys lack active
channels, and instead appear as colluvium-mantled hollows, possibly indicating a change
in sediment storage and discharge that accompanied the Pleistocene-Holocene transition
[Reneau et al., 1986].
The dominant drainage direction of Gabilan Mesa is to the southwest, and the
roughly planar surface defined by ridgetops throughout the mesa dips 1.5' to 2'
southwest. The landscape is incised into the Paso Robles formation, which is composed
of moderately consolidated conglomerates, sandstones, and siltstones that
73
Legend
a)
Alluvium
Paso Robles Formation
mudstone, and limestone)
tN
(sandstone, conglomerate,
Pancho Rico Formation (sandstone, conglomerate,
mudstone, diatomite, andporcelaneousrocks)
Hames Member of the Monterey Formation
(siliceousmudstone, porcelanite, chert, and
dolomite)
Figure 3.2. (a) Shaded relief map of Gabilan Mesa, CA with lithological map overlay.
Outline of California in the lower left of the frame shows the location of Gabilan Mesa
marked with a star. (b) The south-facing hillslopes appear more regularly and deeply
incised than the north-facing hillslopes (36.069' N, 120.863' W). Image courtesy of
Google Earth. Location of image marked as Photo 1 in (a). (c) Some valleys at Gabilan
Mesa exhibit evidence of southward lateral channel migration and undercutting (35.913'
N, 120.8360 W). This high degree of undercutting is not typical of every basin at Gabilan
Mesa. Location of image marked as Photo 2 in (a).
74
were originally deposited as a bajada. The dominant dip of beds in the Paso Robles
formation is 1.5' to 3' to the southwest [Durham, 1974]. The Paso Robles formation is
Pliocene to Pleistocene in age and is underlain conformably by Pliocene marine deposits.
The Paso Robles formation has not been internally deformed by tectonics despite the
proximity to the San Andreas Fault and several other minor regional faults [Dohrenwend,
1978]. This is likely due to the strength of the basement rocks, which are primarily
composed of granitic intrusive and metamorphic rocks [Durham, 1974].
Gabilan Mesa is classified as a semi-arid, steppe-type climate in the Kppen
climate classification [McKnight and Hess, 2008]. The summers are hot and dry, while
the winters are mild and wet. The mean annual rainfall in the nearby town of Paso
Robles is 374 mm. Interior Live Oaks (Quercus wislizeni) are common on the mesic
(moderately moist) north-facing slopes. Both the north-facing slopes and the xeric (dry)
south-facing slopes are blanketed with a mixture of grasses that includes both introduced
(Bromus, Avena, and Festuca) and native genera (Stipa, Poa, and Aristida) [Kane, 1970].
Evidence from marine sediments, plant fossils, pollen, soil caliche and charcoal suggests
that the climate has changed since the Pleistocene, which was likely wetter and cooler
relative to present conditions [Johnson, 1977].
3.1.3.2 Proposed origins of the asymmetric topography at Gabilan Mesa
At Gabilan Mesa, significant differences in hillslope morphology are welldocumented and correlate with modem differences in aspect-controlled microclimates
and vegetation. However, the specific erosional mechanisms that lead to the differences
75
in morphology are not well understood. I seek to determine the mechanism or
mechanisms that dominantly control the topographic asymmetry.
Residents of the area have long noted the topographic asymmetry, and one
popular idea was that that the asymmetry was due to preferential aeolian erosion and
deposition due to the dominant wind direction (Figure 3.1). Reed [1927] was the first
author to write a scientific paper addressing the topographic asymmetry of Gabilan Mesa.
He noted that the dominant wind direction was inconsistent with the orientations of the
asymmetric slopes and suggested that, independent of the dominant wind direction, the
asymmetry in vegetation caused the differences in aeolian erosion and transport. The
north-facing slopes of Gabilan Mesa are generally more heavily vegetated and steeper,
and he suggested that the vegetation was able to trap aeolian sediment, causing northfacing slopes to steepen relative to the sparsely vegetated south-facing slopes. This
hypothesis considers the topography to effectively behave as a set of large dunes. This
idea was later abandoned as more reasonable alternatives were proposed.
Kane [1970] came to a different conclusion to explain the valley asymmetry at
Gabilan Mesa. In Sarah Canyon, a highly asymmetric valley, Kane interpreted qualitative
infiltration rate estimates as evidence that differences in erosional efficiency on slopes
with different aspects were responsible for the valley asymmetry. Additionally, Kane did
not find any evidence that preferential aggradation was correlated to the presence of
asymmetry, and doubted that slope undercutting could lead to significant valley
asymmetry in semi-arid environments.
In stark contrast, Dohrenwend [1978] argued that systematic undercutting of
north-facing slopes was the primary mechanism driving the formation of asymmetric
76
valleys and concurred with Melton's [1960] conclusion that differences in the efficiency
of erosion processes are not sufficient to cause valley asymmetry. Dohrenwend [1978]
argued that other characteristics of the site's topography support the slope-undercutting
hypothesis, including beheaded streams and the capture of southern tributaries that may
record the southward migration of north-facing hillslopes. Recently, Garcia and
coworkers [2011] suggested that tectonic tilting instead of microclimates controls the
asymmetry of Peachtree Valley, a major northwest-southwest trending valley at Gabilan
Mesa.
3.1.3.3Approach and outline
In Chapter 2, I used a numerical model to make unique topographic and erosion
rate predictions for different asymmetry-forming mechanisms, including aspectdependent erosional efficiency and lateral channel migration. These predictions can be
tested using a combination of high-resolution topographic data and cosmogenic
radionuclide-derived erosion rates. Furthermore, field measurements of soil properties
and topographic evidence of drainage network reorganization can be used to test for
evidence of the hypothesized mechanisms described in the previous section.
I take a multi-faceted approach to determine the possible causes of asymmetry at
Gabilan Mesa. I carry out terrain analysis in section 3.2 and identify locations of river
capture and beheaded channels. I also address the applicability of ridgetop Laplacian
analysis developed in Chapter 2. In section 3.3, I consider the possible role of initial
tilting and the resulting background slope at Gabilan Mesa as a possible mechanism that
contributes to asymmetry. In section 3.4, I present results for cosmogenic radionuclide-
77
derived erosion rates for opposing north-facing and south-facing slopes at Gabilan Mesa.
In section 3.5, I present numerical landscape evolution modeling experiments that include
different asymmetry-forcing mechanisms and compare the topographic and erosion rate
predictions with the erosion rate estimates and topography of Gabilan Mesa.
3.2 Terrain analysis
3.2.1 Evidence of drainage network reorganization
I mapped beheaded valleys and stream captures at Gabilan Mesa from aerial
imagery and digital elevation data. I identified 27 previously unidentified stream captures
or beheaded valleys (Figure 3.3). I focused on identifying stream captures and beheaded
valleys in the Paso Robles Formation.
Three large drainage basins in or near my study area-Powell Valley, Portuguese
Valley, and Indian Valley-all exhibit physical evidence of lateral channel migration in
the form of beheaded channels or stream piracy (Figure 3.2a and 3.3). Near the outlet of
Indian Valley where it joins the Salinas River (Figure 3.2a), evidence of westward
migration and valley beheadings in the neighboring basin serve as strong evidence of
lateral channel migration and undercutting of an east-facing slope. In contrast, Portuguese
Valley mostly experiences undercutting of its northwest-facing slope. This lends
evidence to the idea that lateral channel migration is an important mechanism for the
reorganizing of drainage networks, but does not clearly point towards a microclimatic
origin since the channels have migrated in different directions.
78
3.2.2 Metrics for measuring asymmetry
I use the asymmetry indices developed in Chapter 2 and modify them specifically
for the northern hemisphere. I use the bulk slope asymmetry measurement to quantify
the asymmetry in slope length across a valley. Bulk slope asymmetry is defined as
BSA
=
log 2 Sf
(3.1)
s~f
Where S is bulk slope and is calculated as the hillslope relief divided by the slope length.
Subscript nfrefers to north-facing while sfrefers to south-facing and denotes the aspect
of the slope. I measure BSAnfsf across valleys, as opposed to hillslopes, and split the
valleys along the channel, separating the valley into north-facing and south-facing zones.
Within each zone, I measure slope length as the horizontal distance from the channel to
the ridgeline along a transect that is oriented perpendicular to the average channel
direction. I make this measurement at each pixel location along the channel and define
slope length for the zone as the mean of the slope length measurements. The relief is
calculated as the vertical difference in the elevation of the ridgeline and the channel at
each transect measurement and I use the mean of the relief measurements as the valley
relief for the zone.
I also measure the ridgetop Laplacian asymmetry, defined as
RLA,_1S 1 = log 2
V 2z
2
(3.2)
"
R,s#
79
Figure 3.3. Shaded relief map created from 30m NED data with sites of stream captures
or valley beheadings that were identified in this study and in previous studies. Field sites
where infiltration rate and soil shear strength measurements were made are also marked.
Field Site 1 (FS-1) is located at 36.9180 N, 120.8270 W. Field Site 2 (FS-2) is located at
35.9150 N, 120.7670 W.
80
where V2 zR is the ridgetop Laplacian of the slope denoted by the second subscript (nfor
sj). If a ridgeline has responded to base level conditions then RLAnjgcan be used as a
proxy for erosion rate asymmetry. If the slopes on opposing sides of a valley are eroding
at the same rate then RLAnf-f is 0. If the hillslope has completely responded to the base
level lowering rate and RLA nfsf > 0, the south side of the valley (north-facing slope) is
expected to be eroding faster than the north side of the valley (south-facing slope).
In order to estimate V 2 zR,, I bin V 2 z values into 20 bins spaced logarithmically in A 0 3 5S,
calculate the median in each bin, and use the most negative median as V2 zR (Figure 3.6).
I exclude bins with less than 25 data points. I use the binned value with the most negative
median for two reasons. First, the ridgelines of Gabilan Mesa may be still be
experiencing a transient response to the initial incision of the original mesa surface and
may have not fully responded to the base level lowering condition. The most negative bin
should represent the portion of the hillslope that has responded the most, which is
generally on the thinner interfluves or on the portion of the ridgeline furthest from the
main divide but still dominated by soil creep. Second, if lateral channel migration is
occurring at Gabilan Mesa then differences in V2 zR are expected to occur near the
ridgeline and are unrelated to overland flow or channel incision on the hillslope (Chapter
2). I estimate V2 zR within each zone by splitting the valley into north-facing and southfacing regions and estimating
V 2 ZR
separately on the north-facing and south-facing
ridgeline. It is important to isolate the ridgelines for this analysis, so I exclude the valley
bottom by mapping channels with drainage area greater than 10,000 m 2 and also
excluding pixels within a 50 m radius and that are within 5 m of the elevation of the
81
excluded channel pixels. Where significant alluvial deposits exist, I use a similar
technique and exclude all of the sediment in the valley from the analysis.
3.2.3 Ridgetop Laplacian asymmetry
I analyzed ridgetop Laplacian asymmetry in 9 zones at Gabilan Mesa where
high-resolution topographic data derived from LiDAR (gridded to 1 m) are available
(Figure 3.4 and Table 3.1). I chose to analyze zones within the Paso Robles Formation
where north-facing and south-facing tributaries are approximately perpendicular to the
main channels and span at least a few low-order tributaries. I also measured BSAfg
within these zones.
The magnitude ofV2 zR varies significantly at Gabilan Mesa, with some ridgelines
appearing as if they have not responded fully to the base-lowering rates while other
hillslopes appear to have responded. For example, for ridgelines within zone R6, the
north-facing and south-facing ridgetops appear relatively gentle and wide and have a low
magnitude of V 2 z R (-5.95 0.07x10-3 and -4.67 0.03x103, respectively). This hillslope
appears as if it has only partially responded to the boundary lowering rates and still
exhibits relict characteristics of its history as a mesa. For zone R2, the ridgelines have
responded more significantly and the magnitude of V 2 zR is considerably higher on both
the north-facing (-9.72 0.19x 10~3) and south-facing ridgetops (-13.02 0.03 x 10-3).
I measured positive RLAgfgf in all analyzed zones except zone RI and R2, which
exhibit negative RLAfjg(Table 3.1). Bulk slopes are steeper on south-facing slopes than
north-facing slopes in zone RI, while zone R2 exhibits relatively low BSAfg in
comparison to the other zones that I analyzed.
82
Figure 3.4. LiDAR-derived shaded relief map showing ridgetop Laplacian asymmetry
for each analyzed zone. The site name is listed next to each zone. For reference, the
downstream edge of R6 is located at 36.929' N, 120.808' W.
Table 3.1. Estimates of the ridgetop Laplacian and bulk slope asymmetry. Uncertainty is
reported as I standard error of the mean.
Zone
Ri
2
V zR,nf
(X10-
3
i2
R,sf
RLAnjgg
BSAnyff
-0.25 +/- 0.02 / 0.02
-0.51 +/- 0.02 / 0.02
0.35 +/- 0.01 /0.01
2.30 +/- 0.02 /0.02
1.20 +/- 0.02 /0.02
1.15 +/- 0.01 /0.01
0.56 +/- 0.01 /0.01
1.43 +/- 0.01 /0.01
0.86 +/- 0.01 /0.01
1.77 +/- 0.01 /0.01
-1)
(X10-3
0.19
0.13
-8.11
-13.02
-7.68
0.09
0.03
1.41
-7.22
0.18
0.04
-13.29
-5.35
0.08
0.03
-0.42 +/- 0.01 /0.01
1.61 /-0.25 /0.31
0.11 /-0.01 /0.01
0.43 +/- 0.01 /0.01
R6
-5.95
0.07
R7
-11.10
0.09
R8
R9
-12.22
-18.15
0.04
0.11
-4.67
-10.58
-8.71
-10.48
0.03
0.04
0.06
0.03
0.35
0.07
0.49
0.79
-6.82
0.18
-9.72
-23.5
R4
R5
-14.39
R2
R3
83
+/- 0.02
+/- 0.01
+/- 0.01
+/- 0.01
/0.03
/0.01
/0.01
/0.01
3.3. Field measurements
I measured infiltration rates and soil shear strength during a field campaign to
Gabilan Mesa carried out from December 30, 2012 until January 9, 2013. I made
measurements on north-facing and south-facing slopes at two field sites (Figure 3.3).
Gabilan Mesa receives the majority of its annual precipitation in the winter months, but
no significant storms had occurred yet during that winter.
3.3.1.1 Infiltration measurements
To determine if runoff varies on north-facing and south-facing slopes at Gabilan
Mesa, I estimated the field-saturated hydraulic conductivity, Ks, on north-facing and
south-facing slopes at two field sites following established procedures [Reynolds and
Elrick, 1990; Mertens et al., 2002]. Kfs describes the infiltration rate of water due to
gravity under a zero-pressure head. Multiple ponding-depth measurements were made in
order to independently solve for Kf, without needing to explicitly solve for the matrix flux
potential, which describes the infiltration of water due to capillary forces [Reynolds and
Elrick, 1990].
I measured the infiltration rates with a single-ring infiltrometer at two ponding
depths (5 cm and 10 cm). Once I completed the 5 cm ponding depth measurements, I
added water to the infiltrometer to achieve a ponding depth of 10 cm and additional
measurements were made to calculate q,, the field-saturated infiltration rate, at the 10 cm
ponding depth. At each ponding depth, I measured the length of time that was required
for 200 ml of water to infiltrate into the soil repeatedly until infiltration rates were
84
approximately the same for multiple, contiguous measurements.
For each site, the best-fit line to the cumulative infiltration rate for the quasi-steady
infiltration measurements against time was chosen as q. From Reynolds and Elrick
[1990], Kfs can be calculated as
Kf = a H2 - H,
(3.3)
where
G=0.316 (
+0.184
a
(3.4)
is an empirical, dimensionless parameter dependent on d, the depth of insertion of the
infiltrometer, and a, the infiltrometer radius. G describes the 3-dimensional flow
geometry beneath the infiltrometer.
Q, (L 3/T)
and Q2 (L 3/T) are the quasi-steady-state,
saturated flow rates and H1 and H 2 are the depth of ponding from the two infiltration
measurements [Reynolds and Elrick, 1990].
3.3.1.2 Infiltration rate results
My estimates of Ks at Gabilan Mesa range over two orders of magnitude with
higher rates generally on north-facing slopes, especially at FS-2. I measured infiltration
rates at 25 hillslope locations at FS-1. Thirteen of those locations were on the
south-facing side of the valley and 12 were on the north-facing side of the valley. I did
not measure a statistically significant difference in Ks on north-facing and south-facing
sides of the valley at FS-1. Two of the south-facing measurements produced negative
estimates of Ks and are excluded from the analysis. Negative estimates of Ks are nonphysical, but are not uncommon when estimating Ks in the field using two head heights
85
[Elrick and Reynolds, 1992], as I did. Phillips [1985] carried out two numerical
experiments for unsaturated flow and showed that heterogeneities in soil conductivity
with depth or uncertainty in the infiltration rates could lead to negative estimates of K.
Furthermore, increased flow through macropores activated by the increased pressure at
the higher head height may lead to negative estimates of Kfs [Wu et al., 1993; Mertens et
al., 2002].
At FS-2, I measured infiltration rates at 20 sites. I made 11 measurements on the
north-facing side of the valley and 9 measurements on the south-facing side of the valley.
Kfs differs significantly on the north- and south-facing sides of the valley at FS-2. The
mean Kfs on the south-facing side of the valley was 0.5
the north-facing side of the valley was 7.6
0.1 cm/hr while the mean Kfs on
2.1 cm/hr.
Kfs can vary with hillslope gradient [Casanovaet al., 2000], so I regressed Ks
against the local slope gradient (Figure 3.5). I measured the local gradient from National
Elevation Dataset topography gridded to -10 m/pixel at each location where I estimated
Ks. At both FS-I and FS-2, log-transformed Kfs on south- facing slopes exhibited
moderate to low dependence on slope gradient (R2 = 0.14, 0.35 and p-value = 0.14, 0.09,
respectively). At FS-1, the log-transformed K, on north-facing slopes exhibited moderate
dependence on slope gradient (R2 = 0.32, p-value = 0.06) while the log-transformed Ks on
the north-facing slopes at FS-2 did not exhibit dependence on slope gradient (R 2 = 0.005,
p-value = 0.83). If the two outliers with low Kfs are excluded at FS-2, the north-facing
log-transformed Ks at FS-2 does exhibit dependence on gradient (R 2 = 0.44, p-value =
0.05). Outliers are a common result from double-ponded infiltration measurements and
may be caused by an increase of flow through macropores that are activated at deeper
86
ponding-depths due to expansion of the saturated bulb [Wu et al., 1993; Mertens et al.,
2002].
* FS-1 n-facing
o FS-1 s-facing
AA
& FS-2 n-facing
10-
A FS-2
s-facing
FS-2n-fin
n
OA
100
10-
0
0.1
0.2
0.3
0.4
Ivi
0.5
0.6
0.7
0.8
Figure 3.5. K against hillslope gradient. Best-fit lines for the log-transformed K, and
hillslope gradients on the north-facing and south-facing hillslopes at the two field sites.
3.3.2.1 Soil shear strength measurements
At each field site, I made multiple measurements of soil shear strength to
determine if aspect-dependent differences exist in soil shear strength.. I measured shear
strength of the soil surface with a shear vane (Humboldt H-4212MH) at the same
locations where I estimated Kf at FS-1 and FS-2. Zimbone and coworkers [1996] and
Leonard and Richard [2004] used a similar device to measure soil shear strength and
found the measurements to be reasonable indicators of soil shear strength. At each site
87
where I measured the soil shear strength, I made 10 measurements and used the mean as
the representative value for the site. Measurements were made on bare soil and vegetated
soil. For the vegetated soil measurements, I clipped the vegetation down to the surface
before making the measurement to limit the entanglement of the shear vane blades with
above-surface vegetation.
3.3.2.2 Soil shear strength results
At FS-1, the bare soil measurements on the south-facing slope were comparable
to the bare soil measurements on the north-facing slopes (Table 3.2). This is also the case
for the measurements made in vegetated soils. When the south-facing and north-facing
slope measurements are considered together, the vegetated soil exhibited higher soil
strength than the bare soil (p-value: 0.02).
At FS-2, The differences between bare soil and vegetated soil were less
pronounced and not statistically meaningful (p-value: 0.43). However, the vegetated soil
strength measurements on the south-facing slope are significantly higher than the
vegetated soil strength measurements on the north-facing slopes (p-value: 0.002). I also
measured a significant difference in soil shear strength of the bare soils on north-facing
and south-facing slopes (p-value: 0.05). I measured a small dependence on soil strength
with slope gradient for the vegetated shear strength on north-facing slopes (R2 = 0.26, pvalue= 0.015), with slopes with higher gradients exhibiting slightly lower shear strengths.
The south-facing soil shear strength exhibited weak dependence on slope (R 2 = 0.117, pvalue = 0.13). The north-facing and south-facing bare soil shear strength both exhibited
88
weak dependence on slope gradient (R2 = r-squared = 0.1, 0.09, and p-values
=
0.17, 0.2,
respectively).
Table 3.2. Field measurements of field-saturated hydraulic conductivity and soil
shear strength. Uncertainties are reported as 1 standard error of the mean.
BSAnf-sf
Ks (cm/hr)
2
Soil shear strength (kg/cm
Solsertenh(k C2
Vegetated soil
Bare soil
)
Field site
FS-1
south-facing
north-facing
0.69
0.69
0.03
0.03
2.6
2.7
1.2 (11)
0.5 (12)
0.13
0.14
0.01 (12)
0.02 (11)
0.17
0.17
FS-2
south-facing
north-facing
2.01
2.01
0.10
0.10
0.5 0.1 (9)
7.6 2.1 (11)
0.16
0.09
0.03 (9)
0.01 (9)
0.18 0.02 (9)
0.11 0.01 (11)
0.01 (12)
0.02 (12)
3.4 Cosmogenic radionuclide-derived erosion rates
I determine cosmogenic radionuclide-derived erosion rates at Gabilan Mesa in
order to test the predictions made in Chapter 2 by the landscape evolution models that
incorporate different asymmetry-forming mechanisms.
3.4.1 Cosmogenic radionuclide methods
Analyses of cosmogenic radionuclides (CRNs) have been used successfully at
many sites around the world to determine long-term denudation rates for landscapes
[Hancock et al., 1999; Balco and Stone, 2005; Ferrieret al., 2005]. I used CRNs to
estimate erosion rates from (1) catchment-averaged sediment samples collected from
small, fluvially deposited fans at the mouths of hollows [Grangerand Kirchner, 1996]
[Bierman, 1996], and (2) from bedrock samples collected at or just below the soil89
bedrock contact [Heimsath et al., 1997; DiBiase et al., 2010]. The samples were
processed and analyzed at the Purdue Rare Isotope Laboratory (PRIME Lab) following
the methods developed at PRIME lab for '0 Be processing [Clifton et al., 2005].
I collected two samples in March 2010 and 23 samples in December 2013. For the
two samples collected in 2010, I collected quartz pebbles from fluvial fans, which I
crushed and processed at PRIME Lab for accelerator mass spectrometry (AMS) analysis.
During the 2013 trip, I collected sediment from fans and hollows at 20 sites. Ten of those
sites were from small south-facing catchments while the other 10 were from small northfacing catchments. I also collected bedrock samples at three of the sites-two on northfacing slopes and one from a south-facing slope. Pebbles and sediment less than 2 mm in
diameter were crushed and recombined for AMS analysis.
For the catchment-averaged samples, I used 10 m NED data to calculate a basinaveraged shielding value. For the depth samples, I calculated the shielding factor at the
location where the sample was collected. I used the basin-averaged coordinates and
elevation to calculate the soil production rate. For the depth samples, I used the
coordinates and elevation to calculate the soil production rate and used the slope-normal
depth of the sample to calculate the depth-corrected production rate.
Due to the young age of the Paso Robles formation, it is necessary to account for
the inherited
10 Be
concentration, N,,h,, from previous exposure of the sediment. The
concentration of 1 0Be in previously-buried sediment that was recently exposed at the
surface along road cuts has been determined [Perron,2006] and is used to constrain N,.
The total concentration is N,,
=
N,,, + N,.e where N,0, is the total 10Be concentration
measured with an accelerator mass spectrometer and Nrec is the
90
10 Be
concentration due to
recent exposure of the rock to cosmic rays. I measured N, and used it to estimate N
.
I
used the CRONUS calculator to solve for the long-term denudation rates [Balco et al.,
2008].
3.4.2 Erosion rate asymmetry metric
I measured the asymmetry in erosion rates by comparing the paired erosion rates
for low-order basins that directly oppose one another on north-facing and south-facing
slopes. I define the erosion rate asymmetry as
ERAf
S
= log2
(3.5)
Where E is the erosion rate of the slope denoted by the subscript. I use ERAnf-fto
describe the difference in the erosion rates at Gabilan Mesa and I test the values against
the LEM predictions.
3.4.2 Erosion rate results
Catchment-averaged bedrock erosion rates on south-facing slopes range from
46 5 m/Myrs to 87 12 m/Myrs while catchment-averaged bedrock erosion rates on
north-facing slopes exhibit a wider range from 42 4 m/Myrs to 266 110 m/Myrs. I
report the inheritance-corrected erosion rates and uncorrected erosion rates in Appendix
1.
91
a)
0
2.5 I- o
2
Field Evidence of LCM
No field evidence of LCM
-<
1.5
1
0.5 I
0
-0.5 F
-1.5
'
-1
0.5
1
1.5
BSA/f
2
2.5
Figure 3.6. (a) Erosion rate asymmetry against bulk slope asymmetry for sites shown in (b)
at Gabilan Mesa. Uncertainty bars show 1 standard error of the mean. (b) Hillshade created
from -10 m NED data showing sites where samples were collected for CRN analysis. Sites 3
and 9 exhibit evidence of lateral channel migration (LCM). The black circles mark the
sample locations. Topography along the A-A 'transect is analyzed in section 3.5.4. For
reference, the end of the transect at A is located at 35.930' N, 120.7890 W.
92
Two samples that I collected at the bedrock-soil interface are from north-facing
slopes (GAB13023 and GAB13024) and had low concentrations of 10Be. Their
concentrations of 10Be are similar to a sample that was recently exposed along a road cut
that has not experienced modern exposure and production of 10Be [Perronet al., 2012].
Applying an inheritance correction to GAB 13023 and GAB 13024 is difficult because a
large uncertainty is introduced due to the low
10 Be
concentrations of the samples and the
high uncertainty in the inherited concentration that I estimate from the deeply buried
samples. The other sample collected at the bedrock-soil interface (GAB 13022) was from
a south-facing slope and the erosion rate at that location (53 7 m/Myrs) was comparable
to the catchment-averaged erosion rate for the basin (63 6 m/Myrs). I exclude them
from the analysis.
In three of the valleys (sites 2, 8, 9 in Figure 3.6a), north-facing slopes erode
faster than south-facing slopes. In two other valleys (sites 3, 5 in Figure 3.6a), the southfacing side of the valley erodes faster. For the other five erosion rate pairs, the erosion
rates on the north-facing and south-facing sides are comparable.
In Figure 3.6a, I plot erosion rate asymmetry against bulk slope asymmetry. There
is no clear trend between them at Gabilan Mesa. Valleys with low BSAfg (~0.5 to 1)
exhibit insignificant differences in erosion rates on north-facing and south-facing slopes.
Valleys with higher BSAnfg1 exhibit a much larger range in erosion rate asymmetry. The
two sites that exhibit physical evidence of lateral channel migration both have higher
north-facing erosion rates relative to south-facing slopes. In addition, site 8 (Figure 3.6b)
also has high erosion rate asymmetry, with the north-facing catchment eroding
considerably faster (161 43 m/Myrs) than the south-facing catchment (55+6 m/Myrs). At
93
site 5, which has the highest BSAnf.f of the sites where I estimated erosion rates, the
south-facing catchment erodes faster (77 11 m/Myrs) than the north-facing catchment
(42 4 m/Myrs).
3.5. Landscape evolution model
As in Chapter 2, I modified a simple LEM to include asymmetry-forming
mechanisms. Here I briefly summarize the model framework from Chapter 2.2. The
general form of the governing equation is
az
DV 2z+ E
A"m jVz" s OC(36
-
--
A' 1 Vz
t at DV z K l +EK
Vz"+ E A' Vz >6
2
2V Z
(3.6)
where z is elevation, D is soil transport efficiency, K is the fluvial incision coefficient
[Perronet al., 2008], A is drainage area, 0, is the fluvial incision threshold, and E is the
uplift rate or boundary lowering rate [Howard, 1994; Perronet al., 2008]. I assume that
the channel incision rates scale with the bed shear stress and not the excess shear stress.
The shear stress threshold (K6c) is often subtracted from the shear stress term
(KA" Vz l), but there is a lack of field evidence in support of either approach for small
drainages. By not subtracting shear stress, the calibration of the model with Oc > 0 is
significantly simplified. I discuss the calibration of the fluvial incision threshold in
section 2.2.
94
3.5.1 Aspect-dependent LEMs
Following the same procedure as in section 2.2.2, I adapted the governing
equation in order to model either differences in regolith strength or differences in runoff.
Differences in vegetation and microclimates on south-facing and north-facing slopes at
Gabilan Mesa may lead to differences in regolith strength. Increased vegetation density
on the north-facing slopes may lead to an increase in regolith strength and make initial
gullying more difficult relative to the south-facing hillslopes. The vegetation and
microclimatic differences may also influence infiltration rates and runoff rates when
precipitation exceeds the infiltration capacity.
I incorporated a weighting function into the governing equation to account for
aspect dependence of regolith strength and runoff. The weighting function is of the form
(16(cos(#b)
((co
6
1+
CO=
1-61
o
s(
s(#)
cos(ridge)
where
-
-
# is the angle between the surface
1
1
cos(#)
cosr(,,dg,)
(3.7)
cos(#) <cos(n,,)
g'
normal and the sun,
qSdge
is the slope-normal
vector of the ridgeline (always 900 from horizontal) and 6 is the magnitude of the
weighting function. If 6 > 0, o is higher on the south-facing slope. If 6 < 0, w is higher on
the north-facing slope. Increasing the magnitude of 6 causes larger differences in w on
opposing slopes. I parameterize the sun altitude angle for Gabilan Mesa and use 700,
95
which is the angle that minimizes the variance between cos() and the annually averaged
solar radiation.
I included aspect-dependent regolith strength in the LEM by weighting 0, by w.
This changes the value of A Vz required for incision to start on the landscape. I
incorporated aspect-dependent runoff into the LEM by weighting A by w. This
effectively changes the relationship between runoff and drainage area and mimics an
aspect-dependent infiltration rate. Also, by weighting A instead of modifying K, I allow
for non-local effects since A represents the upslope area that drains to a point on the
landscape.
3.5.2 Lateral channel migration
Following the same approach as in section 2.2.3, I model lateral channel
migration by adding a linear advection term that shifts the landscape in the y-direction
towards the positive y-boundary, which represents a bounding stream. This effectively
mimics a migrating channel undercutting the base of a hillslope. The modified form of
the governing equation is
DV 2 z+E-y az
A'" Vz
az _ay
at
DV 2z - KA'" Vz" +E-y az A'" Vz" >0
ay
where y (L T-) is the lateral channel migration rate. I used a fixed lateral channel
migration rate for the modeling experiments. In natural landscapes, lateral channel
96
(3.
(3.8)
migration may be driven by initial tilt, differences in initial slope morphology, or
microclimates. In this scenario, I assume that the necessary mechanisms for driving
lateral channel migration are active, but I do not explicitly model them.
3.5.3 Model parameterization
I calibrated the model from the same section of topography as Perron and
coworkers [2009] and used their estimate of K and m. I assume n =1. I recalibrated D
using a slightly modified technique and also estimate O. Previous numerical models
Table 1. LEM model parameters
(M2
yr-')
0.0138
K (MI-2, yr-1)
m
n
E (in yr-)
Oc
1.x10~ 4
0.35
1
1.47x10~4
1
(mi
7
)
D
of Gabilan Mesa did not include a fluvial incision threshold [Perronet al., 2009; 2012]. I
calibrated the model for a non-zero fluvial incision threshold. I did this for two reasons.
First, it allows me to test if aspect-dependent differences in regolith strength, which can
be described by introducing aspect dependence to O, can explain the asymmetry at
Gabilan Mesa. Second, it allows me to better reproduce the Laplacian near the ridgetop.
If Oc = 0, overland flow will influence the Laplacian near the ridgetop. Here, I impose a
fluvial incision threshold so that overland flow does not contribute to erosion near the
ridgeline, which is supported by topographic evidence [Perronet al., 2009].
Past efforts have generally involved estimating 0, from field measurement or by
calculating best-fit values of 0, for detachment-limited stream incision and channel
97
profiles [Snyder et al., 2003]. These approaches work well for estimating bedrock river
incision thresholds, but here I focus on estimating the threshold that influences the
transition from a ridgetop dominated by soil creep to 1 s-order valleys that experience
episodic incision and fill from colluvium. I estimate 0, by calibrating the other parameters
in the LEM and then choosing a 0, that best reproduces the transition from a constant
Laplacian at low A 0.35 VzI to a spatially variable Laplacian that is influenced by overland
flow and channel incision (Figure 3.7).
-
0.12
-
0.1
0.08
0.06
-
0.04
-0.02
-
-
0.02
-0.04
102
100
10-'
035
A
1VZ
101
(M 0 7
)
10-3
Figure 3.7. Changes in the Laplacian with increasing drainage area and slope. Grey points show
LiDAR-derived data from Gabilan Mesa near site 10 in Figure 3.6b. For clarity, I only show a
random subsample of 25% of the raw data. Green circles show the binned means of the logtransformed data. Crosses show the binned means of the log-transformed data for the calibrated
model.
98
3.5.4 Consideration of tilted initial topography
The background tilt at Gabilan Mesa influences the orientations of the major
tributaries that drain into the Salinas River. The headwaters of the large drainages are
located to the northeast with basin outlets to the southwest. Previous geomorphologists
have excluded tilt as a possible explanation for the topographic asymmetry at Gabilan
Mesa because the orientation of the asymmetry is generally perpendicular to the main
drainages and therefore to the dominant direction of tilt [Reed, 1927; Kane, 1970;
Dohrenwend, 1978].
Nonetheless, I investigated the role of tilt because a background slope is present
for some of the asymmetric hillslopes at Gabilan Mesa. I measured a background slope
from the northwest to the southeast of 0.60-0.65' across a series of highly asymmetric
neighboring basins (Figure 3.6b and 3.8c). To explore the role that the background slope
of the land surface may have on the development of topographic asymmetry, I ran a
series of LEMs calibrated to Gabilan Mesa with a background slope that varied from 0.5'
to 5' (Figure 3.8a) and analyzed the developing topography throughout the evolution of
the model run. The models with the lowest background slopes developed the highest
initial BSAnff. This somewhat counterintuitive result occurred because hillslopes with
higher initial background slopes developed lower relief on the north-facing slope, which
led to relatively low bulk slope gradient on the north-facing slope and therefore low bulk
slope asymmetry.
Figure 3.8b shows the evolution of a model landscape calibrated to the
topography at Gabilan Mesa with the mean background slope and width (890 m) of the
valleys in transect A-A ' (Figure 3.8c). Even though this tilting scenario is capable of
99
initially producing a high degree of topographic asymmetry, the asymmetry is not
maintained throughout the model run. Initially, the north-facing slope erodes faster than
the south-facing slope, causing the main divide to migrate southward until erosional
equilibrium is reached. Once this occurs, typically in less than 1 Myr, the hillslope
exhibits insignificant asymmetry.
a)
2
1.5
Myrs
I
b)
Initial tilt
0.50
10
20
30
40
50
3
0.8
2
0.6
0.4
0
0.5
0.2
0
0
I
0
1
0.1
1.5
2
0
BSA'
Time (Myrs)
c)
Transect
-
400 r
0
1
0.5
-
-
-
-
-
-
Background slope (valley)
Background slope (ridgeline)
350
A'
300
0
1000
3000
2000
4000
5000
Distance along transect (m)
Figure 3.8. (a) Evolution of topographic asymmetry (measured as bulk slope asymmetry)
from 0.1 Myr to 1 Myr for hillslopes with different degrees of initial tilting. (b) Transient
results for a model calibrated from Gabilan Mesa topography and an initial background
tilt that is estimated from transect A-A'. The model topography is initially asymmetric,
but decreases through the model progression. (c) Elevation profile across transect A-A'
shown in Figure 3.5b.
100
3.5.5 Landscape evolution modeling of aspect-dependent process efficiency
I use LEMs that include aspect-dependent runoff and aspect-dependent regolith
strength to explore the transient development of topographic asymmetry. I use the
modern erosion rates and relief measured at Gabilan Mesa to estimate a minimum
amount of time that Gabilan Mesa has been incising and to begin my transient analysis.
The mean bedrock erosion rate for Gabilan Mesa is 78
error of mean) and the mean relief is 80
12 m/Myr (mean
standard
5 m (mean : standard error of mean) for the
zones with erosion rate pairs. If the long-term mean erosion rate is less than twice the
modern erosion rate, then it would require ~0.5 Myr to produce the mean modem relief at
Gabilan Mesa. I analyzed the transient model results from 0.5 Myr to 3 Myr, which is the
maximum time that is generally required for the modeled hillslopes to reach either
steady-state topography in the case of the aspect-dependent LEMs or a steady form for
the lateral channel migration LEM. I ran models with widths of 545 m, 1020 m, and 1860
m, which are the minimum, mean and maximum widths of the valleys in which the
erosion rate pairs were estimated.
I varied 6 in equation (3.7) to reproduce the range of topographic asymmetry that
I measured at Gabilan Mesa. For the LEMs with aspect-dependent runoff and aspectdependent regolith strength, the south-facing slope erodes faster than the north-facing
slope while the hillslope is responding transiently to the different erosional efficiencies.
Eventually, the ridgeline is offset enough that the steeper north-facing slope is able to
match the more efficiently eroding south-facing slope. The aspect-dependent regolith
strength and aspect-dependent runoff LEM produce model results that generally cannot
be distinguished by the relationship between ERAf.g and BSAfnff (Figure 3.8).
101
The aspect-dependent runoff LEM required large differences in the mean co on
north-facing and south-facing slopes to produce the degree of asymmetry at Gabilan
Mesa. A ratio of the mean co on north-facing to south-facing slopes of-30 was required
to reproduce the mean BSAgfgf (1.6) for a hillslope with the mean width (1020 m) of the
zones where erosion rates were estimated. A ratio of the mean (o on the north-facing to
the south-facing slopes of -200 was required to reproduce the maximum amount of
BSAgfgf (2.4) measured at Gabilan Mesa. According to the numerical modeling
.
.o
2.5
2
S a
-U...
1.5
Ib
OV
UL
DRO LEM
A A DRS LEM
CM LEM
A G EM with
ackground slope
Hbilan Mesa (field
ev idence of LCM)
G abilan Mesa (no field
ev idence of LCM)
*U
N
1
*U.
0.5
-."
0
*AA
-0.5
A
0
*.
0i
0.5
A
A
A 00
A
A
4.A
1
*AO
1.5
40
*A
*
-11
0
06
D
AA
2
2.5
BSA
Figure 3.8. Comparison of CRN-derived erosion rate asymmetry results with the results
for the aspect-dependent runoff (ADRO) LEM, aspect-dependent regolith strength
(ADRS) LEM, and the lateral channel migration (LCM) LEM, and the results from the
modeling experiment with background slope. All models are calibrated for Gabilan Mesa.
The orange background color shows the general region for the lateral channel migration
LEM results. The blue background shows the general region for the combination of the
aspect-dependent runoff and the aspect-dependent regolith strength LEM.
102
experiments in Chapter 2, the required difference to produce the same degree of BSAf1 gf
should decrease slightly as hillslope width increases.
The aspect-dependent regolith strength LEM required a considerably smaller
difference in o on the north-facing and south-facing slopes to achieve the same degree of
asymmetry. In order to produce the proper sign of asymmetry as Gabilan Mesa, soil
strength must increase on north-facing slopes, leading to a decrease in fluvial incision,
relative to the south-facing slopes. The aspect-dependent regolith strength LEM required
a ratio of mean w on north-facing to south-facing slopes of -5. The aspect-dependent
regolith strength LEM required a ratio of the mean o on north-facing to south-facing
slope of -10 to reproduce the maximum degree of asymmetry measured at Gabilan Mesa.
This suggests that the wider basins at Gabilan Mesa may require smaller differences in co
on north-facing and south-facing slopes to produce the same degree of BSA, 1f-f relative to
narrower basins.
3.5.6 Landscape evolution modeling of lateral channel migration
For the lateral channel migration LEM, I varied the lateral channel migration rate
to reproduce the range of topographic asymmetry that I measured at Gabilan Mesa.
Similar to the aspect-dependent LEM experiments, I also analyzed the transient results
and compared the asymmetry that develops between 0.5 Myr and 3 Myr. Both the
transient and the steady-state results predict that north-facing slopes erode faster than
south-facing slopes (Figure 3.9). Lateral channel migration rates of -600 m/Myr were
necessary to produce BSAffgof 1.6 and lateral channel migration rates of -750 m/Myr
were required to produce BSAfjgof 2.4. The rate of lateral channel migration required for
103
asymmetry to develop is strongly dependent on the Migration number (Chapter 2). If K is
lower than the estimate made by Perron and coworkers [2012], a slower rate of lateral
channel migration would be required to reproduce the same degree of asymmetry.
3.5.7 Comparison of LEM predictions and erosion rates
The transient modeling results of a hillslope that formed on an initially tilted
surface produced a similar trend between BSAnfjgand ERAngff as the steady-state results
created from the lateral channel migration LEM (Figure 3.9). These trends differed
significantly from the results of the aspect-dependent LEMs. The steady-state results
created from the aspect-dependent LEMs produced no trend between BSAnfjgand ERAnf-f,
and produced negative ERAnfjg while the models were transiently responding (Figure
3.8).
Two of the ERAfpsgvalues from Gabilan Mesa overlap with the lateral channel
migration LEM results within 1 standard error while not overlapping with the results
from the aspect-dependent runoff or aspect-dependent regolith strength LEMs (Figure
3.9). Of the two, one of the basins (Site 2) is directly downstream from a southward river
capture in Portuguese Valley. Six of the ERAnfsf values made at Gabilan Mesa overlap
uniquely within 1 standard error with the results of the aspect-dependent runoff LEM and
aspect-dependent regolith strength LEM (Figure 3.9). One of the ERAnggvalues (Site 9)
does not overlap with either model and occurs in Powell Valley, which exhibits physical
evidence of lateral channel migration.
104
3.6. Discussion
Numerical modeling suggests that even a small degree of initial tilt can lead to the
development of significant topographic asymmetry for young landscapes. The amount of
time that Gabilan Mesa has been incising is not well constrained and I cannot completely
rule out the initial influence of tilt on the development of topographic asymmetry,
especially where a background tilt is present. Two of the most asymmetric zones that I
analyzed (Sites 5 and 9, Fig. 3.6b) have the orientation expected if tilting is responsible
for the asymmetry. In addition, a transect across several of the other highly asymmetric
basins also exhibits a background slope (Figure 3.8). However, the erosion rate signature
does not match the expected signature if tilt is solely responsible for the topographic
asymmetry (Figure 3.9), making it unlikely that initial tilting of the landscape is the sole
driver of the asymmetry.
It is important to consider the transient development of topographic asymmetry in
landscapes that have not reached a steady form because the topographic signatures,
especially in erosion rate asymmetry, are different than the signatures that develop at
steady state. The relationship between BSAgfgf and ERAfpj for the aspect-dependent
runoff LEM and the aspect-dependent regolith strength LEM is consistent with 7 of the
10 measured sites at Gabilan Mesa (Figure 3.9), whereas the relationship between BSAgfg
and ERAflf for the lateral channel migration model only matches 3 of the 10 values
(Figure 3.9). Considering that the results of the aspect-dependent LEMs are a better
match at most of the sites, I conclude that lateral channel migration is likely not the
dominant mechanism causing the topographic asymmetry at Gabilan Mesa.
105
If a discrepancy in soil shear strength is responsible for the valley asymmetry at
Gabilan Mesa, then soil shear strength should be higher on north-facing hillslopes. I find
no difference in soil shear strength at Field Site 1; while I find that the south-facing
slopes at Field Site 2 exhibit higher soil shear strength, not the north-facing slopes. These
findings are not consistent with the hypothesis that soil shear strength controls the
topographic asymmetry at Gabilan Mesa.
Measurements of field-saturated hydraulic conductivity suggest that significant
differences in infiltration rates exist in asymmetric basins. At Field Site 2, Kf, is -15
times higher on the north-facing slope in comparison to the south-facing slope. In order
to reproduce the mean BSAnf-s that I measured at Gabilan Mesa for the sites where I made
erosion rates, the aspect-dependent runoff model required that the drainage area be
weighted so that w is -30 times higher on the south-facing slope relative to the northfacing slope. The differences in Kfs measured in the field cannot be directly compared
with the differences in co required in the model because Ks describes the infiltration rate
while the numerical model addresses runoff. Kfs of the north-facing slope is sufficiently
high (7.6 2.1 cm/hr) that few storms may be intense enough to exceed the infiltration
capacity and cause overland flow. K, of the south-facing slope is considerably lower (0.5
0.1 cm/hr), and therefore this slope may experience runoff much more frequently. This
threshold effect associated with the magnitude of storms and the recurrence interval of
erosive events could lead to an effective difference in runoff on north-facing and southfacing slopes that is much greater than expected if considering infiltration rates alone.
This suite of observations suggests that aspect-dependent runoff production is the
most likely mechanism that consistently contributes to the asymmetry at Gabilan Mesa.
106
However, the model requires extreme differences in runoff on north-facing and southfacing slopes to replicate the most asymmetric slopes seen at Gabilan Mesa, which
suggests that aspect-dependent runoff is probably not exclusively responsible for all of
the topographic asymmetry, especially in the most asymmetric basins. Evidence of lateral
channel migration, the presence of a background slope, or both, is apparent at each of the
most asymmetric sites at Gabilan Mesa, suggesting that the asymmetry may be
polygenetic at some locations.
Of the three sites where the aspect-dependent efficiency models are not able to
match the relationship between BSAgfgf and ERA fs,, physical evidence of lateral channel
migration exists at two. At the other site, the absence of physical evidence such as stream
capture or the presence of beheaded valleys does not preclude the possibility that lateral
channel migration is also happening at that location.
Even though lateral channel migration is probably not the dominant cause of
asymmetry at Gabilan Mesa, the occurrence of stream captures and beheaded valleys
suggests that the drainage network at Gabilan Mesa is experiencing significant
reorganization. Furthermore, spatial variability in erosion rates for nearby sites in
Portuguese Valley suggests that lateral channel migration occurs episodically. Pulses of
lateral channel migration may cause oversteepening to occur more rapidly than it occurs
in the model and might require less overall undercutting than the long-term rate that I
reported.
I excluded aspect-dependent soil creep as a possible asymmetry-forming
mechanism because predictions of the asymmetry signatures (Chapter 2) do not match
well with the predictions at Gabilan Mesa. In order to match the BSAgfgf at Gabilan Mesa,
107
the south-facing slope must experience much higher soil creep rates than the north-facing
slope. Drastically increasing soil creep rates on the south-facing slopes leads to complete
infilling and eradication of valleys. At Gabilan Mesa, the south-facing slopes are deeply
incised. Thus, the model predictions of topography for aspect-dependent soil creep do not
match the topographic characteristics at Gabilan Mesa.
Ridgetop Laplacians vary at Gabilan Mesa, and many of the valleys exhibit
ridgetop Laplacian asymmetry on opposing sides of the valley. There are two possible
factors that may contribute to the RLAgfgf that I measured. One possibility is that lateral
channel migration is causing an increase in the erosion rate on the north-facing slope.
Another possible explanation is that the RLAgfgf is an artifact of the transient topography.
Considering the very low estimates of V 2 zR at some locations and the relict mesa surface
visible in some parts of the landscape, I suggest that much of the asymmetry of ridgetop
Laplacians at Gabilan Mesa is due to the transient response of the ridgeline and does not
reflect lateral channel migration.
There are multiple possible explanations for why the north-facing slopes have
higher Kfs than south-facing slopes. In a compilation study, Ludwig and coworkers [2005]
concluded that in semi-arid environments, vegetation patches often retain more water and
have higher infiltration rates and higher biomass production, which may contribute to the
higher estimates of Kfs on north-facing slopes. In addition to the direct microclimatic
effects, steeper north-facing slopes, which likely experience higher sediment flux locally,
may experience increased soil mixing and maintain more pore space than shallower
slopes that experience lower sediment flux. Thus, infiltration rates could also be
influenced by shallower soil depth on south-facing slopes. I measured shallower soils on
108
the south-facing slopes (Appendix 1), and Reed [1927] observed that bedrock outcrops
generally occur on south-facing slopes rather than north-facing slopes, indicating that
south-facing slopes generally have thinner soils.
3.7. Conclusions
Due to the high degree of topographic asymmetry, Gabilan Mesa is an ideal field
site to test which asymmetry-forming mechanisms are responsible for the development of
topographic asymmetry in semi-arid environments. I tested numerous asymmetryforming mechanisms including aspect-dependent runoff, aspect-dependent regolith
strength, and lateral channel migration. I also investigated the role that initial tiling of the
mesa may have had on the development of the topographic asymmetry. I compared
topographic and erosion rate signatures predicted from the different models with
measurements from Gabilan Mesa. The aspect-dependent runoff and aspect-dependent
regolith strength LEMs are best at reproducing the relationship between topographic
asymmetry and erosion rate asymmetry at Gabilan Mesa.
In order for aspect-dependent soil shear strength to explain the asymmetry at
Gabilan, north-facing slopes should have higher soil shear strength. Field measurements
of soil shear strength do not support higher soil shear strength on the north-facing slope
and actually show that soil shear strength is higher on south-facing slopes at one of the
two sites. Field measurements do show that large differences in field-saturated hydraulic
conductivity exist at Gabilan and that field-saturated hydraulic conductivity is higher by a
factor of ~15 on north-facing slopes. This is consistent with the expectation if aspectdependent runoff is responsible for the asymmetry at Gabilan Mesa. Evidence of stream
109
captures and beheaded valleys is likely to exist in valleys that experience lateral channel
migration. I identified new locations of stream captures and beheaded valleys, but they
are not present in most of the asymmetric valleys.
The aspect-dependent model predicts that differences in aspect-dependent runoff
must be very large if aspect-dependent runoff is solely responsible for the asymmetry at
Gabilan Mesa. For the most asymmetric basins, additional asymmetry-forming
mechanisms may also be present. Many of the most asymmetric basins at Gabilan Mesa
have a background slope, suggesting that initial tilting of the mesa may have influenced
the development of the drainage basins and caused high topographic asymmetry to
develop without the aid of microclimates. Asymmetry due to tilting is short lived (< 1
Myr), but due to the poor age constraints on the history of Gabilan Mesa, it is not
possible to completely rule out the influence of tilting in some valleys. When all of the
evidence is taken together, it seems likely that multiple mechanisms are acting together to
produce the high asymmetry witnessed in some of the basins at Gabilan Mesa, but that
aspect-dependent runoff is dominantly responsible for the bulk of the asymmetry. This
analysis suggests that lateral channel migration should be carefully reconsidered as a
general asymmetry-forming mechanism in semi-arid environments.
Acknowledgements
I would like to thank David DeJong for help building the infiltrometer, Peter
Polivka and Michael Sori for helping with field work, and Scott Miller for help in the
field and insightful discussions about topographic asymmetry. I would also like to
110
acknowledge support from the US National Science Foundation Geomorphology and
Land Use Dynamics program through award EAR-0951672 to Taylor Perron.
111
112
Chapter 4. The influence of climate on hillslope sediment
transport efficiency
113
Abstract
Hillslopes compose the majority of Earth's land surface and are responsible for the bulk
of sediment produced and delivered to the oceans, lakes and seas. The efficiency at which
material can be transported from a hillslope to a channel plays a major role in the
sediment budget of rivers. Therefore, understanding hillslope soil transport efficiency is
important for both reconstructing past sediment budgets and also for understanding how
sediment flux rates may change under different climate conditions. Estimates of soil
transport efficiency, which is often described by a soil transport coefficient, or diffusivity
(D), have been made for many sites globally. I compile previous estimates of D and also
make new estimates at sites where erosion rates have been measured and high-resolution
topographic data are available. Estimates of D vary over 3 orders of magnitude. For the
logarithmically-transformed data, D exhibits a power-law relationship with a slope less
than one with mean annual precipitation and the aridity index, which describes the
moisture available to plants. I compare how D varies with the type of vegetation present
at the site and find that, not surprisingly, D is lowest for arid sites. However, for sites that
exhibit low mean annual precipitation (5 to 25 cm), sites described as desert have
significantly lower estimates of D (17 5 cm 2/yr) than sites described as
grasslands/scrublands (52 5 cm 2 /yr) or as savannah/lightly forested (70 20 cm 2 /yr). For
moderate to high values of mean annual precipitation (50 cm to 150 cm), there is no
difference in D for sites categorized as either grasslands/scrublands, savannah/lightly
forested, or forested. I also find differences in D for sites with different lithology and
where different techniques were used to estimate D. Estimates of D made in
unconsolidated sediments are higher than estimates made for igneous/metamorphic rocks.
This may be due to a bias introduced by the technique that was used to estimate D. Of my
compiled estimates, 23 of the 33 estimates of D made in unconsolidated sediments are
based on models of scarp diffusion. I find that estimates of D made with the scarp
modeling technique are generally lower than the estimates made with other techniques.
Even with the confounding influences of lithology and measurement technique, the
compilation reveals an overall trend in which D increases rapidly with increasing
moisture among relatively dry sites and less rapidly with increasing moisture at relatively
wet sites. This trend suggests that the establishment of life in a landscape substantially
accelerates soil creep, whereas differences in biological communities associated with
different degrees of moisture have a relatively small effect on creep.
114
4.1. Introduction
4.1.1 Motivation
Hillslopes are responsible for producing the vast majority of sediment that is
transported by rivers to the ocean. The rate at which sediment is fluxed into streams and
rivers plays a pivotal role in influencing a myriad of ecological conditions from the
quality of salmon spawning streams [Platts et al., 1989] to the health of marine estuaries
[Wolanski et al., 2004]. Fernandes and Dietrich [1997] suggested that the long response
time of hillslopes makes it unlikely that hillslopes have reached a spatial or temporal
erosional equilibrium during the Quaternary due to fluctuations in climate between
glacial and interglacial periods. Therefore, it is likely that hillslopes have constantly
modified their form during this period and have experienced different sediment flux rates
under different climate conditions. Numerous studies point towards climate and
vegetation influencing sediment transport rates [Fernandesand Dietrich, 1997; Roering,
2004; Hughes et al., 2009; Hurst et al., 2013a; McGuire et al., 2014], but the relationship
is not well understood.
Hillslope sediment flux rates, which are dominantly controlled by hillslope
gradient and disturbance mechanisms that influence sediment transport efficiency, are
challenging to estimate, and estimates generally require site-specific information such as
topographic data in conjunction with field measurements [e.g., Almond et al., 2008;
Jungers et al., 2009], estimates of erosion rates [Perronet al., 2012; Hurst et al., 2013a],
or knowledge of how and when a landform developed [e.g., Colman and Watson, 1983;
McGuire et al., 2014].
115
Culling [1963] developed a mathematical framework to describe how sediment
flux rates relate to landscape topography and influence the form of hillslopes.
Geomorphologists subsequently developed techniques for estimating sediment transport
rates from landscape characteristics and estimates of soil transport efficiency that could
be applied to specific regions [Nash, 1980a; 1980b; Colman and Watson, 1983]. Nash
[1984] suggested that if hillslope characteristics were known, such as the topography,
local climate, hillslope aspect, and the properties of the material being transported, then
sediment transport efficiency, and by extension sediment transport rates, could be
accurately estimated for a site without the need of any additional measurements.
Estimating sediment transport efficiency has proven more difficult. Numerous studies
have been carried out to estimate hillslope sediment transport efficiency since that
prediction, but a simple relationship between hillslope sediment transport efficiency and
hillslope characteristics has not been established. Instead, studies have suggested more
complicated relationships between hillslope sediment transport efficiency, climate,
erosion rates and landscape characteristics [e.g, Hughes et al., 2009; Hurst et al., 2013a]
4.1.2 Background
Hillslope sediment transport efficiency is influenced by myriad factors including
the occurrences of freeze thaw cycles [Anderson et al., 2012], burrowing of mammals
[Thomas and Montgomery, 1991; Gabet, 2000; Yoo et al., 2005], tree throw [Roering et
al., 2010], and fire frequency [Pierce et al., 2004; Roering and Gerber, 2005]. Soil
transport efficiency is often described by a soil transport coefficient (D), a diffusivity-like
116
parameter relating hillslope sediment flux (L 2 T-1) with slope gradient [Culling, 1963], so
that
q, = -DVz
(4.1)
where q, is the sediment flux rate and z is elevation of the land surface. When
incorporated into a conservation of mass framework, a governing equation for the
evolution of hillslope elevation can be derived of the form
p, az-DV2Z
p,
at
(4.2)
Where t is time, U is bedrock uplift rate, pr is bedrock density, and ps is soil density. If the
landscape is in topographic steady state, then
D=
-P
--
(4.3)
p,. V2Z
There is some empirical support for equation (4.1) [McKean et al., 1993], equation (4.2)
and equation (4.3) [Perron et al., 2012; Hurst et al., 2013b]. Modification of equation
(4.1) to include soil depth dependence [Heimsath et al., 2005; West et al., 2014] or
nonlinear dependence on slope gradient [Roering et al., 1999] also has empirical and
theoretical [Furbishet al., 2009] support for some locations.
117
Geomorphologists have noticed that D increases as climate becomes less arid
[e.g., Hanks et al., 1984b; Fernandes and Dietrich, 1997; Hurst et al., 2013a]. Hanks
[1984] observed that sites with low precipitation, such as shorelines of Lake Bonneville,
UT, have low estimates of D while sites with moderate to high precipitation exhibit
higher values. Hanks also noted that the estimated value of D for a poorly-consolidated,
wave-cut bluff in Emmet County, MI is similar to the value estimated for the Santa Cruz
sea cliffs, CA and the Raymond fault [Nash, 1980] in Pasadena, CA even though the
bluff in Emmet County receives higher precipitation. Hanks [1984] suggested that the
higher vegetation cover may offset the effects of high precipitation. Hughes and
coworkers [2009] found that soil transport efficiency at a site with gentle gradients
(<30%) in the Charwell Basin, New Zealand likely increased from conditions during the
Pleistocene as the landscape transitioned from a scrubland/grassland to a forest during the
Holocene. Even though there is some evidence that soil transport efficiency increases as
landscapes become less arid, other studies suggest that the relationship between climate
and soil transport efficiency may be more complicated due to differences in erosion rate,
vegetation, soil depth, temperature and precipitation rates among landscapes.
A global compilation that spans a wide range of climates and includes enough
sites to discern any trends that may exist despite the multiple influences on D is needed to
address how soil transport efficiency varies globally. Estimates of D have been made at
many sites, but limited effort has been made to compile the data or determine the trends
between D and climate. I carry out such an analysis below.
118
4.1.3 Approach
I compiled existing estimates of soil transport efficiency (D) and made new
estimates for sites where both high-resolution topographic data (from LiDAR or
differential GPS) and erosion rate estimates are available. I then compared the estimates
of D against climate proxies, including mean annual precipitation (MAP), an aridity
index (Al), and a measure of seasonality. I then investigated the role of the underlying
lithology and the measurement technique used to estimate D to determine if they
influence D.
4.2. Techniques for estimating D
Numerous techniques have been developed to estimate D. I present a short
summary of the techniques used to estimate D in the data compilation.
4.2.1 Scarp modeling
The first estimates of D were made by modeling the evolution of fault scarps and
paleo-shorelines of known ages [Nash, 1980b; Colman and Watson, 1983; Hanks et al.,
1984a]. Multiple scarp modeling techniques have been developed [Colman and Watson,
1983; Hanks andAndrews, 1989; Avouac et al., 1993] and produce differing results
[Pelletieret al., 2006] depending on the height of the scarp, assumptions about the initial
geometry, and whether linear or nonlinear flux laws are used to estimate D [Pelletieret
al., 2006]. The simplest solution for the evolution of a fault scarp that forms
instantaneously and then evolves gradually due to creep is
119
z(x,t) = a*erf
x)
+bx
(4.4)
2 D
where erf(x, t) is the error function, a is half the initial vertical difference in elevation
along the scarp, b is the is the pre-existing slope, and x is the distance from the center
elevation of the scarp. The function is often evaluated at x=0 and is where the scarp is
predicted to experience the highest slope gradient [Hanks, 2000]. More sophisticated
numerical approaches have been developed that allow the entire profile of the scarp to be
analyzed [Avouac, 1993; Arrowsmith et al., 1998]. Pelletier [2006] found that methods
that incorporate the entire profile of the scarp in addition to uncertainty in the initial scarp
angle yield the most accurate results.
4.2.2. Laplacian and erosion rate
Roering [2002] estimated D for a transient hillslope profile along the Charwell
River on the South Island, New Zealand using the hillslope Laplacian and estimated
erosion rates along the profile. Geomorphologists [Roering et al., 2007; Perron et al.,
2009; Hurst et al., 2012] have used the ridgetop Laplacian and catchment-averaged
erosion rates to estimate D in conjunction with equation (4.3) so that
D= P U
pr V2 ZR
120
(4.5)
where V 2 zR is the Laplacian at the ridgeline. An important assumption required for this
analysis is that the ridgeline is eroding in steady state, such that the uplift rate U equals
the measured erosion rate. However, due to the long response time required for hillslopes
to reach steady state and variability in climate through the Quaternary, this assumption is
rarely perfectly met [Fernandesand Dietrich, 1997]. Hillslopes are typically the last part
of a landscape to respond to changes in channel incision rates or regional tectonics
[Furbishand Fagherazzi, 2001]. Nonetheless, evidence exists that ridgetop Laplacians do
record changes in channel incision rates, albeit with a delay [Hurst et al., 2013b].
4.2.3 Relief and erosion rate
In addition to the ridgetop Laplacian and erosion rate technique, another
relationship has been derived that relates D, topographic characteristics, and erosion rate.
Roering and coworkers [2007] derived an analytical solution relating dimensionless relief
(R*) and dimensionless erosion rate (E*):
R*
(1+(E*
ln I1+ 1+(E*)
1
(4.6)
where R*=E*/4, E* = (-2V2z R LH) / S, , La is the mean hillslope length, and S, is the
critical hillslope angle at which downslope sediment fluxes become infinite. Callaghan
[2012] used equation (4.5) to modify E*, yielding
121
E
2E(p' p,)LH
DS,
(47)
where E is the erosion rate and can be solved for with cosmogenic radionuclide (CRN)
analysis. Callaghan [2012] combined equation (4.6) and equation (4.7) to solve for D for
a series of sites along a strong climate gradient along the Chilean coast.
4.2.4 Colluvial flux and slope
Hughes and coworkers [2009], in a similar fashion to Reneau and coworkers
[1989], estimated the mass of dated colluvium in hollows and used colluvial infilling
rates to estimate D. Gabet [2000] estimated D by measuring the sediment flux from
ground squirrels at a field site near Santa Barbara, CA and by using sediment traps
[Gabet, 2003]. Others [McKean et al., 1993; West et al., 2014] have used meteoric 1Be
to determine sediment flux rates in conjunction with slope gradients and equation (4.1) to
solve for D.
4.2.5 Landscape evolution modeling
Others have estimated D using landscape evolution models (LEMs) and generally
utilize error-minimization techniques to tune D so that other characteristics of the
landscape are reproduced from a LEM [Petit et al., 2009; Pelletieret al., 2011; McGuire
et al., 2014]. Roering and coworkers [1999] estimated D for a field site in the Oregon
Coast Range by picking a value of D that minimized the error between predicted erosion
rates using a nonlinear flux law and a long-term erosion rate determined by CRNs.
122
4.3. Data Compilation
4.3.1 Compilation of values from the literature
Multiple compilations of D have been made by others [e.g., Fernandesand
Dietrich, 1997; Hanks, 2000; Hurst et al., 2013a]. I include these estimates and compile
additional estimates of D that exist in the literature (Appendix 2). I include all estimates
that I found where D was estimated for natural landscapes under modern climatic
conditions. If multiple estimates of D were made at the same site during different
studies, I include all of the estimates [e.g., Roering et al., 2002; Almond et al., 2008;
Hughes et al., 2009]. I exclude an estimate of D made at Gabilan Mesa, CA [Roering et
al., 2007] because a newer estimate of D has been made using a better-constrained
erosion rate [Perron et al., 2012].
In a few of the studies included in the compilation, the data required to estimate D
were reported in the literature, but D was not estimated. In these cases, I use the reported
data to estimate D and include it in the compilation. For example, Reneau and Dietrich
[1991] estimated colluvial transport rates in the Southern Oregon Coast Range and
reported the slope gradient at most of the sites. I used their reported values in conjunction
with equation (4.1) to estimate D.
4.3.2 New estimates of D
I made nine new estimates of D by using existing high-resolution topographic
data and published erosion rates and by solving for D using equation (4.3) (Appendix 3).
Seven of the ridgetop Laplacian estimates were made from topographic data created from
LiDAR that is publicly available through OpenTopography [Krishnanet al., 2011]. I
123
made the other two ridgetop Laplacian estimates from differential GPS surveys of
hillslopes in the Atacama Desert, Chile, provided by Justine Owen [Owen et al., 20111.
150 0 W 120 0 W 90 0 W
60 0 W
30 W
0
30 E
60 0 E
90 0 E
120 E
150 0 E
600 N
3
0
N
00
30 S
600S
Figure 4.1. Map showing site locations where estimates of D have been made. Grey
circles show locations of previous estimates of D. X's show locations for new estimates
of D made in this study.
At each site, I measured the ridgetop Laplacian from soil-mantled portions of the
landscape upslope from where the erosion rate estimates were made following a
technique similar to Perron and coworkers [2012]. I calculated the Laplacian by fitting a
center-weighted, second-order polynomial to elevation data within a 15-by-15 meter
window and summing the second derivatives in the x- and y-directions. To determine a
single value that is representative of the ridgetop, I plotted the Laplacian against the areaslope product and binned the data into 20 logarithmically spaced bins. Starting from the
bin with the lowest area-slope product, I include all additional neighboring bins until the
magnitude of the binned mean decreases.
If more than one erosion rate estimate exists at a site in a suitable location to
estimate D, I estimated D for each erosion rate and assigned the mean of these estimates
124
of D as the site D. I estimated the uncertainty in D as either the standard error of the mean
of D or the sum in quadrature of the standard errors of individual estimates, whichever is
greater. I report the ridgetop Laplacian of each site as the mean of the unique estimates of
the ridgetop Laplacian used to calculate D for the site. If there is no published estimate of
Pr or ps at the site, I use the commonly-invoked density ratio of pr/ps = 2 [Heimsath et al.,
1999; DiBiase et al., 2010; Hurst et al., 2013b].
A few of my new estimates of D differ from previously published values for the
same sites. I briefly comment on these discrepancies here. My estimate of D = 147
+
33
cm 2 /yr for the Oregon Coast Ranges is higher than a previously published estimate of 36
16 cm 2 /yr, the estimate made by Roering and coworkers [1999]. The erosion rates
[Bierman et al., 2001] that I used to calculate D are slightly higher than the erosion rates
Roering and coworkers [1999] use to estimate D. The ridgetop Laplacian where I
estimate D is considerably less negative than the ridgetop Laplacian in the catchment
where Roering and coworkers [19991 estimated D. I use catchment-averaged erosion
rates made by Bierman and coworkers [2001] in the Oregon Coast Range, but they also
estimated one hillslope erosion rate of 81
24 m/Myr, which was measured from a
sample collected at the base of a 300 m hillslope. If the hillslope erosion rate is used to
estimate D instead of the catchment-averaged rate, D is ~80 cm2 /yr. This value is in
better agreement with Roering and coworker's [1999] estimate of D, but is still higher by
a factor of~2.
I used colluvial flux rates and hillslope gradients reported by Reneau and Dietrich
[1991] to make an additional estimate of D (51
13 cm 2 /yr) for the Oregon Coast
Ranges. This estimate is comparable to the estimate made by Roering and coworkers
125
[1999]. However, Reneau and Dietrich [1991] may have underestimated the sediment
mass flux from the hillslopes. They estimated sediment transport rates from the mass of
colluvial fill in dated deposits. If some of the hillslope sediment was fluxed through the
hollows instead of being stored, the sediment flux rates would be underestimated, which
would also lead to an underestimation of D. Reneau and Dietrich [1991] estimated an
erosion rate of 70 m/Myr from the mass of colluvial infilling. Bierman [2001] estimated
CRN-derived erosion rates of 136
43 m/Myr for the same region using catchment-
averaged erosion rates. This suggests that Reneau and Dietrich [1991] may have
underestimated the long-term erosion rate for the Oregon Coast Range, which would lead
to an underestimate of D, or that the erosion rates derived from CRNs are biased high.
Jungers and coworkers [2009] included the necessary data to estimate D for a site
in the Great Smoky Mountains, NC. I used the mean slope that they reported (-14
degrees) and the estimated sediment flux rate (65-100 cm 2/yr) to estimate D for their site
(331 cm 2 /yr). This is considerably higher than my estimate of D (19
1 cm 2 /yr) made
nearby using the ridgetop Laplacian and erosion rate technique. Their estimate assumes
plug flow of the 60 cm thick active layer of soil and their estimated soil velocities of 1.1
to 1.7 cm/yr from meteoric and in situ 10Be data. If soil velocity exhibits a linear
dependence on depth instead of being constant with depth, then the real sediment flux
rates may be considerably lower than their estimate. This would cause a decrease in the
estimate of D.
Petit and coworkers [2009] used a numerical model to estimate D for the Wasatch
Range, UT, and estimated an unprecedentedly high D (1200 cm 2 /yr). Mattson and Bruhn
[2001], using a scarp modeling technique, estimated a much lower value of D for the
126
same region of 28
11 cm 2/yr; while I estimated a value of D of 83
15 cm 2 /yr. Lacking
any reasonable explanation for the discrepancy, the large range in estimates of D made at
the Wasatch Range suggests that one of the estimates is likely incorrect. When
considering that Matson and Bruhn [2001] used a better-established technique and that
the value estimated by Petit and coworkers [2009] is anomalously high in comparison to
other estimates of D in the literature, it seems most likely that the high estimate of D
made by Petit and coworkers [2009] is inaccurate.
4.4. Relationship between D and climate proxies
I compare D with three different proxies for climate in order to determine which
proxy best describes the variability in D. I compare D to mean annual precipitation
(MAP), CGIAR-CSI Global-Aridity Index (Al) [Zomer et al., 2008], and seasonality.
MAP is calculated from global precipitation data from 1950-2000 and is gridded to 30
arc-seconds (~A kM 2 ) [Humans et al., 2005] and is also used in the Al calculation. Al is
defined as MAP divided by mean annual potential evapotranspiration (PET) and is useful
as a proxy for the water available to vegetation. PET describes the ability of the
atmosphere to remove water through evapotranspiration under idealized assumptions
[Allen et al., 1998]. Al is confusingly defined such that landscapes with low Al have high
aridity and landscapes with high Al are less arid. I define seasonality as the difference
between the maximum and minimum monthly precipitation normalized by the mean
monthly precipitation. The monthly precipitation data is derived from the same dataset
used to calculate MAP [Hijmans et al., 2005].
127
Previously published
This study
102
,!
Figure 4.2. (a) Plot of D
against mean annual
precipitation (MAP) with
least-square regression line fit
to log-transformed data. (b)
Plot of D against Aridity Index
(AI) with least-square
regression line fit to logtransformed data. (c) Plot of D
against seasonality where
seasonality is defined as the
difference in precipitation
between the wettest and driest
month divided by the mean
monthly precipitation.
.
a) 10 3
0
00
10'
10"0
R2 =0.33
0
10"
10
MAP (cm/yr)
10-1
b)
102
13
102
)
0
.
0..
10
10-
.
R2 = 0.35
0
10-1 10
0_3
AI
c)
0
102
10
10.
0
0.5
1
1.5
2.5
2
Seasonality
3
3.5
4
4.5
I found a positive correlation between D and both MAP and Al (Figure 4.2). I did
not find a correlation between D and seasonality (p-value of linear regression = 0.17).
Least-squares linear regression of log-transformed values of D against log-transformed
2
MAP and Al reveals that Al is a slightly better predictor of D than MAP (R
128
=
0.35 and
R2= 0.33, respectively). Both MAP and Al exhibit a power-law scaling relationship with
D, with D = 0.14*MAP
58
and D = 1.86*AIo
55
where D is in cm 2 /yr, MAP is in cm/yr
and Al is a dimensionless quantity.
4.5. Effect of vegetation
I split the estimates of D in the compilation into 4 different vegetation categories:
1) arid/desert, 2) grassland/scrubland, 3) savannah/lightly forested, and 4) forested
according to the site descriptions included in the original publications. If modern land use
has changed the vegetation cover present at a site, I categorize the site based on the
vegetation that existed for the majority of the time interval that the estimate of D reflects.
For example, if the land where the measurement was made was recently cleared, but had
been previously forested and the technique used to estimate D required CRN-derived
erosion rates (> 1 kyr timescale), I categorize the site as forested instead of grassland. If a
description of the vegetation was not included, I assigned the category by inspecting
available photographs and satellite imagery of the site.
For sites that experience MAP between 5 cm and 25 cm, D is lower for the
arid/desert sites (17 5 cm 2 /yr, mean
standard error) than for the grassland/scrubland
category (52 5 cm2 /yr), which in turn is lower than D for the savannah/light forested
category (70 20 cm 2/yr) (Figure 3). However, the only statistically significant difference
(p = 0.02) is between the means for arid/desert sites and savannah/lightly forested sites
for the 5 cm to 25 m range in MAP.
For the 50-150 cm range of MAP, the forested sites exhibit a higher mean value
of D (101
26 cm 2 /yr) relative to the savannah/lightly forested category (72 13 cm 2 /yr)
129
19 cm 2 /yr). At the 95% significance level, no difference
and the scrubland/grassland (83
exists in D between the different vegetation categories for sites with MAP between 50
and 150 cm. In the savannah/lightly forested category, I excluded an outlier of D (1200
cm 2/yr) made by Petit and coworkers [2009] in the Wasatch Mountains. However, even if
the outlier is included, a significant difference at the 95% significance level still does not
exist between the categories.
o
o
Desert / arid
Grassland / scrubl and
Savannah / Lightl y for ested
Forested
to
0 C
102
'vs
0
E
10'
0
100
10-
0
c
0
100
101
102
MAP (cm/yr)
Figure 4.3. Plot of D against MAP separated into four different vegetation categories.
The light grey patch highlights the MAP zone between 5 cm and 25 cm. The dark grey
patch highlights the MAP zone between 50 cm and 150 cm.
For the savannah/lightly forested category, estimates of D did not vary
significantly at the 95% significance level for an increase in MAP from the 5-25 cm
range (70 :20 cm 2/yr) and the 50-150 cm range (72 13 cm 2/yr). D increased by a factor
of ~2 between estimates from the grasslands/scrublands category for MAP of 5-25 cm
130
and from the forested category for MAP of 50-150 cm. However, I did not find a
difference between the two categories at the 95% significance level. This suggests that
once landscapes become moderately vegetated, D may not increase significantly even for
landscapes with higher precipitation or increased vegetation cover.
4.6. Effect of lithology
D varies over three orders of magnitude even for comparable values of Al or
MAP (Figures 4.2 and 4.3). In order to hopefully explain some of the variance in D, I
explored the relationship between D and lithology. To complete this analysis, I split
0
10
Igneous / metamorphic
0
-
Sedimentary
40
Un consolidated
102
2 10'
0
100
400
10-
3
10~-
10~
10-2
100
Al
Figure 4.4. Plot of D against Al separated into different lithological categories. The grey
line is the best fit to the log-transformed data for the igneous/metamorphic category. The
black line is the best fit to the log-transformed data for the unconsolidated sediment
category. R2 values are listed next to the respective regression line.
131
the estimates of D into three different categories: 1) Unconsolidated sediments, 2)
Sedimentary rocks, and 3) igneous and metamorphic rocks. I completed regression
analysis of the log-transformed data for each lithology category. The estimates of D for
sedimentary rocks exist over a limited range of Al, which makes them poorly suited for
the regression analysis. I focus on the results for the unconsolidated sediments and the
igneous/metamorphic category.
The estimates of D in unconsolidated material generally exhibit lower estimates
of D when compared to estimates of D where the underlying material is igneous or
metamorphic rock (Figure 4.4).
4.7. Effect of measurement technique
To determine if the method used to estimate D biases the estimate of D, I split the
estimates of D into the five different categories summarized in section 2. I then
performed least-squares linear regression on the log-transformed data and compared the
different method categories (Figure 4.5).
Estimates of D made from the LEM or colluvial flux category (Figure 4.5d)
exhibit a limited range in Al and were excluded from the regression analysis. The scarp
modeling method category produced the lowest estimates of D for a particular value of
Al (Figure 4.5a). The relief and erosion rate method category produced the highest
estimate of D (Figure 4.5c) while the Laplacian and erosion rate method category
produced an intermediate estimate (Figure 4.5b).
132
a) 10a o
b) to,
Scarp modeling
* Laplacian and erosion rate
*
0
102
0 @0
10
10 1
10D
100
0.32
=
c)
1
t10-3
-
to, L
10-
R2 =0.49
*
R2
103
10'
10-2
100
d) 103
0 Relief and erosion rate
102
A
LEM
A Colluvial flux
oQ
10 2
A
101
0
0
A
102
A
(p
100
10'
E
~tkA
10
100
10"
0.47
R2 =
10 0
10'
10'
10
10 0
-
10'
10 3
0I
102
Al
Al
e)
10 3
0 Scarp modeling
* Laplacian and erosion rate
Relief and erosion rate
o
10
E
0
S0"
10
102
10
-
10-1
100
Al
Figure 4.5. Plots of D against Al for D estimated with (a) the scarp modeling technique,
(b) the Laplacian and erosion rate technique, (c) Relief and erosion rate technique, (d)
LEM and colluvial flux techniques. The best-fit regression line and the R2 values of the
log-transformed data are included in (a)-(c). (e) Plot of D against Al for the three
measurement techniques with suitable ranges of Al for comparison. Best-fit regression
lines for the scarp modeling technique (black line), Laplacian and erosion rate technique
(dark grey line), and the relief and erosion rate technique (light grey line) are also shown.
133
4.8. Discussion and conclusions
4.8.1 Influences on D
My compilation shows that D increases with mean annual precipitation and
aridity index as a power between 0.5 and 0.6, which effectively means that the magnitude
of D levels off (within the range of variability) in wetter landscapes. This sub-linear
relationship may indicate that, despite transitions in the dominant creep mechanisms as
landscapes become more heavily vegetated, the new transport mechanisms that are
activated may not significantly increase the sediment transport efficiency. For example,
burrowing mammals may dominate sediment transport in a grassland landscape [Thomas
and Montgomery, 1991]. If climate conditions change and the landscape becomes
forested, the frequency of animal burrowing may decrease while the occurrence of tree
throw increases [Gabet and Mudd, 2010], but this transition may be a tradeoff instead of
increasing sediment transport efficiency.
The more substantial increase in D with precipitation and aridity index among dry
landscapes may reflect a more impactful transition from abiotic creep to biotically
mediated transport mechanisms that more efficiently transport sediment. D increases by
an average factor of ~4 between arid landscapes and savannah/lightly forested landscapes
for sites with low precipitation (MAP of 5-25 cm). As precipitation increases from sites
with low precipitation to sites with high precipitation, the differences in D become
smaller for the same change in mean annual precipitation.
D increases by a factor of -2 between grasslands/scrublands that experience low
precipitation (MAP of 5-25 cm) and forested terrain experiencing higher precipitation
(MAP of 50-150 cm). However, there is significant variability in D for both of these
134
categories and even though D increases, there is not a significant difference between the
two categories. In Charwell Basin, New Zealand, Hughes and coworkers [2002] found a
similar result that D increased by a factor of ~2 as forest colonization occurred during the
Pleistocene-Holocene transition. This result, like mine, counters the idea that flux rates
decrease as landscapes become more forested and experience soil stabilization due to
increased soil cohesion from roots. However, my results also show that the average
increase in D from grasslands to forests is rather small when considering the three-orderof-magnitude range in D reported in the literature.
Multiple factors may influence the generally higher estimates of D in
igneous/metamorphic rocks relative to unconsolidated sediments. First, it is possible that
the apparent correlation of D with lithology may be an artifact, because lithology in our
compilation is correlated with the measurement technique used to estimate D. Of the 25
estimates of D made with the scarp modeling technique, 23 are in unconsolidated
sediments. The other 2 are in poorly consolidated sediments. In stark contrast, estimates
of D made with the relief and erosion rate technique and the Laplacian and erosion rate
technique were primarily made in granitic landscapes. One reason for this is that these
techniques use CRN-derived erosion rates to calculate D, which generally require the
presence of 2 6Al or 10Be found in quartz. A bias from the measurement technique may be
introduced due to the younger and less well-developed soils that may be present on the
scarps relative to possibly better developed soils on older hillslopes in the same region.
Another reason might be that scarps are often composed of coarse sediment such
as alluvial fans or pluvial shorelines. The coarse sediment may inhibit vegetation growth,
especially where the soils are young or poorly developed. For wave-cut shorelines of
135
Lake Bonneville, Pelletier [2006] found that soil texture had a weak but significant
inverse relationship with D. McKean [1993] estimated a high value of D (360
50
cm 2 /yr) in clay-rich soils at a site in northern California. Particle size likely influences a
number of potential transport mechanisms that influence sediment transport efficiency
including shrink-swell cycles of clays while also influencing biotic activity.
Furthermore, a scarp sampling bias may exist for two reasons. First, the presence
of significant vegetation may make it difficult to identify scarps. Second, unlike
hillslopes, scarps have a definite lifespan unless repeated offset occurs for scarps of
active faults. A bias may exist where estimates of D exist mostly for slower evolving,
longer-lived scarps.
Hurst and coworkers [2013] compiled a substantial collection of climate,
vegetation, and geological data for sites with estimates of D. Hurst and coworkers
explored the relationship between climate proxies, D, and lithology. Taking lithology into
consideration did not help explain the variability in D at the different sites. However, at a
new field site that they consider in that study, they do find that lithology likely influences
soil transport efficiency. They found that weak bedrock had higher values of D. However,
this is not necessarily inconsistent with our results. Independent of whether the bedrock
or underlying material is consolidated, the soils may be poorly developed. The key to
high soil transport efficiency may be that sufficient soils exist that are attractive to
vegetation and fauna, which are primarily responsible for physically disturbing the soils
and causing sediment transport.
136
4.8.2 Towards a general explanation for variations in D
Nash [1984] suggested that it may be possible to estimate D from regional
information if the controlling mechanisms are known. If this is the case, it may be
possible to develop an empirically based model to estimate D. In order to do this, the
dominant factors that influence D at different locations must be known. In this study, I
identified multiple factors that correlate with D and could therefore be used to estimate
D. Syvitski [2007] used categorical estimators in conjunction with topographic
characteristics to model global sediment flux. A similar approach could be taken to
estimate D. Being able to estimate D globally from climatic, lithological, and other
controlling factors in conjunction with topographic data with near global coverage would
enable us to better estimate global hillslope sediment fluxes in the past, present and the
future.
Acknowledgements
I would like to thank Naomi Schurr who helped compile some of the data and
helped make some of the topographic measurements. I would also like to acknowledge
the Department of Defense for funding through a National Defense Science and
Engineering Graduate Fellowship. I would like to thank Justine Owen for sharing
topographic data that she collected in the Atacama Desert, Chile.
137
138
Chapter 5. Conclusion
In the three preceding chapters, I investigated the relationship between climate
and landscape evolution. I accomplished this by (1) investigating how erosional
mechanisms that may be sensitive to differences in microclimates can generate
asymmetric topography, and by (2) compiling estimates of the soil transport coefficient,
and then empirically determining important factors, including climate factors, that
influence soil transport efficiency.
In Chapter 2, I incorporated aspect-dependent erosional mechanisms, such as
aspect-dependent regolith strength, aspect-dependent soil creep, and aspect-dependent
runoff, into a landscape evolution model (LEM). I also incorporated lateral channel
migration into the LEM. The LEM with lateral channel migration predicts a unique
relationship between topographic and erosional characteristics for asymmetric landscapes
if lateral channel migration is the root cause of the asymmetry.
The aspect-dependent runoff and aspect-dependent regolith strength LEMs predict
comparable signatures between topographic and erosional characteristics that differ from
the lateral channel migration LEM. The aspect-dependent soil creep LEM predicts a more
complex response to asymmetry in soil creep than the other aspect-dependent efficiency
139
models. In general, the aspect-dependent soil creep LEM is not capable of producing
hillslopes with a high degree of topographic asymmetry while maintaining realistic
topographic characteristics.
I also explored controls on asymmetry and found that topographic asymmetry
increases with an increase in the Peclet number, a value that describes the competition
between fluvial incision and soil creep. This occurred for all of the asymmetry-forming
LEMs except the aspect-dependent soil creep LEM. The practical application of this
knowledge is that for the same magnitude of asymmetry forcing, higher asymmetry is
expected to develop in wider basins. For the LEM with lateral channel migration, I found
that the Pdclet number and another dimensionless number, the Migration number, control
the topographic asymmetry that develops. I also further investigated the controls on
topographic asymmetry for the lateral channel migration model with a 1 -D model that
includes hillslope and channel processes. In the 1 -D model, I modified the lateral channel
migration rule so that the lateral channel migration rate is driven by differences in
sediment flux on opposing sides of a valley instead of occurring at a fixed rate. The 1 -D
model suggests that topographic asymmetry may develop and be sustained in landscapes
without variability in microclimates if differences in sediment flux occur on opposing
slopes for other reasons, such as a difference in initial slope length.
In Chapter 3, I investigated which asymmetry-forming mechanisms are most
likely responsible for the topographic asymmetry at Gabilan Mesa, CA. The aspectdependent runoff and aspect-dependent regolith strength LEMs are best at reproducing
the relationship between topographic asymmetry and erosion rate asymmetry. In a
particularly asymmetric valley at Gabilan Mesa, field-saturated hydraulic conductivity is
140
significantly higher on north-facing slopes than on the opposing south-facing slopes,
suggesting that significant differences in runoff may occur at Gabilan Mesa under current
conditions. My measurements of soil shear strength do not support the hypothesis that
aspect-dependent differences in regolith strength are controlling the asymmetry at
Gabilan Mesa. Physical and erosion rate evidence of lateral channel migration exist in
some basins, but not in all of the asymmetric basins.
For the most asymmetric basins at Gabilan Mesa, the LEM predicts that
differences in aspect-dependent runoff must be quite high if aspect-dependent runoff is
solely responsible for the asymmetry. This suggests that multiple asymmetry-forming
mechanisms may be acting in unison. Initial tilting of the mesa and the corresponding
background slope may have influenced the initial development of the drainages and
caused topographic asymmetry to initially develop. However, the pattern in erosion rates
at Gabilan Mesa does not match the prediction if tilting is solely responsible for the
topographic asymmetry.
When the field measurements and observations are considered alongside the
numerical modeling experiments and the topographic and erosion rate analysis, aspectdependent runoff seems to be the most likely explanation for the bulk of the asymmetry
at Gabilan Mesa. However, the most asymmetric basins may be influenced by additional
asymmetry-forming mechanisms such as initial tilting and lateral channel migration.
This analysis suggests that aspect-dependent differences in runoff are important
for influencing the development of topography at Gabilan Mesa. Aspect-dependent
runoff should also be considered as a likely asymmetry-forming mechanism in other
semi-arid landscapes that exhibit differences in microclimate and topographic
141
asymmetry. Furthermore, this study casts doubt on the role of lateral channel migration as
a dominant asymmetry-forming mechanism and suggests that evidence of lateral channel
migration must be carefully weighed, as its presence at some locations does not indicate
that it is occurring everywhere.
In Chapter 4, I compiled estimates of the soil transport coefficient (D), and also
made new estimates at sites where both high-resolution topographic data and erosion rate
estimates already exist. I found that D has a power-law relationship with an exponent of
-0.5-0.6 with mean annual precipitation and the aridity index, a useful proxy for water
availability in soils. D increases markedly between arid landscapes and more vegetated
landscapes. Among vegetated landscapes, further increases in D with precipitation and
aridity index are relatively minor, especially compared with the observed range of D
among landscapes. This suggests that once a landscape is sufficiently vegetated, increases
in precipitation do not necessarily lead to significant increases in sediment transport
efficiency or significant increases in hillslope erosion rate.
Much work remains to be done to unravel the relationship between climate and
landscape evolution. By focusing on understanding the relationship between climate and
landscape evolution at specific sites and exploiting natural experiments, we can continue
to improve our understanding of how landscape evolution is influenced by climate. We
can also continue to improve our understanding of climate and landscape evolution by
carefully analyzing compilations that enable us to examine a much larger range in climate
than is generally possible for regional studies. In regards to topographic asymmetry, there
are still many fundamental questions left to address. My numerical modeling experiments
suggest that lateral channel migration may be a self-sustaining process in which
142
differences in slope length alone are enough to produce and maintain topographic
asymmetry, but does this actually occur in real landscapes? Determining appropriate field
sites where this might be the case and testing the topographic and erosional predictions
made from numerical modeling experiments should help solve this mystery. Lateral
channel migration has been suggested as a dominant cause of asymmetric topography
[Dohrenwend, 1978], and Gabilan Mesa was considered a prime example of such a
landscape. However, my analysis suggests that lateral channel migration is not the
dominant cause of the asymmetry at Gabilan Mesa. My numerical modeling predictions
provide a useful framework for testing if lateral channel migration is fundamentally
responsible for the asymmetry at other sites. It will be interesting to apply these tests to
other field sites and determine if lateral channel migration is a dominant mechanism in
any landscapes that exhibit topographic asymmetry.
My analysis of the compilation of D suggests that soil transport efficiency
depends on climate. Soil transport efficiency is particularly sensitive in arid regions that
are on the cusp of being able to support vegetation and fauna. An important result of
aspect-dependent runoff causing the topographic asymmetry at Gabilan Mesa is that it
serves as valuable evidence that landscapes can respond dramatically to relatively small
differences in climate-differences that currently exist on opposing slopes. As is the case
for the compilation of D, we once again learn from this natural experiment at Gabilan
Mesa that life is important for determining tipping points in landscapes. Landscapes that
exist on these tipping points have likely experienced the most significant changes due to
climate change in the past and may experience considerable changes due to
anthropogenic climate change in the near future.
143
144
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2), 101-111.
Zomer, R. J., A. Trabucco, D. A. Bossio, and L. V. Verchot (2008), Climate change
mitigation: A spatial analysis of global land suitability for clean development
mechanism afforestation and reforestation, Agric. Ecosyst. Environ., 126(1-2), 6780, doi:10.1016/j.agee.2008.01.014.
157
158
Appendix
159
Appendix 1. Cosmogenic radionuclide-derived erosion rates and related data. All reported uncertainties are one st
ndard
error of the mean.
[IO4ei
Sample
Site
BSA,
Aspect
Type
Location* (*N/*W)
)
(m(AMSL)
(spallation/muons)
[o[hr
"BBe'
Be Carrier
"Be production rate
Elevation'
fantor
(mg)
Quartz (g)
1(
x0)
(atoms/g/yr)
GAB 13003
GAB 13004
GABI3005
GAB 13006
GAB13023
0.99
0.99
0.99
0.98
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.98
1
0.99
0.99
0.99
0.99
0.98
0,98
0.98
1
26.180
24.072
29.020
28.108
23.279
35.247
34.392
33.390
28.979
42.280
32.409
19.808
24.575
43.977
41.996
22.826
39.997
30.265
16.688
29.325
13.743
0.2863
0.2852
0.2821
0.2836
0.2834
0
0
0
0
0
0
0
0
0
0.4
5.69/0.209
5.65/0.208
5.44/0.205
5.23/0.203
5.29/0.203
5.27/0.202
5.24/0.202
5.23/0.202
5.13/0.200
5.08/0.199
5.12/0.200
4.99/0.199
5.44/0.204
5.33/0.203
5.38/0.204
5.34/0.203
5.18/0.201
5.16/0.201
4.79/0,195
4.80/0.196
4.35/0.200
0
0
0
0
0
0
0
0
0
0
Isotoee
8 SiO)
0.15910.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
for inriheitance
-
south-facing
bedrock-soil interface
-
north-facing
bedrock-soilinterface
35.9128/120.7770
354
0.6
3.98/0.203
0.98
12.257
0.2864
21.4
1.6
0.253
0.027
0.159
0.068
2451
1202 1202
north-facing
bedrock-soil interface
35.9119/120.7710
322
1.4
2.75/0.201
0.97
23.316
0.2776
32.0
2.7
0.213
0.022
0.159
0.068
1749 +4185
south-facing
north-facing
south-facing
north-facing
+0.08
-0.08
soath-facing
north-facing
catchment
catchment
+0.06
((7 -0.06
+0.03
2.33 -0.03
south-facing
north-facing
south-facing
north-facing
catcuanrot
catchment
catchment
catchment
2.02
+0.06
-0.05
south-facing
0.73
+0.03
-0.03
south-facing
north-facing
catchment
catchment
catchment
catchment
1.36
+ 0.05
-0.05
south-facing
north-facing
1.66
+0.03
-0.03
south-facing
north-facing
+ 0.03
south-facing
north-facing
1.92
6
8
10
8
0.69
-
-0.03
north-facing
catchment
catchment
catchment
catchment
catchment
catchment
catchment
catchment
catchment
0
0.2837
0.2879
0.2876
0.2930
0.2890
0.2803
0.2834
0.2759
0.2848
0.2834
0.2842
0.2867
0.2850
0.3493
0.3187
0.2856
interface.
0.159 0.069
0.159 0.068
0.159t0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159 0.068
0.159*0.068
0.159+0.068
Erosion rate not
corrected for
inheritance
(M/Myrs)
87t12
78 10
64 7
266 110
63 7
45 4
69 9
58 7
77 11
42 4
55 6
64t8
46 5
42 4
55 6
161 43
51 5
72 9
72 10
93 19
53+7
(I/km2/yr)
219 30
196 25
161 19
666 E 276
158 18
113 11
172 22
145 17
192 27
105 10
136 15
160 21
114 12
105 10
137 14
403 t106
128 13
181 23
179 24
232 47
132 18
3
-0.03
+0.05
2.10 -0.05
locations and elevations nre the means for the samnled hasins
Reported
e
from the bedrock-soil
thickness of small rnins does not cause inificant attenuation of cosmic ravs. so the depth of surface samples is assumed to he zero. For qamoles collected
ratios are standardied accordins to isotonic standard 07KNSTD WNishiibmi et al.. 2007).
rates
production
and
statistics
counting
mass
carrier
in
blank
uncertainties
incorporate
unceetainties
'Rinnk ahumdance wasscaled hvsamnle carrer mass Renorted
'Inherited concentration estimated from "Be concetration of deenhy buried rock that has recently been exposed alona road cuts (Perrone al.- 2012).
TIh
112.8 3.8
113.0 3.9
155.8 5.3
58.0 2.2
125.0 4.5
244.4 6.7
167.1 7.4
185.7 8.1
126.7 6.5
297.9 10.2
191.7 7.2
102.9t5.3
178.4 7.5
323.5 8.1
251.5 7.6
63.9 4.7
244.2 6.7
142.2 4.7
110.4i4.3
60.2 5.2
78.1 4.9
(10' atoms/
g SiA)
0.787 0.028
0.053 0.032
0.978 0.034
0.356 0.016
0.975 0.037
1.287 0.036
0.906 0.041
1.039 0.047
0.021 0.044
1.337 0.047
1.[)78 0.042
0.934 0.051
1.299 0.056
1.378 0.035
1.111 0.034
0.488 0.039
1.145 0.032
0.862 0.030
0.832 0.036
0,686t0.069
1.012 0.068
3
2
GAB13011
GAB13024
441
432
385
350
351
348
340
338
316
303
312
294
373
360
372
363
325
334
246
248
319
fi10' atoms/
35.9287/120.7493
35.9213/120.7481
35.9201/120.7613
35.9157/120.7617
35.9163/120.7739
35.9119/120.7702
35.9086/120.7674
35.9057/120.7645
35.9135/120.7971
35.9084/120.8003
35.9182/120.8102
35.9161/120.8076
35.9279/120.7864
35.9255/120.7845
35.9230/120.7799
35.9190/120.7772
35.9502/120.7928
35.9418/120.7988
35.9202/120.8278
35.9165/120.8255
35.9128/120.7731
1.+0.03
89
GAB13009
GAB13012
GAB 13013
GAB 13014
GABI3015
GAB13016
GAB13017
GAB13018
GAB 13019
GAB 13020
GABI 3021
GAB13028
GAB 13029
GMIO-03
GMIO-04
GAB13022
catchment
hnierites? [OBeI Erosion rote corrected Bedrockerrsion
rate corrected for
c
+
the denth is mesured as the slone-normal distance from the sample to the soil surface
85
481 +981
-481
+
700 6
1675
(t/km/vr)
174 13
159 12
134 10
367 28
131 10
98 7
141 11
122 10
154 13
92 7
115 9
132 11
100t8
92 6
116t8
270 28
109 8
147 11
144 11
176 21
110+ 10
Bedrock erosion
rate not corrected
for inheritance
(n/Myrs)
69 5
63 5
54 4
147 11
53 4
39 3
56 4
49 4
61 5
37 3
46 3
53 4
40 3
37 3
47 3
108 11
44 3
59 4
5814
70 9
44+4
440
55
176 22
431
52
173
21
Appendix 2. Estimates of the soil transport coefficient (D) made in this study.
Site
ON
Location (lat/lon
0)
Bedrock Erosion Ridgetop Laplacian
3
Rate (m/Myrs)
(x10 1/rM)
Source of erosion rates
Source of topographic data
19 + 1
Rate from Portenga and Bierman
(2011). Rate originally determined
by Matmon et al. (2003).
OpenTopography
Rate from Willenbring et al. (2013).
Rate originally determined by Binnie
et al. (2007).
OpenTopography
2
-28.2
148
-157.3 + 7.3
175
21
-24.7
0.6
83
15
108+ 17
-30.2
0.6
71
12
37.850/-122.550
102
23
-13.8
0.9
174
21
Drift Creek, OR, USA
44.517 / -123.844
155
30
-22.0
1.6
147
33
Blasingame, CA, USA
Atacama Desert, Chile
Atacama Desert, Chile
36.954/-119.631
-24.130/-69.990
-29.770/-71.080
-26.9
-24.6
-29.1
0.4
6.0
1.2
22
3
Great Smokey Mountains, NC, USA
35.621714/-83.204
27
San Bernardino Mountains, CA, USA
34.051351/-116.934
1373
Wasatch Mountains, UT, USA
40.892/-111.865
89+9
San Gabriel Mountains, CA, USA
34.3641/-117.992
Tennessee Valley, CA, USA
30 4
1 0
27 3
4.3
2
D (cm /yr)
1+ 1
16
2
Rate from Willenbring et al. (2013).
Rate originally determined by Stock
et al. (2009).
Rate from Willenbring et al. (2013).
Rate originally determined by
DiBiase et al. (2010)
Rate from Portenga and Bierman
(2011). Rate originally determined
by Heimsath et al. (1997).
Rate from Portenga and Bierman
(2011). Rate originally determined
by Bierman et al. (2001).
Dixon et al. (2009)
Owen et al. (2011)
Owen et al. (2011)
OpenTopography
OpenTopography
OpenTopography
OpenTopography
OpenTopography
J. Owen
J. Owen
Appendix 3. Compilation of the soil transport
Site Loaion
Charwell
*
Sasin, New
AhuriiNew
Zealand
Ahuriri, New
Zealand
Carrizo Plain. CA,
USA
coeflicient (D)
Latitude (c)
Soaree
and site information.
MAP
Longitude(0)&A]
l
Ss
(an/ye)
Underlying lithology
Description
Lithology
Technique
Technique
Vegetation
Vegetation
category'
Description
Cntegsry'
Description
Categnry'
2
Grassland/shrubland
(recently cleared), but
previously bech
2
Previous vegetation
was likely podocarphardwood forest, but
recently repalced by
pasture grasses
Transient hillslope
Laplacian and
mond ef a]. [2008]
-42.450
173-357
30= 0
1.42
11
0.57
Loess underlain by
fluvial gravel terraces
I
Almond er al. [2008]
-43.702
172.584
31
4
0.76
68.8
0.70
Thick loess deposits
underlain by altered
basalt
I
Almond et al. [2008]
-43.702
172.594
70 20
0.76
68.8
0.70
Thick underlain by
altered basalt
I
"'Cs fallout nuclidederived eosion rate
(-50 yr timescale)
and slope Laplacian
2
Previous vegetation
was likely podocarphardwood forest, but
recently repalced by
pasture grasrs;
2
35.271
-119.827
0.33
46.7
2.24
2
Scarp modeling
I
Grasses and shrubs
2
Avouac andPeltzer
(I993)
Avoac et al. (1993)
36.800
80.500
33+ 14
0.03
3.3
2.55
Loose fan gravels
Scarp modeling
I
44.048
86.790
55,20
0.19
18.4
1.57
Loose fan gravels
Scarp modeling
1
Begin (1992)
31.262
34.802
4 +3
0.16
23.3
2.78
Fluvial gravel terraces
Scarp modeling
I
Not vegatated
Bowsan and Gesn
31.386
35.361
4
0.07
10.9
2.97
Gravel
Scarp modeling
I
Not vegatated
35.240
4
0.04
6
2.60
Scarp modeling
I
Not
Arrowsith
(1998)
et al.
86
8
Paso Robles Formation
(poorly consolidated
gravels and sands) and
Holocene alluvial fan
timescale from
beginning of
Holocene to present
Transient hillsope
Laplacian and
timscale ofvoclanic
event (-27ka) to
present
units
Region,
Xinjiang, China
Hotan
Tien Shan, China
Northern Negev'
Israel
Lake Lisan, Dead
Sea, lsrael
oreAaa'
Israel
Chile
(1986)
Goss
Bowman
and
(1989) reported in
Hank (2000)
30.658
Callaghan (2012)
-32.99
-71.42
0.41
55=24
48.2
3.41
Chile
Callaghan (2012)
-32.98
-71.42
70 + 36
043
51.8
3.41
Granitic
Chile
Callaghan (2012)
-32.98
-71.42
41
+ 20
0.43
51.8
3.41
Granitic
Chile
Callaghan (2012)
-32.94
-71.43
46 20
0.34
39.7
3.26
Granitic
58 27
0.45
53.1
3.44
Granitic
vcgatated
vegatated
Relief and erosion
rate
Mostly herbaceous.
Relief and erosion
Mostly herbaceous.
some ttees
'ate
Callaghan (2012)
-33.01
Chile
Callaghan (2012)
-31.12
-71.58
46 + 7
0.14
16.7
3.59
Granrtic
Chile
Callaghan(2012)
-31.12
-71.56
44 13
0.15
16.7
3.59
Granitic
Chile
Chile
Callaghan (2012)
Callaghan (2012)
and erosion
Mostly
rate
Relief and
oen
Relief aderosion
3sone
Herbaceous,
3
Relief and erosion
ate
3
-31.12
-30.55
-71.55
-71.63
49+ 13
68
158
0.16
0.13
18.3
13.8
3.54
Relief and erosion
rate
4.09
Granitic
Relief and erosion
rate
Relief and erosion
rater
Chile
Callaghan (2012)
-30.55
-71.63
212
+92
0.13
13.8
4.09
Granitic
Chile
Callaghan (2012)
-29.62
-71.20
38
+ 13
0.07
7.6
3.47
Granitic
Chile
Callaghan(2012)
-29.62
-71.20
38
+
11
0.07
7.6
3.47
Granitic
Chile
Callaghn (2012)
-29.62
-71.20
35+12
0.07
7.6
3,47
Granitic
Chile
Callaghan (2012)
-29.58
-71.14
20 + 7
0.56
7.3
3.62
Granitic
Chile
Callaghan(2012)
-29.57
-71.16
19+7
0.06
7.4
3.73
Granitic
Chile
Callaghan (2012)
-29.22
-71.18
27 9
0.06
6.5
3,51
Granitic
CHiC
Callaghan (2012)
-29.23
-71.18
14 c 5
0.05
6.5
3.51
Granitic
CHl
Callaghan (2012)
-28.41
-71.05
16 = 7
0.04
4.7
3.57
Granitic
CHIle
Callaghan (2012)
-28.40
-71.06
11 + 5
0.03
4.5
3.73
Granitic
Chile
Callaghan
(2012)
-28.39
-7107
15 7
0.03
4.3
3.91
Granitic
Chile
Callaghan(2012)
-28.36
-71.05
18 9
003
4
3.90
Granitic
Chile
Callaghan (2012)
-26.57
-70.44
2
1
0.02
2
4.20
Granitic
Chile
Callaghan(2012)
-26.56
-70.48
3
1
0.02
2.3
4.17
162
Relief and
erosion
and
roson
rate
Relief
rate
Mostly herbaceous.
3wineetrees
Relief
3
Mostly herbaceous,
few trees, sore bare
ground
3
Mostly herbaceous,
wsoe trees
3
Mostly herbaceous,
bare
few trees,
ground
3
Mostly herbaceous.
bare
few trees,
ground
some
some
Mostly herbaceous,
few trees. some bare
3
ground
and erosion
rate
3
Mostly herbaceous.
fewtrees.soanbare
ground
Relief and
erosion
3
Mostly
hcrbaccous.few
sine bare ground
Relief and
rate
erosion
3
Mostly herbaccous,
bare
few
ground
erosion
3
rate
Relief and
rate
rate
3
Relief
3
rate
Relief snd erosion
rate
Relief and erosion
rate
Relief
and erosion
rate
trees, some
ofherbaceous
groundcovernand bare
ground
Mixture of herbaceous
groundcover and bare
ground
Mosrtly bare ground,
sereeberbeous
and erosion
Relief and erosion
rate
Relief and erosion
trees.
Mixture
ground
3
few trees
Mostly herbaceous,
f some trees
3
Relief and erosion
rate
Granitic
herbaceous,
trees
Mostly herbaceous,
trees
erosion
rates
/
Chile
-71.44
Relief
3
trees
3some
/
M
Not
Grasses and shrubs
cover
3
Bare ground
3
Bare ground
3
Bare ground
3
Bare ground
3
Bare ground
3
3
2
3
Chile
Callaghan (2012)
-26.56
-70.51
4+12
0.02
2.3
4.17
Granitic
Chile
Callaghan(2012)
-26.59
-70.49
4 '2
0.02
2.3
4.17
Gniti
Chile
Callaghan (2012)
-26.57
-70.56
9
i4
0.02
2.4
4.00
Granitic
Chile
Callagh
n (2012)
-40.58
-73.69
58
17
2.23
184
1.42
GUti6
Chile
Callaghan(2012)
-40.58
-73.60
61
20
2.13
178
1.40
Gr
Chile
Callaghan (2012)
-37.90
-73.28
40
14
1.52
169
1.94
Chile
Callaghan (2012)
-36.97
-73.12
93045
1.13
123
2.16
Grtic
Grntic
2.16
Grt
Chile
Callaghan (2012)
-36.97
-73.12
142165
1.13
123
Chile
Callaghan (2012)
-35.84
-72.51
66 23
0.80
90.7
2.74
Chile
Callaghan(2012)
-35.86
-72.48
0.76
85.3
2.76
Chile
Callaghan (2012)
-34.61
-71.58
116 42
19 + 12
0.60
75.5
3.16
Chile
Callaghan (2012)
-33.88
-71.50
65
0.33
42.3
3.23
Chile
Callagha (2012)
-33.90
-71.49
32
0.34
45.2
3.24
Granitic
i
+14
Graniic
Granitic
Graniic
Graniic
Granitic
Granitic
Graniic
Callaghan (2012)
-32.94
-71.42
53
23
0.34
39.6
3.27
Callaghan (2012)
-32.27
-71.41
75
31
0.24
30.1
3.11
Gr
Chile
Callaghan(2012)
-32.27
-71.40
73238
0.23
30
3.04
G
Chile
Callaghan (2012)
-32.08
-71.42
58,*28
0.20
25.9
3.0)
Grtiti=
Chile
Callaghan(2012)
-31.56
-71.42
61+
16
0.15
18.8
2.81
Chile
Callaghan (2012)
-31.52
-71.42
16 = 4
0.17
20.8
3.06
Chile
Callaghan (2012)
-30.52
-71.66
71
0.12
12.6
4.00
Chile
Callaghan (2012)
-30.53
13
3.97
-30.55
-71.62
84=37
0.13
4
4.11
Chile
Callaghan (2012)
-30.57
-71.63
200 t 88
0.13
14
4.11
Chile
Callaghan (2012)
-29.65
7.5
4.00
Chile
Callaghan (2012)
-29.67
-71.16
Bugd fault
system. Mongolia
Lane Bonneville.
UT. USA
Southern Arava
Cartir
et al.
(2002)
44.840
100.303
23
8
19.7
0.07
3
Bare ground
Forested
33
33rate
3
3
Relief
and erosion
re
rate3
erosion
Relief and
3
3
Relief and
33rate
G ii
3
3
rate
3
erosion
Forested
erosion
Relief and erosion
3
Relief and
rate
3
3
Forested
3
3
3
3
Relief
3
Relief
and erosion
and crosion
Relief
r ecrosion
and
Graniic
itic
Graniic
iti
Forested
Forested
3
3
Forested
3
Mostly herbaceous.
few
33
3
rt3r
at3r
3
3
erosion
Relief and
3
Herbaceous
3
Herbaceous
3
3
33rate
3
Relief
33
Relief
and erosion
and erosion
Granitic
3
R
ate
Gr
3
at3a
Relief and erosion
rate
and crosion
rat.
Relief and erosion
rate
3
Relief
3
andeerosion
33
erosion
3
ic
Graniic
3
3
Graniic
3
Graniic
Granitic
G
3
Graniic
3
3
Relief
3
Relief and
Mostly
3
r
3
tiRelief
Granitie
3
at3r
33
aderso
reic
trees
Mostly herbaceous.
some trecs
Mostly herbaceous.
some trees
Graniic
ate
Mostly herbaceous.
some
Mostly herbacau..
some
trees
3
Graniic
Graniic Graniic
-71.11
3
Graniic
Granitic
Callaghat(2012)
Reliefradt
Graniic
Graniic
Chile
erosion
Relief and erosion
33
Bare ground
3
R .liefand
erosion
Graniic
0.12
Bare ground
trees
Gran(i,
Chile
74=30
andateerosion
rate
Graniic
Chile
-71.66
Relief
rate
3
3
Forested
Grtiti=
Granilti,
29
and erosion
3
Granitic
29
Relief
3
herbaceous
Mostly herbaceous.
some
trees
Mostly herbaceous.
sine trees
Mostly herbaceous.
few trees
3
3
Mostly herbaceous,
some
trees
Mostly herbaceous.
few Ite.
Mostly bare ground
3
Mixture
and esion
of herbaceous
and bae
3
at.
3
Gravel
1
Scarp modeling
I
Not vegetated
I
0.78
Gravel
I
Scarp modeling
I
Orsses and shrbs
2
3.10
Sandy gravel
I
Scarp
modeling
I
Not vegetated
I
2.46
Paso Robles Formation
(poorly consolidated
sands)
gravels
2
4
Coastal
Coarse alluvial deposits
I
Scarp
modeling
I
I
I
scrubland visible in
photographs ofsit
I
Grass and sme sparse
vegetation visible in
0.07
7.7
3.74
17
0.18
13.9
3.63
1
0.16
19.9
0.02
3,)
groundcover
ground
2
Gurvan
Valley,
Trssts
Israel
Ranges.
CA, USA
Colman and
(1983)
Enzel
at4son
t al. (1996)
Gabt (2000)
33
39.625
-113.211
9f
29.612
34.983
3
34.693
-120,041
74
0.38
49.2
Sediment flux
and
estimated from
gopher burrows and
Sage
2
slope
grasses and sparse
Rtvytnd Fau
Hankes r al. (1984)
LA. CA. USA
Scarp.
34.119
-118.131
160
0.33
46.2
2.60
trac
tt
.ovettiihl
ateite and aerial
images
Lost River. ID. USA
Haks (2000)
44.166
-113.870
10
0.31
28.3
1.06
Alluvial gravels
I
I Scar
modeing
Soarpttmotdtling
tkt Lahstta. NV.
USA
Hanks andifilace
(1985)
40.152
-117.925
11
0.14
18.8
0.83
Alluvial gravels
I
Scarp
Lake Bonneville.
Hanks
r al. (1984)
UT. USA
modeling
2
2
2
satellite images
39.613
-112.299
11
0.24
29.5
I
Gravels
0.61
Scarp modeling
I
Grasscs
and shrubs
Lower ttrraos
2
are
farmed. upper terraces
Santa Cruz sea cliffs. Hanks or at (1984)
CA. USA
36.984
-122.127
110
0.72
79.8
2.62
2
Mudston
am grassland; unlikely
that the lower terraces
Scarp modeling
were
2
ever Forested
(Rosenbloom and
Anderson. 2004)
Low
Drum Mtnts.. UT.
USA
Haks ot at (1984)
39.650
-112.136
11
0.26
32.6
0.59
Alluvial gravels
I
Scarp
modeling
I
SE
Australia
-36.605
149.493
40
0.74
86.9
0.69
Gratnodiorite
3
of
Heimsathor al.
(2005)
-36.605
149.493
28
0.74
86.9
0.69
Granodiorite
3
depth-integrated soil
production rates
Huhso t(09
4.5
Heimsath e
(2000)
at'
and CRN-derived
rate
SE
2
erosion
Sediment flux
Nunnock River.
Australia
and
shadescale)
Hillslope Laplacian
Nunnock River.
shrubs
(sagehsh
Schlerophyll forest
(lightly forested)
rm
and
5
Schleophyll
forest
(lightly forested)
depth-gradient
Product
Cherwell Basin. New
Zealand
Feather River. CA.
USA
htghes tt
tO (2009)
Hurstt ral
(2012)
-42.40
39.652
173.357
-121.312
88 1 30
80
1.42
(.01
116
117
Loss underlain
0.57
2.47
163
fluvial
gravel
Sediment flux from
by
terraces
Granitic
3
deposits
and slope
ridetp
Laplacian
and CRN-drivtd
erosion rates
2
Mixed
conider forest
4
Feather River. CA.
USA
Hurst et al. (2013)
Feather River, CA.
USA
Hurst e al.(2013)
39.724
39.710
-121.285
-121.262
48
88
18
1.10
33
1.15
113
2.43
ridgetop Laplacian
and CRN-derived
3
Metavolanics
2
Mixed conifer forest
4
2
Mi
Mixed conif
4
crosion rates
150
Granodiorite
2.30
Laplacian
ridgetop
and rsion rates
3
sediment
flux estimated from
s-it velocity
. es
Related
Smokey
Great
Mountains, NC.
USA
Jungers ei al. (2009)
LakeBonneville.
UT. USA
MattsonandBruhn
(2001)
-83.176
331
1.93
70
185
(determined
3
Quartzite
0.33
situ and
5
by in-
meteoric
4
Deiduous forest
"oBe) and hillslope
Wasatch Fault Zone,
UT, USA
San Francisco
40.489193
Mn ason andBruhn 40.723594 -111.8232455
(2001)
(2014).
Springville Volcanic
McGuire et al.
-112.3262747
12
3
0.4097
28 I
0.4203
43.7
49.1
Al
Al
0.82
gradient
uvial shoreline
I
deposits
A Iluvial
0.95
gravels
I
35.390
Scarp modeling
-111.570
0.44
40
49.3
1.36
Basaltic cinder cones
I
34.190
and aerial
2
Pinyon pine,
at lower
assumed
sagebrush
age
initial shape and
elevation to Ponderos
4
of cinder cone
LEM with
(2014)
2
Grasses
scrubland visilbe in
satellite
images
(2084).
east-c1ntral
and shrubs
Scarp modeling
LEM with
M uietal
Volcanic Field in
norhtem Arizona
Field in
35.559
-109.570
0.50
50
56.4
1.70
Basaltic cinder
cones
elevation
Ponderosa pin.,
gasibel
oak, alligator
assumed
initial shape and age
S
barkjunipr. Douglas
fir. Pinyon, sagebrush
4
ofcinder cone
Arizona
3
pin. forests at higher
and juniper in lower
elevations
Lodgepole
pine.
offrey
Pandora.,
Medicine Lake
Volcanic Field in
northeastem
3McG.I et
(2014).
al.
41.640
-121.740
0.44
75
45.2
1.46and
4
LEM with assumed
initial shape and age
pin,
sugar pine,
white pine:
western
4
and white fit at
cnderconered
of
.f~ider on.higher clevation;
I
California
Western juniper
East Bay Regional
Park. CA. USA
AcKean st al. (1993)
37.974
-121.865
50
360
0.34
43.1
2
Marine shale
2.53
Emmet County. MI.
USA
NAsh (1980a)
45.575
-85.113
120
0.94
77.9
1.00
ohesionless send and
gravel morain deposits
Drum Mms., UT'
Nash (1980b)
39.650
-112.136
4
0.26
32.6
0.59
Alluvial gravels
USA
flux
sediment
2
slose
at
lower elevations
.P"
0
3
and
2
Grse
5
2
hardwoods
with
white
pine and hemlocks.
Native
Scarp modeling
scattered
4
Law shrubs
h and
(sageb
2
shadescale)
and
spasm coverage of
pine trees visible in
3
photographs of site3
and satellite and aerial
Prairie grasses
Hebge
Lake. MT.
USA
Nash (1984)
44.701
-111.204
20 + 4
0.72
62.2
0.56
47.637
7.516
14
0.88
73
0.76
Staid and gravel
Scarp
I
modeling
Estimate
Upper Rhine Graben. Niviee andarquis
(2000)
Germany
Fluvial gravels and
coarse
sands
I
swarp
from
both
modeling and
estimating
sediment at toe of
from
modeling
Lathr
p WIlls,
NV.
USA
Pelleier andCln
(2007)
36.690
-116.510
39
39
Looswvesicular scoris
0,710.1.43
0.07
80.9
143
numerical
using initial
and
curet shape of
cinder
lapil
cone
cone . Age of
4
Spar.
I
Grasses
vegetation
I
is -77 ka
determined from
8
8diometric dating
Alluvial shoreline
Bonneville.
UT. USA
Lake
Pelletier el al, (2006)
39.400
10
-113.700
0.20
25
0.72
swarps
Scarp modeling
(mostly sand and/or
gravels)
and shrubs
2
Measured soil
thik1nes and known
B nit. lava
flow. Valles Cadets. Pelleterel
NM. USA
Banco
al. (20
11)
36.840
-106.590
1
6
0.44
48.2
1.15
P88848 888 pin.
age of lava flow to
ak
lest a nonlinear.
R6volit
4
numerical
gamble
. and mixed
scbland
LEM and
determine the best-
conifer
3
forest
fit D
AI18ghey
u
P
et al. (2012)
Peron
39.971
-80161
PA. USA
U.8A.
Mesa,
CA.
Perrone , al. (2012)
35.923
-120.826
USA
100 + 8
0.98
105
0.53
124 19
0.18
28.4
2.41
Sandstone
2
Poorly consolidated
2
conglomerate
2
2
Decidious
Laplacian
2
Grasses & 08k8
2
Gass&Ok
and erosion rates
4Ridgat
p
and erosion rates
Used LEM to
parameter inversion
estimate D through
8isib
in
photographs
3
W
UsatAh
Mt..
UT.
Petitel al. (2009)
41.031
USA
-111.894
1200
100
0.53
57.5
8.00
Gneiss88
G8s
a
Monte Carl.
3
and
error
minimization.
Big Lost River
Valley, ID. USA
Pierce and Colman
(1986)
43.809
-113.336
21
61
-20
0,28
28.3
0.98
Carbonate gravels
and
wads
I
forest
Ridgetop Laplacian
Scarp modeling of
analytical solution
w/error function
4
3
Patchy vegetation with
Irmes.
mixture
grasses3
of
sage. and
a
ofsite. satellite, and
image$
aerial
South-facing slopes
ame shrub desert and
north-facing slopes are
2
Praire grassland
Intnsel8y sheared
TCA.es
ee
VUSA8y'
Reneau (1988)
eported in
Heimath
e
thrust
sheets greenstoni'
gr ywwck sandstone
and chert (Franciscan
of
37.863
-122.550
50
0.94
94.2
2.42
al. (2005)
assemblage)
164
of
landslide deposits.
Colluvial infilling
2
Coastal
grassland
scrub
and
2
Uoitys*A
Southern Coast
Range, OR
Reneau (1988)
reported in Heimsith
et al. (2005)
38.047
-122.852
43.788
-123.931
30
0.93
99.1
2.53
+ 13
1.7848
168
2
Quartz diorite and
grantdierilr
Colluvial infilling of
3dBspsits
Iandslidr deoits
5
Bhbp pine forest
4
5
Conifer forest
4
Colluvial infilling
Reneau ndDietrich
(1991)
Clecrwater Sincer
C Reneaunt al. (1989)
WA, USA
Bodmin Moor.
Comnwall, UK
Riggins .1 al. (2011)
Sullixce Cemk. OR
' Roering el al. (1999)
USA
Charwell River'
SouthIsland, New
Zealand
Roering eal (2002)
47.660
-124.000
47 25
4.20
50.508
-4.439
394 7
1.96
43.463
-124.119
36+
16
200
-42.450
173.357
120 + 80
142
Charwell River.
South Island, New Roeringefal (2004)
Zealand
-42.450
Oullivan Cieek, OR
Roeringetal (2007)
u Sa
43.463
USA
51
173.357
-124.119
160 + 60
29
14
1.42
2.00
311
114
(68
I6
Tyre Formaion (Ecer
graywacke sandstone)
1.72
Silts, sandstones and
0.73
Granite
1.96
0.07
2
sandstone)
2
Sediment flux
estimates from
dating hollow
deposits (-10,000 yr
timescale) and
hillslope gradient
0
Westetn hemlock
Pacific silver fie ferest
4
3
Ridgetop Laplacian
and soil production
rate
2
Grasses, but
previously hazel and
rik woodland
4
HillIslope
and
Lois underlain
168
1-96
Tyre Formation (Eocene
graywacke sandstone)
Laplacian
vegetation-driven
creep (-9k yrs)
2
Numerieal modeling
by
fluvial gravel terraces
and
Douglas fir, mixed
conifer forest
timscale of
underlain by
0.57
Minimized error
between modeled
rates and
measured erosion
rates for non-inear
erosion equation
erosion
-
Loess
fluvial
gravel terraces
116
and hillslope
gradient
conglomerates
Tyee Formation (Eocene
graywacke
flux
oftransient
hillslope
4
Podocarp and beech
forest
Podocarp and beech
forest
I
laplacian
erosion rate
Douglas fir, mixed
Ridgetop
and
coifer
Rosenhloom and
Anderson (1994)
36.984
-122.127
WindRiver Ruege.
WY. USA
Small e al (1999)
43.370
-109.750
Laguna
Salads, Baja
Califernia, Mexiu
Spele, al. (2008)
32.075
-115.383
Qilian Shan. China
Tupp9e)ell.
(1990)
39.262
99.608
100
12
176
2
0.72
79.8
2.62
Mudstone
1.00
60.3
0.44
Granite and gneiss
Numerical model
with best-fit D
4
Ridgetop laplacian
and erosion rates
0.04
33+ 17
0.11
8.3
2.02
Gravel
terraces
famed, upper terraces
grassland. Likely
never forested
Non-vegeatated.
alpine
landscape
non-vegetated.
but
vegetation
near active fans and
channel bars.
Mostly
some
Finite-slupe end
0.9
0.4 0.3
forest
terraces are
Lower
Santa Cruz. CA,
USA
3
profile
deinit-lupeca
modeling tecbique
Mostly non-vegetated.
11.9
Fanglomerates
1.39
bedrock, but
blanketed with
Basalt
BlueMountien
WA. USA
Walther e al (2009)
46.148
-117.938
0.82
48 7
74.4
which
sparse
Scrpmsome
2.62
regetation
visible in
photographs of site
Slope ofline
between differential
erosion rate (from
glass age estimate
and peak profile of
Mazama ash) and
differential
lIens,
controls erosion
rate.
coniferusnfet
curvature.
Susquehanna Shale
HilIn Critical
Observatory. PA.
USA
Atacama Desert.
Decidious
.st
et al. (2014)
40.667
-77.903
67
+ 56
-40
0.95
97.6
Shale
0.50
2
Meteoric "Be and
billslope gradient
5
forest on
hillslopes and
hemlock and pine in
vallev (Aaet al.,
4
2013)
Tbin cud
Chile
-24.130
-69.990
1.4+
.5
0.01
0.7
3.43
Granitic (Owen
2011)
el al..
Ridgetop Laplacian
and erosion rates
Ridgetop Laplacian
and erosion rates
Desert
I
Ridgetop Laplacian
and erosion rates
Oak grsIand
3
2
Deer
Atacama Desert.
Chile
Tistd
-29.770
-71.080
16 2
0.07
7.8
3.38
Granitic (Owen ei al..
2011)
Blasingame, CA.
USA
This study
36.954
-119.631
23
3
0.26
38.7
2.23
Tonalite (Dixon el al.,
2009)
3
Dritl Creek. OR.
USA
Tbic sindy
44.517
-123.844
167i37
2.55
223
1.95
Tyee Formation (Eocene
graywacke sandstone)
(Bierman el al., 200 1)
3
This study
35.622
-83.204
1
1.38
154
0.44
Quartzite (3aifan et
al., 2003)
3
Ridgetop Laplacian
and erosion rates
2
riduene feret
4
This
34.051
-116.934
21
0.59
72.9
2.07
and
3
Ridgelep Leplcin
and erosion rates
2
Chapparral and oak
identifed in satellite
3
Pimntly grnitic nd
metcmerpbi reks
(DiBise el al., 2010)
3
Great Smokey
Mountains, NC.
USA
San
Bernardino
Mountains, CA. USA
19+
Ridgetop
ned
Laplacian
erenienres
2
Primarily granitic rocks
study
175
(quartz monzonite
gneiss) (Binnie et al.,
2007)
San Gabriel
Mountains, CA.
USA
This study
34.364
-117.992
71
12
R66
77.1
2.33
.l
images.
Chaparral, decidious
and
visible in
sanellite and aerial
images
.
Intensely sheared
coniferous
Dense
ferrest
conifers
Ridgetop Laplacian
and erosion raetes
thrust
of greenstone.
greywacke sandstone
and chert (Franciscan
sheets
Tennesse Valley.
CA. USA
This study
37.850
-122.550
174
21
0.89
84.4
2.45
assemblage)(Heimsath
el al.. 1997)
165
Ridgetop Laplacian
and erosion rates
2
Coastal grassland and
scrub
4
WasatchMontain.
UT, USA
location
Thin study
40.892
-111.865
used location
literature and
83
3
0.45
1.03
31.0
Gneiss (Stock
2009)
el a..
a region,
a
Ridgetop Laplacian
and erosion rates
lat/lon
2
for the study.
I report the mean
that best matched the site description. If multiple measurements were made for
the
was not able to be identified, I
exact
the standard error D
D were included. I
If raw
standard
standard deviation,
may reflect the
reported in the
the
report that instead.
'Rock category: 1= unconsolidated, 2 =sedimentary, 3 = Igneous/metamorphic.
Technique category: I = Scarp modeling. 2 =Laplacian and erosion rates. 3 = Reliefand erosion rate, 4 = LEM. 5 = Colluvial flux and slope.
forested, 4=frested.
I = Arid/desert, 2 = grasslands/scrublands, 3 =
Xgetation
"Ifihe
'Uncertainties ae
category:
uncertainties
range,
or
error.
savannaMightly
166
estimates of
Patchy vegetation with
mixture trees
sage, and grasses
visible in photographs
of site, satellite, and
aerial image"
calculated
of and
of
3