Climatic Influences on Hillslope Soil Transport Efficiency
ASS
H
ES
OF TECHNOLOGY
by
JUN 10 201
Naomi D. Schurr
LIBRARIES
Submitted to the Department of Earth, Atmospheric and Planetary Sciences
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science in Earth, Atmospheric and Planetary Sciences
at the Massachusetts Institute of Technology
May 12, 2014
Copyright 2014 Naomi D. Schurr. All rights reserved.
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document
in whole or in part in any medium now known or hereafter created.
Signature redacted
Author
DepartmeLo Earth, Atmospheric and Planetary Sciences
Signature redacted
May 12,2014
Certified by_
Signature redacted
J. Taylor Perron
Thesis Supervisor
Accepted by
Richard Binzel
Chair, Committee on Undergraduate Program
Abstract
The soil transport coefficient D represents the relationship between local
topographical gradient and soil flux in the landscape evolution model. This work
presents new estimates of the soil transport coefficient D at 9 sites and compares them,
along with a compilation of 16 previously published estimates of D, against three climate
proxies (mean annual precipitation, aridity index, and mean annual temperature) with the
goal of characterizing climatic influences on soil transport efficiency. The new
measurements were performed at sites that extend the range into both drier and wetter
climates than those published. Together the data suggest that D increases with mean
annual precipitation and aridity in dry climates, and levels off or decreases gradually in
wetter climates.
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2
Acknowledgements
I would like to thank my advisors Taylor Perron and Paul Richardson for sharing their
enthusiasm for surface processes with me, teaching me geomorphology from scratch, and
guiding me through this adventure. Paul has spent countless hours meeting with me
every week, running analyses with and for me, and explaining concepts as many times as
necessary.
I would like to thank Jane Connor for providing moral support and encouragement (and
delicious honey walnut raisin cream cheese at thesis meetings!) in addition to instruction
in communication.
I would also like to thank Hosea Siu for reading drafts, making sure I had enough food in
lab and answering random thesis questions; Anders Kaseorg for help with code to extract
data from the compilations; my roommate Erika Ye for making sure I came home from
lab eventually; and all of my housemates at the Women's Independent Living Group for
supporting me and putting up with replies of "thesis, thesis, thesis!" to any inquiry.
Finally, I would like to thank all my friends and family for their constant encouragement
and support.
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3
Contents
1
2
3
4
Introduction...................................................................................................................
6
1.1
M otivation........................................................................................................
6
1.2
Background ..........................................................................................................
7
8
1.2.1
M athem atical M odels of H illslope Soil Transport......................................
1.2.2
M ethods of Estim ating Soil Transport Efficiency .....................................
11
1.2.3
Existing Estim ates.....................................................................................
12
13
M ethod ........................................................................................................................
2.1
O verview of Approach.........................................................................................
13
2.2
Site Selection ...................................................................................................
14
2.2.1
Topographic Data.......................................................................................
14
2.2.2
Erosion rate estim ates ...............................................................................
15
2.2.3
M easurem ent Sites ....................................................................................
16
2.3
Hilltop Laplacian A nalysis ...............................................................................
17
2.4
Climate D ata ....................................................................................................
21
Results.........................................................................................................................
23
3.1
M ean Annual Precipitation (MA P)..................................................................
25
3.2
A ridity Index (AI) .............................................................................................
26
3.3
M ean A nnual Tem perature (MA T)...................................................................
27
Discussion ...................................................................................................................
29
4.1
G eneral Observations .......................................................................................
29
4.2
Specific Site Notes ...........................................................................................
30
4.3
O ther Factors and Future W ork ......................................................................
31
5
Conclusions .................................................................................................................
34
6
References...................................................................................................................
36
7
Appendix.....................................................................................................................
39
7.1
Selected plots with site identification ..............................................................
40
7.2
Individual m easurem ent summ ary ..................................................................
42
7.3
Sample features to m ask from DEM ....................................................................
45
7.4
Analysis output im ages ....................................................................................
47
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4
List of Tables
Table 1. Summary of Results ........................................................................................
28
Table 2. Extended table showing individual measurement data...................................
42
List of Figures
Figure 1. Control volume analysis ...............................................................................
10
Figure 2: Locations of soil transport coefficient estimate sites .....................................
17
Figure 3. Tennessee Valley Basin 2..............................................................................
19
Figure 4. Tennessee Valley Basin 2 Laplacian map .....................................................
20
Figure 5. Tennessee Valley Basin 2 Laplacian vs area-slope product...........................
20
Figure 6. Tennessee Valley Basin 2 hillshade .............................................................
21
Figure 7. D vs MAP, published estimates.........................................................................
25
Figure 8. D vs MAP, new estimates .................................................................................
25
Figure 9. D vs MAP, all estimates ....................................................................................
25
Figure 10. D vs Al, published estimates ......................................................................
26
Figure 11. D vs Al, new estimates ...............................................................................
26
Figure 12. D vs Al, all estimates.......................................................................................
26
Figure 13. D vs MAT, published estimates .................................................................
27
Figure 14. D vs MAT, new estimates ...............................................................................
27
Figure 15. D vs MAT, all estimates ..................................................................................
27
Figure 16. D vs MAP with sites identified ....................................................................
40
Figure 17. D vs Al with sites identified ............................................................................
41
Figure 18. Laplacians calculated over a DEM that has not been pre-processed....... 46
Figure 19. Ridgetop results for unmasked DEM . ........................................................
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46
5
1
1.1
Introduction
Motivation
There is strong evidence that climate affects Earth's landscape. For example,
precipitation feeds the flow in river channels, which form deep canyons and steep slopes
as they erode through rock. However, quantifying the effects of climate on landscapes is
more challenging because many parameters are coupled and difficult to isolate. In this
work, I seek to determine if a quantitative relationship exists between hillslope soil
transport efficiency and climate.
Landscape evolution is commonly described by a mathematical model that
includes terms for smoothing by diffusive soil transport, incision by streams, and uplift
[Howardet al., 1994; Dietrich et al., 2003]. Characterization of the parameters can
better constrain the model, allowing for more accurate estimation of landscape response
time, interpretation of past conditions that led to existing landscapes, and prediction of
future landscapes as a result of modem inputs.
Much attention has been devoted to climatic effects on rivers [diBiase et al.,
2010; Tucker and Bras, 1998], but there has been relatively little investigation of how
climate affects erosion and sediment transport on hillslopes. While precipitation is
expected to affect erosion rates via soil thickness on hillslopes, past comparisons of
hillslope erosion rates to mean annual precipitation and mean annual temperature have
shown no clear relationship [Riebe et al., 2001 a], likely because erosion rates are also
influenced by tectonics. This work instead examines the soil transport coefficient D,
which represents the relationship between local topographical gradient and soil flux in the
diffusive soil transport term of the landscape evolution model. D is related to the erosion
Schurr
6
rate, but, unlike the erosion rate, is considered to be relatively independent of tectonics,
leaving open the possibility of a discernible relationship with climate.
Much attention has been devoted to climatic effects on rivers [diBiase et al.,
2010; Tucker and Bras, 1998], but there has been relatively little investigation of how
climate affects erosion and sediment transport on hillslopes. While precipitation is
expected to affect erosion rates, past comparisons of hillslope erosion rates to mean
annual precipitation and mean annual temperature have shown no correlation [Riebe et
al., 2004a], likely because erosion rates are also influenced by tectonics. This work
instead examines the soil transport coefficient D, which relates the local topographical
gradient to soil flux on hillslopes. Unlike the erosion rate, D is considered to be
relatively independent of tectonics, leaving open the possibility of a discernible
relationship with climate.
1.2
Background
Soil transport efficiency is a measure of how easily soil is transported downslope
due to slope-dependent processes. Factors thought to affect soil transport efficiency
include bioturbation, precipitation, salt shrink-swell cycles, bedrock geology, and
temperature [Nash, 1980a; Owen et al. 2011].
Bioturbation, the disturbance of soil caused by plants and animals, facilitates soil
transport. Common types of bioturbation that occur on hillslopes include burrowing, root
dilation and shrinkage, and tree throw. Burrowing by gophers has been determined to be
a primary means of soil transport in several landscapes [Gabet, 2000].
Precipitation is expected to have competing effects on soil transport efficiency. In
addition to mechanically perturbing the soil to cause transport, varying degrees of
Schurr
7
precipitation support different biota that interact with the soil. At the dry end, Owen et
al. [2011] observed that erosion rates and vegetation increased together with mean annual
precipitation (MAP) at semi-arid to hyperarid sites in the Atacama Desert. At higher
MAP, the explanation that additional precipitation beyond a threshold reduces stream
erosivity by promoting growth of vegetation [Perronet al., 2009] may also apply to soil
transport efficiency on hillslopes. That is, additional root systems may have an effect of
anchoring the soil to reduce transport efficiency. If both these effects are present, an
increase in soil transport efficiency should be observed with MAP until a threshold is
reached. Once the threshold is exceeded, soil transport efficiency should decrease.
Salt shrink-swell and frost heaving are other types of slope-dependent soil
transport processes whose efficiency is influenced by climate, namely aridity and
temperature. Differences in bedrock geology have also been used to explain variation in
soil transport efficiency [McKean et al., 1993]. Of these factors that affect soil transport
efficiency, this work focuses on precipitation, aridity, and temperature.
The hillslope soil transport model is described in greater detail in Section 1.2.1,
methods of estimating soil transport efficiency are outlined in Section 1.2.2, and existing
estimates are summarized in Section 1.2.3.
1.2.1
Mathematical Models of Hillslope Soil Transport
Soil transport efficiency can be represented by the soil transport coefficient, a
diffusivity-like coefficient with dimensions [length] 2/[time] that arises from a landscape
evolution model where soil flux is proportional to the local topographic gradient.
Landscape evolution is commonly modeled by the equation
Schurr
8
-
= DVzz - KA"IVz + -U
at
PS
where z is elevation, t is time, D is the soil transport coefficient, A is drainage area, K and
m are constants, U is the surface uplift rate, and p and p, are bedrock and soil densities,
respectively [Perron et al., 2009]. The D 2z term represents the smoothing effects of
diffusion-like soil transport, and KA'"IzI is a fluvial incision term representing soil
transport and channel incision by running water.
The diffusion-like form of D Vz results form treating the soil flux q, as
proportional to the local topographical gradient with constant of proportionality D. This
form of the transport law was was presented mathematically by Culling [1960] and is
commonly used in models for hillslope evolution [Dietrich,2003]. Initially considering
the problem in one dimension gives Equation ( 2 ).
qs = -D
dz
-x
dx
(2)
Applying conservation of mass through a control volume of length Ax as in Figure 1
gives
az
qsO
at
- qsin
Ax
which yields
az
-=
at
D
0 2z
ax
2
(4)
in the limit as Ax->0. In the two-dimensional model, by similar arguments, the
relationship
Schurr
9
-=
t
DVzz
(5)
is obtained, where V2 z is the Laplacian of surface elevation and gives a measure of the
topography's curvature. In this diffusive soil transport term, the rate of elevation change
is related to the Laplacian by the soil transport coefficient D, the same constant that
relates soil flux to topographical gradient.
+qsoult
Ax
Figure 1. Control volume analysis. Treating a section of the soil as a control volume and applying conservation
of mass relates rate of elevation change to flux.
The preceding derivation assumed that the soil flux is proportional to
topographical gradient. However, Roering et al. [1999] noted that hillslopes exhibit
convex forms near the ridge but become increasingly flat downslope while the linear
dependence predicts hillslopes of constant curvature, and proposed a nonlinear slope
dependence of the form
D",Vz
qs = (1 - IVzI/sc) 2
(6)
where Dn1 is a coefficient for non-linear transport, and parameter sc is a critical slope near
which flux increases rapidly and landsliding is more prevalent than diffusive transport.
At slopes near se, landslides and non-diffusive soil transport dominate. In regions where
Schurr 10
the gradient Vz is low, however, such as on gentle slopes or on ridgetops, the
denominator is approximately equal to 1, and the dependence on slope can be
approximated as linear.
Returning to equation ( 1 ), the coefficient D can be isolated by imposing two
conditions, namely the assumption that the landscape is in steady state and the restriction
that the equation be applied only on ridgetops. The steady-state assumption removes the
time-dependence term aat and allows the topographical uplift rate to be considered
approximately equal to the bedrock erosion rate Eb, which can be determined as described
in Section 2.2.2. Imposing the ridgetop constraint removes the fluvial incision term since
A approaches zero at the ridgetop. Solving the remaining terms for the soil transport
coefficient as in equation (7 ) gives D in terms of quantities that can be measured.
PbU
PSV2Z
PbEb
(7)
pSV 2z
This approach was used by Perron et al. [2012] and is also used in this work.
Other methods that have been used to estimate the soil transport coefficient are described
in Section 1.2.2.
1.2.2
Methods of Estimating Soil Transport Efficiency
Three main methods have been used so far to estimate soil transport efficiency.
First, there are mass balance approaches, which have been used by Reneau [1988]
and McKean et al. [1993]. Reneau examined infilling of a dated landslide scar, while
McKean et al. used chemical tracers to plot flux against gradient, the slope of which is D.
The second method involves forward numerical modeling from assumed initial
conditions and elapsed time, and selecting D to match the present-day profile. Nash
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[1980b, 1984], Hanks [1984], and Rosenbloom and Anderson [1994] have used this
method on the marine terraces north of Santa Cruz, CA, and scarps in Michigan,
Montana, and Utah.
The third method combines erosion rate data and high-resolution measurements of
the ridgetop Laplacian to estimate D, and has been used by Roering et al. [2007], Hurst,
et al. [2012], and Perron,et al. [2012]. This approach is the basis for the method
described in Section 2 and was used to create the new estimates we present here.
1.2.3
Existing Estimates
Fernandesand Dietrich [1997] compiled 9 estimates of D and classified each
site's climate qualitatively. The data was limited in both number and precipitation range,
but suggested that a trend may be present. Seven additional published estimates have
been included in the compilation presented here.
Previously published estimates fall primarily within the 300 to 1000 mm/yr range
on mean annual precipitation, with no data in the very dry regions or the very wet
regions. These extremes are of particular interest because Owen et al. [2011] observed a
positive correlation between erosion rates and precipitation at low mean annual
precipitation, and because the relationship could be expected to level off or even decrease
as anchoring effects of vegetation increase with MAP.
In summary, a comprehensive data set that relates D to climate over a wide range
of climates has not yet been compiled. The purpose of this work is to extend the range of
climate variability and generate a relationship of D versus climate that holds across a
range of different sites, using published soil transport coefficients and new estimates
calculated with the analysis described in the Method section.
Schurr 12
2
2.1
Method
Overview of Approach
Estimates of the soil transport coefficient from many locations around the world
have been plotted against climate proxies, such as mean annual precipitation and the
aridity index. I present both a compilation of previously published soil transport
coefficient estimates, and a set of new estimates that have been computed from erosion
rate data and topography in locations where prior estimates have not been made. The
method used to create the new estimates is outlined here and described in further detail in
Sections 2.2-2.4.
In order to complete the analysis, an erosion rate, an estimate of the nearby
ridgetop Laplacian, and climate data are required for each site. Erosion rates have been
estimated in many independent studies, and have been compiled in publications including
those by Portengaand Bierman [2011] and Willenbring et al. [2013]. The ridgetop
Laplacian is calculated from high-resolution topographic data. Since modern global
climate data is readily available, the regions for this study were primarily constrained to
where erosion rate and high-resolution topographic data exist.
Once a suitable region was located, the corresponding data set was imported into
MATLAB. Code developed to perform the analyses described in the work of Perronet
al [2009, 2012] was used to identify ridge tops, calculate their Laplacians, and return an
estimate of the soil transport coefficient given an erosion rate estimate for the area.
I completed this procedure for seven sites, and include two sites (Atacama hyperarid and Atacama semi-arid) analyzed by Paul Richardson (personal communication,
2014) in a similar manner. The range in mean annual precipitation (MAP) across the
Schurr 13
sites is 2200 mm/yr and the range in the aridity index (Al) is 2.6. I analyzed the resulting
data to determine whether a relationship could be identified between climate and the soil
transport coefficient.
2.2
Site Selection
Site selection was constrained primarily by the availability of high-resolution
topographical data and erosion rate data at locations with soil-mantled landscapes that
appear to be in steady-state. Hillslopes in steady state are approximately symmetric and
bounded by incising river channels such that material is uplifted at the same rate at which
it erodes. The applicability of the steady-state assumption can be tested when the
Laplacian is computed since the model predicts that landscapes in steady state should
have a spatially uniform Laplacian along the ridgeline.
2.2.1
Topographic Data
Digital elevation models (DEMs) used to make estimates were obtained from
LIDAR surveys available for free download through the Open Topography
(opentopo.sdsc.edu) and USGS National Map Viewer (viewer.nationalmap.gov/viewer)
websites. Data from OpenTopography at Im and 3m resolution were downloaded in
ASCII format. Data from USGS National Map at 1/9 arcsecond (~3m) resolution were
downloaded in IMG format and converted to ASCII format with UTM projection in
ArcGIS. Ground or bare-earth download options were selected where applicable. The
DEMs were examined alongside Google Earth imagery to screen for topographic features
such as transient hill forms that would invalidate the assumptions required for the
measurement.
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2.2.2
Erosion rate estimates
Bedrock erosion rate estimates used to make soil transport coefficient estimates
were obtained from data compiled by Portengaand Bierman [2011], and Willenbring et
al. [2013]. Bedrock erosion rates have been estimated for locations around the world
from measurements of cosmogenic isotopes, particularly
10
Be.
1
Be is naturally rare,
except when produced in the upper few meters of Earth's surface by the interaction of
cosmic rays with Earth's surface [Portengaand Bierman, 2011]. Production and decay
rates of 1 Be can be used with measurements of ' 0Be abundance to estimate erosion rates.
Previously published estimates were recalculated and modified with the standardized
CRONUS method [Balco, 2008] in the compilations for better consistency.
Erosion rates are often calculated from samples obtained in a drainage basin,
giving a catchment-averaged estimate over the region that drains through the sample site.
Erosion rates can also be calculated from outcrop samples at a particular site. Outcrop
erosion rates are slower than catchment-averaged erosion rates on average [Portengaand
Bierman, 2011], but can be used as a lower bound on the soil transport coefficient when
used in conjunction with nearby soil-mantled ridgelines. A few measurements based on
outcrop erosion rates and nearby topography have been included in this work for
comparison.
The soil and rock densities for individual sites were used when found. For
locations where bedrock or soil densities were not reported, a default bedrock density
ratio of 2.7 g/cm3 and a default soil density of 1.6 g/cm3 were used to convert to bedrock
erosion rates to soil erosion rates.
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2.2.3
Measurement Sites
There are three main clusters of published erosion rate data in the United States,
which form approximately north-south strips on the West Coast, in the West through
Utah and New Mexico, and in the East along the Appalachian Mountains. Published
erosion rate data also exists in South America, Europe, Asia, Australia, and parts of
Africa [Portengaand Bierman, 20111, but LIDAR data in these locations are less
accessible or do not exist.
Based on the accessibility of data, measurements were taken using the above
method at seven sites where D had not previously estimated, and one site where a
previous estimate existed (Tennessee Valley, CA). Three of the new sites were in
California, while the rest were in Oregon, Utah, and North Carolina / Tennessee (Figure
2). Two additional measurements were made for the Atacama Desert using Trimble
global positioning system data provided by Owen (personal communication) for the sites
discussed in Owen, et al. [2011] since LIDAR data were unavailable and the sites were of
interest in order to extend the lower range of MAP values.
In total, 16 published values and 9 new estimates of D are reported here.
Schurr 16
*
*
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
00
00
Figure 2: Locations of soil transport coefficient estimate sites in the US
with a close-up view of California. Not pictured: 1 site at the Nunnock
River, Australia, and two sites in the Atacama Desert, Chile.
2.3
Hilltop Laplacian Analysis
The procedure for estimating the soil transport coefficient involves selecting the
basin of interest within the DEM, calculating the Laplacian, gradient, and drainage area
for points in the selection, determining the points that represent ridgelines, and finally,
computing the coefficient.
The DEMs are first masked manually through a graphical user interface.
Ridgelines of the basin that contribute to the sample are included in the selection on
which subsequent calculations will be run, while roads and river bottoms, which may
have outputs that are similar to ridges, are excluded. (Examples of these features and
how they affect ridgeline selection are given in Appendix 7.3). Google Earth imagery,
such as the Tennessee Valley Basin 2 example in Figure 3, may be useful for determining
landscape suitability and identifying features to include or exclude.
The Laplacian at each point is calculated from the coefficients of a twodimensional quadratic surface that is fit to the data over the 15m-by-15m geographic
Schurr 17
region surrounding the point using a least-squares regression with an inverse-distance
weighting scheme. The 15 m window was selected experientially to cover an extent large
enough that the calculation is relatively robust to topographic noise, but not so large that
actual curvature is lost to smoothing. Figure 4 shows the resulting calculated Laplacian
for the topography shown in Figure 3.
The gradient, drainage area, and area-slope product are also computed at each
point. The area-slope product is then binned logarithmically, and the mean value of the
corresponding Laplacian within the bin is defined as the bin Laplacian. The Laplacian is
plotted against the area-slope product in order to allow for the identification of ridgeline
data, which is contained in the bins where the area-slope product is small and the
Laplacian is relatively constant, as predicted by the linear slope dependence that this
analysis assumes. If there is no flat region in the Laplacian versus area-slope product
curve, then the steady-state assumption is unlikely to hold. An example Laplacian vs
area-slope product graph with the ridgeline portion highlighted is shown in Figure 5, and
the corresponding ridgeline is highlighted on a hillshade in Figure 6.
An algorithm was developed to automatically identify ridgeline points since
visual estimation of the appropriate bins can be subjective and tedious. The algorithm
first rejects bins that have less than a threshold number of data points, set at 20 in this
analysis. The first bin accepted, the "low bin," is the bin with minimum area-slope
product after which all bins (excluding the right tail) have more than the threshold
number of data points. The algorithm then finds the "top bin" such that the cumulative
mean of bin Laplacians is most negative. (Note that this algorithm differs from selecting
the bin with the most negative bin Laplacian as the top bin, since this algorithm also
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includes bins that are less negative than the minimum as long as they are more negative
than the cumulative mean up to that bin.) The points contained between the low bin and
top bin, inclusive, are considered to comprise the ridgeline. This algorithm is useful
when a clear transition is not discernible between the portions of the D vs area-slope
product curve. A visual quality-check is performed after the algorithm runs to ensure that
a representative Laplacian selection has been made.
The reported overall Laplacian is the median of the selected bin Laplacians. The
soil transport coefficient is computed by dividing the erosion rate estimate by the overall
Laplacian, and negating the quotient, as in equation ( 7).
Figure 3. Tennessee Valley Basin 2. Outcrops and roads are clearly visible. However, the majority appears to be
soil-mantled with clearly defined ridgelines.
Schurr 19
CA Tennessee Valley Basin 2
I
0.15
0.1
0.05
-0.1
200m
Figure 4. Tennessee Valley Basin 2 Laplacian Map with roads and large outcrops removed. Ridgetops have
negative Laplacians while valleys have positive Laplacians.
CA Tennessee Valley Basin 2
Lap= -0.012958, stdev = 0.0030904
0.251
0.2 F
0.15F
0.1 0.05F
.
A.
0
0
3.
-0.05-0.1-A1
0.C
10-2
100
10
10
106
Area-slope Product, A IVzI (m2)
Figure 5. Tennessee Valley Basin 2 Laplacian vs area-slope product plot showing in green bins identified by the
algorithm as belonging to the ridgetop.
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N
CA Tennessee Vaiey Basin 22
DTV4,TV5.cree2 = 29, 20, 190 [cm tyr]
elev. 300
200m
Figure 6. Tennessee Valley Basin 2 hillshade showing ridgetop points corresponding to those identified in Figure
5 in green.
2.4
Climate Data
The mean annual precipitation (MAP) and aridity index (Al) were used as proxies
for climate. The soil transport coefficient was also plotted against mean annual
temperature (MAT).
The MAP and MAT for sites in the United States were drawn directly from the
total precipitation (rain + melted snow) and temperature 30-year PRISM datasets,
respectively. The MAP and MAT values for the Australia site [Heimsath 2000, 2005]
were taken from the Australian Government Bureau of Meteorology 30-year datasets,
while MAP and MAT values listed by Owen et al. [2011] were used for the Atacama
Desert.
Schurr 21
The Al is calculated from MAP and the potential evapotranspiration (PET), which
is the sum of the evaporation and transpiration that would occur if such quantities of
water were available.
MAP
(8)
Al= annual PET
As in equation ( 8 ), the Al is equal to MAP divided by PET, making Al a more
informative representation of climate since it also reflects the amount of water retained in
the soil. Despite its name, higher Al values correspond to wetter regions, where
precipitation exceeds the demand for moisture. I obtained Al values for all sites from the
CGIAR-CSI Global-Aridity and Global-PET Database [Zomer et al., 2007, 2008],
available at http://www.cgiar-csi.org.
The analysis proceeds with the caveats that using the climate proxy value at the
erosion rate measurement site ignores climatic variations over the basin that influences
the measurement, and that the use of recent MAP, Al, or MAT values in our comparison
assumes that current climate data is representative of the climate at the time in which the
erosion was occurring.
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3
Results
The new and existing soil transport coefficient estimates are shown here plotted
against the mean annual precipitation (Figure 7-Figure 9), aridity index (Figure 10-Figure
12), and mean annual temperature (Figure 13-Figure 15). The data for these plots are
summarized in Table 1, and a full table with data for individual measurements made is
included in the Appendix 7.2 (Table 2). Numbered versions of Figure 9 and Figure 12
with individual sites identified are presented as Figure 16 and Figure 17, respectively, in
Appendix 7.1.
Error bars have been included on the new measurements to show one standard
error of the mean in both directions, reflecting uncertainty in estimates of D and climate
for sites where multiple erosion rate estimates and ridgelines were used to create the site
estimate.
There appears to be an upward trend in both the published and new values of D
versus MAP in the precipitation range from 0 mm/yr to 1000 mm/yr (Figure 7). The new
estimates show a slightly downward trend from 600 to 1600 mm/yr (Figure 8), but the
downturn is not as well-defined, especially when viewed in conjunction with the
published data. Together, the published and new estimates suggest a relationship in
which D rises with precipitation for low MAP and either decreases gradually or stays
approximately constant with precipitation for higher MAP (Figure 9).
Similar trends are visible in the data for D versus Al (Figure 10-Figure 12), in
which there is an upward trend in D for low Al (drier climates) that levels off or
gradually decreases for higher Al (wetter climates).
The plots of D versus MAT (Figure 13-Figure 15) do not suggest any relationship.
Schurr 23
The Oregon Coast Range, which has both the highest mean annual precipitation
and aridity index, appears as an outlier.
Schurr 24
3.1
Mean Annual Precipitation (MAP)
Tr
1o2
E
101
1001
0
1500
1000
Mean Annual Precipitation [mm/yr]
500
2500
2000
Figure 7. D vs MAP, published estimates
0
102
::C
t
E
101
*
100
0
I
I
*
New Estimates (catchment)
New Estimates (outcrop)
1500
1000
Mean Annual Precipitation [mm/yr]
500
I
2500
2000
Figure 8. D vs MAP, new estimates
*
0
102
C4
I:f
E
101
*
10
0
i00
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
1500
1000
Mean Annual Precipitation [mm/yr]
2000
2500
Figure 9. D vs MAP, all estimates
Schurr 25
3.2
Aridity Index (AI)
103
102
E
10
10
0
0
0.5
3
2.5
2
1.5
1
Aridity Index
Figure 10. D vs Al, published estimates
0
102
-v
#.
E
9.0
0
101
New Estimates (catchment)
New Estimates (outcrop)
*
10
I --0
*
L-
1.5
1
0.5
2
2.5
3
Aridity Index
Figure 11. D vs Al, new estimates
'U
0
102
1
E
9.
0
101
*
10
0
0.5
1
1.5
Aridity Index
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
2
2.5
3
Figure 12. D vs AI, all estimates
Schurr 26
3.3
Mean Annual Temperature (MAT)
102
E
0
101
100L
-5
0
15
10
5
20
Mean Annual Temperature [*C]
Figure 13. D vs MAT, published estimates
103
102
E
10
*
*
-5
0
New Estimates (catchment)
New Estimates (outcrop) I
10
5
Mean Annual Temperature [*C]
15
20
Figure 14. D vs MAT, new estimates
10
102
E
10
*
*
10o
-5
0
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
10
5
Mean Annual Temperature (*CJ
15
20
Figure 15. D vs MAT, all estimates
Schurr 27
Table 1. Summary of Results
Published Study Location
1 Emmet County, MI
Long.
(*)
D
[cm 2/yr]
MAP
[mmyr]
Al
MAT
[C]
45.529
39.207
36.984
39.617
44.709
37.863
38.050
37.972
36.971
43.378
43.462
120
4.4
110
10
20
50
30
360
100
180
32
786
329
890
289
563
902
1021
440
792
839
1903
0.94
0.25
0.72
0.24
0.70
0.92
0.93
0.34
0.66
0.87
2.03
6.3
8.9
14.2
9.8
2.25
13.6
13.7
15.0
13.8
-0.1
11.1
Nash (1980a)
Nash (1980b)
Hanks(1984)
Hanks(1984)
Nash (1984)
Reneau (1988)
Reneau (1988)
McKean (1993)
Rosenbloom and Anderson (1994)
Small et al. (1999)
Roering et al. (1999)
Gabet (2000)
Lat.
(0)
Reference
throughout UT
Santa Cruz, CA
Lake Bonneville, UT
West Yellowstone, MT
Tennessee Valley, CA
Point Reyes, CA
Black Diamond Mines, CA
Santa Cruz, CA
Wind River Range, WY
OR Coast Range near Coos Bay, OR
-84.930
-112.702
-122.127
-112.297
-111.161
-122.546
-122.850
-121.861
-122.133
-109.758
-124.135
12
Sedgewick Reserve, CA
-120.035
34.707
74
596
0.39
16.2
13
14
15
16
Nunnock River, Aus.
Allegheny Plateau, PA
Gabilan Mesa, CA
Feather River basin, Sierra Nev., CA
149.479
-80.261
-120.826
-121.3
-36.616
39.971
35.922
39.66
34
100
120
86
D
[cm 2/yr]
800
1053
303
1637
MAP
[mm/yr]
0.73
0.98
0.18
1.08
13.5
9.9
15.9
15.4
MAT
[C
Heimsath et al. (2000,2005)
Perron et al. (2012)
Perron et al. (2012)
Hurst et al. (2012)
16
150
70
54
170
17
110
32
1
D2
[cm /yr]
1537
643
632
634
891
1758
1933
119
2
MAP
[mm/yr]
1.41
0.58
0.53
0.66
0.92
1.15
2.31
0.07
0.01
this study
this study
this study
this study
this study
this study
this study
this study
this study
Al
10.8
11.7
9.6
13.0
13.6
14.2
11.1
13.5
17.0
MAT
[oC]
12
35
1769
903
1.87
0.92
9.8
13.5
this study
this study
2
3
4
5
6
7
8
9
10
11
Catchment Study Location
1 Great Smoky Mountains, NC/TN
2
3
4
5
6
7
8
9
San Andreas / San Jacinto Faults, CA
Wasatch, UT
San Gabriel Mountains, CA
Tennessee Valley, CA
Oroville, CA
Oregon Coast Range, OR
Atacama Desert (semi-arid), Chile
Atacama Desert (hyper-arid), Chile
Outcrop Study Location
1 Great Smoky Mts (Outcrop), NC/TN
2
Tennessee Valley (Outcrop), CA
Long.
()
-83.206
-116.934
-111.865
-117.994
-122.547
-121.332
-117.981
-71.078
-69.994
Long.
(0)
-83.233
-122.547
Lat. ()
35.620
34.051
40.892
34.364
37.862
39.639
36.262
-29.774
-24.125
Lat.
(0)
35.673
37.863
Al
Reference
Reference
Schurr 28
4 Discussion
Both the D versus MAP and D versus Al plots suggest a relationship between D
and wetness in which D increases steeply with MAP and Al in drier climates, and
decreases gradually with MAP and Al in wetter climates. The peak D appears to occur at
an MAP of approximately 500-1000 mm/yr and an Al of approximately 0.5-1.
The upward trend for low MAP and Al is in agreement with the prediction by
Owen et al. [2011]. In very dry climates, there is little biota to agitate the soil. The
semiarid Atacama site with 120 mm/yr had a plant density of 30%, while the hyper-arid
Atacama site with a MAP of less than 2 mm/yr had a plant density of 0. The landscape at
the semi-arid site undergoes bioturbation and chemical weathering processes while the
landscape at the hyper-arid site is too dry for bioturbation and is acted upon primarily by
salt shrink-swell and overland flow, which are less effective at transporting soil. Thus it
seems that the climate is affecting the soil transport efficiency through the biota that it
supports.
The lack of a trend in D versus MAT is not surprising for this range of
temperatures. The new sites in particular have a very limited MAT range where biotic
factors are not expected to be reflected. Even with the published data, which has a larger
MAT range, the lower end where cold-dependent abiotic processes are expected to be
more effective is not well represented.
4.1
General Observations
With the exception of the Oregon Coast Range, the new D estimates show a
cleaner trend than the published values in both MAP and Al. Consistency in the
Schurr 29
estimation method for the new D values may be contributing to the cleaner trend in the
new data, but additional estimates in overlapping climate ranges would need to be
compared to see whether this holds in general.
The assumptions that the landscape is in steady state, that linear transport applies,
and that modern climate is representative of the climate in which the landscapes formed
are also potential sources of uncertainty. The steady state assumption was tested
qualitatively by the area-slope product plot created as part of the Method, and the linear
slope dependence is approximated by applying the analysis only on ridgelines. The
climate assumption is more challenging. The timescale for hillslope evolution depends
on D, but is typically on the order of 105~106 years [Fernandesand Dietrich, 1997],
which is at least as long as a glacial cycle.
One note is that in adding 9 new estimates to the data set over a range of climates,
the range of D remains relatively unchanged since Fernandesand Dietrich [1997] noted
2
that existing estimates of D ranged from 4 to 400 cm /yr. Estimates in the Atacama
2
2
Desert added a new low D of 1 cm /yr, but the upper bound of 360 cm /yr [McKean, et
al., 1993] was not exceeded.
4.2
Specific Site Notes
The estimate presented here for Tennessee Valley is much higher than the existing
estimate presented by Reneau [1988], whose estimate is based on the infilling of a dated
landslide scar. The topographical curvature method used here is considered to be more
precise, but further investigation is required.
The Great Smoky Mountains have a lower D than anticipated in comparison to D
calculated for the Allegheny Plateau [Perronet al., 2012], which is also in the
Schurr 30
Appalachian Mountains. The ridgetops at the Great Smoky Mountains site are relatively
sharp and the erosion rates are very low, which results in a low estimate for D.
The site used for the Oregon Coast Range measurement in this study is located in
the northern tip of the Siuslaw National Forest, approximately 150 km north of Coos Bay,
2
where Roering et al. [1999] estimated D to be 32 cm /yr. The reason why the D value
estimated in this study (110 cm 2 /yr) is so high is currently unclear, and the measurement
at the Oregon Coast Range site will be re-examined. There is, however, a large
variability in erosion rates at this site. Three samples within 500 m of each other have
bedrock erosion rates of 66, 138, and 300 mm/kyr, which suggests that the erosion rate is
not well-constrained for this site.
The estimate for Oroville, which is at the Feather River site studied by Riebe et al.
[2000], is much lower than the estimate presented by Hurst et al. [2012] for the same site.
Hurst et al. used the slope of a Laplacian versus erosion rate trend line over 25 hillslopes
to estimate D for the region as a whole. The estimate presented in this study used only
one hillslope, so it is not unsurprising that it does not match the prediction by Hurst et al.
Performing this analysis on a subset of the hillslopes used by Hurst et al. will give a
better idea of the compatibility of the results.
4.3
Other Factors and Future Work
While several factors have been identified as influencing D (Section 1.2), this
work focused solely on annual climate proxies. As such, this work does not attempt to
account for differences in D caused by differences in rock and soil type or grain size,
which was used to explain variations in D by McKean et al. [1993]. The sites presented
here could be classified by bedrock type to determine whether an effect is visible.
Schurr 31
This study also does not track biota directly. In the indirect sense, MAP and Al
affect the populations that a region can support, but this relationship is not explored
quantitatively here.
By using annually averaged climate proxies, seasonality and higher-frequency
variations are not considered. Two sites with similar MAP may experience different soil
transport processes if one site has distinct wet and dry seasons and the other does not, just
as two sites with similar MAT may experience different soil transport processes if one
has temperatures that vary significantly over the course of a day or a year while the other
has less variation. Interpreting the D values presented here in terms of seasonality may
provide further insight.
In addition to including seasonality, understanding of the potential relationship
between D and climate could be improved by considering sites with even higher MAP,
and by making comparisons of D across a smaller region that still varies significantly in
MAP.
While the new sites analyzed here extended the MAP values through the 0-300
and 1000-2300 mm/yr range, a lack of data remains for the high precipitation values
above 2300 mm/yr. Erosion rate estimates have been made for basins in northern Kauai
near Hanalei Bay [Ferrieret al., 2013ab] (K. Huppert and K. Ferrier, personal
communication, 2014) and in Luquillo, Puerto Rico, both of which have MAP of
approximately 3000 mm/yr. LIDAR also exists for both sites, though the ground return
for Luquillo is sparse due to dense vegetation. The value of D is expected to be low for
the Hanalei sites since the ridgelines are sharp and the estimated erosion rates are not
unusually fast.
Schurr 32
Kauai alone has a wide range of MAP (700 to 7000 mm/yr) at sites where erosion
rate estimates have been made. Estimating D at various sites that have soil-mantled
landscapes and seeing whether the relationship holds throughout Kauai alone would
likely be informative.
Schurr 33
5
Conclusions
This work presents new estimates of the soil transport coefficient D at 9 sites and
compares them, along with a compilation of 16 previously published estimates of D,
against three climate proxies (mean annual precipitation, aridity index, and mean annual
temperature) with the goal of characterizing climatic influences on soil transport
efficiency. The previously published data was primarily clustered at sites with MAP of
300 to 1000 mm/yr, while the new measurements were performed at sites that extend the
range into both drier and wetter climates.
The results show no relationship between D and mean annual temperature.
However, the results do suggest a relationship between D and "wetness" measured by
both the mean annual precipitation (MAP) and the aridity index (Al). At low MAP and
Al, D steeply increases with these climate proxies, and at higher MAP and Al, D
decreases gently with these climate proxies. The peak occurs near MAP values of 500
and 1000 mm/yr, and Al values of 0.5 and 1. This is consistent with ideas proposed by
Owen et al. [2011 ] and Perron et al. [2009].
Not all sites in the compilation follow this trend. In particular, the new estimate
for the Oregon Coast Range departs from the downward trend of the other data with
MAP above 600 mm/yr. Verifying the quality of the new estimates, particularly at sites
with over 1000 mm/yr, and adding data at sites with high MAP (above 2500mm/yr)
should better constrain the behavior in wetter climates.
While the relationship is not yet quantifiable, and the data is not complete for the
higher ranges of MAP and AI, the data presented here leads to the conclusion that climate
influences hillslope soil transport efficiency in a discernible way. Additional data should
Schurr 34
better clarify a relationship between D and climate that would allow for improvements in
landscape evolution modeling and the understanding of the ties between landscape and
the climate in which it forms.
Schurr 35
6
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accessible means of calculating surface exposure ages or erosion rates from ' Be and Al
measurements. Quat. Geochronol. 3, 174-195.
Culling, W.E.H., (1960) Analytical theory of erosion, J. Geol., 68, 336- 344.
DiBiase, R. A., K. X. Whipple, A. M. Heimsath, and W. B. Ouimet (2010) Landscape
form and millennial erosion rates in the San Gabriel Mountains, CA, Earth and Planetary
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Dietrich, W. E., Bellugi, D. G., Sklar, L. S., Stock, J. D., Heimsath, A. M. and Roering, J.
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Prediction in Geomorphology (eds P. R. Wilcock and R. M. Iverson), American
Geophysical Union, Washington, D. C.. doi: 10.1029/135GM09
Fernandes, N. F., and W. E. Dietrich (1997) Hillslope evolution by diffusive processes:
The timescale for equilibrium adjustments, Water Resources Research, 33(6), 1307-1318.
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Gabet, M. J. (2000) Gopher bioturbation: field evidence for non-linear hillslope diffusion,
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Wave-Cut and Faulting-Controlled Landforms, Journalof GeophysicalResearch,
89(B7), 5571-5590.
Howard, A. D. (1994) A detachment-limited model of drainage basin evolution. Wat.
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Schurr 38
7 Appendix
Appendix Contents:
7.1 Selected plots with site identification
7.2 Individual measurement summary
7.3 Sample features to mask from DEM
7.4 Analysis output images
This section contains satellite views, hillshades, Laplacian maps, Laplacian vs
area-slope product plots, and ridgeline selection map for each site at which
calculations were made.
Schurr 39
7.1
Selected plots with site identification
10I
10.5
'15
'1
.9
102
*14
-16
1&
.6
.11
-,13
E5
.9
*1
101
,_v4
r
10-0
*
I
500
10
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
2500
2000
1500
Mean Annual Precipitation [mm/yr]
Figure 16. D vs MAP with sites identified
1
2
3
4
5
6
7
8
Published Study Location
Emmet County, MI, Nash (1980a)
throughout UT, Nash (1980b)
Santa Cruz, CA, Hanks (1984)
Lake Bonneville, UT, Hanks (1984)
West Yellowstone, MT, Nash (1984)
Tennessee Valley, CA, Reneau (1988)
Point Reyes, CA, Reneau (1988)
Black Diamond Mines, CA, McKean (1993)
9
10
I1
12
13
14
15
16
Published Study Location
Santa Cruz, CA, Rosenbloom and Anderson (1994)
Wind River Range, WY, Small et al. (1999)
Coast Range near Coos Bay, OR, Roering et al. (1999)
Sedgewick Reserve, CA, Gabet (2000)
Nunnock River, Aus., Heimsath et al. (2000,2005)
Allegheny Plateau, PA, Perron et al. (2012)
Gabilan Mesa, CA, Perron et al. (2012)
Feather River, Sierra Nev., CA, Hurst et al. (2012)
1
2
3
4
Catchment Study Location
Great Smoky Mountains, NC/TN
San Andreas / San Jacinto Faults, CA
Wasatch, UT
San Gabriel Mountains, CA
Tennessee Valley, CA
Catchment Study Location
8 Atacama Desert (semi-arid), Chile
9 Atacama Desert (hyper-arid), Chile
5
6 Oroville, CA
7 Oregon Coast Range, OR
8 Atacama Desert (semi-arid), Chile
I
Outcrop Study Location
Great Smoky Mts (Outcrop), NC/TN
2 Tennessee Valley (Outcrop), CA
Schurr 40
015
5512
.7
10
39
102
gi416
3
.4
$8
.2
q,13
_9
11
Z
Q
.1
*1
10
*
0
1000
*
0.5
1
2
2
1.5
Aridity
Index
2.5
Published Estimates
New Estimates (catchment)
New Estimates (outcrop)
3
Figure 17. D vs Al with sites identified
I
2
3
4
5
6
7
8
Published Study Location
Emmet County, MI, Nash (1980a)
. UT Mah (loe8i
U
troug 0u
Santa Cruz, CA, Hanks (1984)
Lake Bonneville, UT, Hanks (1984)
West Yellowstone, MT, Nash (1984)
Tennessee Valley, CA, Reneau (1988)
Point Reyes, CA, Reneau (1988)
Black Diamond Mines, CA, McKean (1993)
,
Published Study Location
9 Santa Cruz, CA,'Rosenbloom and Anderson (1994)
10 Wind River Range , WY ,ISmall et al. (1999)
11 Coast Range near Coos Bay, OR, Roering et al. (1999)
12 Sedgewick Reserve, CA, Gabet (2000)
13 Nunnock River, Aus., Heimsath et al. (2000,2005)
14 Allegheny Plateau, PA, Perron et al. (2012)
15 Gabilan Mesa, CA, Perron et al. (2012)
16 Feather River, Sierra Nev., CA, Hurst et al. (2012)
1
2
3
4
5
6
7
8
Catchment Study Location
Great Smoky Mountains, NC/TN
San Andreas / San Jacinto Faults, CA
Wasatch, UT
San Gabriel Mountains, CA
Tennessee Valley, CA
Oroville, CA
Oregon Coast Range, OR
Atacama Desert (semi-arid), Chile
Catchment Study Location
8 Atacama Desert (semi-arid), Chile
9 Atacama Desert (hyper-arid), Chile
Outcrop Study Location
I Great Smoky Mts (Outcrop), NC/TN
2 Tennessee Valley (Outcrop), CA
Schurr 41
7.2
Individual measurement summary
Table 2. Extended table showing individual measurement data
Site
no.
Location
Long.(0)
1
Great Smoky Mountains, NC/TN
-83.193
MAT
[0C]
V 2z
1.466
10.6
1600
1540
1.343
1.381
1520
1.317
D
2
[cm /yr]
MAP
[mm/yr]
AI
35.629
15
1600
35.629
Lat.(0)
U
[m/Myr]
Pb/P,
Compilation
ID*
-0.0288
26.34
2.7/1.6
GSRF-2P,
10.6
11.0
-0.0288
-0.0288
19.52
27.28
2.7/1.6
2.7/1.6
GSRF-3
GSRF-5
P
11.0
-0.0288
28.64
2.7/1.6
GSRF-6
P,
[m
1
]
WTS10002
1
1
1
Great Smoky Mountains, NC/TN
Great Smoky Mountains, NC/TN
Great Smoky Mountains, NC/TN
-83.194
-83.199
35.623
11
16
-83.2117
35.622
17
1
Great Smoky Mountains, NC/TN
-83.2081
35.618
14
1500
1.379
10.8
-0.0288
1
Great Smoky Mountains, NC/TN
-83.2133
35.613
18
1500
1.466
10.8
1
Great Smoky Mountains, NC/TN
-83.2243
35.608
19
1500
1.487
2
San Andreas / San Jacinto Faults,
-116.928
34.050
160
660
-116.9401
34.053
130
I
WTS10005
23.40
2.7/1.6
GSRF-7 ,
-0.0288
31.49
2.7/1.6
10.9
-0.0288
31.92
2.7/1.6
0.560
10.7
-0.1507
1460.72
2.7/1.6
GSRF-8 P,
WTS10007
GSRF-9 ,
WTS10008
WTS26003
630
0.593
12.6
-0.1645
1284.58
2.7/1.6
WTS26004
KC',
WTS39001
StC',
I
WTS10006
CA
2
San Andreas / San Jacinto Faults,
CA
3
Wasatch, UT
-111.9012
41.107
58
756
0.568
8.1
-0.0210
71.81
2.7/1.6
3
Wasatch, UT
-111.8713
40.976
65
590
0.560
10.6
-0.0201
77.87
2.7/1.6
610
0.463
10.0
-0.0168
113.08
2.7/1.6
WTS39005
3
Wasatch, UT
-111.8698
40.934
110
3
Wasatch, UT
-111.8627
40.917
77
570
0.491
10.9
-0.0160
72.83
2.7/1.6
3
Wasatch, UT
-111.819
40.521
38
630
0.592
8.5
-0.0496
110.97
2.7/1.6
San Gabriel Mountains, CA
-117.992
34.367
58
600
0.658
13.3
-0.0302
107.77
2.7/1.6
4
P
FCP,
WTS39006
CC",
WTS39007
BC",
WTS39015
I_
SG131",
WTS40023
N
Schurr 42
4
San Gabriel Mountains, CA
-117.996
34.362
50
670
0.658
12.7
-0.0411
126.19
2.7/1.6
5
Tennessee Valley, CA
Tennessee Valley, CA
-122.546
37.863
160
910
0.924
13.4
-0.0102
79.20
2.8/1.4
SG205 ,
WTS40040
creek1
-122.548
-121.332
37.861
190
21
880
0.924
13.8
-0.0130
125.30
2.8/1.4
creek2
1760
1.154
14.2
-0.0208
28.05
2.7/1.6
FR-6 P
5
6
Oroville, CA
39.639
6
7
Oroville, CA
Oregon Coast Range, OR
-121.331
39.639
14
1760
1.154
14.2
-0.0208
19.61
2.7/1.6
FR-7 P
-123.852
44.537
64
2130
2.629
10.8
-0.0252
113.11
2.7/1.6
7
Oregon Coast Range, OR
-123.867
44.524
110
2210
2.642
10.8
-0.0232
180.98
2.7/1.6
7
Oregon Coast Range, OR
-123.859
44.509
59
2160
2.595
10.9
-0.0160
65.82
2.7/1.6
7
Oregon Coast Range, OR
-123.818
44.519
100
2160
2.561
10.9
-0.0191
137.75
2.7/1.6
7
Oregon Coast Range, OR
-123.818
44.516
110
2160
2.589
10.9
-0.0191
153.56
2.7/1.6
7
Oregon Coast Range, OR
-123.821
44.514
110
2140
2.589
10.8
-0.0191
146.44
2.7/1.6
7
Oregon Coast Range, OR
-123.854
44.508
120
2160
2.583
10.9
-0.0160
138.31
2.7/1.6
7
Oregon Coast Range, OR
-123.859
44.507
270
2160
2.556
10.9
-0.0160
300.41
2.7/1.6
8
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
-71.078
-29.774
23
120
0.070
13.5
-0.0159
20
2.7/1.35
dc-29 ,
WTS55007
dc-30,
WTS55008
dc-31] ,
WTS55009
dc-35 ,
WTS55010
dc-36P,
WTS55011
dc-37p,
WTS55012
dc-38 ,
WTS55013
dc-40,
WTS55014
SGA-1
-71.078
-71.078
-29.774
-29.774
38
40
120
120
0.070
0.070
13.5
13.5
-0.0159
-0.0159
33
35
2.7/1.7
2.7/1.5
SGA-2
SGA-3
-71.078
-29.774
40
120
0.070
13.5
-0.0159
35
2.7/1.4
SGA-4
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
-71.078
-29.774
32
120
0.070
13.5
-0.0159
28
2.7/1.5
SGA-06-28
-71.078
-71.078
-29.774
-29.774
25
20
120
120
0.070
0.070
13.5
13.5
-0.0159
-0.0159
22
17
2.7/1.51
2.7/1.49
SGA-06-17
SGA-06-16
Atacama Desert (semi-arid), Chile
Atacama Desert (semi-arid), Chile
Atacama Desert (hyper-arid), Chile
Atacama Desert (hyper-arid), Chile
-71.078
-29.774
20
120
0.070
13.5
-0.0159
17
2.7/1.38
SGA-5
SGA05-14b
YH-05-16c
YH-17-4
8
8
8
8
8
8
8
8
9
9
-24.125
39
1.1
120
2
0.070
0.005
13.5
17.0
-0.0159
-0.0302
34
0.95
2.7/1.6
2.7/0.8
-24.125
0.97
2
0.005
17.0
-0.0302
0.84
2.7/0.81
-71.078
-69.994
-29.774
-69.994
Schurr 43
Atacama Desert (hyper-arid), Chile
Atacama Desert (hyper-arid), Chile
Atacama Desert (hyper-arid), Chile
9
9
9
-69.994
-24.125
2
1.1
-0.0302
1.7
2.7/0.79
YH-05-44b
U
pb/ps
Compilation
-24.125
1.4
2
0.005
17.0
Al
Temp
Site
Location
Long.
Lat. (0)
D
-83.24
35.61
6.4
Precip
[mm/yr]
1550
-83.13
35.7
23
-83.18
35.63
-83.19
[cmt/yr
no.
1
2.7/0.6
YH-19-C
YH-20-C
-69.994
2.0
1
YH-18-4
2.7/0.81
0.005
0.005
-24.125
I
2.7/0.81
0.91
1.2
2
-69.994
1
0.94
-0.0302
-0.0302
1.1
Atacama Desert (hyper-arid), Chile
I
-0.0302
17.0
17.0
-24.125
9
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Great Smoky Mountains (Outcrop),
NC/TN
Tennessee Valley (Outcrop), CA
Tennessee Valley (Outcrop), CA
17.0
-69.994
2
1
0.005
[*C]
--
17.56
2.7/1.6
GSC-3
1680
1.933
9.5
--
38.75
2.7/1.6
GSDV-10P
10
1640
1.669
10.6
--
22.58
2.7/1.6
GSDV-1 1"
35.73
9.4
1680
1.756
10.8
--
47.83
2.7/1.6
GSDV-2
-83.24
35.72
15
1850
1.978
9.1
--
54.80
2.7/1.6
GSDV-3
-83.27
35.69
9.6
1970
2.207
9.0
--
34.41
2.7/1.6
GSDV-4 P
--
38.14
2.7/1.6
GSDV-7
-0.0102
39.23
2.7/1.6
TV-2
P
I
8.0
2020
1.984
9.1
-122.545
37.856
77
900
0.906
13.5
-122.548
37.866
29
910
0.924
910
20
37.866
-122.547
2 Tennessee Valley (Outcrop), CA
*Compyilation ID:superscript p indicates Portenga & Bierman compilation ID, prefix WTS
indicates a study ID outside the compilations. Values for Ds in italics were not used.
0.924
2
ID*
10.6
35.63
2
[)m/Myr]
1.591
-83.38
1
7Z
[(f
indicates
TV-4
2.7/1.6
-0.0130 18.71
TV-5"
2.7/1.6
13.4 -0.0130 12.72
identification
separate
no
and
et
al.,
Willenbring
13.4
Schurr 44
Sample features to mask from DEM
7.3
Figures Figure 18 and Figure 19 show the results of running the analysis directly on
a DEM that is not pre-processed to select ridges or remove valleys and roads. Figure 18
shows the calculated Laplacians, while Figure 19 shows the resulting ridge selection using
the criteria described in Section 2.3.
Several topographical features that make it difficult to distinguish ridgetops
through the Laplacian and slope-area product distribution include valley bottoms, roads,
flat regions, and outcrops. Examples of these features, how they appear in the Laplacian
map, and how they affect ridge selection are explained below.
1.
Valley bottoms, which can have negative Laplacian values similar to ridgetops, and
may have similar slope-area products. This problem is illustrated in the bottom of
some valleys in Figure 19, where portions adjacent to streams are selected in green
though they are clearly not ridgelines.
2. Roads, which may have negative Laplacian values similar to ridgetops and may
also have similar slope-area products. The curving road with both positive and
negative Laplacians (red and blue colors) is most visible in Figure 18.
3. Flat regions, like the portion on the west side of the sample region, having low
gradient and low drainage area, contributing near-zero Laplacians with low slopearea product. As shown by the green ridgetop selection in Figure 19, flat regions
can be difficult to distinguish numerically from ridgetops.
Schurr 45
4. Outcrops, particularly along ridgelines, that cause irregular ridgetop Laplacians at
low slope-area product. The red and blue mottled areas visible in Figure 18 are
outcrops.
5.
Map Discontinuity. A discontinuity like the straight-lined staircase visible in
Figure 18 is not present in most DEMs, but can contribute significant noise if
included in the analysis.
Figure 18. Laplacians calculated over a DEM that has not been pre-processed for ridgeline selection. In principle,
ridgetops should be differentiable from other topographical features by their negative Laplacian value (indicated
in blue), but clearly there are other features meet this criterion.
Figure 19: Ridgetop results for unmasked DEM. Green indicates regions that were selected automatically as
ridgetop candidates by their low slope-area product and relatively low Laplacian. While most ridgetops were
indeed selected successfully, large regions including flat areas, stream bottoms, and roads have also been included,
on which the subsequent calculations for estimating soil transport efficiency cannot be applied directly.
Schurr 46
7.4
Analysis output images
For each of the new measurement sites, the following pages contain:
*
Satellite view of site (Google Earth)
" Hillshade
* Laplacian map
* Laplacian vs area-slope product
* Ridgeline selection
Schurr 47
NC TN Great Smoky Mountains
NC TN Gregt
N
Smoky Mwfrtins
7
0.15
0.1
0.05
7
0
8
9
-0.05
-0.1
'0
1000m
NC TN Great Smoky Mountains
Lap- -0.028803, stdev = 0.011495
N
-
I
NC TN GatmoyMoquftna
02.3.5.68.691141,171418, 19 (cm Ionr
0.01
0.6
*1.
*95
0.2V
0
-0.2
1000m
-n
10
10
4
12
Area-slope Product, A IVzI
2
(m )
Figure 20: Great Smoky Mountains
Schurr 48
Son Andeas 3
N1
"
CA San Andreas 3
I
015
0.1
0.05
0
-0.1
400m
20Cm
CA San Andreas 3
Lops -0.15072, stdev = 0.014558
elev. 30
0.4
Sn
"GA
SSo
1*
r)3
0.2
4
0
4.J
-0.2 -U
-0.4
-0.6
-n.0
100
10
10
10
2
Area-slope Product, A IVzl (m )
Figure 21: San Andreas 3
Schurr 49
San Andes 3N
kA
1
CA
San Andras 4
I
0.15
0.1
0.05
0
.0.1
loom
CA San Andreas 4
Lap= -0.16452, stev = 0
0.6 -
CA San Anias 4
D3- 130 .cm tA
Obv. 30'
0.4-
0.2
N1
L
0
.E-0.21
-0.4-0.6
-n
R'
100
101
102
103
2
Area-slope Product, A IVzI (m
loom
Figure 22: San Andreas 4
Schurr 50
A
UT Wasatch
N
I
I.
UT Wasatch 1
0.15
0.1
0.05
0
-0.05
-0.1
400m
UT Wasatch I
Lap- -0.021015, sidev = 0.0052757
n A.
NI
0.2
*W. 30'
UT Was"c I
D,= 58 (cm tAf
0.1
0
0-
-0.1
-0.2[
fO
-0.4
400m
-0.5
0
10
10
1
2
10
102
3
10
4
Area-slope Product, A |VzI (m)
Figure 23: Wasatch 1
Schurr 51
N
N
UT Wasatch 5
0.15
UT Wsatch 5
0.1
-0.05
'0
5
-0.05
-0.1
1000m
UT Wasatch 5
Lap= -0.020144, stdv - 0.0093295
N
UT Wastcp 5
05- 65 [anm
ev. 3O
0.2
0.1 [
>-4.
C
2 -0.1
*5
-0.2
-0.3
1I000m
-0
10
10
l02
Area-slope Product, A IVz|
4
2
(m
Figure 24: Wasatch 5
Schurr 52
N
UT Wasatch 6
1
UT Wasatch 6
I
0.15
0.1
0.05
0
-0.05
I
-0.1
100tmT
UT Wasatch 6
Lap- -0.016813, stdev = 0.0081277
N
UT Wasam 6
Do=l1i0 cm 4ir
0.2-
.elv. 30*
0.1
-0.1
-0.2
j-0.3
-0.4-
-0.5
1000m
-0.6
-n 71
.02
100
102
Area-slope Product, A IVzI (m)
Figure 25: Wasatch 6
Schurr 53
N
I
N
I
UT Wasatch 7
0.15
UT Wasatch 7
0.1
0.05
0
-0.05
-0.1
1000m
UT Wasatch 7
Lap= -0.015965, sidev 0.0080568
0.4
0.2
NI
elev. 30
UT Was"t. 7
D7, 77 J- /r
0
,
-0.4
.1-0.6
.9 -0.8
-1
100tm
-1.2
-1.4
'
12
10
102
Area-slope Product, A IVzI
10
2
(m
)
Figure 26: Wasatch 7
Schurr 54
N1
t
N
UT Wasatch 15
a _
J.15
UT Wasatch 15
15
0.05
.0.05
200Cm
-. 1
400m
UT Wasatch 15
Lap- -0.049588, stdev 0.6,
UT Wasatch5
0.010861
N
015 38[c1I
'
elv.301
0.4 -
Lae
0.2
A
0
.3
0~
0.
-0.4
-0.6
-me
-2
16,
4
102
Area-slope Product, A IVzI
2
(m
400m
)
Figure 27: Wasatch 15
Schurr 55
CA San GmbrWe 40023
N
N
N
CA San Gabde 40023
0.15
I
0.1
0.05
0
-0.05
-0.1
10m
23
loom
CA San Gabriel 40023
Lap- -0.030235, stdev = 0.0013638
0.15
0.1
Wv. 30 *
-
CA San Gab"
023
58 1-
P0M
F,
0.05
0
CL
-0.05
.5
201'
*23
loom
-0.15F
-0.2'10
-e
104
1022
id1
100
Area-slope Product, A jVzI
2
(m
)
Figure 28: San Gabriel 40023
Schurr 56
CA Ban Gabie 4004
N
CA San Gabriel 40040
I
0.15
0.1
0.05
0
-0.05
loom
-0.1
CA San Gabriel 40040
Lap= -0.041121, stdev = 0
0.11
0.08
OWa.
0.06
30'
CA Son Gabiel PM4
D,= 50 (em Ojrj
0.04
0.02
*
0
-0.02
-0.04
-0
0
-0.06
-0.08
50m
-0.1
10
-3
102
-
1"
10
10
10
2
Area-slope Product, A jVzI (m)
102
Figure 29: San Gabriel 40040
Schurr 57
23
N
CACTAmTns
VaVaeay
N
CA Tennessee Vay Basin 1
--
0.15
ro.
if1
0.20
00.1
0.0.0
-0.10.-
FiCA
1
Tennessee Valley
FiuA30 Tennessee
Basin 1
Valley Basin
Schurr 58
0.15
CA TwwMftVSISY
N
N
CA Twvwnn Vdey B"n 2
0.15
0.1
-0~o
200m
0.25N
CA Tennessee Valley Basin 2
Lap= -0.012958, stdev - 0.0030904
CAT
T
0.2
Bah
elev. 30o
0.15
E
0.1
-Tvi
0.1
0.0502
-0.1
-0.1
-4
Area-slope Product, A jVzI
(M
2
)
Figure 31: Tennessee Valley Basin 2
Schurr 59
CA Oro~IsCAe
IN
N
I
CA OrcANe
0.15
0.1
0.05
S
0
-0.05
.0.1
6
400M
CA Oroville
Lap= -0.020837, stdev - 0.0022089
N I
CA Om2y
D,., 21.,14 ln
Ov. 30
0.15F
/
0.1
0.05
0
-J
-0.05 F
*a
-0.1F
-0. 15'
10
I10Cm
s-2
102
P
2
Ares-slope Product, A |VzI (in )
Figure 32: Oroville
Schurr 60
OR COWs Range
N
OR Coast Range IX
N
0.15
0.1
0.05
0
-0.05
12
0.1
400fm
ORCoast RangeIX
OR Coast Range IX
Lap- -0.019127, stdev - 0.010209
0.4
Ow. 30~
0.3F
0.20.1}
0-
2
N1
*.0
A
-0.1
-0.2
-034-
0
-2
10-2
10
2
2
Area-slope Product, A IVzI
14
(M
2
40Dm
)
Figure 33: Coast Range IX
Schurr 61
N
OR Coast Ram
N
,
OR Coast Range 07
0.15
<0.1
-0.05
07
-0.1
400M
OR Coast Range 07
N
Lap= -0.025203, stdev 0.01583
0.5
0.4-
elev.3O
OR Coast Rany 07
D0 = 64 cm/i
0.30.2
ev0.1-
407
_j -0.1
-0.2-0.3-0.4
-2
4
2
2
Area-slope Product, A IVzI (m
Figure 34: Coast Range 07
Schurr 62
OR Coast Ronam
N
OR Coast Range 0
0.15
0.1
0.05
0
-0.05
-0.1
08
IGOOm
OR Coast Range 08
Lap= -0.023211. stdov m 0.013771
05
I
0.4
OR Coast Range 0
.eV. 30*
0.3
0.2
CE
.19
0.1
0
0
00
-0.1-0.2-
Ifl
*08
1 000M
-0.3-
10-2
102
10
Area-slope Product, A IVzI
4
(m
2
)
Figure 35: Coast Range 08
Schurr 63
N
OR Coast Range
I.L
N
OR Coast Range r
I
0.15
0.1
0.05
0
-0.05
14
13
-0.1
1000M
OR Coast Range r
Lap= -0.015962, stdev 0.011564
023
Wev. 30*
0.2
2
ORCostR1.
,r
r
09,13,140 5910
0.1 [
-
.ew-M&L-21
Ir
,<kI
0
IN,
e
.
j
-
7X
-0.1-
*9,4
-0.2-
4V
-13
1000m
-0.3-0.4'
10,
107
10,
102
2
Area-slope Product, A IVzI (m )
4
Figure 36: Coast Range r
Schurr 64