Download Does climate change create distinctive patterns of

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, F04008, doi:10.1029/2009JF001562, 2010
Does climate change create distinctive patterns
of landscape incision?
Cameron W. Wobus,1,2 Gregory E. Tucker,2,3 and Robert S. Anderson3,4
Received 12 October 2009; revised 19 July 2010; accepted 23 July 2010; published 14 October 2010.
[1] Incised fluvial systems are typically interpreted as recording geologically recent
changes in either climate or tectonics. However, few diagnostic tools exist to evaluate
whether particular incised landscapes primarily reflect climatic or tectonic perturbation.
Here we summarize the results of a simple fluvial sediment transport model that
allows us to contrast patterns of fluvial incision driven by changes in hydrology and
sediment flux (“climate”) with those driven by changes in rock uplift patterns relative to
sea level (“tectonics”). Our modeling suggests that there may be diagnostic differences
between the spatial and temporal patterns of incision caused by these different processes.
In particular, incision driven by climate change is most commonly accompanied by
downstream migrating waves of incision and decreases in channel gradient, while
under most circumstances incision driven by tectonics will be accompanied by upstream
migrating incision and increases in channel gradient. We apply our modeling to a case
study of the North American High Plains, where regionally elevated surfaces east of the
Rockies have been incised up to 500 m by the fluvial systems draining the core of the
range. Although this incision has been interpreted as reflecting a tectonic rejuvenation
of the High Plains, our analysis suggests that climate change is at least as plausible
an explanation to explain the incision of this landscape. Diagnostic differences between
the climate and tectonic end‐member scenarios might be obtained via detailed study of the
spatial and temporal patterns of terrace abandonment, providing a potentially fruitful target
for field investigation.
Citation: Wobus, C. W., G. E. Tucker, and R. S. Anderson (2010), Does climate change create distinctive patterns of landscape
incision?, J. Geophys. Res., 115, F04008, doi:10.1029/2009JF001562.
1. Introduction
[2] Landscape form is a reflection of the integrated history
of the tectonic processes that build topography and the climatically modulated erosional agents that denude it. Quantifying how these processes interact to shape landscapes is
one of the primary goals of tectonic geomorphology. Efforts
have been made to quantify the relative roles of tectonic
rock uplift and climate change in driving landscape dissection in many settings around the world, including the Alps
[e.g., Champagnac et al., 2007], the western United States and
the Middle East [Bull, 1991], and the Great Plains of central
North America [e.g., McMillan et al., 2002; Leonard, 2002].
However, our understanding of how climatic signals differ
from tectonic signals remains incomplete, in part because
1
Stratus Consulting, Inc., Boulder, Colorado, USA.
Cooperative Institute for Research in Environmental Sciences,
University of Colorado at Boulder, Boulder, Colorado, USA.
3
Department of Geological Sciences, University of Colorado, Boulder,
Colorado, USA.
4
Institute for Arctic and Alpine Research, University of Colorado at
Boulder, Boulder, Colorado, USA.
2
Copyright 2010 by the American Geophysical Union.
0148‐0227/10/2009JF001562
we lack a set of simple diagnostic criteria to quantify the
differences in fluvial response between tectonically and
climatically modulated changes. A related problem is that
“climate,” as it relates to fluvial evolution in particular,
has been interpreted to reflect many different parameters,
including aridity [e.g., Molnar, 2001], changes in sediment
loads due to glacial‐interglacial cycles [e.g., Hancock and
Anderson, 2002], variations in precipitation intensity [e.g.,
Tucker, 2004], changes in the spatial distribution of discharge [e.g., Zaprowski et al., 2005], and changes in vegetation dynamics [e.g., Istanbulluoglu and Bras, 2005]. A more
rigorous framework is needed, both for defining what “climate” means to a geomorphic system and for quantitatively
evaluating how climatic and tectonic signals of incision can
be distinguished in natural systems.
[3] Our approach here is to formulate a generic model of
river longitudinal profile evolution in a piedmont adjacent to
a mountain range, and to systematically vary the parameters
within the fluvial system that might most reasonably be associated with changes in climate. These model results allow us
to evaluate the conditions under which perturbations in water
and/or sediment delivery to piedmont rivers create patterns
of landscape dissection that are diagnostically different from
those driven by tectonic changes. Because the governing
equations of fluvial incision in these systems depend on
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downstream changes in water and sediment flux, perturbations to these two parameters represent the most direct avenue
through which climate change could influence river evolution. Indeed, all of the hypothesized relationships between
climate and fluvial incision described above ultimately
relate to changes in these two key parameters. For example,
glacial‐interglacial cycles are hypothesized to affect the
magnitude and timing of sediment flux from glacial headwaters [e.g., Hancock and Anderson, 2002]; changes in aridity
have been assumed to influence the frequency‐magnitude
distribution of storms and therefore water discharge [e.g.,
Molnar, 2001; Molnar et al., 2006]; and vegetation influences the ability of hillslopes and channel banks to retain
sediment [e.g., Istanbulluoglu and Bras, 2005]. In addition,
changes in temperature or humidity could have a direct effect
on the pace of sediment production by influencing physical
and/or chemical weathering rates in headwater catchments
[e.g., Anderson, 1998; Hales and Roering, 2007; West et al.,
2005; White and Blum, 1995].
[4] In our study, model runs driven by changes in water
and sediment flux are contrasted with models in which
differential rock uplift relative to local base level is the
dominant perturbation. We use comparisons between these
sets of models to explore the diagnostic differences between
rivers incised due to climatic versus tectonic change. This
framework is then used to reevaluate the origin of late
Cenozoic incision of the North American High Plains, east
of the Rocky Mountain front. These analyses provide a new
set of predictions that might be tested against field observations to evaluate the relative roles of tectonics and climate
in driving landscape dissection in this setting as well as in
other dissected mountain piedmonts.
2. Modeling Framework
2.1. Model Setup
[5] Our study was initially motivated by the morphology
of the North American High Plains. The major rivers in this
physiographic province, the North Platte, the South Platte
and the Arkansas, flow across a substrate of soft, easily
eroded marine sedimentary rocks, but must transport resistant clasts delivered from the crystalline core of the adjacent
Front Range. We therefore cast our fluvial incision model in
terms of transport‐limited incision: the ability of these rivers
to incise is limited by their ability to transport these resistant
clasts, rather than their ability to etch into the soft sedimentary rocks underneath. This assumption will be valid in
other settings adjacent to crystalline ranges, provided that
the capacity to detach and transport the local sedimentary
bedrock is greater than the capacity to entrain and transport
coarse, abrasion‐resistant sediment delivered from the adjacent range. Using this transport‐limited assumption, the rate
of change in elevation with time reflects the downstream
divergence of sediment flux [e.g., Whipple and Tucker,
2002]:
dz
dqs
¼U
dt
dx
ð1Þ
where z is the elevation of the bed; t is time; U is the rock
uplift rate relative to the river outlet; qs is the volumetric
specific bed load sediment discharge [L2/T]; and x is distance along the channel. Here we ignore the density difference between sediment clasts and bulk sediment.
[6] The simplest formulation for bed load sediment transport is a generalized Meyer‐Peter Müller bed load transport
relationship, in which the bed load sediment flux is a power
function of the excess shear stress [e.g., Meyer‐Peter and
Muller, 1948]:
qs ¼ Kf ðb c Þ
3
=2
ð2Þ
where Kf is a dimensional constant, t b is the shear stress on
the bed, and t c is the critical shear stress required to entrain
sediment. Other bed load transport equations could also be
employed here; however, the basic power law form with
respect to shear stress is in most cases similar among these
other formulations [e.g., Bagnold, 1977; Fernandez Luque
and van Beek, 1976; Wiberg and Smith, 1989]. We approximate the boundary shear stress using the depth slope product,
b ¼ gHS
ð3Þ
where r is the density of water, g is the acceleration due
to gravity, H is the flow depth, and S is the local channel
gradient. Note that because this approximation neglects wall
stresses, it is valid only for rivers that are very wide relative to
their depth [e.g., Wobus et al., 2008]. Width‐to‐depth ratios
in alluvial rivers are typically substantially greater than 10
[e.g., Leopold and Maddock, 1953], allowing us to neglect
wall stresses and use this common simplifying assumption.
[7] We can eliminate flow depth from equation (3) using a
Manning‐Strickler resistance formulation for the boundary
shear stress:
"
2
b ¼ Cf u ¼ 2r
1 =3 #
H
u2
ks
ð4Þ
where ar is a dimensionless constant with a value of 8–9
[Parker, 1991]; Cf is a roughness coefficient; ks is a length
scale equal to twice the diameter of the 90th percentile size
fraction; and u is the mean velocity of the flow. When combined with a momentum conservation constraint, this leads
to a boundary shear stress approximation based only on the
water flux, gradient, and a dimensional constant that bundles
the resistance coefficient, the roughness length scale, the
gravitational constant, and the density of water (G. Parker,
1D sediment transport morphodynamics with applications to
rivers and turbidity currents, 2004, available at http://vtchl.
uiuc.edu/people/parkerg/morphodynamics_e‐book.htm):
1
=
ks 3 q2w
b ¼ g
2r gS
!3 =10
3
S ¼ Kt qw=5 S
7
=10
ð5Þ
where qw is now the water flux. The parameter Kt provides a
convenient bundling of constants.
[8] By combining equations (1), (2), and (5) and normalizing all variables by reference values, we can formulate
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the entire system of equations in nondimensional terms. Our
normalization proceeds as follows:
x′
z′
So
S′
t′
q′
= x/L;
= z/R;
= R/L;
= S/So;
= t/t ref ;
= q/qo; H 7/10
;
t ref = Kt q3/5
o
L
t′ = t/T ;
L = river profile length;
R = total relief along profile;
T = reference timescale;
U = reference uplift rate.
Here qo and So are the input water flux and slope, and the
superscript ′ represents nondimensional variables [e.g.,
Willgoose et al., 1991]. This results in a single nondimensional formulation describing the elevation history of a
transport‐limited river:
3 = 2
3 =
0 3=5 0 7=10
c0
TKf Kt qo3=5 So7=10 2 d q S
dz 0 TU
¼
dt 0
HL
dx0
H
ð6Þ
[9] Inspection of equation (6) reveals that the dynamics of
this system are controlled by the downstream changes in the
variables q′, S′, and t′c . For our application to landscapes in
which the goal is to decipher differences between tectonic
and climatic forcings, the spatial patterns of evolution are of
greatest interest. The characteristic time, length, and elevation scales T, L, and H, and the reference slope and discharge values So and qo in equation (6), control the rate of
change of the model channels, rather than the spatial patterns of evolution. Thus we explore in our modeling changes
in the downstream distribution of fluvial discharge (which
modulates sediment transport capacity); of input sediment
supply (which propagates through the system via the ratio of
sediment transport rate to transport capacity at the range
front), and of rock uplift rate (which modulates downstream
patterns in S′). Note that downstream changes in sediment
size (which modulate the downstream patterns in t′c ) will
also influence patterns of incision throughout the system;
however, without an a priori means of characterizing downstream patterns of sediment size [e.g., Attal and Lave, 2006],
we leave these analyses as topics for future research.
[10] The downstream increase in water discharge is controlled by a combination of drainage basin geometry and
the spatial distribution of water inputs to the system. The
former is described by the inverse of the Hack exponent, h,
which describes the empirical relationship between drainage
area and distance along the stream:
A ¼ ka xh
ð7Þ
We use an inverse Hack exponent h of 1.6, consistent with
observations from many drainage basins around the world
[e.g., Hack, 1957]. The second relationship describes the
increase in fluvial discharge with drainage area:
qw ¼ kq Ac
ð8Þ
In our baseline models we use an exponent c of 1, implying
that all the portions of a drainage basin contribute equally to
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gathering precipitation and exporting it as fluvial discharge
[e.g., Dunne and Leopold, 1978]. Note that it is the product
of the exponents h and c in (7) and (8) that determines the
rate at which discharge increases downstream. Perturbations
to the model are parameterized as changes in the product of
these two exponents. The choice of initial values for h and c
is therefore not as important to the model results as the way
in which their product is perturbed during model runs.
[11] Finally, river cross‐sectional geometry is parameterized as a power function of drainage area,
W ¼ kw Ab
ð9Þ
where W is channel width, and kw is a dimensional constant.
Although the controls on channel width for bedrock rivers
are complex [e.g., Turowski et al., 2008; Wobus et al., 2008]
a large body of empirical data supports a value of ∼0.5 as
an appropriate exponent on the channel width relationship
for alluvial rivers [e.g., Leopold and Maddock, 1953]. We
employ a value of 0.5 for the width exponent b.
[12] Our model channels are assumed to begin at the
interface between the crystalline rocks of the Laramide
ranges and the piedmont. Thus the upstream boundary condition is dictated by the water and sediment fluxes delivered
to the piedmont and High Plains by the bedrock channels
of the Rockies. The elevation of this upstream boundary
condition is assumed to be free to change; incision of piedmont channels to the east of the Front Range, for example,
would result in knickpoint propagation into the bedrock
channels of the Rockies. While these bedrock channels are
not modeled here, observations of knickpoint migration and
increasing Cenozoic relief along the Front Range are consistent with incision that initiated in the Piedmont channels
as they etched into the softer rocks east of the mountain
front [Anderson et al., 2006].
[13] Our reference model was initiated with a linear ramp
(constant slope) of 0.002. Sediment and water were fed into
the upstream end of the model channels, representing the
contribution of a crystalline range to its adjacent piedmont
river system. The model was run with a slow, uniform background rate of rock uplift and a steady supply of water and
sediment until it reached steady state, at which point the
longitudinal profile was smooth and concave up. Using this
steady state longitudinal profile as an initial condition, we then
individually modified (1) the patterns of rock uplift, (2) the
spatial distribution of fluvial discharge, and (3) the total input
sediment flux. Changes in uplift patterns included scenarios
in which rock uplift was increasing either linearly or exponentially from the channel outlet to the mountain front, and
patterns in which the rate of rock uplift was increased equally
along either the entire channel, or just the upper half. To
examine the spatial patterns of incision that arise from pulsed
uplift, each of these tectonic scenarios was also tested by
ceasing uplift halfway through the model run.
[14] In the fluvial discharge case, we examined the effects
of changing the exponent c on the discharge‐drainage area
relationship so that the system had the same total water
discharge at the downstream end of the study reach, but with
a larger fraction of this discharge coming from the headwaters. This scenario would be consistent with increased
aridification on the piedmont accompanied by enhanced orographic precipitation over the adjacent range, or with regional
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cooling leading to enhanced snow storage in the headwaters,
which would increase the proportion of discharge coming
from the headwaters during geomorphically important events
[e.g., Pelletier, 2009]. We also changed the input sediment
supply to explore how a decrease in sediment flux from the
crystalline range influences profile evolution. Such changes
would be consistent with changes in vegetation dynamics
enhancing slope stability, storage of sediment during interglacial periods, or temperature‐ or aridity‐modulated changes in weathering mechanisms that might decrease regolith
production on hillslopes. Note that the goal of these sensitivity analyses is not to make a priori assumptions about
how changes in climate influence fluvial incision in any particular system, but to examine a range of possible scenarios
that might be climatic in origin.
[15] Finally, we note that our model does not explicitly
consider changes in sediment inputs from tributaries and
hillslopes. However, the spatial distribution and direction of
changes in sediment flux across the landscape would be the
same in a two‐dimensional model as in the one‐dimensional
framework considered here: incision in our model channels
creates a local increase in sediment delivery that is fed to
downstream nodes, just as incision in a two‐dimensional
model would generate additional sediment flux that must be
transported downstream from the incising zone. Results
from our simple modeling framework thus provide a conceptual understanding of how a fully two‐dimensional model
would behave, and can be used as a foundation for future
modeling studies.
2.2. Application to the North American High Plains
[16] Our study was motivated by the spatial patterns of
incision in the North American High Plains. The tectonic
and elevation history of the Rockies and western High
Plains have been topics of considerable debate over the past
few decades [e.g., Gregory and Chase, 1994; McMillan et al.,
2006]. From this debate, only two data points are without
question. First, thick sequences of shale at the top of the Cretaceous sedimentary package clearly demonstrate that the
region was below sea level prior to the Laramide orogeny.
And second, the modern elevation profile of the High Plains,
a long ramp from only a few hundred feet above sea level
at the Mississippi River to approximately 5000 ft at the foot
of the Rockies, requires nearly a mile of up‐to‐the‐west
tilting since that time. This broad tilting must be sustained
by some geophysical anomaly at depth, which is almost
certainly related to the Laramide orogeny [e.g., Mitrovica
et al., 1989]. However, the timing of High Plains surface
uplift, and in particular the possibility that there has been
additional uplift in the late Cenozoic, is not well constrained.
[17] Superimposed on this broadly tilting High Plains
ramp is an unambiguous pattern of incision that increases
toward the Rocky Mountains [e.g., McMillan et al., 2002;
McMillan et al., 2006; Leonard, 2002]. Late Cenozoic
incision along the North Platte, South Platte and Arkansas
rivers is up to 500 m along the edges of the crystalline
ranges of central Colorado and Wyoming, and tapers eastward to nearly zero at the longitude of the Colorado‐Kansas
border (Figure 1). Field relationships indicate that much of
this incision is also quite young, as the Miocene‐Pliocene
Ogallala Group, once spatially continuous across the western Great Plains and smoothly grading onto the crystalline
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range, has clearly been truncated by this incisional pulse,
severing the Ogallala deposits from their source terrain. This
incision has also penetrated through the remainder of the
Cenozoic stratigraphic pile and into the soft Cretaceous
sediments beneath the Ogallala in the High Plains and
Piedmont, and it has generated knickpoints that are currently
propagating into the crystalline core of the Rockies [e.g.,
Anderson et al., 2006].
[18] Because the incision of the High Plains clearly
postdates deposition of the late Cenozoic Ogallala Group, at
least three observed changes to late Cenozoic climate can be
evaluated as potential climatic drivers for incision. First, the
global d 18O record begins a ∼2‰ negative shift near the
Miocene‐Pliocene boundary [Zachos et al., 2004], which
could have created a shift toward more snowmelt‐dominated
hydrologic systems, modified the type and extent of vegetative cover in the Rockies, and/or changed atmospheric
circulation patterns and the frequency distribution of storms.
Second, the d 13C record from the High Plains begins a
regional ∼6‰ positive shift at about this time [Fox and
Koch, 2003], consistent with an increase in aridity to the
east of the Rockies. Finally, the terrestrial record shows the
first major advance of ice sheets into the central United
States around this time [e.g., Balco et al., 2005], which was
most likely accompanied by changes in alpine glaciation in
headwater systems as well. Although direct evidence of how
documented late Cenozoic climatic changes would have
influenced the hydrology of Piedmont and High Plains river
systems is lacking, any of these changes in climate would
certainly have influenced hydrology and sediment transport
along these rivers. We therefore focus our modeling on such
potential changes.
3. Modeling Results
3.1. Changes in Hydrology
[19] In the nondimensional framework described above,
hydrology is parameterized by the exponents h and c in
equations (6) and (7). Together, these two exponents
determine the relative contribution to fluvial discharge of
each segment of the model channel. Because stream length
varies from zero to 1, an increase in the exponent c provides
relatively less water to the channel from the upstream
reaches, while a decrease in the exponent c provides relatively more water to the channel from the upstream reaches.
We note that in either case, the total water at the outlet remains the same in our nondimensionalized framework.
[20] For a given initial gradient, increases in the water
discharge will result in excess stream power and incision
relative to the baseline case. Thus, an increase in the relative
amount of water delivered from upstream generates incision
that initiates near the top of the channel, where the mismatch
between initial and perturbed water flux is greatest. As
incision proceeds downstream, more sediment is entrained
from the channel until the mismatch between sediment flux
and transport capacity returns to zero. Decreases in the
exponent c therefore result in a wave of incision that initiates at the headwaters (the crystalline mountain front in
our model framework) and migrates downstream (Figure 2).
This downstream migrating wave of incision is accompanied by decreases in channel gradient between the mountain
front and the channel outlet.
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Figure 1. Incision of the North American High Plains. (a) Map extent of remaining Ogallala Group
(light gray shading) shows planview patterns of incision into this surface. Thin dashed boxes show extent
of swath profiles; thick dashed lines show extent of gradient measurements on major rivers in Figure 6.
(b and c) Swath profiles show vertical patterns of incision driven by the Arkansas and South Platte rivers,
relative to the Palmer Divide interfluve. Solid lines show average elevation as a function of distance
within each swath shown in Figure 1a; dashed lines show minimum and maximum elevations. Note that
the South Platte swath is oblique to the course of the river; orientation was chosen to run downdip along
the Ogallala surface.
[21] In the context of the North American High Plains,
climate change could therefore have generated post‐Ogallala
incision simply by redistributing the sources of water to
the river systems draining the Rockies. For example, the
cooling global temperatures documented in the oxygen
isotope record [Zachos et al., 2004] could have resulted in
relatively more water exiting the Rockies as snowmelt
[Pelletier, 2009]. Documented changes in the vegetation
blanketing the High Plains, as documented in the carbon
isotope record [Fox and Koch, 2003], are consistent with
increasing aridity (i.e., relatively less water falling on the
High Plains) or with changes to the mechanisms of water
uptake by plants. While we currently have no documentation of fluvial discharge patterns through the late Cenozoic,
it is likely that these late Cenozoic climate changes would
have been accompanied by the types of hydrologic changes
parameterized by our model.
3.2. Changes in Sediment Supply
[22] The gradient of a transport‐limited channel is adjusted
to just carry the sediment delivered to it: all else equal, a
natural channel must steepen if sediment supply is increased,
and decline in slope if sediment supply is decreased. In our
simple modeling framework, the channel gradient is set in
large part by the quantity of sediment supplied at the
upstream end, which represents the mouth of the bedrock
channels exiting a crystalline range like the Colorado Front
Range. If sediment supply is decreased, the system has
excess transport capacity relative to the baseline case. As in
the example of hydrologic changes, a decrease in sediment
supply also generates an incisional signal that initiates in the
headwaters and propagates downstream (Figure 3). As this
incisional signal propagates downstream, the channel will
continue to reduce its gradient via incision until the transport
capacity matches the supply of sediment from the adjacent
range.
[23] In the context of the High Plains, a number of
mechanisms can be envisioned that would have decreased
sediment supply in the late Cenozoic. For example, changes
in vegetative cover in the headwaters could have stabilized
hillslopes and decreased sediment supply; or changes to
temperature and moisture availability could have reduced
rates of chemical and/or physical weathering and therefore
regolith production. Counterexamples can also be envisioned; for example, glaciation could increase local erosion
rates while also increasing sediment storage in overdeepened
basins and moraines. However, to the extent that climate
change could have decreased the long‐term sediment supply
from the headwaters, climatic changes can also generate
downstream migrating incision in High Plains river systems.
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Figure 2. Spatial and temporal patterns of incision driven by a decrease in the exponent c in equation (8).
(a) The initial longitudinal profile (solid gray line), intermediate time steps as incision progresses (gray
dashed lines), and the final profile (black dashed line). (b) The patterns of incision depth as a function of
distance, again with gray dashed lines showing intermediate time steps and the black dashed line
showing the final pattern. (c) Qualitative illustration of the temporal progression of incision, expressed as
the time required for incision to reach threshold percentages of the initial elevation.
3.3. Changes in Rock Uplift
[24] While incision brought on by changes in water flux
and sediment input both generate downstream migrating
incision and decreasing gradients, incision driven by an
increasing rock uplift rate most commonly generates upstream
migrating incision and increasing channel gradients. For
example, in models set to mimic the broad tilting of the
High Plains envisioned by previous authors [McMillan et al.,
2002; McMillan et al., 2006; Leonard, 2002], incision
initiates near the base of the model channel and migrates
upstream (Figure 4). If this uplift pattern is maintained, the
new equilibrium channel must be steeper than its initial
condition. If uplift stops midway through the model run, the
channel relaxes to its initial gradient but abandons a newly
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Figure 3. (a–c) As in Figure 2 but for spatial and temporal patterns of incision driven by a halving of the
input sediment flux at the mountain front.
uplifted paleosurface that preserves the steeper gradients
required to match the higher uplift rates.
[25] Models in which tilting is strongly asymmetric are
capable of generating incisional waves that migrate downstream, similar to the results from changes in hydrology or
sediment supply. For example, if rock uplift rate exponentially increases toward the mountain front, incision initiates
near the headwaters before the mouth (Figure 5). In this
case, the diagnostic difference between incision driven by
changes in hydrology and changes in tectonics lies in the
evolution of channel gradient. Incision driven by sustained
rock uplift creates channels that are everywhere steeper than
their initial gradients, while incision driven by an increase
in discharge or a decrease in sediment supply creates channels
that are everywhere less steep. As described below, this
can provide an additional constraint on the mechanism of
incision in situations where modern and paleogradients can be
compared.
4. Discussion
[26] The case of the High Plains is complicated by the fact
that regardless of whether climate change or a change in
rock uplift patterns drove the initial incision of the region,
the excavation of the western High Plains itself would have
provided an isostatic “kick” to the system that would manifest as a down‐to‐the‐east regional tilt [McMillan et al.,
2002; Leonard, 2002]. The debate is therefore whether
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Figure 4. (a–c) As in Figure 2 but for spatial and temporal patterns of incision driven by simple linear
tilt of the initial profile, as envisioned by McMillan et al. [2002]. Additional thin lines in Figure 4a
represent abandoned paleosurfaces as the channels incise into the uplifted landscape.
changes in hydrology and sediment supply (“climatic” drivers) could have played a leading role in incision, while the
isostatic (“tectonic”) response was secondary.
[27] Arguments for late Cenozoic tectonic tilting of the
High Plains rest primarily on differences between estimated
paleoslopes of preserved paleochannels within the Ogallala
group [McMillan et al., 2002], and modern slopes of the
remnant Ogallala surface. It has been argued that if the
modern slopes are greater than the paleoslopes (beyond
what would be expected from simple isostatic tilting in
response to erosion) there must have been a post‐Ogallala
rock uplift pattern that generated the necessary tilt.
[28] Our modeling places two additional constraints on
the mechanisms of incision of the High Plains. First, the
model suggests that except in the extreme case where
uplift rates increase exponentially upstream, tectonically
generated tilting generates upstream migrating waves of
incision, while climate change generates downstream migrating waves of incision. Depending on the rate at which
this incision migrated, the spatial pattern of incision could
be reconstructed from the rock record. For example,
reconstructing the spatial patterns of incision could potentially be accomplished through detailed geochronology
of abandoned paleosurfaces in the form of gravel‐capped
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Figure 5. (a–c) As in Figure 2 but for spatial and temporal patterns of incision driven by an exponentially upstream increasing tilt of the initial profile. Additional thin lines in Figure 5a represent
abandoned paleosurfaces as the channels incise into the uplifted landscape.
strath terraces across the High Plains. Although our model
does not speak directly to the rates of incision, it seems
likely that the excavation of the western High Plains was
sufficiently protracted that these spatial patterns could be
resolved with the proper suite of geochronologic tools.
[29] Second, the model suggests that tilting of the High
Plains should have created modern rivers that are steeper
than the paleochannels that preceded them. In fact, the
gradients of modern river channels draining the High Plains,
generally between 0.5 and 2.0 m/km, are at the low end of
the uncertainty range on paleoslopes reported by McMillan
et al. [2002], which ranges from ∼0.5 to 4 m/km (Figure 6).
If indeed the piedmont experienced up‐to‐the‐west tilting
during the Pliocene, then the presently low gradients of the
North Platte, South Platte and Arkansas Rivers would require
an explanation such as erosional relaxation following the
cessation of active tilting, or a substantial reduction in erosional resistance of the underlying bedrock after the Ogallala
was breached. Of the available models, the observation that
modern gradients are near the low end of paleogradient estimates best supports the climatic case in which incision is
due to relaxation of river slope due to changes in water or
sediment supply.
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Figure 6. Gradients of the North Platte, South Platte, and Arkansas rivers across the central United
States (black dots), compared with the full range of uncertainty on paleoslopes as reported by
McMillan et al. [2002] (gray shading), and modern slope of the Ogallala from topographic swath profiles (hatched) (see text). Note that modern river gradients have not increased relative to paleogradients
and that modern and paleoslope estimates of the Ogallala surface overlap.
[30] Finally, models invoking tilting of the High Plains
require that the modern slope of the Ogallala surface should
be steeper than the slope of the paleochannels that deposited it. Topographic profiles extracted along the top of the
Ogallala surface perpendicular to the Front Range indicate
modern gradients of approximately 3.5 m/km (Figure 6).
Using post‐Ogallala basin fill thicknesses reported by
McMillan et al. [2006] to reconstruct the base of the Ogallala,
this estimate is as high as 4.4 m/km across the western High
Plains (see auxiliary material).1 The full range of uncertainty
on the paleoslope of Ogallala channels reported by McMillan
et al. [2002] is 0.5 to 4.0 m/km (shading in Figure 6). Thus,
1
Auxiliary materials are available in the HTML. doi:10.1029/
2009JF001562.
while the modern slope of the Ogallala sediments (3.5–
4.4 m/km) is at the high end of this range of uncertainty,
there is overlap between the two measurements. This leaves
open the possibility that the modern and paleoslopes of the
Ogallala are the same.
[31] Again, regardless of the mechanism driving the initial
excavation of the western High Plains, incision itself would
have generated an isostatic response that would manifest as
“tectonic,” i.e., driven by lithospheric rather than surficial
processes. The magnitude and spatial distribution of such
isostatic uplift depends strongly on the flexural rigidity of
the lithosphere [e.g., Leonard, 2002]. Given the poor constraints on this parameter, we have left this isostatic response
out of our simple model. However, the close overlap between
modern and paleogradients of the Ogallala surface, and the
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observation that modern channels are no steeper than the
paleochannels within the Ogallala, suggest that this isostatic
response may have been the only tectonic “kick” to the
system.
5. Conclusions
[32] Our modeling suggests that, along a mountain piedmont, there may be diagnostic differences between the spatial and temporal patterns of fluvial incision driven by
changes in climate versus changes in tectonics. In particular,
fluvial incision driven by climate‐induced increases in water
or decreases in sediment flux is accompanied by downstream
migrating incisional waves and decreases in channel gradient, while incision driven by tectonics generates upstream
migrating incision and increases in channel gradient.
[33] Conceptually, the reason for these differences lies in
the mechanism driving incision. In all cases, incision occurs
due to local changes in the ratio of sediment supply to sediment transport capacity. Climatically modulated incision,
driven by decreases in the input sediment supply or increases
in the relative contribution of discharge from the upstream
reaches of the channel, creates conditions in which the rivers
have excess transport capacity at their point of exit from the
crystalline mountain front, and therefore erode; this is
analogous to the situation in which clear water exits at the
base of a dam [e.g., Williams and Wolman, 1985]. Incision
therefore migrates downstream until the river’s transport
capacity matches the sediment supply from upstream, at
which point incision stops. The final channel gradient in the
incised upstream reaches is less steep than the initial gradient because a lower channel slope is capable of conveying
the reduced sediment supply from upstream.
[34] Incision driven by accelerated rock uplift occurs
because of increases in gradient along the fluvial profile.
This increased gradient will push an initial equilibrium
profile into an incisional regime, provided that the shear
stress on the steepened channel exceeds its critical value. In
the case of simple block uplift, the downstream edge of the
uplifting zone incises first due to the fault‐ or fold‐generated
steepening of the longitudinal profile. In the extreme case of
a strongly upstream increasing rock uplift rate, incision may
actually begin in the headwaters. In this case, the diagnostic
differences between incision driven by changes in hydrology and changes in tectonics lie in the temporal evolution of
channel gradient. All else being equal, incision driven by an
increase in rock uplift rate creates channels that are everywhere steeper than their initial gradients, while incision
driven by changes in hydrology creates channels that are
everywhere less steep.
[35] Against this modeling backdrop, we have reevaluated
the late Cenozoic incision of the North American High
Plains. Given that (1) modern channels draining the High
Plains are no steeper than those estimated from Ogallala
paleochannels, (2) the modern slope of the Ogallala surface
is within error of its estimated paleoslope, and (3) the incision of the High Plains coincides with documented changes
in regional and global climate, we suggest that climate
change remains a plausible explanation for the fluvial incision of this physiographic province. Based on our modeling results, detailed geochronology from abandoned terraces
and paleosurfaces could help to unravel the spatial and
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temporal patterns of incision across the High Plains, providing an additional test of the hypothesis that this incision
was climatically induced.
[36] Acknowledgments. Funding was provided by NSF grant EAR‐
062199 to G.E.T. and NSF grant EAR‐0724960 to Suzanne P. Anderson.
We thank P. Heller, E. Leonard, W. Bull, and four anonymous reviewers
for their comments on various versions of this manuscript.
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R. S. Anderson, Institute for Arctic and Alpine Research, University of
Colorado at Boulder, 1560 30th St., Campus Box 450, Boulder, CO
80309, USA.
G. E. Tucker, Department of Geological Sciences, University of
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C. W. Wobus, Stratus Consulting, Inc., 1881 9th St., Boulder, CO 80302,
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