Does climate change create distinctive patterns of landscape incision?

Authors

  • Cameron W. Wobus,

    1. Stratus Consulting, Inc., Boulder, Colorado, USA
    2. Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, Colorado, USA
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  • Gregory E. Tucker,

    1. Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, Colorado, USA
    2. Department of Geological Sciences, University of Colorado, Boulder, Colorado, USA
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  • Robert S. Anderson

    1. Department of Geological Sciences, University of Colorado, Boulder, Colorado, USA
    2. Institute for Arctic and Alpine Research, University of Colorado at Boulder, Boulder, Colorado, USA
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Abstract

[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.

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 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 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]:

equation image

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]:

equation image

where Kf is a dimensional constant, τb is the shear stress on the bed, and τc 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,

equation image

where ρ 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:

equation image

where αr 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):

equation image

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 the entire system of equations in nondimensional terms. Our normalization proceeds as follows:

x

= x/L;

z

= z/R;

So

= R/L;

S

= S/So;

τ

= τ/τref;

q′

= q/qo;

τref

= Ktqo3/5equation image7/10;

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:

equation image

[9] Inspection of equation (6) reveals that the dynamics of this system are controlled by the downstream changes in the variables q′, S′, and τc. 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 τc) 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:

equation image

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:

equation image

In our baseline models we use an exponent c of 1, implying that all the portions of a drainage basin contribute equally to 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,

equation image

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 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 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].

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.

[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 δ18O 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 δ13C 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.

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.

[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.

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.

[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.

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 uplifted paleosurface that preserves the steeper gradients required to match the higher uplift rates.

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.

[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.

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.

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 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 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.

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). 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, 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 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 temporal patterns of incision across the High Plains, providing an additional test of the hypothesis that this incision was climatically induced.

Acknowledgments

[36] 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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