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Keywords:

  • Rocky Mountains;
  • late Cenozoic;
  • erosion

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] The high relief of the modern Rocky Mountain landscape formed in the late Cenozoic by downcutting of a fluvial network that links a series of easily eroded sedimentary basins across relatively resistant crystalline cores of adjacent ranges. Using a numerical model of fluvial erosion and the flexural isostatic response to the associated unloading, we first calculate the expected pattern and pace of incision caused by rock uplift related to migration of the Yellowstone hot spot and to growth of the northern portion of the Rio Grande rift. Calculated incision rates are <60 m/Myr, and total depth of erosion of sedimentary basins is <300 m, well below the long-term incision rates and amounts of erosion interpreted from the geologic record. Broad-scale tilting of the region toward the east, accomplished by a gradient in rock uplift of ∼1 km along the north-south axis of the central Rockies, declining to zero 1000 km to the east, can account for the additional erosion needed to match observations. In each modeling scenario, stream incision is nonsteady, with rock uplift outpacing erosion for <1 Myr in perimeter basins and 1–5 Myr in interior basins. Three factors dominate the spatial and temporal pattern of regional landscape evolution: (1) the time since uplift began, (2) the uplift pattern, and (3) the distribution of relatively resistant bedrock within the region. Our results suggest that the spatial variability in late Cenozoic exhumation can be explained by a long-lived transience in the stream network response to these various late Cenozoic geophysical events.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] The dramatic mountain landscapes of the central Rocky Mountains formed during the late Cenozoic, well after the end of the Laramide orogeny, with a transformation from a middle Cenozoic landscape of low local relief to one with extensively exhumed basins and deeply incised ranges [e.g., Mears, 1993]. The processes responsible for landscape evolution in the central Rockies have been enigmatic, with debate focused on the potential effects of regional tectonic processes versus climate change [e.g., Eaton, 1986; Epis and Chapin, 1975; Gregory and Chase, 1994; McMillan et al., 2006; Molnar and England, 1990]. A paucity of relevant geomorphic and geophysical field data has hindered the testing of these models. Numerical and analytical models of bedrock streams represent a new tool to distinguish between tectonic and climatic causes of fluvial incision in the Rockies. Landscape evolution models have shown that both climate change and tectonic uplift can drive erosion [e.g., Anderson, 1994; Gregory and Chase, 1994; Herman and Braun, 2006; Whipple, 2001], but the expected spatial and temporal patterns of erosion produced by climate change and tectonic uplift differ [Whipple et al., 1999; Whipple and Meade, 2006]. The differences between model simulations can be used to give a quantitative context to field data and can guide future data collection efforts.

[3] One limitation of many conceptual models of Rocky Mountain landscape evolution is their implicit assumption of a one-to-one correlation between the forcing and the resulting stream incision, with streams producing erosion rates that are in equilibrium with the concurrent tectonic or climatic conditions. While numerical model results demonstrate that stream systems trend toward equilibrium [cf. Willett and Brandon, 2002], transient behavior may persist over timescales >50 kyr in coastal landscapes such as the King Range, California [Snyder et al., 2000], and >10 Myr in continental interiors such as eastern Tibet [Clark et al., 2006; Kirby et al., 2002]. Abundant knickpoints or knickzones along streams in the Rockies [Anderson et al., 2006; Zaprowski et al., 2001] and detailed dating of geomorphic surfaces [Riihimaki et al., 2006] indicate that many of the streams, particularly tributaries to the major rivers in the region, do not have steady state stream profiles over 1 Myr timescales. Therefore proper interpretation of the evolution of this region requires accounting for the regionally relevant factors that introduce complex geomorphic responses to tectonic and/or climatic forcing. These factors include the geometry of the drainage network, the major variations in rock erodibility, and the regional isostatic response to exhumation. Streams draining the central Rockies are likely to exhibit long-lived transience and a complex pattern of incision because the drainage network does not reach sea level for >1000 km and crosses dramatically different lithologies as it passes from crystalline ranges through sedimentary basins and in some cases across additional crystalline reaches. Regional exhumation of large volumes of sediment from easily eroded sedimentary basins has also likely added complexity to the incision history of the Laramide region.

[4] In this paper, we quantitatively evaluate stream incision in response to three scenarios in which geophysical and climatic drivers are prescribed by (1) steady climate and rock uplift due to the short-wavelength (100 km length scale) geophysical features of the Rio Grande rift and Yellowstone hot spot, (2) steady climate and the Rio Grande rift and Yellowstone hot spot with additional long-wavelength (1000 km length scale) epeirogenic tilting of the region, and (3) the Rio Grande rift and Yellowstone hot spot with climate change modeled as a gradual increase in water discharge since the Pliocene. We then assess whether the geomorphic response to each scenario matches the spatial variation in the magnitude of exhumation and the rate of stream incision recorded in the geologic record. While the modeled scenarios that produce results matching observed patterns of landscape evolution are not unique, they quantify the implications of previously proposed elements of the tectonic and climatic history of the Rockies, and guide future collection of critical information from the field.

2. Setting

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[5] The central Rocky Mountain landscape is an irregular patchwork of high mountains and intervening sedimentary basins, stretching across ∼300,000 km2 of Wyoming, Colorado, Montana, Utah, and South Dakota (Figure 1a). The narrow crystalline-cored ranges (<50 km across) include the Wind River, Bighorn, Uinta, Laramie, Medicine Bow, Owl Creek, Granite, and Front ranges, and the Black Hills. Most of these ranges have distinctive, broad, high-elevation surfaces of subdued local relief (so-called “subsummit surfaces”). Some investigators [e.g., Epis and Chapin, 1975; Evanoff, 1990; Gregory and Chase, 1994; McMillan et al., 2006; Mears, 1993] have argued that these bedrock surfaces once merged smoothly with the top of the adjacent basin fills. The broad basins (>100 km across) include the Wind River, Bighorn, Uinta, Laramie, Green River, Denver, and Powder River basins. A striking aspect of these basins is the abundant evidence of late Cenozoic incision within each. The modern drainage network (Figure 1a) has partially exhumed most basins, creating broad depressions up to ∼1.5 km deep in easily eroded, fine-grained sedimentary strata. Some interior parts of the Laramide province remain unexhumed. For example, the Granite Mountains, central Wyoming, have experienced exhumation of only ∼100 m [Jaworowski, 1991], basin fill laps onto the range, and local relief is relatively low. Miocene subsidence partially accounts for the small amount of exhumation, but headward eroding drainage divides, such as the Beaver Rim, demonstrate that exhumation is greater in regions downstream of the Granite Mountains landscape.

image

Figure 1. (a) GTOPO-30 digital elevation map of the modern Rocky Mountain landscape, showing the geometry of the modeled fluvial network. Also included are the locations of sedimentary basins (yellow circles) and resistant bedrock reaches (black line segments). To increase the processing speed of calculations, we applied a filter to coarsen each cell size from ∼700 m to ∼3.2 km; on a regional scale the model results are insensitive to this increase in cell size. (b) Final amount of short-wavelength uplift in model experiments. Uplift in the southern part of the model space occurs steadily through the model run, while uplift in the northwest region is a function of the advection of Yellowstone hot spot topography. BHB, Bighorn basin; DB, Denver basin; LB, Laramie basin; HB, Hanna basin; NPB, North Park basin; PRB, Powder River basin; YS, confluence of Yellowstone-Bighorn Rivers; WRB, Wind River basin.

Download figure to PowerPoint

[6] Tributaries of the Missouri and Green rivers drain the region, ultimately flowing to the gulfs of Mexico and California 6000 and 3000 km away, respectively. Although the Great Divide basin is the only major Laramide basin that is internally drained today, some areas are relatively isolated due to the drainage network topology. Interior basins, such as the Bighorn and Wind River basins, are drained by rivers that have sawed their way through ranges at the downstream basin margin. Perimeter basins, such as the Denver and Powder River basins, are drained by streams that flow directly to trunk rivers without crossing crystalline bedrock reaches downstream of the basins [Dickinson et al., 1988].

2.1. Amounts and Rates of Late Cenozoic Erosion

[7] The spatial patterns of late Cenozoic erosion and erosion rates are poorly constrained because regional erosion has removed nearly all of the deposits and landforms that mark the maximum height of basin fill and the remaining deposits and landforms are often difficult to date precisely. McMillan et al. [2006] present a map of exhumation amounts by interpolating between the oldest preserved geomorphic features, such as buttes composed of remnant basin fill deposits, formed during exhumation. They find two major loci of exhumation in the central Rockies: the area near the confluence of the Bighorn and Yellowstone rivers (henceforth referred to as the Yellowstone basin), with 1000–1200 m of exhumation, and sedimentary basins along the eastern margin of the Front Range in Colorado, with exhumation totals of 600–800 m. Basins in the interior of the landscape tend to have smaller amounts of exhumation: exhumation increases from the interior Wind River basin to the perimeter Yellowstone basin. Interior regions such as the North Park and Hanna basins and the Granite Mountains, have experienced exhumation of <400 m. The ages of the mapped landforms indicate that the onset of regional incision occurred some time after 8 Ma and before 3–4 Ma [McMillan et al., 2006]. This finding is consistent with the age of the top of the Ogallala Formation (∼5 Ma [Heller et al., 2003]), which is the youngest sedimentary unit that indicates widespread post-Laramide deposition on the Great Plains. Assuming that the exhumation has occurred since 5 Ma, exhumation rates in the region range from <80 m/Myr to 250 m/Myr.

[8] Average late Quaternary rates of fluvial incision, constrained by deposits of the 640 ka Lava Creek B ash (Yellowstone origin) preserved within gravel caps of fluvial terraces, vary by greater than an order of magnitude across the region, from <20 m/Myr to ∼300 m/Myr [Dethier, 2001]. The magnitude and spatial distribution of rates are broadly similar to average exhumation rates since the Pliocene [McMillan et al., 2006]. A few older Yellowstone ash deposits constrain local incision rates prior to Lava Creek B deposition. For example, a deposit of 2.02 Ma Huckleberry Ridge ash in a terrace above the Shoshone River can be correlated to Indian Arrow Bench, ∼295 m above the Yellowstone River, yielding an incision rate of 150 m/Myr [Reheis et al., 1991]. Fission track ages of clinker, rock that has been thermally metamorphosed by coal fires, in the Powder River basin indicate that Little Thunder Creek, a tributary to the Powder River, has incised at 140 m/Myr since 700 ka [Mears et al., 1991]. Preliminary results from zircon (U-Th)/He ages of clinker in other parts of the Powder River basin indicate that incision rates average 150–200 m/Myr since 100–600 ka but locally may be as high as 300–400 m/Myr since ∼100 ka [Reiners and Heffern, 2002].

2.2. Late Cenozoic Uplift

[9] Debates about the causes of fluvial incision in the central Rockies have partially focused on estimates of the paleoelevations of the region. Cretaceous marine strata indicate that much of the region was at or below sea level when the Laramide orogeny began (∼80 Ma [Dickinson et al., 1988]). The current basin floor elevations of >1 km indicate that significant change in surface elevation of the region must have occurred since ∼80 Ma. High scarps at the mountain front, coincident with the lithologic break between crystalline rocks of the mountain cores and sedimentary strata of the basins, indicate rock uplift of the ranges along thrust and reverse faults during the Laramide orogeny.

[10] For the Great Plains, restored isopach maps of Upper Cretaceous sedimentary rocks showing tilting to the west and maps of modern topography showing tilting to the east have been used to argue that the region experienced long-wavelength, epeirogenic tilting in the Cenozoic. Total rotation of rocks to the east was ∼3 m/km, with maximum rock uplift of ∼3 km along the north-south axis of the Laramide region and a hinge line ∼1000 km to the east in the Great Plains [Mitrovica et al., 1989]. Numerical modeling results suggest that the long-wavelength tilting is the surface expression of a subducting Farallon Plate, with subsidence during flat slab subduction under the Laramide province and subsequent uplift at the end of the Laramide orogeny as the angle of subduction increased [Mitrovica et al., 1989]. In such a scenario of subsidence followed by rock uplift, deposition of sediment derived from Laramide ranges would have dominated until regional gradients became sufficiently high that fluvial systems became integrated and incisional. In the Great Plains, this geophysical event could account for both the deposition of a thick, generally coarsening upward sedimentary sequence (including the White River, Arikaree, and Ogallala Groups) through the Miocene and regional exhumation since the Pliocene. In the interior of the central Rockies, tilting to the east could have allowed a steepening stream network to become integrated, overcoming local gradients that kept some regions internally drained.

[11] Comparisons of the modern gradient of Ogallala Group deposits with either modern stream gradients [Leonard, 2002] or paleohydraulic reconstructions of Ogallala age stream gradients [McMillan et al., 2002] also show evidence of tilting on the western Great Plains. Calculations of postdepositional tilting at the western edge of the Great Plains along the North Platte–South Platte River interfluve imply 1.8–3.6 m/km of rock tilting to the east since ∼5 Ma, equivalent to 400–815 m of rock uplift at the mountain front with an assumed hinge line 225 km to the east [Leonard, 2002; McMillan et al., 2002]. The amount of uplift at the mountain front would be larger if the hinge line of tilting were farther to the east. Tilting increases to the south, implying ∼1 km of relative uplift at the mountain front at the Arkansas-Canadian River interfluve [Leonard, 2002]. Leonard [2002] proposed that this pattern of southward increasing tilting and hence uplift at the mountain front is related to the northward propagation of the Rio Grande rift; if this is correct, the rift has potentially affected elevations as far north as the Wyoming-Colorado border. However, the location of the northern extent of the rift remains debated [cf. Leonard et al., 2002].

[12] Tilting of fluvial terraces in the Bighorn basin, first recognized by Mackin [1937], has been attributed to short-wavelength tilting caused by the Yellowstone hot spot [Pierce and Morgan, 1992]. The Yellowstone topographic anomaly, with a maximum amplitude of ∼700 m and a radius of ∼300 km [Smith and Braile, 1993], has moved to the northeast at ∼4.5 cm/yr from 16 to 0 Ma [Rogers et al., 1990], although this rate may have slowed to 1.3–3.3 cm/yr since 8 Ma [Smith and Braile, 1993].

[13] The magnitude, timing, and causes of post-Laramide uplift continue to be studied with various methods, including basalt vesicularity [Sahagian et al., 2002a, 2002b], oxygen isotopes [Dettman and Lohmann, 2000], and leaf physiognomy [Gregory and Chase, 1992]. Each method has uncertainties that allow calculation of paleoelevation only to within several hundred meters. Therefore rock and/or surface uplift of <1 km may be undetectable. Recent studies suggest that the Rockies in Wyoming [Dettman and Lohmann, 2000] and northern Colorado [Gregory and Chase, 1992] attained modern, high elevations by the Eocene. However, these studies cannot rule out more recent uplift of <1 km. Studies of uplift of the Colorado Plateau [Sahagian et al., 2002a, 2002b] suggest that certain edges of the plateau surface have been uplifted by up to 2 km since 25 Ma, with slow uplift rates (40 m/Myr) from 25 to 5 Ma and fast uplift rates (220 m/Myr) since 5 Ma [Sahagian et al., 2002a]. Unfortunately, these results do not clearly constrain the uplift history of more northern or eastern portions of the Colorado Plateau or central Rockies.

[14] Geophysical models suggest that erosional unloading of the central Rockies should have led to isostatic uplift of the region [Pederson et al., 2002; Small and Anderson, 1998a]. Rock uplift due to glacial canyon erosion has likely been small enough to be balanced by bedrock weathering rates [Small and Anderson, 1998a], resulting in no net surface uplift of the cores of the mountain ranges. However, exhumation of the broad intermontane basins may have driven larger amounts of isostatic uplift because of their regional extent and the large volume of exhumed sediment. McMillan et al. [2002] and Leonard [2002] calculate that exhumation of the Denver basin has caused ∼100–200 m of isostatically driven rock uplift along the basin periphery. In interior regions of the central Rockies with a more complicated basin distribution (e.g., northern and central Wyoming), two-dimensional calculations are necessary to quantify patterns of isostatically driven rock uplift.

2.3. Late Cenozoic Climate Change

[15] In addition to the regional tectonic perturbations described above, the central Rockies have experienced significant climatic changes during the Cenozoic. Ocean-based paleoclimate proxies, such as oxygen isotopes, provide a high-resolution record of global cooling during the Cenozoic [e.g., Raymo and Ruddiman, 1992; Zachos et al., 2001], with cooler temperatures leading to the intensification of Northern Hemisphere glaciation at 2.7 Ma [e.g., Haug et al., 2005]. The mid-Miocene climatic optimum (17–15 Ma) marked the warmest period of the Neogene [Zachos et al., 2001], while the middle Pliocene (∼3 Ma) was the most recent period of sustained warm temperatures [Thompson and Fleming, 1996]. General circulation models suggest that global average temperatures in the Pliocene were ∼3°C warmer than present values [Haywood and Valdes, 2004]. Since the end of the Pliocene, global temperature has been characterized by glacial-interglacial cycles.

[16] Local climatic history in the central Rockies since the Pliocene is difficult to reconstruct, largely because the extensive exhumation has led to poor preservation of post-Eocene fossils in most central Rockies basins. Fossil flora indicate that local temperatures cooled and seasonality increased since the early Eocene [Fricke and Wing, 2004]. Oxygen isotope values in soil carbonates of the Great Plains are consistent with cooling temperatures since the Miocene [Fox and Koch, 2004]. Paleobotanical reconstructions and paleolake deposits indicate that western North America was more humid during the mid-Pliocene than today [cf. Thompson and Fleming, 1996]. For example, stable isotopes in soil carbonates in southeastern Arizona and lacustrine highstand deposits at Tulelake and Searles Lake, California, indicate that conditions in the Pliocene at ∼3 Ma were wetter than today [Smith et al., 1993]. General circulation models and regional circulation models provide better spatial resolution of regional climate dynamics. Recent modeling results indicate spatially variable cooling by 5°–10°C and a decrease in precipitation rates of 70–700 mm/yr since the mid-Pliocene in the Northern Hemisphere midlatitudes [Haywood and Valdes, 2004]. However, a decrease in annual precipitation does not necessarily correlate with a decrease in flood probability distributions. Modern arid climates are associated with more frequent large floods than are more humid climates [Turcotte and Greene, 1993], and streams may therefore be more erosive in arid climates [Molnar, 2001], although this conclusion is questioned by Molnar et al. [2006]. Likewise, a change in the type of precipitation from rainfall to a mixture of rain and snow can change the timing of delivery of runoff to stream systems, thereby changing flood probabilities.

[17] Glacial deposits and landforms indicate that alpine glaciers in the central Rockies oscillated during the Quaternary in response to global glacial-interglacial fluctuations [e.g., Chadwick et al., 1997]. Glaciation was primarily limited to the ranges, with glacial ice extending into the edges of some basins, such as the Wind River basin, during glacial maxima. Long-term fluvial incision downstream of alpine glaciers paused during glacial periods in response to increased sediment loads [Hancock and Anderson, 2002]. In the Great Plains, the Laurentide Ice Sheet extended south to approximately the present location of the Missouri River, forcing its course south of its preglacial route [cf. Wayne et al., 1991].

3. Numerical Modeling Methodology

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

3.1. Numerical Modeling Framework

[18] The geomorphic evolution of the central Rockies is controlled primarily by fluvial incision patterns that respond to the tectonic and climatic drivers described above. To explore quantitatively the implications of these proposed forcing mechanisms, we develop and apply a numerical model of regional stream incision for the eastern slope of the central Rockies and compare its predictions with two documented, broad-scale patterns of geomorphic change: Quaternary fluvial incision rates [Dethier, 2001] and total erosion since the middle to late Tertiary [McMillan et al., 2006]. While glacial erosion has impacted the highest elevations in the landscape in the Quaternary, we focus on downstream areas and timescales longer than glacial-interglacial cycles. Therefore we do not attempt to model headwater glaciers and their associated erosional, sedimentological and hydrological effects.

[19] The model is structured to incorporate several important aspects of the landscape and its geologic history.

[20] 1. The streams cross dramatically different lithologies as they flow from the crystalline ranges into the highly erodible sedimentary basins (Figure 1).

[21] 2. The ranges and basins reside in close proximity, and therefore exhumation of one range-basin pair may drive isostatic uplift that influences exhumation of nearby pairs (e.g., exhumation of the Bighorn basin may result in isostatic uplift of that basin and nearby basins such as the Wind River basin).

[22] 3. The onset of late Cenozoic exhumation varied across the region but was ongoing in most places by 3–4 Ma [McMillan et al., 2006]. Prior to this time, we assume that streams maintained steady profiles across the adjacent basins while sculpting subsummit surfaces in most ranges.

[23] 4. Stream profiles within and adjacent to the crystalline cores of the ranges have knickpoints that indicate that this portion of the landscape has not attained a steady state morphology [Anderson et al., 2006; Safran et al., 2005; Zaprowski et al., 2001]. Therefore we do not assume that erosion rates are in equilibrium with rock uplift rates.

[24] 5. The streams have incised into bedrock and therefore can be considered bedrock streams over million year timescales.

[25] We use a quasi-two-dimensional, finite difference model (Table 1) of bedrock streams in which stream incision is a function of specific stream power ω, the rate of energy generated per unit area of channel bed by the loss of potential energy as water flows downhill [e.g., Bagnold, 1977; Burbank and Anderson, 2001; Hancock and Anderson, 2002; Howard and Kerby, 1983]. Each model experiment begins at 5 Ma, allowing the onset of incision in most basins to begin by 3 Ma. The two-dimensional topology of the model space is based on the modern landscape, with model stream channels located in their modern orientation as extracted from the GTOPO-30 digital elevation model (Figure 1a). As the streams are kept in a fixed location, incision calculations are one-dimensional. We represent the plan view geometry of major basins in the model space as circles and calculate erosion as if it occurred as a uniform “slab” of sediment (i.e., a disc load) [Lambeck, 1988; Wessel and Keating, 1994].

Table 1. Model Equations and Parameters
ModelEquation or Value
Channel elevation change, m/yrdz/dt = Ut + Uf − ɛ
Basin elevation change, m/yrdz/dt = Ut + Uf − 0.75ɛ
Channel incision, m/yrɛ = k(ωωc)
Specific stream power, N/s mω = ρwgQS/W
Tectonic uplift, m/yrUt = “Yellowstone” + “Rio Grande Rift”
Flexural uplift, m/yrUf = analytical solution for disc loads
Drainage area, km2A = 0.712x1.785
Upstream channel distance, kmx = distances extracted from GTOPO-30
Discharge, m3/sQ = PA
Channel width, mW = 3.0Q0.55
Stream incision time step100 years
Rock uplift time step0.1 Myr
Model duration5 Myr
Precipitation P0.1 m/yr
Gravitational acceleration g9.81 m/s2
Water density ρw1000 kg/m3
Rock erodibility in basins kb1.5 × 10−12 m s2/kg
Rock erodibility in ranges kr5 × 10−14 m s2/kg
Threshold stream power ωc25 N/s m
Crust density ρc2600 kg/m3
Mantle density ρm3300 kg/m3
Flexural rigidity D1024 N m

[26] Specific stream power is proportional to the product of the effective stream discharge Q (the volume of water available per unit time) and the local slope S (the proportion of the distance traveled that is downward), and is inversely proportional to channel width W:

  • equation image

where ρw is the density of water, and g is gravitational acceleration. A fraction of the excess specific stream power (specific stream power above a threshold value ωc) is available to drive incision of the streambed:

  • equation image

where z is elevation of the channel bed and k is the proportionality coefficient that accounts for factors such as the efficiency of the flow in delivering energy to the bed and the susceptibility of the bed to erosion. We employ a rule in which incision is linearly related to stream power, and we allow a finite threshold (i.e., ωc ≠ 0). Because sinks and flat areas of the digital elevation map prevent accurate extraction of drainage areas over such a large region, we use a power law relationship to express drainage area A as a function of upstream channel distance x, constrained by the drainage areas of USGS stream gages in the central Rockies. At tributary junctions, the upstream distance for each stream is added, resulting in a stepped increase in drainage area. We use power law relationships to express Q and W as functions of A [Hancock and Anderson, 2002; Roe et al., 2002; Snyder et al., 2000].

[27] We use Equation (1) to calculate stream erosion because it explicitly incorporates effective discharge, which can be adjusted in climate change scenarios. However, we note that our incision rule is equivalent to excess shear stress rules for stream incision, in which dz/dt = KAmSn (summarized by Tucker and Whipple [2002]), where m = 0.45 and n = 1 and K incorporates ρw, g, and coefficients of the power law equations Q = f1(A) and W = f2(A). The concavity index, θ = m/n = 0.45, is well within the 0.11–1 range of indices reported for a variety of drainage basins [Tucker and Whipple, 2002]. As a first-order approximation, we hold concavity steady spatially and temporally, although analysis of digital elevation models of the Great Plains indicates that modern concavity varies spatially [Zaprowski et al., 2005]. We use two values for k, 1.5 × 10−12 m s2/kg for highly erodible basin fill and 5 × 10−14 m s2/kg for resistant crystalline bedrock, the same values used by Anderson et al. [2006] in modeling incision of Boulder Creek, which drains a portion of the Front Range. The parameters we employ are similar to the lithology coefficients used in excess shear stress incision models (converting k to K, our basin value is K = 2.25 × 10−5 m0.1/yr; Whipple and Tucker [2002] use K = 2.00 × 10−5 m0.1/yr when n = 1), and the lithology contrast is well within the four-orders-of-magnitude range of K values reported by Stock and Montgomery [1999].

3.2. Initial and Boundary Conditions

[28] The detailed morphology of the Laramide stream network prior to the onset of late Cenozoic exhumation is poorly known. Stream captures have rearranged several drainages [e.g., Mackin, 1937; Reheis et al., 1991; Ritter, 1972; Wayne et al., 1991; Zaprowski et al., 2001], and initial stream gradients are known only in localized areas [McMillan et al., 2002]. The eastern slope of the central Rockies has undergone long-wavelength rock subsidence producing tilt down to the west during the Laramide orogeny and subsequent rock uplift with tilt down to the east since the mid-Tertiary [Mitrovica et al., 1989]. During this time interval, the landscape evolved from one characterized by deposition and relief reduction to one characterized by incision and relief enhancement. Presumably, during active subsidence and during initial recovery from the subsidence, low regional stream gradients prevailed and streams could not incise into bedrock except perhaps locally and temporarily within the crystalline ranges. Long-term persistence of such conditions would have promoted lateral planation that carved subsummit surfaces within the ranges. The ubiquity of these surfaces suggests that the stream network was below the threshold for incision for many millions of years [Epis and Chapin, 1975; Mears, 1993]. Long-term sediment deposition and rock uplift eventually produced regional gradients that were sufficiently great that the stream network must have been at the threshold for incision. Any subsequent rock uplift and/or climate change would have caused stream power to exceed the incision threshold.

[29] In the modeling scenarios we present here, we assume that the streams at 5 Ma were on the cusp of beginning to incise, with ω = ωc. Because initial conditions are set such that starting stream incision rates are 0 m/Myr, incision is driven only by rock uplift or climate change imposed during the model run; this was confirmed by a run in which no tectonic or climatic forcing was imposed, and indeed no incision occurred. Therefore the model results can be considered sensitivity tests to the imposed forcing. There are no published values of ωc for the central Rockies, despite the recognized importance of erosional thresholds [e.g., Snyder et al., 2003]. McMillan et al. [2002] calculate that the preexhumation slope of the ancestral Platte River system in the western Great Plains was ∼0.001. Setting S = 0.001 and using reasonable discharge and channel width values for the Platte River, Q = 100 m3/s and W = 40 m, we find that ωc = 25 kg/s3. Sensitivity studies in which ωc values were varied over several orders of magnitude indicated that calculated stream incision in this model is not sensitive to ωc, although the initial stream gradient is.

[30] We do not attempt to reproduce stream captures and drainage reconfigurations that have occurred in the central Rockies since 5 Ma. While changes in the plan view morphology of the stream network have affected local erosion rates, it is unlikely that these changes have caused regional incision. Stream capture and/or migration may drive incision if there is a corresponding increase in channel gradient. The expected incision is Δz = SΔx, where S is the steady state channel gradient and Δx is the change in channel length generated by the capture/migration. For a stream system with a gradient of 0.001, a 200–1200 km decrease in channel length would be required to drive 200–1200 m of incision, as suggested for the amount of erosion in the large Laramide basins. Sufficiently large changes in channel lengths have not been proposed.

[31] We dictate that no erosion occurs at the downstream node of the modeled drainage network, consistent with minimal late Cenozoic erosion rates in the eastern Great Plains [Dethier, 2001; McMillan et al., 2006]. Because erosion at this downstream boundary is prevented from occurring, the boundary does not generate incision upstream.

3.3. Short-Wavelength, Tectonically Driven Rock Uplift

[32] In the southern part of the model space, short-wavelength rock uplift is based on calculated tilting of the Ogallala Formation. Leonard [2002] presents profiles of tilting to the east and north. We reproduce this pattern of tilting by multiplying two Gaussian curves to capture decreasing uplift to the north and east, choosing parameters to match the uplift profiles presented by Leonard [2002]:

  • equation image

where A1 is the maximum amplitude of the uplift, 600 m; Dn and De are the distances north of the southern model boundary and east of the western model boundary, respectively; and σn and σe are the length scales over which the uplift decreases to 1/e of its maximum, 500 km and 800 km, respectively (Figure 1b). Rock uplift tapers both to the east and north, becoming negligible at the eastern edge of the model space and decreasing to only ∼200 m at 41°N (the Colorado-Wyoming border) [Leonard, 2002]. We assume northward tapering of 100 m per degree of latitude suggested by Leonard [2002] continues; therefore rock uplift becomes negligible at ∼43°N. Uplift in the southwest part of the model space possibly overestimates true uplift, but because there are no modeled streams in this region, the model results are unaffected by the imposed uplift in this region. We assume that the uplift has occurred steadily since 5 Ma.

[33] Short-wavelength rock uplift in the northwest part of the model space is based on the observed Yellowstone topographic anomaly [Smith and Braile, 1993], a radially symmetrical bulge that can be approximated by

  • equation image

where dz is the amplitude of the anomaly, A2 is the amplitude of the center of the hot spot, 700 m; Dr is the radial distance from the hot spot center; and σr is the radial length scale over which the topographic anomaly decreases, 250 km. The center of the hot spot, migrates at 4.5 cm/yr with a bearing of 56°; surface uplift associated with the migrating hot spot at time i is Δz = dzidzi−1 (Figure 1b). We assume that the corresponding rock uplift is equal to the surface uplift, although this is not well constrained in the geologic record. A remnant deposit of the White River unit near the southern border of Yellowstone National Park indicates that erosion here has been <100 m [Love et al., 1976; McMillan et al., 2006]. We calculate hot spot migration in 0.1 Myr time steps, with rock uplift imposed at the beginning of each time step.

3.4. Long-Wavelength, Epeirogenic Rock Uplift

[34] The magnitude and cause of long-wavelength, epeirogenic uplift in the central Rockies and Great Plains has been debated. As stated above, Mitrovica et al. [1989] propose that post-Laramide tilting to the east occurred after the cessation of the Laramide orogeny as the region recovered from subsidence caused by passage of the subducting Farallon slab. A large fraction of this uplift likely occurred prior to the onset of late Cenozoic incision. We use a pattern of tilting similar to that suggested by Mitrovica et al. [1989], with maximum rock uplift at the western boundary of our model space and a hinge line 1000 km to the east (500 km west of the eastern boundary of the model space). Because the magnitude of Pliocene through Quaternary tilting is unconstrained, we present results for a variety of scenarios in which the final magnitude of uplift at the crest of the pattern ranges from 0 to 2 km (corresponding to tilting of 0–2 m/km) (Figure 2a).

image

Figure 2. (a) Long-wavelength tilting toward the east implemented in epeirogenic uplift experiments, plotted in an east-west transect across the model space. Because the projection is equal area, longitude values for the x axis are approximate. The east-west location of the center of each basin is plotted (abbreviations defined in the caption for Figure 1). (b) Oxygen isotope values from Zachos et al. [2001] (dashed line) and discharge time series relative to the initial discharge Q0 for the climate change experiments. Final discharge is 2–6 times greater than Q0.

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3.5. Climate Change

[35] Ideally, a quantitative assessment of how late Cenozoic climate change has affected stream processes would include reconstructions of flood probability distributions along each stream [Lague et al., 2005; Molnar, 2001; Molnar et al., 2006; Snyder et al., 2003; Tucker and Bras, 1998]. However, this is an unrealistic expectation of the geologic record, particularly given the extensive erosion that has removed much of the late Cenozoic sedimentary record in the Rockies. We therefore attempt to keep our climate change scenario as simple as possible to illustrate the sensitivity of landscapes to basic changes in climate. Our implementation of climate change does not encompass all of the possible ways in which climate could have affected late Cenozoic erosion rates. We use a simple forcing in which streams gradually become more erosive through time, accomplished by linearly increasing effective discharge over the model runs. This pattern mimics the gradual increase in global oxygen isotopes since 5 Ma [Zachos et al., 2001] (Figure 2b). We present the results of several scenarios in which the final discharge increase is 2–6 times the initial discharge.

3.6. Isostatically Driven Rock Uplift

[36] We employ an analytical solution to calculate two-dimensional isostatic uplift due to removal of disc loads [Lambeck, 1988; Wessel and Keating, 1994] (Figure 3). We use a uniform flexural wavelength l of ∼100 km, corresponding to a flexural rigidity D of 1024 N m [Angevine and Flanagan, 1987; Lowry and Smith, 1995]. For Young's modulus E = 100 GPa and Poisson's ratio ν = 0.25, the effective lithospheric thickness Te ≈ 48 km. We assume a mantle density of 3300 kg/m3, a basin fill density of 2600 kg/m3, and an air density of 1.22 kg/m3. We perform this calculation every 0.1 Myr, sufficiently long for the landscape to achieve the full isostatic response to the unloading (of order 10 kyr [Adams et al., 1999]) and for significant, but still small, amounts of rock uplift to occur (<10 m per time step for all experiments).

image

Figure 3. (a) Schematic exhumation of a sedimentary basin and the modeled disc load approximation used for isostatic uplift calculations, shown in one dimension. The basin floor elevation lowers from the initial elevation (solid black line) to the final elevation (dashed gray line) in response to river incision in the center of the basin. We treat the material exhumed as a uniform slab of sediment, with a thickness 75% of the river incision (solid gray line). We expect the greatest error in this approximation at the basin edges. (b) Plot of the expected uplift generated by removing a disc with a radius of 100 km and thickness of 100 m from a sedimentary basin in the Laramide region. A maximum of 67.3 m of rock uplift occurs at the center of the exhumed basin; 33.5 m of uplift is generated along the basin periphery. For basins with smaller radii the amount of calculated uplift is smaller.

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[37] The thickness of each sediment slab removed depends on the mean lowering of the basin floor, which is a function of the rate of trunk stream incision (which we explicitly calculate), the response of tributaries to this incision, and the drainage density within the basin. The detailed relationship between trunk stream incision and mean basin exhumation is complicated in any basin. In the central Rockies, we make a first-order approximation that the basin floor experiences a mean erosion rate that is 75% of the trunk-stream incision rate. Our choice of the 75% value acknowledges that the basin floors are not perfectly flat, that tributaries do not cover the entire basin, but that the volume of uneroded basin fill is small relative to the volume of eroded sediment, as can be seen in the modern basins of the region. We expect the greatest error at the basin edges, where the approximation of circular basins does not capture more complex basin shapes and where tributary response times are longest [Riihimaki et al., 2006]. However, given the high flexural rigidity of the region, modeled stream incision rates and amounts are insensitive to the simplified basin geometries.

[38] We do not calculate rock uplift due to erosion of canyons within ranges. Small and Anderson [1998a] argue that this rock uplift was likely small enough to be balanced by slow bedrock weathering rates. Because the volume of material eroded from basins was much greater than the volume eroded from the adjacent ranges, the regional isostatic uplift should be driven primarily by uplift in response to basin erosion [Small and Anderson, 1998b].

4. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

4.1. Scenario 1: Short-Wavelength Uplifts Only

[39] Short-wavelength uplift produces erosion rates of 0–75 m/Myr, with maximum erosion rates in each basin closely corresponding to maximum rates of rock uplift (Figure 4). The Yellowstone, Denver, and Bighorn basins show the highest incision rates, corresponding to the highest imposed uplift rates. The time series of erosion rates for each basin displays an initial transience, as erosion rates gradually increase until they match rock uplift rates. Erosion rates increase most rapidly in the perimeter Denver basin, reaching steady state values after 4 Ma, whereas erosion rates in the most interior basins, Hanna and North Park, remain low until after 3 Ma and do not attain steady state values until after 1 Ma. In the Yellowstone hot spot region, time series of erosion rates have additional transience because rock uplift caused by the migrating hot spot is nonsteady; erosion rates in the Bighorn and Wind River basins decrease after 2 Ma as uplift caused by the migrating hot spot decreases in these basins, while erosion rates in the Yellowstone basin increase through the end of the model run because uplift rates in this basin continue to increase.

image

Figure 4. Model results of (a) erosion rates, (b) uplift rates, and (c) total erosion and uplift due to short-wavelength uplift (scenario 1). Observations from the geologic record for erosion are from McMillan et al. [2006]; we assign 200 m error bars to accommodate uncertainty in the reconstructed pre-eroded topography and variable erosion within each basin. Observed late Quaternary erosion rates are 50–300 m/Myr for most of the Laramide region [e.g., Dethier, 2001], but Pliocene rates are poorly constrained.

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[40] Modeled incision rates reflecting geomorphic response to short-wavelength tectonic drivers are well below observed late Quaternary incision rates of 50–300 m/Myr for most of the central Rockies [e.g., Dethier, 2001]. This result is expected, given the slow rate of rock uplift imposed. Therefore this result serves, in part, to illustrate the need for a separate or additional mechanism for stream incision. A comparison between modeled erosion rates and Pliocene–early Quaternary rates cannot be done because these rates are poorly constrained in the geologic record.

[41] The rock uplift pattern sets the upper limit on the total depth of incision in each basin, but interior basins experience 20–55% less incision than the local rock uplift whereas perimeter basins experience only 4–11% less incision. Amounts of incision in the model range from 90 m in the Powder River basin to 290 m in the Denver basin. The relatively small amounts of incision and associated basin exhumation result in only minor amounts of isostatic uplift. The largest effect of isostasy can be seen in the 10 m/Myr increase in uplift rate from 5 to 4 Ma in the Denver basin, but other basins, which have lower exhumation, experience less isostatic uplift (Figure 4b). Modeled incision amounts are 35–85% below values interpreted from the geologic record [McMillan et al., 2006], with the greatest mismatch for basins in the northern part of the model space, where rock uplift is caused by the Yellowstone hot spot.

[42] An initial mismatch between erosion and uplift rates causes a steepening of river gradients until erosion rates increase to uplift rate values. The amount of steepening is sensitive to k, with greatest amount of steepening along crystalline reaches, which require large river gradients to compensate for low rock erodibility (Figure 5). As these reaches steepen, they act as local base level for upstream basins, further delaying the onset of enhanced erosion rates in interior regions. The interior basins therefore experience the greatest amount of surface uplift in the model.

image

Figure 5. Modeled longitudinal profiles of the Wind-Bighorn-Yellowstone rivers at 1 Myr intervals. Shaded areas show regions of resistant crystalline bedrock. Minor surface uplift occurs in the perimeter Yellowstone basin, as erosion rates match uplift before 4 Ma, but significant steepening of the river at the Bighorn-Pryor Mountains occurs through 3 Ma during the long response time of the interior basins to rock uplift. Steepening of the river in the Wind River Range continues through the model run.

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4.2. Scenario 2: Short-Wavelength and Long-Wavelength Uplift

[43] Simulations in which both short- and long-wavelength uplift affect the modeled region, produce greater depths of incision and faster incision rates in all of the Laramide basins than those produced in scenario 1 (Figure 6), as expected from the greater amounts of rates of rock uplift imposed. The scenario in which the region is tilted by 1 m/km (maximum uplift of 1 km) produces results that best match the amounts of erosion recorded in the geologic record (assessed using reduced χ2): incision ranges from 400 to 1100 m, with greatest incision in the Yellowstone and Bighorn basins. This amount of tilting matches the 1 m/km estimate of tilting of the Ogallala Formation by Heller et al. [2003], which they attribute to the dynamic topographic affect of Farallon-Plate subduction [e.g., Mitrovica et al., 1989]. The greatest misfit to observations in the 1 km scenario is in the Denver and Laramie basins, where modeled exhumation is 375 m and 325 m greater than observations, respectively. This can partially be explained by removing the short-wavelength uplift associated with the Rio Grande rift; exhumation decreases by 290 m in the Denver basin and by 140 m in the Laramie basin when the Rio Grande rift uplift is removed from the 1 km scenario. These results indicate that tilting of Great Plains strata [Leonard, 2002; McMillan et al., 2002] can be explained by long-wavelength epeirogeny. Additional mismatch can likely be attributed to the simplified uplift pattern and lithology parameters implemented in the model.

image

Figure 6. Results from scenario 2. (a) Erosion rates from the modeling scenario in which long-wavelength tilting toward the east, with uplift at the western edge of the model space of 1000 m at the range crest (Figure 2a), is coupled with short-wavelength uplift. Other epeirogenic uplift experiments show similar spatial and temporal patterns of erosion, although the magnitude of erosion rates are scaled to the amount of uplift imposed. (b) Modeled amounts of erosion for epeirogenic-uplift scenarios. Values in the legend show the amount of epeirogenic rock uplift prescribed at the western border of the model space. Erosion without epeirogeny (“0 m”) is given for reference, as are observations from the geologic record [McMillan et al., 2006]. The 1000 m scenario provides the best statistical fit, although results exceed observations in regions affected by short-wavelength uplift from the Rio Grande rift and are below observations for the Yellowstone basin.

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4.3. Scenario 3: Short-Wavelength Uplifts and Climate Change

[44] Simulations in which we couple short-wavelength uplift with a gradual increase in discharge also produced enhanced erosion rates and total depths of erosion (Figure 7). Erosion rates have short-term variations caused by short-term changes in the discharge time series. The rates also show longer-term transience: perimeters basins display a rapid increase followed by a more gradual decrease in erosion rates, while interior basins initially experience only a moderate increase in erosion rates followed by steady erosion before the rapid increase to fast erosion rates. The erosion rates match observations of Quaternary erosion rates for at least part of each model run, but exhumation amounts do not match geologic observations. Despite increasing discharge by up to a factor of 6, exhumation remains below 1100 m for all basins. The greatest mismatch between model results and observations is in the Yellowstone basin, where calculated exhumation is >400 m below observations. The relatively uniform amount of modeled exhumation across all of the basins also fails to reproduce the observed variation of >500 m from the Yellowstone River to interior regions such as North Park basin [McMillan et al., 2006].

image

Figure 7. Results from scenario 3. (a) Erosion rates from the climate change scenario in which there is a threefold increase in discharge. Erosion rates in most basins reach their maxima at 4–2 Ma and decrease thereafter. Other climate change experiments show similar spatial and temporal patterns of erosion, although the magnitudes of these maxima are scaled to the amount of discharge increase imposed. (b) Modeled amounts of erosion for climate change scenarios, in which effective discharge increases gradually to 2–6 times the initial effective discharge. Erosion with no change in discharge (“1X”) is given for reference, as are observations from the geologic record [McMillan et al., 2006]. Model results show less regional variability than seen in the geologic record.

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[45] In summary, estimates of short-wavelength rock uplift associated with the Yellowstone hot spot and Rio Grande rift alone can explain neither the incision rates constrained by Lava Creek B ash deposits [Dethier, 2001] nor the erosion amounts constrained by late Cenozoic landforms [McMillan et al., 2006]. Regional tilting of 1 m/km, in combination with short-wavelength uplift, can produce results that better match the geologic record. Climate change scenarios, in which discharge gradually increases since 5 Ma, cannot produce erosion patterns that are consistent with highly variable erosion amounts across the region. While the tested climate change scenarios do not span all possible effects of climate change, they provide guidance for future scenarios by highlighting the need for a climate mechanism that produces greater regional variability in erosion patterns.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[46] Interpretation of the late Cenozoic geologic history of the Rocky Mountain region has been confused by assumptions of one-to-one correlations between post-Laramide exhumation and geophysical or climatic forcing mechanisms. Such assumptions are problematic in the face of increasing geologic evidence that incision has been unsteady and nonuniform in the late Cenozoic. Our results suggest that long-lived transience in the region's stream network can explain much of the spatial and temporal variability in late Cenozoic exhumation. Incision rates in our simulations do not immediately balance uplift rates. Instead, uplift outpaces incision from the beginning of the modeled period at 5 Ma through 3 Ma for several basins and through 1 Ma for the Hanna and North Park basins (Figure 8). The perimeter basins (Denver, Powder River, and Yellowstone basins) respond most rapidly, with erosion rates balancing uplift rates before 4 Ma. The long response time of interior basins reflects the time required for the geomorphic response of the fluvial system to propagate from high-drainage area, downstream reaches to headwater localities. The rate of headward response propagation is further delayed in several places by sills of hard rock that the river must cross (e.g., the Wind River gorge as it crosses the Owl Creek range between Wind and Bighorn basins). Therefore lower total exhumation of interior basins at the end of the simulation occurs because the onset of exhumation was delayed in these basins. For example, despite increasing amounts of imposed epeirogenic uplift from the Yellowstone to Bighorn to Wind River basins (Figure 2a), the amounts of exhumation at the end of the model run decrease (Figures 4c and 6b) because the Wind River basin is the most interior of these three basins.

image

Figure 8. Difference between uplift rates and incision rates for each basin from the modeling scenario in which long-wavelength tilting toward the east, with uplift at the western edge of the model space of 1000 m at the range crest (Figure 2a), is coupled with short-wavelength uplift. Incision in perimeter basins balances uplift earlier in the model run than incision in interior basins does. Negative values in the Bighorn basin after 2 Ma occur as uplift rates caused by the Yellowstone hot spot decrease (Figure 4b) but erosion rates remain high.

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[47] We predict that a second period of imbalance between erosion and uplift rates will occur as uplift rates decrease. Interior basins again will exhibit long response times, but now erosion rates will be greater than uplift rates. On a local scale, this effect can be seen in the difference between erosion and uplift rates in the Bighorn and Wind River basins (Figure 8), which experience a decrease in uplift rates from advected Yellowstone topography after 3–3.5 Ma (Figure 4). Erosion rates exceed uplift rates after 2.5 Ma in the Bighorn basin, and after 0.5 Ma in the Wind River basin. Erosion in each basin will continue until the amount of exhumation is proportional to the total rock uplift experienced since the stream gradients matched or exceeded the threshold gradient for incision.

[48] Despite the 106 year timescale to the region's response to rock uplift, our results indicate that the major streams in the study basins should presently be in an equilibrium state in which erosion rates balance local uplift rates. This does not mean that the modern morphology of the entire region is in steady state, however. Instead, small tributaries within the crystalline ranges may still show geomorphic evidence of a mismatch between uplift and erosion because they have a low stream power and flow across crystalline bedrock with low erosivity. The many knickpoints along streams within the Front Range [Anderson et al., 2006] and other central Rockies ranges [Safran et al., 2005], and a scarcity of knickpoints within the adjacent basins, are consistent with this interpretation. Knickzones along the Black Hills [Zaprowski et al., 2001] may reflect recent climatic or tectonic forcing, stream capture events, or subtle spatial variability in lithology.

[49] Our model results suggest that even if the central Rockies underwent a fairly simple history of rock uplift and/or climate change, the resulting pattern of incision would have been quite complex. We suggest that (1) a fairly simple geomorphic sequence may explain the general features of the landscape morphology, (2) some interior basins, and crystalline reaches bounding many basins, may still have erosion rates below uplift rates, even if uplift began in the Pliocene, and (3) the timing and amount of exhumation in a given basin within the central Rockies depends on the basin's location within the drainage network. Thus lower amounts of exhumation in interior basins such as the Hanna and North Park basins may be attributed to the long response time of the basins to geophysical events, rather than to small amounts of uplift in the region.

[50] A spatially complex erosional response to rock uplift requires a contrast in erodibility between basin fill deposits of sedimentary basins and crystalline bedrock of adjacent ranges (Figure 9). Numerical models predicting the rate of knickpoint propagation in the mountain ranges can provide additional constraints on the appropriate contrast in erodibility as the response to uplift propagates upstream from basins into ranges. We use a contrast in k based on model results of knickpoint propagation in the Front Range [Anderson et al., 2006]. Numerical models for other range-basin pairs are needed to explore whether k has a more complicated spatial and temporal pattern than that implemented herein. To ground truth these models, additional high-resolution ages of landforms generated during incision, such as strath terraces and pediments [Hancock et al., 1999; Riihimaki et al., 2006] and clinker [Reiners and Heffern, 2002], are needed. Stream gradients in canyons carved into ranges that form the downstream boundary of interior basins (e.g., Bighorn and Wind River canyons) also could provide constraints on k; unfortunately, dams and reservoirs in many of these areas confound this signal. Field measurements of rock strength can also provide constraints, but care must be taken when extrapolating these measurements to regional length scales and million year timescales. Changes in sediment load on multimillion year [Carroll et al., 2006] or glacial-interglacial [Hancock and Anderson, 2002] timescales may introduce additional complexity into the regional response to uplift and/or climate by effectively causing temporal variability in k (through variable mantling of the bed with sediment). A combination of modeling and geochronological studies should help provide limits on the role of sediment in modifying bedrock erodibility.

image

Figure 9. (a) Incision rates for the Bighorn and Wind River basins assuming two values of k (solid lines) and one value of k (dashed lines) and imposing only short-wavelength uplift. Incorporating a lithology contrast between basins and ranges (i.e., two values of k) results in a longer response time to uplift. The stepped increases in incision rates in the 2k scenario are caused by low erosion rates along downstream crystalline (low k) reaches; basin erosion rates are low as canyons are carved through these reaches. (b) Uplift pattern experienced by each basin during the 1k and 2k scenarios.

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6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[51] Incision rates and totals implied by modeling experiments in which incision is driven only by the proposed tectonic uplift due to the Rio Grande rift and Yellowstone hot spot are much lower than the rock record suggests. Our numerical modeling suggests that a combination of short- and long-wavelength rock uplift more successfully explains the pattern of late Cenozoic exhumation and late Quaternary incision rates along the east slope of the central Rocky Mountains. While we stress that this is unlikely to be a unique solution, it appears that regional tilting across an area on order 1000 km wide may better account for observed patterns of geomorphic response.

[52] Drainage network topology should play a major role in the pattern and timing of basin exhumation in complex orogens such as the Laramide. Spatially and temporally variable incision is a natural consequence of the spatial distribution of resistant ranges and more easily eroded basins. The timing of basin exhumation should provide an additional test of the nature of the tectonic and/or climatic forcing, particularly for basins that have similar amounts of exhumation in climate change and tectonic uplift scenarios. Therefore better constraints on the history of exhumation in each of the Rocky Mountain basins would aid in making more useful the natural experiment that this landscape represents.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[53] This work was supported by grants from the National Science Foundation (OPP98-18251 and EAR-0003604), a NSF Graduate Student Fellowship (to C.A.R.), and a University of California Presidential Postdoctoral Fellowship (to E.B.S.). We thank Eric Kirby and Joel Pederson for insightful reviews.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Setting
  5. 3. Numerical Modeling Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
jgrf289-sup-0001-t01.txtplain text document1KTab-delimited Table 1.

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