An Uplift History of the Colorado Plateau and Its Surroundings from Inverse Modeling of Longitudinal River Profiles G

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TECTONICS, VOL. 31, TC4022, doi:10.1029/2012TC003107, 2012

An uplift history of the Colorado Plateau and its surroundings from inverse modeling of longitudinal river profiles G. G. Roberts,1 N. J. White,1 G. L. Martin-Brandis,2 and A. G. Crosby3 Received 10 February 2012; revised 22 June 2012; accepted 27 June 2012; published 16 August 2012.

[1] It is generally agreed that a region encompassing the Colorado Plateau has been uplifted by sub-crustal processes. Admittance calculations, tomographic studies and receiver function analyses suggest that dynamic support is generated by some combination of convective upwelling and lithospheric thickness changes. Notwithstanding advances in our understanding of present-day setting, uplift rate histories are poorly constrained and debated: an improved history will aid discrimination between proposed models. Here, we show that a regional uplift rate history can be obtained by inverting longitudinal river profiles. We assume that the shape of a river profile is controlled by uplift rate and moderated by erosion. In our model, uplift rate is allowed to vary smoothly as a function of space and time, upstream drainage area is invariant with time. Simultaneous inversion of river profiles from the Colorado, Rio Grande, Columbia and Mississippi catchments shows that three phases of regional uplift occurred. The first phase occurred between 80 and 50 Myrs, when 1 km of uplift was generated at a rate of 0.03 mm/yr. A second phase occurred between 35 and 15 Myrs, when 1.5 km of uplift was generated at a faster rate of 0.06 mm/yr. A final phase of uplift commenced 5 Myrs ago. These distinct phases of Late Cretaceous and Oligocene uplift are corroborated by stratigraphic considerations, by thermochronometric data, and by stratigraphic evidence of periodic clastic efflux delivered into the Gulf of Mexico. An episodic uplift history is consistent with staged removal of thick lithospheric mantle beneath a large region, which is currently centered on Yellowstone. Citation: Roberts, G. G., N. J. White, G. L. Martin-Brandis, and A. G. Crosby (2012), An uplift history of the Colorado Plateau and its surroundings from inverse modeling of longitudinal river profiles, Tectonics, 31, TC4022, doi:10.1029/2012TC003107.

1. Introduction the thickness, temperature or composition of lithospheric mantle generate the required surficial elevation. Such chan- [2] The magnitude, timing and cause of Late Cretaceous ges could be produced by small-scale convection or by and Cenozoic regional uplift centered on western North erosion/delamination of the base of the plate [e.g., Bird, America has been debated for over 100 years [e.g., Burchfiel 1979; van Wijk et al., 2010]. Heating of the lithosphere, et al., 1992, and references therein]. In recent years, atten- thinning of the thermal boundary layer and melt extraction tion has focussed on the Colorado Plateau, which sits in the on the margins of the plateau might also play a role [Roy middle of the southern half of the uplifted zone (Figure 1). et al., 2009]. Chemical modification of lithospheric mantle The most popular models of uplift can be divided into could be facilitated by hydration during subduction of the crustal, lithospheric and sub-lithospheric categories. The Farallon plate [Humphreys, 1995; Humphreys et al., 2003]. first category of models suggests that elevation of a region A final category emphasizes the importance of sub-plate encompassing the Colorado Plateau can be explained by an processes such as large-scale convective upwelling and the increase in crustal thickness generated by, say, Late Creta- changing geometry of the subducting Farallon plate [e.g., ceous to Early Cenozoic lower crustal flow or magmatic Thompson and Zoback, 1979; Spencer, 1996; Lowry et al., underplating [e.g., Wolf and Cipar, 1993; McQuarrie and 2000; Moucha et al., 2009; Liu and Gurnis, 2010; Chase, 2000]. A second category argues that changes in Karlstrom et al., 2012]. [3] There have been significant advances in our under- 1Bullard Laboratories, Department of Earth Sciences, University of standing of the crustal, lithospheric and sub-lithospheric Cambridge, Cambridge, UK. structure beneath western North America. Crustal thickness 2Royal Opera House, London, UK. 3 measurements are a key constraint. The most reliable mea- BP Exploration, Sunbury-on-Thames, UK. surements come from modern wide-angle seismic surveys Corresponding author: G. G. Roberts, Bullard Laboratories, Department and from receiver function analyses. Crustal thicknesses are of Earth Sciences, University of Cambridge, Madingley Rise, Madingley 30–45 km across the Colorado Plateau [e.g., Gilbert and Road, Cambridge CB3 0EZ, UK. ([email protected]) Sheehan, 2004; Wilson et al., 2005] (Figure 1). The most ©2012. American Geophysical Union. All Rights Reserved. striking observation is that crust thicknesses beneath the 0278-7407/12/2012TC003107

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Figure 1. Topographic map of North America, which summarizes present-day crustal and lithospheric thickness data. Colored circles = crustal thickness estimates based upon receiver function analyses com- piled from literature (see text); solid numbered lines = lithospheric thicknesses (LT) from Priestley and McKenzie [2006]; heart-shaped dashed line marks CP = outline of Colorado Plateau where crust is 35– 45 km thick; BR = Basin and Range province; RG = Rio Grande rift; GP = Great Plains where crust is 35–60 km thick; RM = Rocky Mountains; YS = Yellowstone; A-A′ = location of schematic cross-section shown in Figure 15.

Great Plains are similar to, or exceed, those beneath the compensation occurs in regions such as the Rocky Colorado Plateau, even though their respective elevations Mountains where thickened crust is encountered. Nonethe- are < 500 m and > 2000 m (Figure 2). This elevation dif- less, the admittance value at long wavelengths is indicative of ference can only be maintained by crustal isostasy if crust regional sub-crustal support. This support encompasses beneath the Great Plains is 0.15 Mg/m3 denser than crust Yellowstone, the Colorado and Rocky Mountains plateaux, beneath the elevated plateaux. Magmatic underplating is one and the Basin and Range province (Figures 3 and 4) obvious mechanism for generating a dense lower crust but [McKenzie and Fairhead, 1997; Lowry et al., 2000; Li et al., the regional history of magmatism suggests that under- 2002b; Roy et al., 2005]. Seismic tomographic models show plating is much more likely to have occurred beneath the that regional dynamic support is generated by convective elevated plateaux. The required density difference also upwelling beneath the western edge of the North American means that crustal velocities should be faster by 1 km/s. plate. For example, the S40RTS shear velocity model shows Neither wide-angle seismic surveys nor receiver function that a large negative velocity anomaly sits beneath western analyses indicate that sufficiently large differences in crustal North America [Ritsema et al., 2011]. This widespread velocity exist [Thompson and Zoback, 1979; Braile, 1989; anomaly is largely confined to the upper mantle, although in Sheehan et al., 1995; Snelson et al., 1998; Li et al., 2002a; places it appears to extend beneath the 670 km discontinuity. Ramesh et al., 2002; French et al., 2009; Rumpfhuber et al., The anomaly also spreads horizontally beneath the thickened 2009; Wilson et al., 2010]. edge of North American lithosphere. Surface wave tomo- [4] These isostatic constraints suggest that the topographic graphic models suggest that 240 km thick lithosphere elevation of western North America is supported by density occurs beneath the Great Plains, thinning westward [West variations within the lithospheric and/or the sub-lithospheric et al., 2004; Priestley and McKenzie, 2006]. Beneath the mantle (Figure 2). This conclusion is corroborated by large- Colorado Plateau, receiver function analyses indicate that the scale geophysical observations. A +40 mGal long wave- 410 km discontinuity is often deeper than the global average length free-air gravity anomaly is centered on Yellowstone [Gilbert et al., 2003]. The depth to the 670 km discontinuity (Figure 3). Spectral analysis of free-air gravity and topo- also varies. Although the topography of these two dis- graphic signals show that the admittance, Z, at wavelengths continuities does not correlate, it is consistent with patches of of > 2000 km is 14 3 mGal/km (Figure 4). This value is higher than average ambient temperatures [Shen et al., 1998]. smaller than the +30 mGal/km expected for dynamic These and other seismological observations suggest that a support, which suggests that partial crustal isostatic region encompassing the Colorado Plateau overlies thinner

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notably the Gulf of Mexico, provides a tangible means for estimating uplift history [Galloway et al., 2000, 2011; Alzaga-Ruiz et al., 2009]. [6] Our principal objective is to show that longitudinal profiles of the trunk rivers and their tributaries, which drain North America (e.g. Colorado, Rio Grande, Columbia, Mississippi) can be jointly inverted to determine a meaningful spatial and temporal pattern of uplift rate of a region which surrounds and includes the Colorado Plateau. We suggest that the observed drainage pattern of western North America provides useful clues about the temporal evolution of uplift, which can be integrated with incision rate records,

Figure 2. Crustal thickness estimates plotted as a function of elevation above mean sea level. Black, grey and white circles show where LT ≥ 200 km, 200 > LT > 120 km and LT ≤ 120 km, respectively. Labeled gray bands = relationship between crustal thickness and elevation which is calculated by equalizing lithostatic pressure at base of 30 km thick (band a) and 40 km thick crust (band b). Width of gray band reflects range of crustal density (2.8 0.05 Mg/m3). Litho- spheric mantle density is 3.3 Mg/m3. Poor correlation suggests that topography is partially supported by sub-crustal density variations. lithosphere, beneath which convective upwelling occurs [Sine et al., 2008; Moucha et al., 2008, 2009]. [5] This broad geophysical framework places important constraints on uplift models. The temporal evolution of the dynamically maintained topography is of equal importance but poorly understood. Late Cretaceous marine sedimentary rocks crop out along a corridor running through western North America, which suggests that there is negligible pre-existing topography and sets an overall time scale for regional uplift [Hunt,1956;Sahagian,1987;Fenton et al., 2001]. The temporal distribution of uplift within this 95 Myr period, stretch- ing from Late Cretaceous times to the present day, can be determined using three different approaches. First, the geo- morphological evolution of the uplifted landscape places Figure 3. Long wavelength free-air gravity anomaly maps of broad, albeit largely qualitative, constraints on uplift history. North America extracted from GRACE dataset [Tapley et al., Geomorphic analysis of the Colorado River and its catchment 2005]. Sub-plate density variations are accentuated by band- emphasizes the importance of young (<6 Myr) uplift [e.g., pass filtering gravity data between 800 and 2500 km: red shad- Karlstrom et al., 2008, 2012]. A key part of this geomorphic ing = positive gravity anomalies; blue shading = negative evidence is the youthfulness of incision along the Colorado gravity anomalies; green line = zero value contour; contour River [McMillan et al., 2006]. Secondly, thermochronometric interval = 10 mGal. Heart-shaped black line labeled CP = methods are increasingly used to determine rates of unroofing Colorado Plateau; YS = Yellowstone. Note long-wavelength at spot locations across the elevated plateaux [Flowers et al., positive anomaly of 40 mGal centered on Yellowstone region. 2008]. Although these data are still sparse, they suggest that (a) White circles and gray dots = epicenters of earthquakes at least two phases of cooling have occurred since Late with body wave magnitudes ≥6 and <6, respectively (IRIS Cretaceous times, which could be related back to the history and CMT catalogues, 1973–2010). (b) Distribution and timing of uplift [Huntington et al., 2010]. Finally, the average flux of western North America magmatism after 26 Myrs [van Wijk of eroded products into surrounding sedimentary basins, et al., 2010] (NAVDAT database).

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Figure 4. (a) Admittance, Z, which is ratio of free-air gravity anomaly and topography plotted as function of wavenumber, for a box enclosing western North America. Upper horizontal scale shows equivalent wavelength. Solid circles with vertical error bars = observed values of Z; solid line = predicted values of Z, calculated using elastic model, which best fit observed values (elastic thickness = 15 km, upper crustal thickness and density = 20 km and 2.7 Mg/m3, lower crustal thickness and density = 20 km and 2.9 Mg/m3;[McKenzie, 2003]). Note observed admittance of 14 3 mGal/km at longest wavelengths, indicative of dynamic support. (b) Coherence between free-air gravity and topography plotted as a function of wavenumber. with thermochronometric observations, and with sedimen- [9] Cook et al. [2009] noted that steep sections (i.e. knick- tary flux estimates. zones) of the Colorado River and its tributaries traverse different lithologies. In many places, the top of a knickzone does 2. North America Drainage Patterns not occur at a lithologic contact. In Figure 7, the relationship between lithologic boundaries, knickzones and knickpoints 2.1. Longitudinal River Profiles is shown for the Colorado, Columbia, Rio Grande and Mis- [7] A digital elevation model of North America was gen- sissippi rivers and their principal tributaries. At outcrop scale, erated using the 3 arc-seconds (90 90 m resolution) short wavelength knickpoints often correlate with lithologic Shuttle Radar Topographic Mission (SRTM) dataset [Farr boundaries but on wavelengths >10 km this correlation et al., 2007]. Anomalous spikes and sinks were removed breaks down and broader knickzones rarely correlate with and drainage networks were extracted using the ArcGIS lithologic boundaries. In Figure 7, we compare slope or cur- software package (Figure 5). Away from deep and narrow vature and maximum change in tensile strength, which is channels, the vertical and horizontal accuracy of this edited regarded by Sklar and Dietrich [2001] as a proxy for erod- dataset is notionally 20 m [Hancock et al., 2006]. However, ibility, within a 6 km moving window for all four catchments. elevations along reconstructed river profiles can err by A majority of longer wavelength changes in slope or curva- hundreds of meters. For example, in the vicinity of Lees ture do not correlate with changes in bedrock lithology. This Ferry along the Colorado River, elevation is overestimated surprising and perhaps unexpected result suggests that the by about 300 m. As well as correcting for the presence of size and position of longer wavelength (>10 km) knickzones man-made dams along the Colorado River and elsewhere, we might be controlled by the amplitude and timing of regional have also benchmarked the position and elevation of extrac- uplift. An uplift event produces a gradient change at, say, the ted drainage networks wherever possible by employing mouth of a river, which propagates upstream at a rate which is Landsat imagery and published longitudinal profiles of pre- determined by the average or integrated discharge along the dammed rivers (Figure 6) [Cook et al., 2009]. Morphologic river. From an erosional perspective, the existence of frac- details of our drainage inventory are given in Appendix A. tured rock and regolith may be more significant than changes in lithology per se. 2.2. Colorado River and Rio Grande Catchments [8] Two large catchments drain the Colorado Plateau: the 2.3. Inverse Modeling Colorado River, the Rio Grande, and their tributaries. The [10] We are interested in exploring general methods for Colorado, Green, San Juan and Little Colorado rivers flow inverting longitudinal river profiles to extract surface uplift westward and drain most of the plateau and the surrounding rate histories [Pritchard et al., 2009; Roberts and White, highlands. The Rio Grande and Rio Puerco flow southeast- 2010; Hartley et al., 2011]. It is accepted that the rate of ward and drain highlands adjacent to the eastern edge of the change of elevation along a river profile, ∂z/∂t, is given by Colorado Plateau. All six rivers have irregular, convex- ∂z upward, longitudinal profiles (Figure 6). Within the Colorado ¼ UxðÞþ; t ExðÞ; t ; ð1Þ catchment, each tributary has at least two broad (200–400 km ∂t wide) knickzones which separate zones of lower relief. Numerous sharp (<10 km) knickpoints also occur. Within the where U is the rate of regional uplift and E is the rate of Rio Grande catchment, two knickzones are observed at erosion [e.g., Rosenbloom and Anderson, 1994; Whipple similar upstream distances but their amplitudes are smaller. and Tucker, 1999]. We assume that the shape of a longitudinal river profile is controlled by U and moderated by E.

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Figure 5. Topographic map centered on Colorado Plateau. Numbered blue lines = major rivers extracted from SRTM dataset. Drainage inventory in Table A1.

In general, U varies as a function of space and time but for during the Cenozoic Era [e.g., Cather et al., 2008; Wernicke, now we will assume that upstream drainage area is invariant 2011]. Since integrated discharge cannot easily be measured and that river capture events are not important. Neither of on geologically meaningful timescales, we exploit the well- these assumptions is likely to be correct in detail but it is known empirical model where important to investigate simple models before developing ∂z n ∂2z very sophisticated ones. We also assume that all rivers grade ExðÞ¼; t vAm þ k ; ð2Þ to a fixed mean sea level. Synthetic modeling shows that ∂x ∂x2 glacio-eustatic fluctuations have much shorter periods and amplitudes compared with the time and length scales con- where m and n exert a significant control on river profile m sidered here. The longer period sea-level fall since Late shape. n is often assumed to be 1–2. A is a proxy for the Cretaceous times is probably less than 100 m and has little integrated discharge at any position x along a river [e.g., affect upon our results [Miller et al., 2005]. To extract Hack, 1957; Whipple and Tucker, 2002]. m is typically information about U from an observed river profile, E must 0.35–0.6, although values as low as 0.1 have been cited be appropriately parameterized. E might be controlled by [Tucker and Whipple, 2002; Schoenbohm et al., 2004]. k is integrated discharge, which varies as a function of upstream erosional ‘diffusivity’ which mimics downwearing caused drainage area, A [e.g., Whipple and Tucker, 2002]. This by transport-limited erosion [Whipple and Tucker, 1999, assumption implies that integrated discharge is more sig- 2002]. We will initially assume that n = 1 since there is no nificant than instantaneous discharge. Undoubtedly, the evidence for shockwave behavior when knickzones retreat discharge of rivers draining the Colorado Plateau has varied [e.g., Berlin and Anderson, 2007; Pritchard et al., 2009]. If

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Figure 6. Longitudinal river profiles and their upstream drainage areas from Colorado River and Rio Grande catchments (see Figure 5 for locations). Solid lines = Colorado (C), Green (G), Little Colorado (LC), San Juan (SJ), Rio Grande (RG) and Rio Puerco (RP) river profiles; man-made dams were removed. Dotted lines = upstream drainage area of Colorado River and Rio Grande only. Horizontal bars along base = lithology along river bed : black bar = Precambrian/Paleozoic rocks, gray bar = Mesozoic rocks, white bar = Cenozoic rocks, red bar = igneous rocks [from Choubert and Faure-Muret, 1990]. n = 1 and m = 0, then v is the advective (i.e. knickpoint) river profiles by using an integrative methodology such as velocity. If n ≠ 1 and m > 0, the advective velocity is a non- that described here. linear function of local slope and upstream drainage area. [12] In its general form, equation (1) is not amenable to Together v, m, and n control the value of the advective term, analytical attack but Pritchard et al. [2009] showed that if which sets the knickpoint velocity and governs the transient k =0,ifn = 1, and if Am is replaced by, say, x0.5, U(t) can be shape of a river profile. We assume that k does not vary recast as along the river profile itself. : ∂z [11] If a river profile is at steady-state (i.e. ∂z/∂t =0; UðÞ¼t v x0 5 ; ð Þ x ∂x 3 U = E) and if k = 0, it is widely assumed that U can be ∂ ∂ estimated by measuring log( z/ x) as a function of log(A) where measurements [e.g., Schoenbohm et al., 2004; Whipple, pffiffiffi pffiffiffi 2004; Wobus et al., 2006; Karlstrom et al., 2012]. The L x t ¼ : ð4Þ slope of this function is m/n and its intercept along the y 0:5vx (i.e. log(∂z/∂x))axis at log(A)=0is1/n log(U/v), which yields U. There are two fundamental and serious drawbacks t is the time taken for a knickzone to retreat to a given of this form of slope-area analysis. First, observed river position after an uplift event, L is the total length of the river profiles may not have achieved steady state (i.e. ∂z/∂t ≠ 0). in meters, and x is the distance in meters from the source of Secondly, and more critically, slope-area analysis is predi- the river to the knickzone. Note that vx is not the same as v. cated upon differentiation of discrete and noisy measurements. The present-day Colorado River is 2300 km long and there In Appendix B, we show that slope-area analysis is inherently are two prominent knickzones located 200 and 1000 km unstable and can yield unreliable values of both m/n and U. downstream which yields t = 43 and 21 Myrs if, for 0.5 1 t More robust uplift histories can be instead be obtained from example, vx =50m Myr . These approximate values of suggest that at least two phases of uplift occurred during

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Figure 7. Relationship between slope and lithology for Colorado, Columbia, Rio Grande and Mississippi rivers and their tributaries. (a–c) Curvature, slope and lithology along Colorado river. (d–f) Conchos river (tributary of Rio Grande). Black, gray, white and red bars = Precambrian, Paleozoic/Mesozoic, Cenozoic and igneous rocks (i.e. surface rocks crudely divided into four categories based on likely erosional resis- tance [Choubert and Faure-Muret, 1990]). (g and h) Differences in tensile rock strength along each river, Dst, plotted as function of slope and curvature measured from SRTM dataset. Maximum change in tensile strength, slope and curvature are binned within a 6 km moving window. Cell shading = number of data points which fall within cell.

Cenozoic times and that these knickzones were probably not this position along the Colorado River, the local slope and created within the last few million years. A similar result is upstream drainage area are 1/375 and 3.6 1011 m2, obtained by plotting knickzone distances as a function of respectively. If n =1,v ≈ 4.16 104(2.78 1012)m.If river length on a template which was created by solving a m = 0.2, v = 203 25 m0.6 Myr1 (equation (D1)). The version of equation (1) for a set of idealized longitudinal uncertainty in v was estimated by error propagation where river profiles. This template assumes that knickpoint retreat slope and drainage area were assumed to have uncertainties 0.5 is only governed by vxx (Figure 8). of 10% and 20%, respectively. v and m trade-off negatively [13] These approximations are a helpful guide but it is against each other to some extent which means that different more useful to solve the generalized inverse problem: what is combinations of these parameters will produce similar uplift the smoothest uplift rate history, which yields the best fit rate histories (Appendix D). Our chosen values generate best- between calculated and observed river profiles? Equation (1) fitting river profiles within the time period constrained by suggests that if we know the shape of a river profile and if we stratigraphic control. Note that k can range over many orders can parameterize E, it is possible to extract U(t). To invert for of magnitude up to 107 m2 Myr1 without significantly U, we have devised a trial function with suitable penalties, affecting our results. which measures the difference between an observed river [14]Ifk = 0 and n = 1, the time taken for a knickzone to profile and a synthetic river profile calculated for any given propagate upstream, tG, is given by U. This trial function is minimized by systematically varying Z x dx Xx Dx U as a function of time alone. Our goal is to find the t ¼ ≈ i : ð Þ G vAm vAm 6 smoothest temporal distribution of U, which produces a best- 0 i¼1 i fitting synthetic river profile (Appendix C). The solution k obviously depends on the chosen values of v, m, n, and . If In Figure 9, isochrons of tG have been plotted for the Rio n =1,v and m directly control knickpoint velocity. 40Ar/39Ar Grande, Colorado and Columbia catchment areas. All three ages of basalts and U-Pb dates from speleothems located in catchments have strikingly similar landscape response times the Grand Canyon provide a well-constrained record of local which suggests that they may have evolved in a similar way. ∂z/∂t [e.g., Pederson et al., 2002; Polyak et al., 2008; Karlstrom et al., 2007, 2008, 2012]. If U = 0 and if k =0,we 2.4. Uplift as a Function of Time can rearrange equation (2) so that [15] To start with, we modeled the Colorado River and its major tributaries by permitting U to vary as a function of ∂z ∂z n 1 v ¼ Am : ð5Þ time alone. For the Colorado River itself, the starting misfit, ∂t ∂x c2, was 54 which reduced to 2 after optimization. Joint ’ Karlstrom et al. s [2007] mean vertical incision rate in the inverse modeling of the Colorado River and its principal Grand Canyon is 111 7 m/Myr (note that we have averaged tributaries suggests that three phases of uplift produced the the results from the eastern and western Grand Canyon). At large-scale knickzones (Figures 10a–10c). The first phase of

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Figure 8. Look-up chart for gauging timing of uplift events from knickzone distances along river profile. 0.5 1 vx =50m Myr . (a) River length plotted as a function of knickzone distance. Numbered lines are isochrons in Myrs which yield timing of uplift event for a given knickzone distance-river length pair. Mag- nitude of uplift event given by knickzone relief. Open circles with error bars = uplift for named rivers; solid circles with error bars = knickzone estimates for Colorado River. (b) Colorado River. Solid circles = two knickzones plotted in Figure 8a. uplift occurred between 80 and 50 Myrs. The rate of uplift our earlier assertion that knickzone retreat does not exhibit was 0.03 mm/yr which yields a cumulative uplift of 1 km. shock wave behavior. The influence of m can be tested in a The second phase of uplift occurred between 35 and similar way. A series of inversions were carried out with 15 Myrs. The rate of uplift was 0.06 mm/yr, which yields a 0 ≤ m ≤ 1. In each case, the value of v was chosen to ensure cumulative uplift of 1.5 km. A final phase of uplift started that Karlstrom et al.’s [2007] incision rate data from the 5 Myrs ago at a slower rate of 0.02 mm/yr. Inverse mod- Grand Canyon were honored. The residual misfit has a broad eling of the Rio Grande and its tributaries suggests that three global minimum at 0.2 ≤ m ≤ 0.4, which vindicates our discrete phases of uplift also occurred on the eastern side of original choice of value (Figures 11h–11n). We also tested the Colorado Plateau, although uplift rates are smaller the sensitivity of calculated uplift histories to changes in v (Figures 10d–10f). and A (Figures 11o–11bb). Unsurprisingly, residual misfit is [16] An important advantage of inverse modeling is that insensitive to moderate changes in either parameter (e.g. uncertainty in the four erosional parameters can be mapped 175 ≤ v ≤ 225, A 0.5A ≤ A ≤ A + 0.5A). Changes in v and A into calculated uplift rate histories. Different inversions are do change the calculated uplift rate history particularly at run using different values of v, m, n and k randomly selected greater times. For example, the change in v shifts the older from the ranges given in Table 1. This form of Monte Carlo phase of uplift by 5 Myr. This form of systematic testing inversion allows uncertainty envelopes to be constructed for shows the power of an inverse modeling approach which U(t). Our results suggest that the uncertainty in U(t) permits model space to be explored in systematic ways and decreases toward the present day. Inverse modeling can also allows uncertainties in parameters to be mapped into the be used to directly investigate the effect of varying an indi- model. vidual parameter. For example, we initially assumed that [17] Our one-dimensional inversion scheme is of limited n = 1. However, some studies have suggested that n could be practical use since uplift rate varies as a function of both greater or less than 1 [e.g., Whipple and Tucker, 1999; time and space, U(x, y, t). This more general problem can be Harkins et al., 2007; Ouimet et al., 2009]. We can easily test tackled by determining a smooth temporal and spatial his- the influence of n by running a series of inversions with tory of uplift which yields the best fit between calculated and 0 ≤ n ≤ 2 (Figures 11a–11g). The residual misfit has a pro- observed river profiles. nounced global minimum centered on n = 1, which confirms

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Figure 9. Landscape response time, tG, calculated for Rio Grande, Colorado and Columbia catchments using SRTM digital topography (see equation (6)). Dashed line = less certain divide in Basin and Range province which might drain internally. Uplift signal originates at river mouth. Contour interval = 10 Myr; gray shading = topography; black lines = loci of drainage divides.

2.5. Uplift as a Function of Time and Space and observed river profiles is sought. In this way, we have [18] Consider a grid of X Y T vertices, which repre- simultaneously inverted nearly 100 river profiles from North sent spatial and temporal nodes at which U can vary America (Figure 12). The mean residual misfit between cal- (Appendix C). A starting model of uplift rate is then chosen, culated and observed river profiles decreases from 29 for example U(x, y, t) = 0. The uplift rate history for a spe- Rto 8 after optimization. The history of cumulative uplift, t UxðÞ; y; t dt cific river is interpolated from this grid. Based upon our , is shown in Figure 13a. Our results show that previous experience, we chose v = 200, m = 0.2, n = 1 and a large region, encompassing Yellowstone and the Colorado 4 k =10. During inversion, the smoothest distribution of Plateau, has experienced two significant phases of regional U(x, y, t) which yields the smallest misfit between calculated uplift. The initial period of uplift had a maximum amplitude

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Figure 10. Inverse modeling of river profiles shown in Figure 6. Each river profile was inverted 50 times with erosion parameters assigned random values within bounded ranges (2 102 ≤ k ≤ 7 102, 200 ≤ v ≤ 210, 0.19 ≤ m ≤ 0.21, 1 ≤ n ≤ 1.05). (a) Smooth uplift rate history which yields the best-fitting river profile. Solid line = uplift rate as a function of time, which was calculated by inverse modeling; gray band = 1 s uncertainty resulting from variation in erosion parameters. (b) Cumulative upliftR history. t Udt Solid line = uplift as function of time obtained by integrating uplift rate through time (i.e. ); gray band = 1 s uncertainty. (c) Four river profiles from Colorado catchment: LC = Little Colorado, SJ = San Juan, C = Colorado, G = Green. In each case, gray band = observed river profile and solid line = best-fitting river profile calculated by inverse modeling (see text and Appendix C). (d–f) Inverse modeling of 2 river profiles from Rio Grande catchment: RP = Rio Puerco, RG = Rio Grande. of 1 km and occurred 80–50 Myrs at a rate of 0.03 mm/yr. It was then uplifted by an additional 1 km from 35–15 Myrs at 0.06 mm/yr. Table 1. Units and Range of Parameter Values Used in This Study [19] Inverse modeling indicates that the Colorado, Columbia, Mississippi and Rio Grande river catchments Symbol Parameter Value Units contain self-consistent sets of knickzones which can be k Diffusive coefficient of erosion 102–104 m2 Myr1 interpreted as a co-ordinated response to multiple phases of v Advective coefficient of erosion 175–225 m1–2m Myr1 regional uplift (Figure 12). The Columbia and Colorado (general model) 0.5 1 catchments contain at least two broad knickzones, which vx Advective coefficient of erosion 50 m Myr (simplified model) suggest that separate phases of uplift propagated upstream – – n Slope exponent 0 2 dimensionless from a coastline located somewhere to the west (rivers 7 9 m Area exponent 0–1 dimensionless and 44–48, respectively). In contrast, the Rio Grande and t Time Myr t Mississippi catchments have smoother river profiles which G Landscape response time Myr nonetheless are disequilibrated at the longest wavelengths x Distance along river m – – z Elevation of river m (rivers 59 62 and 72 76, respectively). These profiles are A Upstream drainage area m2 consistent with phases of uplift which have been inserted U Uplift rate m Myr1 into the upper reach of each catchment rather than at the E Erosion rate m Myr1 coastline. We suggest that a common history of uplift

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Figure 11

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Figure 12. Inverting for uplift as a function of space and time (see Appendix C for method). 93 rivers were jointly inverted for a smooth, temporal and spatial history of uplift (Figure 5 and Table A1). Gray lines = observed rivers; dotted lines = calculated river profiles (Figure 13). Residual c2 misfit = 7.9.

centered upon western North America is the unifying probably developed in response to a temporal and spatial framework which accounts for the river profiles within all pattern of regional uplift which has similarly affected other four catchments. river catchments. The exact timing and amplitude of different [20] Despite these striking patterns, we acknowledge that phases of uplift depends upon the erosional history, and there is considerable debate about the longevity of river especially on the values of v and m (Appendix D). Our cal- catchments. In recent years, this debate has been focussed on culated uplift history makes important and testable predic- the Cenozoic history of the Colorado River and its tributaries tions, which can be addressed by examining a range of [e.g., Wernicke, 2011; Karlstrom et al., 2012]. One possi- geologic observations. bility is that the present-day planform of the Colorado River catchment did not exist prior to 6 Myrs. If so, the results of 3. Independent Constraints our inverse modeling could be adversely affected by rapidly changing drainage patterns. A simple test of this hypothesis [21] Four sets of published observations are used to test is to remove the Colorado River and its tributaries from our the results of inverting longitudinal river profiles. First, database and rerun the inverse model. The resultant uplift thermochronometric analyses carried out on samples of rate history is largely unchanged (compare Figures 13a remnant stratigraphy provide spot estimates of unroofing. and 13b). We conclude that long wavelength knickzones of Secondly, paleontologic and geomorphic studies of the the Colorado River and its principal tributaries have Colorado River and Plateau help to constrain the history of

Figure 11. Testing erosional parameter values. (a–g) n was varied systematically to determine which value yields smallest residual misfit between theoretical and observed river profile. Figures 11a–11c show different values of n effect the shapes of theoretical river profiles. Gray line = profile of Colorado River; dotted line = theoretical river profile. Value of n in each case is shown bottom left. Figures 11d–11f show calculated uplift histories for best-fitting theoretical river profiles shown in adjacent panels. Figure 11g shows misfit between theoretical and observed river profiles as a function of n. Note position of global minimum at n =1.(h–n) Tests for varying m. Note global minimum at 0.2 ≤ m ≤ 0.4. (o–u) Tests for varying v between 175 and 225 which fit observations equally well. Note systematic increase in age of predicted uplift events as v increases. (v–bb) Tests for varying A by 0.5 A–1.5 A. Note trade-off between A and v.

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Figure 13. InvertingR for uplift as a function of space and time. Set of panels showing calculated cumu- t ¼ UxðÞ; y; t dt lative uplift history, . Blue and red lines = rivers modeled in this study. Location of vertices where uplift rate is input into the model U(x, y) are shown in Appendix C2. Time step, Dt = 5 Myrs. (a) Colorado Plateau is progressively uplifted by 1 km from 80–50 Myrs and by a further 1.5 km from 40–5 Myrs. Red lines = Colorado River and tributaries. (b) Calculated history of uplift when rivers from Colorado catchment are excluded which yields similar result as in Figure 13a. regional elevation. Thirdly, estimates of the volumes of (Figure 14). These two episodes were separated by a pro- clastic sediment transported from the elevated plateau and tracted period of negligible cooling between 50 and 30 Myrs. deposited in surrounding sedimentary basins, notably the Flowers et al. [2008] note that the rim and base of the Grand Gulf of Mexico, track the progression of regional unroofing. Canyon have similar Early to Middle Cenozoic cooling his- Finally, the Cenozoic magmatic history of western North tories, which suggests that a significant proportion of the America places an important constraint on the relationship present-day relief existed by the Eocene epoch. They suggest between lithospheric thickness, asthenospheric temperature, that only one of the four unroofing episodes, which occurred and decompression melting. from Late Jurassic to Recent times (i.e. the 80–50 Myr event), can be directly linked to rise of the Colorado Plateau. 3.1. Thermochronometry [23] Earlier apatite fission track studies by Kelley et al. [22] The most convincing evidence comes from the ther- [2001] and Naeser et al. [2001] favor a two-stage history mochronometric study of Flowers et al. [2008] who ana- of unroofing. Kelley et al. [2001] argue that 1–1.5 km of lyzed and modeled rock samples from Proterozoic basement denudation occurred between 70 and 55 Myrs. Temperatures within the Grand Canyon and from Triassic and Permian remained constant until 5 to 15 Myrs when a second phase sandstones and Cenozoic Rim gravels from the southwestern of cooling (i.e. unroofing) occurred. Naeser et al. [2001] quadrant of the Colorado Plateau. They obtained 230 single also suggested a two stage unroofing process: their first grain apatite ages from (U-Th)/He measurements, which event occurred at 60 Myrs and a second event occurred at suggest that unroofing of the plateau occurred in a series of 35–40 Myrs. In southern Colorado and northern New well-defined denudational episodes. Their best-fit thermal Mexico, fission-track data record cooling ages of 70–45 and histories show that peak temperatures at the end of Creta- 30–25 Myrs [Roy et al., 2004]. Thus a series of thermo- ceous marine sedimentation were followed by at least two chronometric studies, starting with Dumitru et al. [1994], episodes of rapid cooling at 80–60 Myrs and 20 Myrs

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Figure 14. Cumulative uplift history of western North America. Black line and gray band = cumulative uplift history calculated by inverting profiles from Colorado catchment; dashed line = thermochronologic history of crystalline basement from Upper Granite Gorge, Grand Canyon [Flowers et al., 2008]; dotted line = uplift history of southern interior of Colorado Plateau from combination of age of marine deposition, local relief inferred from (U-Th)/He dating, and elevation of lacustrine Bidahochi Formation [Huntington et al., 2010]; dash-dot line = change in dynamic topographic uplift inferred from reconstructed sub-plate flow by Moucha et al. [2009] and pinned at 30 Myrs using Huntington et al.’s [2010] estimate. Squares = uplift inferred from outcrops of Cretaceous shorelines [Sahagian, 1987]; dia- monds = uplift values from paleochannel incision observations and from Rim Gravel deposition and erosion on Hualapai Plateau [Elston and Young, 1991]; triangle = erosion of Chuska erg from central Colorado Plateau [Cather et al., 2008]; red histogram = distribution of K-Ar and 40Ar/39Ar ages for magmatic activity in New Mexico (vertical axis shows number of sites [Chapin et al., 2004; van Wijk et al., 2010]); black bars = periods of increased siliclastic deposition in Gulf of Mexico [Galloway et al., 2000, 2011]; solid circle = initiation of clastic infill on Coastal Plain, Eastern Mexico [Alzaga-Ruiz et al., 2009].

consistently favor two major stages of denudation between from overlying volcaniclastic conglomerates indicate that Late Cretaceous times and the present day. 2–3 km of uplift occurred before Late Eocene times and that [24] Huntington et al. [2010] combine these thermo- post-35 Myr uplift was minor [Gregory and Chase, 1992]. chronometric measurements with estimates of depositional Paleobotanical estimates of elevation are notoriously impre- temperatures obtained from Cenozoic lacustrine sedimentary cise. Pederson et al. [2002] and McMillan et al. [2006] rocks which crop out on the plateau. These estimates are identified a Late Cenozoic surface and argued that it was extracted from the temperature-dependent clumping of formed during the transition from net deposition to net deg- 13C-18O bonds in carbonate rocks. Their results imply that radation. If present-day topography is subtracted from this there has been little or no elevation change of the plateau surface, >1 km of incision (and surface uplift) is inferred for since 16 Myrs. Instead, the bulk of uplift and denudation is the last 8 Myrs. Unfortunately, there is little information thought to have occurred in Late Cretaceous and Early about the elevation at which this surface formed and so this Cenozoic times. It is important to emphasize that these value could be smaller. Upper Miocene-Pliocene sedimen- thermochronometric studies constrain denudation alone and tary rocks (i.e. Bouse Formation, Hualapai Limestone) are that uplift events which drive denudation must be inferred exposed on the flanks of the Colorado River southwest of the using, for example, isostatic considerations. Colorado Plateau. These deposits have been interpreted as either low-elevation lacustrine or estuarine facies [Lucchitta, 3.2. Paleontologic and Geomorphic Observations 1979]. They now sit at 460 m and 700–900 m, which implies [25] The most significant paleontologic observations are that up to 900 m of uplift occurred after 4–9 Myrs. Unfor- concerned with two important questions. First, to what tunately, high 87Sr/86Sr ratios extracted from carbonate layers extent can paleobotanical data be used to estimate the history and invertebrate shells in the Bouse Formation indicate that of elevation? Secondly, are Cenozoic carbonate deposits at no marine incursions occurred [Spencer and Patchett, 1997]. high elevations of marine origin? Moreover, the absence of the Bouse Formation and Hualapai [26] The size and shape of fossil leaves from the Florissant Limestone in similar low-lying areas of southwest and central Lake Beds of central Colorado combined with K-Ar dates Arizona favor a lacustrine origin. If so, this constraint on

14 of 25 TC4022 ROBERTS ET AL.: UPLIFT HISTORY OF COLORADO PLATEAU TC4022 timing of uplift is weakened [Spencer, 1996]. Sahagian et al. which was delivered along, for example, the paleo-Rio [2002] suggest that the size distribution of vesicles in young Grande [Alzaga-Ruiz et al., 2009]. This and later periods of (<25 Myrs) basalts around the edge of the Colorado Plateau sediment flux are often attributed to the onset of uplift and is consistent with an acceleration of uplift throughout Late subsequent erosion of the southwestern North America Cenozoic times, yielding 2000 m of uplift over the last 5– during the Laramide Orogeny [Galloway et al., 2000; 25 Myrs. Libarkin and Chase [2003] pointed out that these Alzaga-Ruiz et al., 2009]. There have been three significant vesicle data are open to alternative interpretations. periods of flux: Late Paleocene-Early Eocene, Oligocene, [27] For more than 75 years, geomorphic arguments have and Pliocene-Recent times [Galloway et al., 2011]. The been used to argue that the plateau landscape was recently location of other major sinks is difficult to determine and is created. Excavation of the 1.6 km deep Grand Canyon can complicated by extensional and strike-slip deformation on be attributed to uplift and incision during the last 6 Myrs the western flank of the uplifted plateaux. [e.g., Pederson et al., 2002; Karlstrom et al., 2008]. How- [30] Cather et al. [2008] have shown that during Early ever, cooling histories at the rim and base of the canyon Oligocene (34–27 Myrs) times, 300–500 m of eolian suggest that its morphology is at least partly inherited [e.g., deposition, known as the Chuska erg, occurred across the Flowers et al., 2008; Wernicke, 2011]. U-Pb dates from central and southern Colorado Plateau. The age of this speleothems imply that the Grand Canyon is older than Chuska erg is bracketed by 40Ar/39Ar dates of interbedded 17 Myrs [Polyak et al., 2008]. Alternative explanations have ash layers and overlying lavas. By comparing the present- also been suggested [Pearthree et al., 2008; Pederson et al., day elevation of erg remnants with the height of the younger 2008]. Four observations are invoked to support youthful Bidahochi Formation, Cather et al. [2008] propose that incision. First, fluvial sedimentary deposition is not recorded 1200 m of erosion occurred between 27–16 Myrs in within the 13–6 Myr Muddy Creek Formation which blan- response to uplift of the Colorado Plateau. They suggest that kets the Grand Wash trough at the mouth of the Grand this erosional event is the source of an Oligocene increase in Canyon [Lucchitta, 1972; Faulds et al., 2001]. Secondly, the sedimentary flux in the Gulf of Mexico [e.g., Galloway oldest sedimentary rocks, which contain detrital zircons et al., 2011] (Figure 14). from Rocky Mountain sources, were deposited in the newly [31] There is excellent evidence for proximal deposition opened Gulf of California at 5.3 Myrs [Dorsey et al., 2007]. which blankets the western flanks of the uplifted plateau. Thirdly, gravel deposits, which overlie the Hualapai Lime- These ‘rim gravel’ deposits present both a challenge and an stone and sit beneath the 4.4 Myr Sandy Point basalt, imply opportunity: their existence records uplift and denudation to that the Colorado River only became established along its the west [Elston and Young, 1991]. The fact that the same present course between 6 and 4.4 Myrs [Howard and deposits are incised by later drainage testifies to the exis- Bohannon, 2001]. Finally, if extrapolated over the last few tence of separate phases of uplift and erosion. Unfortunately, Myrs, Ar39/Ar40 dating of basalts which overlie terraces they are terrestrial and it is difficult both to date them and to within the Grand Canyon itself are consistent with 690– determine their elevation at time of deposition. In several 850 m of incision during the last 6 Myrs [Pederson et al., places, up to 1200 m of Paleogene relief is indirectly recor- 2002; Karlstrom et al., 2007, 2008]. None of these obser- ded by channels which incise Paleozoic strata. On the Hua- vations preclude the existence of a pre-13 Myr Grand lapai Plateau, at the southwest edge of the Colorado Plateau, Canyon [e.g., Wernicke, 2011]. Thermochronometric data these incised channels were later infilled by rim gravel show that little unroofing occurred between 13 and 6 Myrs deposits. Coeval development of a low-relief erosion surface but that kilometer-scale relief might have existed prior to is recorded by a regional unconformity which crops out 13 Myr [Flowers et al., 2008]. The detrital zircon record and beneath the widespread gravels. In northwestern Arizona, gravel deposits can be interpreted in several different ways. rim gravels could be of Paleocene or Early Eocene age, Incision rates calculated from the age and height of basalt- based on in situ gastropods and on K-Ar dates from exotic covered terraces, originally deposited along the thalweg of volcanic clasts. the paleochannel, are consistent with retreat of a broad [32] In general terms, rim gravel deposition records a knickzone, which might be related to regional uplift and period of extensive aggradation, producing a thick blanket base-level lowering since 40 Myrs (Figure 13). over north and central Arizona. Widespread erosion of these [28] These direct geologic observations, which help to gravels occurred in Late Eocene times since Late Oligocene- constrain the history of vertical motions of the Colorado Miocene deposits unconformably overlie them [Elston and Plateau, are of obvious value. Nonetheless, the modest set of Young, 1991; Gregory and Chase, 1992; Potochnik, 2001; geologic observations used to favor significant Late Ceno- Cather et al., 2008]. This regional geometry might suggest zoic uplift is equivocal. We concur that uplift is probably that a first phase of uplift affected a smaller circumference ongoing but that its amplitude is difficult to constrain. and that a second phase of uplift was of greater regional extent. 3.3. Proximal and Distal Deposition [29] The eroded products of regional uplift represent an 3.4. Magmatism important, albeit indirect, test of competing uplift rate his- [33] Late Cretaceous and Cenozoic magmatism dominates tories. In western North America, the most obvious distal western North America [Chapin et al., 2004] (Figure 3). Its sink for eroded sediment is the Gulf of Mexico, which has distribution, age and composition yields important informa- been rapidly subsiding since Cretaceous times. During Early tion about the interplay between lithospheric thickness, Cenozoic times, carbonate reef deposition was interrupted asthenospheric melting, decompression melting and the by the influx of large quantities of siliciclastic material importance of subduction zone processes [e.g., Fitton et al.,

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1991; Kempton et al., 1991]. In New Mexico, there is [Humphreys et al., 2003], or dynamic topography associated excellent evidence for Late Cretaceous and Paleocene (75– with slab foundering [Liu and Gurnis, 2008, 2010]. Each of 54.8 Myrs) magmatism [Chapin et al., 2004]. On the Col- the described processes may have contributed to the uplift orado Plateau itself, the earliest recorded magmatism occurs history of the Colorado Plateau, however, it is worth con- in Middle Cenozoic times (28–19 Myrs [Laughlin et al., sidering the arguments for uplift due to crustal thickening in 1985]). Coeval uplift has often been attributed to the asso- light of better crustal thickness estimates. McQuarrie and ciated ‘ignimbritic flare up’ [e.g., Humphreys, 1995; Chase [2000] argue that a pressure gradient from over- Humphreys et al., 2003]. K-Ar and 40Ar/39Ar dated Middle thickened and overheated crust of the Sevier orogenic belt Cenozoic intermediate-silicic and Late Neogene basic mag- drove intracrustal flow east toward a low-elevation proto- matism crop out on the plateau and its surroundings Colorado Plateau. Their argument hinges on evidence which (Figure 3b). Middle Cenozoic basic rocks across the region shows that the present-day crustal thickness is 45 km, indi- have relatively high abundances of Ba and low amounts of cating that isostatic equilibrium prevails [see Zandt et al., Nb and Ti [Fitton et al., 1991; Kempton et al., 1991; Chapin 1995; Mooney et al., 1998]. They suggest that crustal et al., 2004]. Fitton et al. [1991] argue that the chemical and thickness must have been much lower (30 km) to maintain isotopic characteristics of the basic magmas is consistent the plateau close to sea level in pre-Cenozoic times. In light with interaction between OIB-like magma originating in the of new data, the crustal thickness of the Colorado Plateau is asthenosphere and lithospheric mantle enriched by subduc- as much as 10 km less than some older estimates [e.g., tion-derived fluids. Late Neogene (<5 Myrs) mafic rocks McQuarrie and Chase, 2000] (Figure 1). Thus, elevated generally show no Ba enrichment or depletion of Nb and Ti; topography of the Colorado Plateau cannot be explained a composition similar to that of ocean island basalts [Fitton solely by crustal thickening. Observed crustal thicknesses et al., 1991; van Wijk et al., 2010]. A simple explanation is and long wavelength free-air gravity anomalies indicate up that these rocks were derived from a source or sources to 1 km of dynamic support (Figures 1–4). These observa- beneath the lithosphere. tions are consistent with calculations of viscous flow [34] Thus the magmatic history of the plateau and its beneath the Colorado Plateau, with major and trace element surroundings are consistent with the presence of hotter than geochemistry of basic magmatism across the western United normal asthenosphere sitting beneath a lithospheric plate States, and with receiver function analysis which suggest which may have become thinner over time. This history is that the plateau currently sits on top of an asthenospheric broadly consistent with the multi-phase history of uplift upwelling [Fitton et al., 1991; Lowry et al., 2000; Gilbert extracted from drainage. et al., 2003; Moucha et al., 2008, 2009; Liu and Gurnis, 2010; van Wijk et al., 2010; Wilson et al., 2010]. 4. Discussion [37] If crustal thickness does not change and if the density of the crust and lithospheric mantle at standard temperature [35] The history of uplift calculated by inverse modeling and pressure (s.t.p) can be estimated, then, the evolution of of river profiles has the same temporal distribution as phases plate thickness beneath the Colorado Plateau can be calcu- of unroofing estimated by (U-Th)/He and fission track lated as a function of topographic growth. In Figure 15, the thermochronometry [Kelley et al., 2001; Naeser et al., 2001; change in plate thickness is tracked through time by assum- Flowers et al., 2008]. Our calculated history of uplift is ing that a steady-state geotherm applies, that the temperature consistent with cumulative uplift estimated by clumped at the base of the crust and lithosphere are 500 and 1480C isotope thermometry and physiognomy of fossil flora [see respectively, and that the density of the crust at s.t.p. is Gregory and Chase, 1992; Huntington et al., 2010] (Figure 14). between 2.7 and 2.8 g cm3. Topography was smoothed and This uplift history coincides with denudation of the Colorado varied as a percentage of modern elevation (Figure 14). Plateau and with episodes of increased clastic flux into the Gulf Calculated plate thickness is sensitive to assumed crustal of Mexico [Galloway et al., 2000, 2011; Cather et al., 2008; density and elevation of topography. Increasing mantle Alzaga-Ruiz et al., 2009]. Explanations of Colorado Plateau potential temperature and/or the density of the crust raises the uplift must account for a series of related observations (e.g. base of the lithosphere. Our plate thickness estimates are surprisingly low values of surface strain [Bird, 1979]; present- – consistent with mantle xenoliths from the Colorado Plateau day crustal thicknesses of 35 45 km (Figure 1); a long which indicate that by 30–20 Myrs the plateau had a cool wavelength free-air gravity anomaly of +30 mGal [Lowry mantle to a depth of at least 140 km [Riter and Smith, 1996]. et al., 2000] (Figure 3); more than 2 km of uplift since Late These thickness estimates are also broadly consistent with Cretaceous times [e.g., Sahagian, 1987]; (U-Th)/He thermal surface wave studies which indicate that a 120–140 km thick histories which require phases of Late Cretaceous and lithosphere exists beneath the Colorado Plateau [West et al., Cenozoic cooling (e.g., Figure 14) [Flowers et al., 2008; 2004; van Wijk et al., 2010]. Basaltic magmatism became Huntington et al., 2010]; and the consistent convex-upward widely established across the Colorado Plateau and sur- shapes of river profiles which drain a region encompassing rounding region at 25 Myrs [Chapin et al., 2004]. Our the plateau). calculations suggest that the 1480C isotherm intersected the [36] The lack of measurable horizontal strain across the dry solidus, at a depth of 110 km, at approximately this Colorado Plateau suggests a deeper mechanism of uplift time. A lack of significant surface deformation [Spencer, [Bird, 1979; Spencer, 1996]. Uplift during Late Cretaceous 1996], a thinner lithosphere, and magmatism with a and earliest Cenozoic times has previously been related to decreasing lithospheric signature during late Neogene times crustal thickening by lateral flow of deep crust [McQuarrie [Fitton et al., 1991] all suggest that the present configuration and Chase, 2000], hydration of the mantle lithosphere due of the Colorado Plateau is due to the staged convective to volatile flux from a newly arrived Laramide flat slab removal of the lower half of the lithospheric mantle.

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function of the gradient of long wavelength gravity anomalies (Figures 3 and 5). A surface fitted to major drainage divides correlates with the long wavelength gravity anomaly which reflects the pattern of convective circulation (Figure 16). By subtracting the modern landscape from this surface, we obtain a minimum estimate of the amount of rock removed since Late Cretaceous times: 9.8 106 km3 has been removed from western North America and 0.6 106 km3 has been removed from the Colorado Plateau. Mean exhumation across the Colorado Plateau is at least 700 m. At long (1000 km) wavelengths, flexural support of topography is not significant and rock uplift due to erosional unloading is simply a function of crustal buoyancy (Figure 4). If the density of the lithospheric mantle and crust are 3.3 g cm3 and 2.5 g cm3, 700 m of exhumation produces 170 m of surface lowering and 530 m of rock uplift. Alternatively, a reconstructed Late Cretaceous surface suggests that there has been 200 m of surface lowering [Pederson et al., 2002].

5. Conclusions

[39] We have reconstructed the uplift rate history of a region which encompasses the Colorado Plateau by inverting a set of longitudinal river profiles as a function of time and space. This inverse strategy is predicated upon an Figure 15. Schematic lithospheric cross-section traversing empirical model which uses a non-linear advective-diffusive Rocky Mountain and Colorado plateaux (see Figure 1 for formulation to match the shape of a river profile. In most location). (top) Gray stripe = observed topographic profile; cases, the fit between theory and observation is good and the dotted numbered lines = long wavelength topographic pro- uplift rate histories suggest that three principal phases of files calculated every 20 Myrs from cumulative uplift his- uplift have occurred. The first phase started toward the tory shown in Figure 14; BR = Basin and Range province; end of Cretaceous times (80–50 Myrs). Between 50 and CP = Colorado Plateau; RM = Rocky Mountains; GP = 30 Myrs, the uplift rate was negligible. A second phase of Great Plains. (bottom) Colored circles = crustal thickness uplift occurred during Oligocene times (35–15 Myrs). measurements within 100 km wide corridor (see Figure 1); Finally, there is some evidence for a more recent minor black line = best-fitting crustal thickness variation used in phase of uplift which started about 5 Myrs ago. isostatic calculation; gray bands = lithospheric thicknesses [40] Despite uncertainties in the values of erosional con- calculated from topographic and crustal thickness profiles stants, this multi-phase history broadly agrees with inde- shown in Figure 15 (top) by isostatically balancing against pendent thermochronological analyses and with the history lithospheric column beneath Great Plains (width of band of siliciclastic flux into the Gulf of Mexico. Agreement reflects crustal density uncertainty of 2.8 0.05 Mg/m3 at suggests that hitherto irreconcilable geomorphic and ther- 0C). Density of lithospheric mantle at 0C estimated beneath mochronometric observations from the Colorado River are Great Plains = 3.33 Mg/m3. Temperatures at base of crust and consistent with multi-phase regional uplift. There are many lithospheric mantle were fixed at 500C and 1480C, respec- conflicting views concerning the establishment of the Col- tively [e.g., Fitton et al., 1991; Jaupart and Mareschal, orado catchment but we have shown that an inverse model 1999]. Solid circles = Priestley and McKenzie’s [2006] esti- which excludes this catchment has a similar uplift history. mate of lithospheric thickness along edge of Great Plains; We acknowledge that drainage networks undoubtedly triangles = lithosphere thicknesses from surface wave anal- evolve through time and space. Nevertheless, we believe that yses [West et al., 2004]; dashed red line = locus of solidus it is both useful and important to fully explore the con- for dry peridotite at potential temperature of 1480C. Base sequences of simple transparent models by inverting large of lithospheric intersects this solidus at 27 Myrs when datasets. We conclude that eroding landscapes may contain magmatism intensifies. important clues about the spatial and temporal evolution of regional uplift. Beneath western North America, gradual convective removal of thick lithosphere appears to have [38] Many authors, starting with Powell [1875], have played a decisive role in creating and sculpting the present- pointed out that the Colorado River follows an improbable day physiography. course: along much of its path, the river flows against the dip of underlying rocks, bisects major uplifts, and rarely follows Appendix A: Drainage Inventory faults [e.g., Potochnik, 2001]. Given the long wavelength free-air gravity anomaly, which probably reflects the pattern [41] Table A1 shows attributes of North American rivers, of convective circulation beneath the plate, the present-day numbered clockwise from North (see Figure 5). Longitude drainage planform is logical. Major rivers flow radially as a and latitude of river mouths are shown in decimal degrees;

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Figure 16. (a) Map of calculated cumulative uplift (Figure 13a: 0 Myr). Black lines = modeled rivers; red, blue, and green contours = positive, negative and zero free-air gravity anomaly values (interval = 10 mGal; Figure 3); stippled pattern = Basin and Range province and Baja California where inversion is poorly constrained. (b) Map showing long-wavelength surface draped over loci of drainage divides; black lines = drainage divides extracted from calculated drainage network. Draped surface calculated using continuous curvature method [Smith and Wessel, 1990]. Note coincidence between cumulative uplift, draped surface and gravity anomaly. also shown are maximum elevation and area of drainage By calculating the linear regression of log(∂z/∂x) and log(A), basin calculated from the SRTM dataset. uplift rate, U, can be determined (e.g. [Schoenbohm et al., 2004]). In Figure B1, we show an example of slope-area Appendix B: Slope-Area Analysis analysis for a synthetic river profile which is in steady state (i.e. ∂z/∂t = 0) for known values of U, v, m, n and A. In the ∂ ∂ [42] If a river is assumed to be at steady-state, z/ t =0, absence of random and/or systematic noise, the uplift rate k and = 0, equations (1) and (2) can be rearranged so that history can be reliably retrieved from a slope-area plot. If ∂z m U modest amounts of random noise are added, neither m/n nor ¼ ðÞþA 1 : ð Þ log ∂x n log n log v B1 U can be reliably determined. Our analysis clearly

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Table A1. (continued) Table A1. Attributes of North American Rivers, Numbered Elevationc Length Basind Clockwise From North (See Figure 5) Name Number Longitudea Latitudeb (km) (km) (km2) c d Elevation Length Basin a b 2 Chowan 91 76.70 35.92 0.3 500 23,000 Name Number Longitude Latitude (km) (km) (km ) Rivanna 92 77.27 37.33 0.2 200 17,000 Columbia River 123.51 46.24 1,026,000 Potomac 93 77.04 38.87 0.6 400 29,000 Willamette 1 1.7 500 a Methow 2 1.0 1000 Longitude of river mouth in decimal degrees. bLatitude of river mouth in decimal degrees. Okanogan 3 1.6 1700 c Pend Oreille 4 1.0 2100 Maximum elevation. d Spokane 5 1.6 1600 Area of drainage basin calculated from the SRTM dataset. Salmon 6 2.5 1500 Snake 7 2.7 2300 Owyhee 8 1.9 2100 demonstrates the great peril of differentiating discrete and Deschutes 9 1.6 820 noisy data. West Coast rivers Umpqua 10 124.08 43.71 1.5 400 11,000 Coguille 11–12 124.43 43.12 0.8 100 3,000 Appendix C: Numerical Methods Rogue 13–14 124.42 42.42 1.7 300 13,000 Trinity/Klamath 15–19 124.07 41.54 2.5 500 38,000 [43] Equation (1) was solved using numerical methods. Eel 20–21 124.31 40.64 1.3 300 9,000 Distance from the head of a river, x, and time, t, are dis- Sacramento 22–30 121.95 38.04 2.2 700 147,000 San Joaquin 31–38 121.95 38.04 3.6 800 147,000 cretized so that Salinas 39–40 121.80 36.86 1.3 300 12,000 Santa Barbara 41–42 120.64 34.97 1.6 100 2,000 xj ¼ x∘ þ jDx; j ¼ 0; 1; …; J Colorado River 114.81 31.82 768,000 ðC1Þ ti ¼ t∘ þ iDt; i ¼ 0; 1; …; I: Virgin 43 2.1 1000 Green 44 2.5 2600 Colorado 45 2.8 2200 Gunnison 46 2.9 2100 We used a Crank-Nicolson scheme, which is second-order San Juan 47 2.8 1900 accurate and stable for any Dt, to solve the diffusive term. Little Colorado 48 2.8 1700 Gila 49 2.7 1100 Thus Mexican rivers 01 iþ iþ iþ i i i Conception 50 112.98 30.54 1.5 400 25,000 iþ1 i z 1 z 1 þ z 1 þ z z þ z zj zj k jþ1 2 j j1 jþ1 2 j j1 Sonora 51 111.51 28.40 1.4 400 21,000 ¼ @ A: Yaqui 52–53 110.09 27.13 2.3 1000 70,000 Dt 2 ðÞDx 2 Fuerte 54–55 109.04 25.63 2.7 600 33,000 Sinaloa 56 108.31 25.26 2.5 400 13,000 ðC2Þ Culiacan 57 107.72 24.51 2.8 400 16,000 San Lorenzo 58 107.40 24.25 2.4 300 9,000 Rio Grande 97.40 26.36 800,000 An upwind differencing scheme is used to solve the advec- Conchos 59 2.3 1900 tive term. Thus Rio San Jose 60 2.2 2400 !n ziþ1 zi zi zi Rio Grande 61 2.7 2600 j j ¼vAm jþ1 j ; ð Þ Pecos 62 2.7 2100 Dt Dx C3 West Gulf of Mexico rivers Nueces 63 97.53 27.90 0.7 700 41,000 where the stability criterion is Colorado 64 95.75 28.80 1.4 1600 105,000 Brazos 65 95.25 29.09 1.4 1900 113,000 n Trinity 66 94.74 29.79 0.3 700 44,000 zi zi 1 vAm jþ1 j Dt Sabine 67 93.85 29.71 0.2 700 48,000 Dx Mississippi River 90.54 30.05 2,856,000 ≤ 1: ðC4Þ Canadian 68 2.7 2900 Dx Arkansas 69 3.0 3200 White 70 0.4 1500 Republican 71 1.7 3600 The steepest slope, (zi zi)/Dx, and maximum drainage South Platte 72 3.0 4100 j +1 j North Platte 73 2.2 4400 area are used to set the timestep required for stability. Both Cheyenne 74 1.5 4300 numerical schemes are combined using operator-splitting Yellowstone 75 3.0 5300 Missouri 76 2.2 5900 techniques [Press et al., 1992; Roberts and White, 2010]. Des Moine 77 0.4 2500 [44] In the inverse model, different distributions of U(x, y, t) Mississippi 78 0.5 3100 are used to calculate M river profiles, which are then com- Illinois 79 0.3 2300 Ohio 80 0.4 3100 pared to the M observed river profiles. In our starting model Cumberland 81 0.3 2300 U(x, y, t) = 0 and z(x)=0.U(x, y, t) is systematically varied East Gulf of until calculated and observed rivers agree within error. To Mexico rivers Pearl 82 89.64 30.16 0.1 500 21,000 implement this scheme, U(x, y, t) is parameterized by Tombigbee 83 87.98 30.96 0.1 600 106,000 selecting X Y T discrete values, Uk. X Y vertices Alabama 84 87.98 30.77 0.4 1000 106,000 D D – Chattahoochee 85 85.37 30.04 0.4 700 47,000 are arranging in a regular grid, where x = y, typically 50 Appalachian rivers 500 km, with a time interval of Dt, where Dt is typically 1– Ocumugee 86 81.41 31.34 0.3 600 36,000 5 Myrs. Optimal values of Uk are bilinearly interpolated Savannah 87 80.98 32.08 0.4 500 27,000 Santee 88 79.26 33.16 0.7 500 38,000 along each river to determine U(x, t) (Figure C1). To stabilize Great Pee Dee 89 79.27 33.39 0.4 500 44,000 the inversion algorithm, smoothing is imposed upon U(x, y, t). Cape Fear 90 77.96 34.19 0.3 700 14,000

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Figure B1. Synthetic slope-area analysis. (a) Black line = steady-state theoretical river profile calculated using v =200m1–2m Myr1, m =0.2,n =1andU(t) = 25 m Myr1. Gray line = upstream drainage area; red and pink sections = location of slope-area data shown in Figure B1b. (b) Crosses = slope as function of drainage area for river shown in Figure B1a. Black line = linear regression of log(∂z/∂x)andlog(A)data;m/n =gradientof 1/n regression line (i.e. concavity index); intercept = (1/n)log(U/v), which yields ks =(U/v) (i.e. channel steepness index). In absence of noise, uplift rate history of this steady-state river is reliably retrieved (see values in left- hand corner). (c and d) 5 m of random noise added to river profile. m/n and uplift rate history are no longer reliably retrieved. (e and f) 10 m of noise. (g and h) 20 m of noise.

o c Since this problem is non-linear and since U ≥ 0, we have znm and znm are the observed and calculated river elevation and chosen to minimize a trial function, H, by varying Uk where N is the number of data points along each river. The first term "# N;M 1 on the right-hand side of equation (C5) is zero when the cal- 1 X zo zc 2 2 H ¼ nm nm þ P: ðC5Þ culated and observed values of znm agree along a given river NM sn s n;m¼1 profile. Dividing the difference between them by n, the variance, ensures that each term in the summation has unit

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Figure C1. Forward and inverse modeling of river profiles. (a) Map showing idealized drainage network. Thick black numbered lines = rivers draining to north; thin black lines = drainage divides; white numbered circles = vertices where uplift is input into model. Dirchlet boundary conditions are set at vertices 7–9: U(t) = 0. Black lines = edges; dotted line = coastline. Uplift as a function of distance along a river, U(x, t), is bilinearly interpolated from uplift history of surrounding vertices, U(x, y, t). (b) Idealized uplift rate history of each vertex, U(t). Location of each vertex shown in Figure C1a.R In this example, uplift ¼ t Udt rate was increased twice. (c) Cumulative uplift history of each vertex, CU . (d) Map showing cumulative uplift at final timestep (i.e. 0 Ma). Contoured surface = cumulative uplift; contour interval = 250 m. (e) Calculated longitudinal river profiles, z(x), at final timestep. In this example, v = 200 m1–2m Myr1, m = 0.2, n =1,k =102 m2 Myr1. variance. To stabilize the inversion algorithm, a set of penalty were given weighting coefficients of 100. The positivity pen- functions, P,isincluded.P ensures that the first and second alty function was given a weighting coefficient of 5. Our derivatives of U are smooth and that U ≥ 0[Roberts et al., results are not significantly affected by changing these 2012]. The spatial and temporal smoothing penalty functions weightings by several orders of magnitude. To invert, a

Figure C2. Inverting synthetic data for U(x, y, t). (a) Map showing location of modeled rivers (blue lines); vertices where uplift rate is input into model (numbered circles); solid black lines = convex hull of model cells. (b) Results from inverting synthetic river profiles. Red lines = uplift rate history used to create synthetic river profiles; black lines = calculated uplift rate history for each vertex, numbered in Figure C2a. Uplift rate history is reliably retrieved. Synthetic river planform shown in Figure C2a.

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Figure C2

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Figure D1. Trade-off between v and m. (a) Values of v and m are constrained by Karlstrom et al.’s [2007] and Karlstrom et al.’s [2008] measurements of incision rate at Grand Canyon (see equation (5)). Black line indicates where v = 4.16 104(2.78 1012)m; black box = location of Figure D1c. (b) Blue, red, and black lines = advective velocity, vAm, for m = 1.1, 0.5, and 0.2, respectively. Lowest residual misfit between theoretical and observed rivers occurs when m ≤ 0.5. (c) Misfit between immature river (cross- hair) and rivers calculated as v and m are co-varied. Black line = relationship between v and m shown in Figure D1a; red numbered lines = contours of root mean squared misfit [Roberts and White, 2010]. starting solution is chosen (e.g. U(x, y, t) = 0) and a conjugate t time (T). gradient method is used to minimize H [Press et al., 1992]. tG Landscape response time (T). Figure C2 shows the results of a test in which synthetic data U uplift rate (L T1). was inverted. This joint inversion scheme can reliably retrieve E erosion rate (L T1). uplift rate histories. v advective coefficient of erosion (L1–2m T1). 0.5 1 vx advective coefficient of erosion (L T ). Appendix D: Erosion Parameter Values m area exponent, dimensionless. n slope exponent, dimensionless. [45] Measurements of incision rate at the Grand Canyon k diffusive coefficient of erosion (L2 T1). constrain the values of the erosional parameters in our model s variance of data (L). [e.g., Karlstrom et al., 2007]. Unfortunately, v and m trade-off 2m/n ks Channel steepness index (L ). negatively against each other such that v ≈ 4.16 4 12 m 10 (2.78 10 ) (Figure D1). Therefore, different com- [46] Acknowledgments. This work is supported by a BP-University binations of v and m can be used to successfully invert river of Cambridge research project funded by BP Exploration. We thank profiles. Uncertainty in v, dv, can be estimated by propagat- P. Allen, G. Apps, R. Corfield, K. Czarnota, M. Davis, L. Mackay, J. Paul, J. Wilson, and J. Winterbourne for their help. We are especially grateful to ing errors through equation (5) so that Brian Wernicke for his careful and wise review. Department of Earth sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSciences contribution esc.2533. dðÞ∂z=∂t 2 jjn dðÞ∂z=∂x 2 jjm dðÞA 2 dv ¼ jjv þ þ : jj∂z=∂t jj∂z=∂x jjA References ðD1Þ Alzaga-Ruiz, H., M. Lopez, F. Roure, and M. Séranne (2009), Interactions between the Laramide Foreland and the passive margin of the Gulf of Mexico: Tectonics and sedimentation in the Golden Lane area, Veracruz In this study, we chose values of v and m which yield the State, Mexico, Mar. Pet. Geol., 26, 951–973. smallest residual misfit. Berlin, M. M., and R. S. Anderson (2007), Modeling of knickpoint retreat on the Roan Plateau, western Colorado, J. Geophys. Res., 112, F03S06, doi:10.1029/2006JF000553. Bird, P. (1979), Continental delamination and the Colorado Plateau, Notation J. Geophys. Res., 84(B13), 7561–7571. Braile, L. W. (1989), Crustal structure of the continental interior, Mem. z elevation of river (L). Geol. Soc. Am., 172, 285–315. x distance along river (L). Burchfiel, B. C., P. W. Lipman, and M. L. Zoback (1992), The Cordilleran 2 Orogeny: Conterminous U.S., Geol. of North Am., vol. G-3, Geol. Soc. of A upstream drainage area (L ). Am., Boulder, Colo.

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