Rates of river incision and scarp retreat in eastern and central Grand Canyon over the past half million years: Evidence for passage of a transient knickzone

Because the Colorado River is the master stream that drains the bulk of the American Southwest, knowledge of Grand Canyon’s incision history is of regional geomorphic significance. The spatial and temporal details of this history provide information about the relative importance for canyon formation of base-level change, climate variability, bedrock strength, recent tectonic activity, and erosion-induced isostatic rebound (e.g., Pederson et al., 2002, 2013a, 2013b; Karlstrom et al., 2008, 2012b; Darling et al., 2012; Crow et al., 2014).

Whether or not the majority of Grand Canyon was carved by the Colorado River or by ancestral rivers remains unresolved (e.g., Pederson et al., 2002; Karlstrom et al., 2007, 2008, 2013a, 2014; Flowers et al., 2008; Wernicke, 2011; Flowers and Farley, 2012, 2013; Lee et al., 2013; Lucchitta, 2013). Broad consensus does exist, though, that drainage became integrated across the Colorado Plateau–Basin and Range transition at the Grand Wash Cliffs (Fig. 1) ca. 5–6 Ma, thereby creating an integrated Colorado River that has been responsible for subsequent Grand Canyon incision (e.g., Young and Spamer, 2001; Karlstrom et al., 2012a). This drainage integration event likely lowered base level by ∼1000 m, inevitably producing a knickzone. Many authors conclude that most or all of Grand Canyon was carved during upstream migration of that transient knickzone, with its attendant wave of rapid incision (e.g., Pederson et al., 2002; Cook et al., 2009; Pelletier, 2010; Darling et al., 2012). The speed at which that knickzone migrated and its current location are matters of keen interest.

Other processes might also contribute to Grand Canyon incision. Examples include epeirogenic surface uplift produced by increased mantle buoyancy (e.g., Karlstrom et al., 2008, 2012b; Crow et al., 2014), isostatic rock uplift in response to Canyon widening (Pelletier, 2010) or regional exhumation (Lazear et al., 2013; Pederson et al., 2013a, 2013b), local base-level fall triggered by down-to-the-west slip along the Hurricane and Toroweap faults (Fig. 1; Hamblin et al., 1981; Fenton et al., 2001), and increases in stream discharge triggered by climate change (Wobus et al., 2010; Darling et al., 2012). In addition, along-stream differences in the incision rate could be modulated by spatial differences in rock strength and/or sediment cover (Sklar and Dietrich, 2004; Hanks and Webb, 2006; Cook et al., 2009; Pederson and Tressler, 2012). Data that record incision rates in both space and time throughout the past 6 m.y. are needed so as to discriminate between various potential incision mechanisms and rate modulators.

Prior to 2014, no direct incision-rate data, using dated river terraces, existed for central Grand Canyon between River Mile¹ (RM) 57 and 179 (Fig. 1). Such direct rate measurements spanned only the past ∼400 k.y. in eastern Grand Canyon and the past ∼700 k.y. in western Grand Canyon. These data revealed that eastern Grand Canyon (at RM 56–57; Fig. 1) has been incising at a constant rate of 150–175 m/m.y. over the past ∼400 k.y., the same rate has held since ca. 500 ka at RM 179 in the Toroweap fault footwall, and rates of 50–75 m/m.y. have been sustained since 600–700 ka west of RM 179 on the Toroweap fault hanging wall (Lucchitta et al., 2000, 2001; Pederson et al., 2002, 2006; Karlstrom et al., 2007, 2008). Pederson et al. (2002) concluded from these data that down-to-the-west Toroweap fault slip has dampened late Quaternary western Grand Canyon incision. Karlstrom et al. (2007) concluded that Grand Canyon spans two crustal blocks, an Eastern Grand Canyon block from Lees Ferry to the Toroweap fault and Western Grand Canyon Block from that fault to Grand Wash Cliffs (Fig. 1); they considered both blocks to have experienced a steady rate of surface uplift since 6 Ma, with the Eastern Grand Canyon Block having risen 750–900 m during that time.

Longer-term Grand Canyon incision rate data came from only one study, which employed a proxy technique. Polyak et al. (2008) obtained U/Pb ages ranging from 0.8 to 17 Ma for cave mammilaries, which form at the water table, from ten Grand Canyon area caves. These ages track the rate of water table descent, which the authors considered a proxy for river incision rate. Their proxy incision rates range widely, between 166 and 411 m/m.y. for eastern Grand Canyon (RM 32–109) over time spans of 0.8–3.7 m.y. and a slower 55–123 m/m.y in western Grand Canyon (RM 190–277) for time intervals of 2.17–17 m.y. Polyak et al. (2008) concluded that these data reveal initiation of an eastward-propagating transient knickzone at 17 Ma at the Grand Wash Cliffs. Other workers questioned the validity of the speleothem proxy (Pearthree et al., 2008; Pederson et al., 2008). Karlstrom et al. (2008) argued that it provides only an upper bound on incision rates and noted that the lowest proxy rates for caves as old as 3.87 Ma are similar to the shorter duration rates reported in Karlstrom et al. (2007) for a given reach. Based on this similarity, Karlstrom et al. (2008) concluded that “semi-steady” incision rates of 175–250 m/m.y. in eastern Grand Canyon and 50–80 m/m.y. in western Grand Canyon have been maintained for the past 3–4 m.y. in response to dynamic surface uplift produced by upwelling asthenosphere.

Karlstrom et al.’s (2008) conclusion that Grand Canyon incision rates since 4 Ma are steady and mirror surface uplift rates requires that the Colorado River through Grand Canyon has been in an equilibrium state throughout that interval; in other words, no transient knickzone migrated through the canyon during that time. In contrast, Cook et al. (2009) combined incision rate data from Glen Canyon (Fig. 1) with a detachment-limited bedrock incision model to conclude that the Colorado River is in a transient state, with a headward-advancing knickzone having passed Lees Ferry ca. 500 ka. A knickpoint exists today at Lees Ferry (Fig. 1). Cook et al. (2009) considered it to be the downstream of two knicks that formed when a previously solitary Grand Canyon knick bifurcated upon reaching the lithologic interface between resistant rock downstream of Lees Ferry and weaker rock upstream. The lower knick remained pinned at Lees Ferry, while the upper one propagated upstream through the weaker rocks. Darling et al. (2012) concurred and noted a sixfold incision rate increase in Glen Canyon ca. 290 ka, which they interpreted as the transient knick’s arrival there. Pederson et al. (2013a) concluded that the Colorado Plateau’s regional incision pattern is a product of transient river response to 6 Ma drainage integration augmented by isostatic rock uplift triggered by erosion of weak Mesozoic rocks. Pederson and Tressler (2012) considered the Lees Ferry knickpoint and the Grand Canyon knickzone downstream of it to be pinned, equilibrium features produced by high bedrock resistance.

Discrimination between these various hypotheses requires the collection of longer-term incision rate data at new locations throughout Grand Canyon. Crow et al. (2014) presented the first such data. They concluded that incision rates at three eastern Grand Canyon locations between RM 56 and RM 69 have been a nearly constant ∼160 m/m.y. since ca. 600 ka, and rates at two central Canyon locations (RM 116 and RM 135) have held steady at ∼97 m/m.y. since ca. 650–700 ka. The rate at one western Canyon location (RM 246) has been 95 m/m.y. since ca. 575 ka, consistent with rates found by previous studies. Following Karlstrom et al. (2008), they combined their data with selected proxy data from Polyak et al. (2008) to conclude that incision rates in eastern Grand Canyon have remained an essentially constant 160 m/m.y., and those in central and western Grand Canyon have been a constant 101 m/m.y. for at least the past 4 m.y. They argued that this incision rate pattern precludes passage of a transient knickzone through Grand Canyon during that time and considered the pattern to reveal epeirogenic uplift caused by an eastward-propagating zone of buoyant upper mantle. Here we present incision rate data for two new locations, at RM 96 and RM 159 (Fig. 1). These data, contrary to Crow et al.’s (2014) conclusion, indicate passage of a transient knickzone through central and eastern Grand Canyon at ca. 500 ka.

We identified nine remnant surficial deposits between Hermit and Boucher creeks (RM 96, Figs. 1 and 2) that form resistant outcrops due to travertine cementation. All outcrops consist of conglomerate, breccia, and sandstone interbedded with layers of massive and laminated travertine (Fig. 3). We assign each outcrop to one of three groups based on their relative geomorphic position (Fig. 2).

Grand Canyon here consists of a ∼12-km-wide outer canyon, cut from nearly horizontal Paleozoic sedimentary layers, into which is inset a ∼500-m-wide, 250-m-deep “Inner Gorge” composed mainly of Precambrian crystalline rocks (Figs. 2 and 4). The outer canyon meets the Inner Gorge at the Tonto Platform, a bench formed in easily eroded Bright Angel Shale. The Bright Angel is underlain by Tapeats Sandstone, which forms the Inner Gorge’s nearly vertical rim. The Redwall and Muav limestones form a 150-m-tall, irregular cliff above the Tonto Platform that is set back ∼500–700 m from the rim of the Inner Gorge. This limestone forms a karstic aquifer, from which emerge the springs that produced the travertine (Crossey et al., 2006).

Our three travertine groups (Figs. 2 and 4) are: (1) two outcrops that mantle hillslopes from the Tonto Platform into the Inner Gorge (Inner Gorge Outcrops I1 and I2); (2) four outcrops perched atop the Tonto Platform (Perched Outcrops P1 to P4); and (3) three outcrops confined to tributary valleys (Tributary Outcrops T1 to T3).

We interpreted each outcrop’s depositional environment based on their facies successions and collected 34 travertine samples for U/Th age analysis so as to place those environmental interpretations into chronostratigraphic context. Samples were georeferenced using a handheld geographic positioning system (GPS) device, or, where the GPS signal was not obtained, by reference to nearby GPS-located samples through careful measurement. Differential correction of the handheld GPS data (referenced to the Fredonia, Arizona, base station) allowed us to determine sample elevation to ±2 m.

Selection of high-quality travertine samples is critical to obtaining reliable U/Th ages. Massive travertine is common (Fig. 3B) but unsuitable for U/Th analysis because it contains abundant clastic detritus. Laminated travertine is less common but is widely distributed (Figs. 3A and 3C). It contains minimal clastic material and produces reliable U/Th age data.

Our sample preparation and analytical techniques are described in detail in the Supplemental File². We employed standard anion resin-based chromatographic separations (Edwards et al., 1987) followed by mass analysis using either thermal ionization mass spectrometry (TIMS) or multicollector–inductively coupled plasma mass spectrometry (MC-ICPMS) (Sims et al., 2008). We analyzed isotopic ratios using ISOPLOT (Ludwig, 2003). Measured ²³⁰Th/²³²Th values for all samples were 43–4694, indicating the absence of significant detrital ²³⁰Th (Szabo, 1990). Our detrital corrections were, therefore, minimal, and assumed whole-earth U and Th isotopic ratios. We measured two subsamples from each of six hand samples (Table 1), and in every case the subsample isotopic ratios were consistent, indicating that sample heterogeneity does not adversely affect our results.

Dating of eastern Grand Canyon river terraces, and hence calculation of incision rates, has long relied on U/Th dating of interbedded travertine (Pederson et al., 2002, 2006). Therefore, in the quest to construct longer eastern and central Grand Canyon rate histories, both Crow et al. (2014) and our study have relied in part on travertine samples whose ages lie at or even beyond the upper limit for reliable U/Th dating. The reliance in both studies on these “old” ages makes it necessary here to explore the method’s details.

U/Th dating exploits isotopic disequilibrium that develops when ²³⁸U decays (through two short-lived nuclides) to ²³⁴U. ²³⁴U, with a half-life of 245 k.y., decays to ²³⁰Th (with a half-life of 75 k.y.) (Cheng et al., 2013). Incorporation of groundwater-derived uranium but not thorium into precipitating calcite causes (²³⁰Th/²³⁴U) and (²³⁰Th/²³⁸U) activity ratios (an isotopic ratio in parentheses denotes an activity ratio) to initially be very near zero (Fig. 5A). As ²³⁴U decays to ²³⁰Th over time, accumulation of ingrown ²³⁰Th moves (²³⁰Th/²³⁴U) toward a value of 1.0 (secular equilibrium). After ∼5–6 half-lives (375–450 k.y.), secular equilibrium is reached (Bourdon et al., 2003). This fact seemingly places a 450 ka upper bound on U/Th dating. However, in a useful complication, groundwater flow and reaction often result in significant ²³⁴U/²³⁸U disequilibrium, making it possible for closed-system samples to possess a (²³⁰Th/²³⁴U) greater than 1.0. For this reason, samples as old as 550–600 ka can be reliably dated using the U/Th technique (Edwards et al., 1987). In addition, the technique computes the isotopic ratio of the water from which the travertine precipitated (denoted (²³⁴U/²³⁸U)_i—the initial ratio).

Measured activity ratios are functions of both the sample’s age and the value of (²³⁴U/²³⁸U)_i. This fact is illustrated by (²³⁴U/²³⁸U) versus (²³⁰Th/²³⁸U) plots, which are the standard way to depict U/Th age data (Fig. 5A; Ludwig, 2003). The activity ratios measured at time = t₁ in a sample that possessed a given (²³⁴U/²³⁸U)_i will plot progressively farther down and right as sample age increases. As it approaches 550–600 ka (i.e., approaches ²³⁰Th/²³⁴U equilibrium), the (²³⁴U/²³⁸U) and (²³⁰Th/²³⁸U) ratios change little, approaching the equiline asymptotically (Fig. 5A). So, the older the sample is, the less precise its U/Th age. By ca. 600 ka, and certainly beyond 650 ka, U/Th ceases to be a useful dating tool.

However, even for samples older than 650 ka, the presence of any ²³⁴U/²³⁸U disequilibrium can still provide a useful maximum age constraint. When travertine incorporates uranium with groundwater-induced ²³⁴U/²³⁸U disequilibrium, (²³⁴U/²³⁸U) will return to secular equilibrium (i.e., 1.0) in 5–6 half-lives of ²³⁴U (1.2–1.5 Ma.; Fig. 5B) The useful time scale depends on the ability to discriminate slight ²³⁴U excess from secular equilibrium. Because ²³⁴U/²³⁸U analyses typically have relative errors less than 0.5% (2σ), in theory it is possible to identify samples younger than 1.5 Ma. However, in reality, slight changes in ²³⁴U/²³⁸U may occur within samples from leaching or other interaction with water. Thus, a conservative view would conclude that differences from secular equilibrium can only be detected when ²³⁴U/²³⁸U >1.02. We therefore interpret samples with a ²³⁴U/²³⁸U ratio greater than 1.02 to be younger than ca. 1.2 Ma (Fig. 5B).

Furthermore, if one could know the (²³⁴U/²³⁸U)_i of the sample, its precise age could be computed. This is not possible because (²³⁴U/²³⁸U) of groundwater commonly varies over short distances and through time. In Grand Canyon, for example, modern groundwater (²³⁴U/²³⁸U) ranges between 1.87 and 4.76 (Stewart et al., 1988). One can, however, compute a ²³⁴U “model age” by assuming an initial (²³⁴U/²³⁸U)_i value, as Crow et al. (2014) did for several Grand Canyon samples by assuming an initial value of less than 8.0.

The effects of diagenesis on U and Th isotopic ratios. As water flows through a travertine outcrop, fluid interactions can result in open-system behavior. If diagenesis has altered a sample’s U and Th budgets, it will typically plot to the right of the equiline (called the field of diagenesis on Fig. 5A) in a field where age determination is impossible. The reason is that U is more fluid-mobile than Th, causing U to leach preferentially during diagenesis, thereby increasing (²³⁰Th/²³⁸U). Typically, it is assumed that isotopic ratios for a given element are not fractionated at percent levels during dissolution and precipitation. However for U, because an atom of ²³⁴U is more likely to reside in a radiation damaged site than is an atom of ²³⁸U, ²³⁴U is more likely to be mobilized during water-rock interactions than will ²³⁸U. Thus, if U is leached, (²³⁴U/²³⁸U) will typically decrease, causing a sample to plot below the equiline (Fig. 5A). Both processes likely occur simultaneously, causing an altered sample to plot down and right of where it otherwise would. In most cases, then, mild diagenesis will make a young sample appear older or cause a sample whose true age is near the ca. 550–600 ka upper limit for U/Th dating (i.e., lies close to the equiline) to plot in the diagenesis field (Fig. 5A).

Pederson et al. (2002, 2006) and Karlstrom et al. (2007) recommended that to calculate an incision rate where data exist for only one terrace, workers use the elevation difference between the dated strath and the inferred position of the modern river’s bedrock surface. Karlstrom et al. (2007) considered the maximum pool depth (defined as mean depth of the ten deepest pools in a 15-mile-long reach centered on the dated strath) to be the best approximation for modern bedrock surface elevation, and to thus yield the “preferred” incision rate. Pool depths were measured by sonar (Wilson, 1986). To account for geologic uncertainty, these authors also computed minimum (by using the mean pool depth) and maximum (by using the bedrock depth determined from seismic studies and drill data) (Hanks and Webb, 2006) incision rates. Grand Canyon mean and maximum pool depths are found in Crow et al. (2014). Incision rates presented here follow this protocol, with all geologic, GPS, and 2-σ U/Th age uncertainties propagated to obtain preferred, minimum, and maximum incision rates for each location (Fig. 6; Table 2).

The modern Redwall/Muav escarpment has a ragged outline that follows tributary valleys, but where it faces the Colorado River, it exhibits collinear, straight segments that parallel the river’s straight course in this reach (Fig. 2). We used differential GPS to map the base of these collinear escarpment segments. The modern escarpment trends at 322°. We define the scarp retreat distance as the distance from our paleoscarp datum to the modern escarpment trend as measured perpendicular to that trend (i.e., at an azimuth of 232°). We then calculate the maximum and minimum scarp retreat rates using that distance and the 2-σ uncertainties in our travertine depositional ages (Fig. 6; Table 2).

Here we describe the facies associations present in each outcrop group and, from them, interpret its depositional environment. We report travertine U/Th ages and use the resulting chronostratigraphic data to interpret timing and rates of incision, aggradation, and scarp retreat. Outcrops are shown on Figure 2; sample locations are listed on Table S1 in the Supplemental File (see ^{footnote 2}); and isotopic data and ages are shown on Figure 7 and Table 1.

Two outcrops of travertine-cemented colluvium, consisting of locally-derived, clast-supported, angular to subrounded cobble to boulder conglomerate interbedded with travertine, drape across the edge of the Tonto Platform and extend down into the Inner Gorge (Figs. 2 and 4). They unconformably overlie bedrock units from the Bright Angel Shale to the Vishnu Schist and Zoroaster Granite, and their beds dip steeply toward the river at angles similar to that of modern hillslope colluvium (Fig. 8 and Figs. S9 and S10 in the Supplemental File [see ^{footnote 2}]).

We cannot constrain the exact elevation of the Colorado River at the time of I1 and I2 deposition because neither outcrop possesses Colorado River–derived material. However, the river must have stood at an elevation below the toe of each outcrop during their accumulation. We can, therefore, constrain the Colorado River’s maximum incision rate since deposition of the basal travertine beds (Fig. 6). Outcrop I2 extends farther into the Inner Gorge than does I1 and is also older; so it provides the more robust constraint on the rate of Colorado River incision.

We collected travertine U/Th samples from three different locations within I2’s basal bed and three more samples at stratigraphically higher levels. One U/Th sample comes from the base of I1 and another from near the top (Table 1; Fig. 7; Table S1 in the Supplemental File [see ^{footnote 2}]). Outcrop I2’s sample I2-3, from a basal 15 cm bed of dense, laminated travertine 23 m upslope from the outcrop toe, yields a high-precision age of 394 ± 32 ka. The other two basal samples yield poor-resolution ages that are identical, within analytical error (562 ± 177 ka for sample I2-1 at the outcrop toe and 468 ± 166 ka for sample I2-2 25 m up the slope). The three stratigraphically higher samples (I2-4 through I2-6) have all endured diagenesis and return no ages. The base of outcrop I1 is either the same age as I2 or likely younger (sample I1-1 with an age of 293 ± 98 ka). Sample I1-2, from laminated travertine 28 cm below the I1 outcrop crest, dates the youngest I1 accumulation at 192.8 ± 1.6 ka.

The toe of I2 lies 59 m above the river (at a river stage of 283 m³/s). Using modern bedrock depths (Table 2), outcrop age of 394 ± 32 ka, and the methods described above, the Colorado River has incised no more than 88 m since ca. 400 ka at a maximum rate of 210 _{+42 –49} m/m.y. This maximum rate is consistent with the more precise 150–175 m/m.y. eastern Grand Canyon incision rate computed for the same time interval by all previous studies (Pederson et al., 2002, 2006; Karlstrom et al., 2007; Crow et al., 2014).

Four travertine outcrops perch atop the Tonto Platform. In contrast to the steeply dipping beds of the Inner Gorge outcrops, most Perched Outcrop beds are subhorizontal. All beds in three of these (P1–P3; Figs. 2 and 4) are restricted to the Tonto Platform. So too are the majority of P4 beds, but its uppermost layers dip northeast at ∼15°, parallel to the slope of the uppermost Inner Gorge. The Perched Outcrop beds form separate topographic knobs, rising 12–25 m above the local landscape. P1 is separated from the rest by Travertine Canyon, and smaller gullies separate the other three outcrops from one another (Figs. 2 and 4).

Outcrop P1, the largest at 55 m tall and 200 m long, stands just meters from the lip of the Inner Gorge and 500 m from the confluence of Hermit Creek and the Colorado River (Figs. 2 and 9A). Its subhorizontal, lenticular beds onlap the underlying Bright Angel Shale (Figs. 3B, 9, and 10B). Based on this onlapping relationship, we interpret the outcrop as filling a large channel form, the northeastern half of which has been removed by erosion (Fig. 9A). The lowest preserved fill lies at 949 m elevation. The axis of this channel form is oriented northwest, parallel to the flow direction of the modern Colorado River.

Outcrop P2, the next largest outcrop at 150 m long, is a knob of remnant travertine-cemented surficial material unconformably overlying Bright Angel Shale northwest of P1 (Figs. 2 and 4; Fig. S4 in the Supplemental File [see ^{footnote 2}]). It stands less than 100 m from the Inner Gorge, with its lowest fill at 976 m elevation. Outcrop P3 is a similar but smaller remnant 100 m to the west of P2 across a gully (Fig. S5 in the Supplemental File [see ^{footnote 2}]), and P4 is a travertine knob 150 m east of P2 (Fig. S6A in the Supplemental File [see ^{footnote 2}]), across another gully.

Perched Outcrop sedimentology and inferred depositional environment. Outcrops P1–P3 are composed mainly of subhorizontal, lenticular, medium-to-thick beds of subangular to subrounded pebble to cobble conglomerate alternating with travertine. Some conglomerate beds are clast supported; others are matrix supported. Both facies are poorly sorted and consist of locally derived clasts. Local crude pebble imbrication yields northwest to southwest paleocurrent directions (Fig. 11A; Fig. S3C in the Supplemental File [see ^{footnote 2}]). Thin, 1–3 cm sand layers possess tabular-planar cross lamination with southwest-dipping foresets. We interpret these clastic facies as tributary stream deposits by analogy with similar deposits left by modern Grand Canyon tributaries (Fig. 11B; see also Anders et al., 2005).

Outcrop P4 is anomalous in that it contains comparatively little clastic material (it is ∼80% travertine). Its lower beds consist of subhorizontal, 10-cm- to 2-m-thick travertine layers interbedded with rare pebble to cobble conglomerate (Fig. S6B in the Supplemental File [see ^{footnote 2}]). Its uppermost, northeast-dipping layers are also dominated by travertine, with a few beds of colluvium (Fig. S6C in the Supplemental File [see ^{footnote 2}]).

The southwestern portion of outcrop P1 (i.e., facing the modern Redwall/Muav cliff) consists of unstratified boulder breccia with angular to subangular clasts of Redwall and Muav limestone and Supai Group sandstone as large as 3 m (Figs. 10 and 12). We interpret it as talus shed from the Redwall/Muav cliff, which, based on the breccia’s large clast size and unstratified nature, must have stood directly above P1 during breccia deposition. Likewise, outcrop P2’s lowest beds (up to 5 m thick) consist of boulder conglomerate and breccia that dip north, parallel to slope. Clasts are angular to subrounded, locally derived, and as large as 1.5 m. We interpret these as rock fall and rock avalanche deposits shed from the Redwall/Muav cliff face when it stood closer to P2 than it does today. This talus is overlain by the subhorizontal tributary stream deposits discussed above. Both P1 and P2 breccias thus provide data points from which we can determine the rate of Redwall/Muav scarp retreat.

Outcrop P1 possesses one additional facies that is absent from the other Perched Outcrops. Several lenses high on P1’s 55-m-tall northern cliffs (in the deepest part of the paleochannel) consist almost entirely of travertine-encased, well-rounded pebbles (Fig. 13A). Because transport distances on Grand Canyon tributaries are insufficient to achieve such a high degree of rounding, this facies is absent from modern tributary gravels. It is, however, a significant component of paleo–Colorado River gravels (Fig. 13B; Pederson et al., 2006). Anders et al. (2005) determined that the vast majority of clasts in paleo–Colorado River gravels near Tanner and Unkar creeks (Figs. 1 and 13B) consist of local lithologies. Only a few percent are far-traveled clasts, such as volcanic porphyry or quartzite. Our examination of P1 did not reveal any far-traveled clasts. However, the cliffside location of these well-rounded pebble lenses prevented us from reaching them to conduct detailed clast examination, even from our rappel down the outcrop’s northwest face (Figs. 9B and 9C).

Any depositional environmental interpretation for the Perched Outcrops must take into consideration the presence of on-lapping, subhorizontal beds right to the lip of the Inner Gorge, the abundance of boulder breccia in the cliff-facing and lower portions of P1 and P2, respectively, the dominance of tributary stream deposits in outcrops P1–P3, and the presence in outcrop P1 of well-rounded pebbles likely transported by the Colorado River. A setting that would juxtapose these facies is the debris fan that formed at the confluence of Hermit and Travertine creeks with the paleo–Colorado River prior to the cutting of the Inner Gorge (Fig. 14). The Redwall/Muav cliff band rose directly behind the debris fan. The Perched Outcrops are, we believe, remnants of such a fan that were preserved even during subsequent incision of the Inner Gorge thanks to the precipitation of travertine from several springs. Outcrop P1 preserves the thickest part of the fan, including Colorado River gravels, right at the confluence. Outcrops P2 and P3, whose bases lie 25+ m above the base of P1, were deposited in the fan’s upper reaches and hence don’t contain Colorado River gravels. The paucity of clastic material in P4 indicates that it constitutes a former spring mound. The change from subhorizontal travertine at P4’s base to slope-parallel beds upsection records continued activity of this spring during initial carving of the Inner Gorge.

If the Perched Outcrops comprise portions of a single paleo-Hermit debris fan, that fan would have fronted 1.2 km of the Colorado River. But Hermit Creek’s modern debris fan fronts the river for only 450 m, and other modern Inner Gorge debris fans have similar dimensions. Is our inferred fan dimension reasonable? Consider that during paleofan growth the river did not occupy a narrow canyon like the modern Inner Gorge, but rather a broad, gentle valley cut in soft Bright Angel Shale (Fig. 14). The best modern analog for this setting is the wide, gentle valley near Tanner and Unkar creeks (Fig. 1), where large paleo–Colorado River outcrops have been identified (Fig. 13B; Anders et al., 2005; Crow et al., 2014). Modern tributary fans there are much larger than those of the modern Inner Gorge. For example, Unkar Creek’s fan fronts more than a kilometer of river, and even the tiny, unnamed creek near Cardenas Butte has built a fan that spreads along a kilometer of riverfront. It is likely that similarly large fans flanked the paleo–Colorado River when it meandered across the gentle Tonto Platform past Hermit Creek.

Considering this depositional environment for the Perched Outcrops, if we can date the basal channel fill of P1, we can use it as a datum from which to calculate both the Colorado River’s incision rate during carving of the Inner Gorge and the rate of Redwall/Muav scarp retreat (Fig. 6). Although P2 and P3 do not provide tight constraints on Colorado River incision, they do serve as datums for scarp retreat.

Age of the Perched Outcrops—U/Th dating of travertine samples. We analyzed 13 travertine U/Th samples from outcrop P1, four each from P2 and P4, and one sample from P3 (Table S1 in the Supplemental File [see ^{footnote 2}]). Eight of the P1 samples (P1-1 through P1-8) come from our rappel line (Figs. 9B and 9C), and the remaining five are from elsewhere in the outcrop (Fig. 10). Only the two stratigraphically lowest samples, P1-1 and P1-9, produced valid U/Th ages (see discussion below). All four P2 samples come from the stratigraphically lowest 1.5 m, and the single P3 sample was collected from the basal bed. The four P4 samples span the outcrop’s entire stratigraphic thickness.

The basal beds in outcrops P1, P2, and P3 all return the same high precision, ca. 500 ka ages within 2-σ uncertainty. Outcrop P4’s base is slightly older, but its top is the same age as P1–P3. These age data strongly support the interpretation that all Perched Outcrops are remnants of the same paleodebris fan.

We describe below those samples that best constrain the age of each datum, beginning with outcrop P2; additional sample descriptions are in the Supplemental File (see ^{footnote 2}).

Outcrop P2. Sample P2-4 comes from a 5-cm-thick, laminated travertine that overlies Bright Angel Shale at P2’s southwest toe. It is dated as 497 ± 21 ka (Fig. 7; Table 1). Field examination shows it to be part of a normal upward-younging stratigraphic sequence (Fig. 11A), indicating that it was precipitated just prior to deposition of the overlying clastic beds, not during a later event. The ages of samples P2-1 and P2-2 are the same within large error bars, and P2-3 plots in the diagenesis field (Fig. 7; Table 1).

Outcrop P3. Sample P3-1, which lies at the Bright Angel–P3 contact, is dated at 499 ± 25 ka. Therefore, the base of P3 is the same age as the base of P2 (Fig. 7; Table 1).

Outcrop P4. Samples P4-1 through P4-3 all come from the outcrop’s southwest side. P4-1, the stratigraphically lowest sample, has endured diagenesis (Fig. 7; Table 1). P4-2, which lies ∼5 m stratigraphically above P4-1, is 591 ± 24 ka. Sample P4-3 lies 0.7 m stratigraphically above P4-2 and 1.8 m below the outcrop’s top. Its age is 489 ± 24 ka. Sample P4-4 lies 50 cm above the P4–Tapeats contact near the outcrop’s northeast toe. It returns a low-precision age of 339 ± 139 ka. We interpret P4 as a spring mound. The P4-2 age indicates that travertine began accumulating here earlier than it did elsewhere along the Tonto Platform. Sample P4-3 records activity of the spring mound during the same travertine-producing episode that cemented outcrops P1–P3.

Outcrop P1. Samples P1-1 and P1-9 both come from within 1.5 m of the outcrop’s base. P1-9 is the outcrop’s stratigraphically lowest sample, lying as it does at the base of the deepest part of the channel. P1-1 is the lowest sample along the line of rappel, higher in the onlapping sequence (Fig. 10B). Both samples yield the same age within 2-σ uncertainty, but P1-9 returns an age of 506 ± 33 ka, while P1-1 is 484 ± 26 ka (Table 1; Fig. 7), suggesting that P1-9 may be slightly older, as expected given its stratigaphically lower position.

Sample P1-1 is a core drilled 7 cm into a dense travertine lens 1.5 m stratigraphically above Bright Angel Shale (Fig. 15). The 30 cm lens possesses distinct 2–4 cm laminated beds. The lens is surrounded by cobble conglomerate. Field examination indicates that it is the oldest material in a normal, upward-younging stratigraphic sequence, not a more recent precipitate. It is not a drape and contains no veins or void-filling cement.

Sample P1-9 consists of dense, laminated travertine collected 1.5 m stratigraphically above the outcrop’s northeast toe. Like P1-1, field evidence suggests it is part of a normal, upward-younging sequence. The underlying Bright Angel Shale is obscured by rubble, but ledges of Tapeats Sandstone crop out 5 m stratigraphically down the slope.

None of outcrop P1’s 11 stratigraphically higher travertine samples yielded U/Th ages. The two highest samples (Fig. 10B), P1-12 and P1-13, plot far into Figure 7’s diagenesis field, indicating that they have been heavily altered. The other nine P1 samples all plot close to the equiline (Fig. 7) and possess (²³⁴U/²³⁸U) between 1.041 and 1.109 (Table 1). The fact that their U isotopes have not yet reached secular equilibrium indicates that each is younger than ca. 1.2 Ma. The fact that they cluster near the equiline can be explained one of two ways. Either they are isotopically closed systems with ages of ca. 600 ka–1.2 Ma, or they experienced mild diagenesis, which shifted their isotopic ratios just enough to cause them to plot slightly outside the datable region (see schematic sample trajectory in Fig. 5A). Any such alteration must have been mild, because it is unlikely that samples subjected to strong diagenesis would cluster near the equiline. Even if they are altered, the samples are likely younger than 1.2 Ma, because the concentration of ²³⁴U near radiation-damaged sites means diagenesis would likely reduce (²³⁴U/²³⁸U), not increase it (see discussion above).

As P1’s stratigraphically lowest sample, P1-9’s 506 ± 33 ka age seemingly constrains the formation age for the underlying strath terrace, thereby providing the necessary datum from which to calculate river incision and scarp retreat rates. However, before reaching this conclusion we must first explain why nine stratigraphically higher samples cluster along the equiline but do not return U/Th ages. As noted above, either they are altered or their ages are ca. 600 ka–1.2 Ma. If the latter, then the younger but stratigraphically lower samples P1-1 and P1-9 don’t provide a useful age datum because, despite field evidence to the contrary (Fig. 15), they must have precipitated during a later event.

A test for whether or not these samples have remained closed chemical systems is to plot them on a (²³⁴U/²³⁸U) versus (²³⁰Th/²³⁴U) diagram (Fig. 16; Burnside, 2010). This diagram looks very similar to Figure 7 and is interpreted the same way, but because it employs the shorter-lived ²³⁴U on its x-axis, samples that have undergone mild diagenesis shift away from the equiline compared to Figure 7. Notice that samples P1-1 and P1-9 have not shifted position on Figure 16, suggesting they are closed systems, but that all other P1 samples shift slightly right of the equiline, revealing that they have endured mild diagenesis.

Why have only the two basal P1 samples remained closed systems? P1 is an isolated knob underlain by low-permeability Bright Angel Shale (Figs. 4, 9, and 10), which makes it difficult for fluid to migrate laterally into the outcrop. Instead, most diagenetic work must be done by meteoric water introduced from above. A down-section decrease in carbonate diagenesis is to be expected from the downward percolation of this water through the vadose zone, because the water becomes saturated during its migration (James and Choquette, 1990; D. Budd, 2013, personal commun.). This pattern of expected diagenesis supports the field evidence that samples P1-1 and P1-9 precipitated during accumulation of P1’s basal clastic fill; we therefore conclude that the P1 strath terrace did indeed form at 506 ± 33 ka.

Rate of Colorado River incision. Based upon the above analysis, we conclude that the Colorado River flowed at the elevation of the Tonto Platform during construction of the Hermit-Travertine Creek debris fan at 506 ± 33 ka. Fan construction could have occurred prior to the cutting of the Inner Gorge or, alternatively, on the shore of a lake that filled the Inner Gorge. Hamblin (1994, 2003) hypothesized that several such lakes formed within the past 600 k.y. due to temporary impoundment of the Colorado River behind lava dams. None of the Perched Outcrops contain the fine-grained sediment one would expect to accumulate in such a lake, despite an abundance of travertine precipitation that could be expected to preserve accumulating lake sediments. We therefore conclude that no such lake existed during accumulation of the Hermit-Travertine debris fan and that the Inner Gorge has been cut during the past ∼500 k.y. (Fig. 14).

Using the methodology described above (Fig. 6) and the strath elevation, modern bedrock elevation, and age data listed in Table 2, we obtain an incision rate of 519 _{+55 –58} m/m.y. since 506 ka. This compares to the maximum rate of 210 _{+42 –49} m/m.y. since 394 ka computed from outcrop I2. It is clear from these results that the incision rate during the ∼500–400 k.y. interval was much faster still, between 1 and 4 km/m.y. If these data are correct, they require a minimum fivefold decrease of incision rate at RM 96 between 500 and 400 ka.

Rate of Redwall/Muav scarp retreat. We interpret the unstratified breccia in outcrop P1 to mark the position of the Redwall/Muav scarp at 506 ± 33 ka (Figs. 6 and 12). Using the protocol outlined above, the escarpment has retreated 383 m since then, a retreat rate during the past ∼500 k.y. of 710–810 m/m.y. (Table 2). Outcrop P2 also contains abundant boulder breccia likely shed from the Redwall/Muav cliff when it stood nearby at 497 ± 21 ka. However, those beds’ comparatively gentle 12° dips indicate that the cliff was close to but not adjacent to this part of the fan. Outcrop P2, therefore, provides only an upper bound on the scarp retreat rate. The modern cliff lies 403 m southwest of P2, meaning that the scarp there must have been retreating at less than 847 m/m.y. during the past ∼500 k.y. (Table 2). This value is consistent with the rate computed from P1. The scarp must also have stood southwest of P3 when it was accumulating at 499 ± 25 ka. Today the escarpment stands 288 m to the southwest. Assuming the minimum possible outcrop age produces a maximum scarp retreat rate of 606 m/m.y., a bit slower than that for P1.

Our 600–800 m/m.y. retreat rate since 500 ka for the Redwall/Muav cliff at RM 96 is broadly similar to the upper end of Cole and Mayer’s (1982) 180–720 m/m.y. since 13 ka and slightly faster than the 500–600 m/m.y. determined for the Kaibab cliff since 19 Ma (Lucchitta and Jeanne, 2001). Our faster rate over 0.5 m.y. is to be expected because scarp retreat rates measured over short time intervals tend to be higher (Gardner et al., 1987).

Three travertine-cemented surficial deposits lie in tributary valleys (Fig. 2). Outcrop T1 lies near the headwaters of a first-order, fault-controlled, tributary to Boucher Creek. Outcrop T2 lies along the same fault as T1, in the midsection of Travertine Canyon, an ephemeral tributary with a drainage area of ∼4 km². Outcrop T3 lies 1 km downstream of T2, where the Tonto Trail crosses Travertine Canyon (Fig. 2).

Outcrops T2 and T3 are dominated by interbedded clast-supported and matrix-supported gravel (Fig. S9 in the Supplemental File [see ^{footnote 2}]) that strongly resembles both modern tributary stream deposits (Fig. 11B) and the Perched Outcrop facies we interpret as tributary stream deposits (Fig. 11A). We, therefore, interpret T2 and T3 likewise, as did Anders et al. (2005) for similar deposits in the Tanner/Unkar area (Fig. 1). Outcrop T2 unconformably overlies bedrock of the Muav Limestone. Outcrop T3 unconformably overlies Bright Angel Shale in the southwest (Fig. S9 in the Supplemental File [see ^{footnote 2}]) and Tapeats Sandstone in the northeast (Fig. S10 in the Supplemental File [see ^{footnote 2}]). Outcrop T3 is capped by 80 cm of dense, laminated travertine (Fig. 3C; Fig. S8 in the Supplemental File [see ^{footnote 2}]) that contains leaf impressions. The Supplemental File (see ^{footnote 2}) contains additional descriptions of these deposits and of T1’s lithology and age.

We collected two U/Th samples from outcrop T2 and six from T3 (Fig. 7; Table 1; Table S1 in the Supplemental File [see ^{footnote 2}]). The basal fill of both T2 and T3 is 52–53 ka, marking the onset of an aggradational episode on Travertine Creek. At T3 a total of 21.6 m of alluvium accumulated between 53 and 11 ka (a rate of 0.5 m/k.y.), when the capping travertine was precipitated. Onset of the Travertine Canyon aggradational episode at 52–53 ka is simultaneous with onset of tributary aggradation in the Tanner/Unkar area (Fig. 1; the S3 event of Anders et al., 2005). The S3 episode ended at 34 ± 5 ka; whereas Travertine Canyon aggradation continued until 11.3 ka. Deposits from this aggradation episode were later incised and are now truncated at the cliff (knickpoint) where Travertine Creek enters the Inner Gorge (Fig. S10 in the Supplemental File [see ^{footnote 2}]). Therefore, the cliff reached its present location, 800 m upstream of the Colorado River confluence (Fig. 2), after 53 ka.

Our second new incision rate location is at RM 159 (Fig. 1), where Wenrich et al. (1997) and Billingsley (2000) mapped two basaltic dikes they called the “159-Mile Dikes” and associated necks, lava flows, and pyroclastic deposits on the adjacent Esplanade Platform (Figs. 17 and 18). Today the river flows at the bottom of the narrow (500 m) Muav Gorge, which is inset into a ∼6-km-wide outer canyon whose floor is the Esplanade Platform. Billingsley (2000) concluded that at the time of dike emplacement the river flowed atop the Redwall Limestone, at ∼914 m elevation, just below the Esplanade Platform. The river subsequently cut the precipitous, 375-m-deep Muav Gorge. If this is correct, one can calculate the incision rate since the time of dike emplacement.

Other workers disagree. Ryan Crow (2013, written commun.) hypothesizes that the 159-Mile Dikes intruded into an extant Muav Gorge. He cites as analogs the injection of dikes into cliff faces during modern eruptions of Kilauea and Mount Etna. Joel Pederson (2013, written commun.) suggests a chronology of Muav Gorge cutting, filling of the gorge with loose sediment that accumulated behind a temporary lava dam (Hamblin, 1994, 2003), dike intrusion into the loose sediment, then reexcavation of the Muav Gorge. If either hypothesis is correct, the 159-Mile Dike age tells us nothing about Grand Canyon incision.

The igneous rocks in the 159-Mile Dike association are collinear on a N45°W trend and span 10.8 km along strike (Fig. 18). They include: (1) the two dikes themselves and a neck of welded pyroclastic tuff that we call the “159-Mile Neck” (this neck stands in lower Supai Group rocks 100 m from the rim of Muav Gorge); (2) “Yumtheska Vent West” and “Yumtheska Vent East”—two vents with cinders and minor basalt flows that erupted on the Esplanade Platform 2.4 and 4.1 km south of the river, along strike, respectively; (3) “The Cork,” a vent/dike with associated cinders and basalt flows on the Esplanade Platform 2.2 km north of the river; and (4) an unnamed neck in an eastern tributary to Tuckup Canyon, 6.7 km north of the river along strike. Wenrich et al. (1995) dated Yumtheska Vent West at 780 ± 150 ka and the Cork at 407 ± 70 ka using K/Ar. Ryan Crow recently dated the 159-Mile Dikes themselves at 517 ± 16 ka using ⁴⁰Ar/³⁹Ar (R. Crow, 2013, written commun.).

The widths of the 159-Mile Dikes are variable, but near the river they are only 50 cm (Fig. 17). They cut through all rock layers from river level to the Muav Gorge rim and are coplanar on both sides of the Colorado River. This latter fact contrasts with the modern volcanic examples cited by Crow (see above), in which dikes intrude just one steep volcanic flank (e.g., Mount Etna; Bonaccorso and Davis, 2004).

The extrusive rocks record the location of the land surface during their eruption at ca. 520 ka. They reveal that the Esplanade Platform comprised the land surface on both sides of the Colorado River. The topography sloped gently down toward the river, with lower Supai Group rocks comprising the land surface at the 159-Mile Neck, 100 m from the rim of the modern Muav Gorge. But the question remains: did Muav Gorge exist at 520 ka?

Consideration of two mechanical issues related to dike emplacement—stress orientation and dike propagation—can assist in answering this question (Martel and Muller, 2000; Muller et al., 2001; S. Martel, 2014, written commun.). If Muav Gorge existed during dike emplacement, it would act as a stress concentrator. Depending on the ambient stress state, the canyon bottom stress concentration could be tensile or compressive. If the former, the dikes would be directed toward the canyon bottom. If the latter, they would avoid it. Initial cutting of the canyon is the event that perturbs the stress state; filling the canyon later with loose sediment impounded in a lava-dammed lake would not change these arguments. The dikes crosscut the canyon; so clearly they didn’t avoid it. But neither were they directed toward it, as evidenced by the associated vents that lie several kilometers from the canyon (Fig. 18).

During emplacement, the dikes could have propagated either up toward the surface or laterally. If they were propagating upwards and Muav Gorge existed, the dikes would have encountered a free surface (the canyon) 375 m below the main land surface to either side (the Esplanade Platform). In this case, the canyon would likely act as a drain, robbing the dikes of pressure necessary to continue rising. This would make eruption on the Esplanade Platform, 375 m higher, difficult. But the magma did just that, including at 159-Mile Neck, a mere 100 m from the canyon rim. Bonaccorso and Davis (2004) argued that an analogous depressurization was responsible for the absence of lava extrusion from a 7-km-long dike emplaced in Mount Etna’s southern flank during the 1989 eruption.

If, instead, the 159-Mile Dikes propagated laterally, it is easy to envision them venting on one Muav Gorge cliff face and also on the adjacent Esplanade Platform (analogous to the modern Kilauea example cited by Crow). But how could they propagate across the canyon to maintain a collinear trend on the opposite canyon wall? The pattern of vents and dikes is far easier to explain if the canyon did not exist during dike emplacement. Therefore, like Billingsley (2000), we conclude that 159-Mile Dike emplacement predates Muav Gorge incision. This implies 394.5 m of incision in Muav Gorge (when maximum pool depth is included) since 517 ka, an average rate of ∼763 m/m.y. (Table 2).

Our data indicate that between ca. 500 and 400 ka the rate of Colorado River incision at RM 96 was 1000–4000 m/m.y. By just after 400 ka, it had decrease to less than 210 _{+42 –49} m/m.y., a value consistent with the post–400 ka eastern Grand Canyon rates determined by previous studies. There seems only one reasonable explanation for this greater than fivefold decrease in incision rate—the passage of a transient knick.

The ∼763 m/m.y. incision rate since ca. 520 ka at RM 159 provides independent evidence for passage of this knick. Karlstrom et al. (2007) concluded that a 160 m/m.y. incision rate has been in force between RM 57 and RM 179 during the past 400–480 k.y., and Crow et al. (2014) argued for an even lower rate (97 m/m.y.) west of RM 116. Slowing of incision sometime between 400 and 520 ka is required to reconcile this with the faster 520 k.y. rate.

Evidence that the knickzone was simultaneously active at RM 159 and RM 96 might seem to imply an unreasonably rapid rate of upstream knickzone migration. But, as the modeling of Cook et al. (2009) showed, that isn’t the case because each incision rate provides just one snapshot of an ever-changing rate regime. The measured rate depends on the knickzone breadth, when it passed, and the age of the rock datum used. Figure 19 is an annotated version of Cook et al.’s (2009) model results (their fig. 12) that illustrates how potentially complex the incision rate data can become in the presence of a migrating knick. Their model simulates the upstream migration of the knick initiated by river integration ca. 6 Ma at the Grand Wash Cliffs (Fig. 1). It explores the effect on that knick’s behavior of the interface between strong and weak bedrock at Lees Ferry. The model was not intended as a quantitative prediction of incision rate history at a specific location; so it is important to view the ages and rates shown on Figure 19 only in relative terms.

Figure 19A illustrates changes in instantaneous incision rate at a given location during upstream migration of a knick under Cook et al.’s (2009) prescribed model conditions. Curves 1, 2, and 3 represent points in the western, central, and eastern Grand Canyon, respectively. Curve 2 approximately represents our RM 159 site and curve 3 our RM 96 site. Incision at both locations is through hard Precambrian or Paleozoic rock. Curve 4 is the signal in Glen Canyon, where the presence of weaker rock results in a lower peak incision rate. Figure 19B illustrates the time-integrated incision rate that would be recorded by a rock datum, such as a river terrace or cave mammillary, of a given age at each of points 1–4. Note that even during a time of high instantaneous uplift rate, if a datum lies in a zone of weak rock, it may record a lower incision rate than will a datum outside the high rate zone but where incision has been through stronger rock (compare curves 3 and 4 on Fig. 19B).

Examination of point A on Figure 19B illustrates that the simultaneously high incision rates we obtained at RM 96 and RM 159 do not imply an almost instantaneous 105 km upstream migration of the knick. Curves 2 and 3 here record the same high rate over the same interval despite their spatial separation. The slower post–ca. 400 ka incision rates observed by all workers between RM 57 and RM 179 are illustrated by point B. Such slow, uniform rates exist downstream of the knickzone, where the river profile has returned to equilibrium.

Cook et al. (2009) concluded that the Grand Canyon knick reached Lees Ferry at ca. 500 ka. They also noted that eastern Grand Canyon’s incision rate should decrease in tandem with a rate increase in Glen Canyon. Darling et al. (2012) documented a sixfold incision rate increase in Glen Canyon at 290 ± 170 ka. We see a fivefold decrease in eastern Grand Canyon nearly simultaneously, just as Cook et al. (2009) predicted.

Crow et al. (2014) is the only study besides ours to calculate eastern and central Grand Canyon incision rates directly from dated river terraces older than ca. 400 ka. They employed the same U/Th dating techniques we did but applied them to different terraces. For central Grand Canyon terraces older than 600–650 ka, they either calculated ²³⁴U model ages or dated them using cosmogenic burial techniques. They then combined data from three eastern Grand Canyon sites and two central Grand Canyon sites and fit linear regressions to each, with the slope revealing the incision rate. Lastly, they combined their results with cave proxy data to extend their history back to 4 Ma. Unlike us, they concluded that Grand Canyon incision rates have been steady over million-year time spans. Why are the conclusions from the two studies so starkly different?

Crow et al.’s (2014) terrace age data are, at their oldest, 650 ka–1.5 Ma. In order to extend their incision rate compilations back to 3.7 Ma, they included selected cave proxy data from Polyak et al. (2008). Because they considered cave proxy incision rates to be maxima, they followed Karlstrom et al.’s (2008) practice of including in their compilations only those cave data that yield the lowest incision rates. But Polyak et al. (2008) considered each cave proxy to be equally valid, concluding that passage of a transient knick will result in variable incision rates. We share Karlstrom et al.’s (2008) concerns about the reliability of cave proxy data (for example, it is difficult to reconcile the paleoriver elevations implied by Polyak et al.’s (2008) points 5 and 6), but the data from each cave must be evaluated on its own merits. A degree of circular reasoning is necessary to accept as valid only those cave proxy data points that yield the slowest incision rates and to then use those data to argue that incision rates were never higher. Points C and D on Figure 19B illustrate an alternative interpretation. Point C represents Polyak et al.’s (2008) Site 8 (at RM 32), which yielded an incision rate of 374 m/m.y. since 0.8 Ma. Point D represents their Site 7 (at RM 57), which indicated a rate of 166 m/m.y. since 2.7 Ma. In this interpretation, both proxies record accurate snapshots of the Canyon’s incision history despite their different incision rates.

Our data are clearly incompatible with Crow et al.’s (2014) interpretation of steady incision on a million-year time scale. But could their data fit with our migrating knick hypothesis? Crow et al.’s (2014) 160 m/m.y. eastern Grand Canyon rate for samples younger than ca. 450 ka is comparable to our post–400 ka results at RM 96. The apparent discrepancy arises only for older samples. But Cook et al.’s (2009) model reveals that large incision rate differences can arise because of differences in rock strength (Fig. 19), making it at least possible that both studies could be recording the passage of a migrating knick.

Crow et al.’s (2014) comparatively slower pre–500 ka incision rate comes from terraces between RM 56 and RM 69, a reach composed of easily eroded Tonto and Chuar Group rocks. This reach has low stream power of 179–331 W/m² (Pederson and Tressler, 2012). By contrast, our faster 500 ka rate at RM 96 comes from the reach containing the canyon’s most resistant rocks and highest unit stream power (630 W/m², Pederson and Tressler, 2012). Cook et al.’s (2009) model illustrates that lower incision rates are to be expected for a reach underlain by softer rocks and higher rates will occur in a reach with stronger rocks. For example, our 500 ka average rate at RM 96 could plot on Figure 19B at point E, whereas Crow et al.’s RM 56–69 rate during the same time interval could plot at point F.

Although both Crow et al.’s (2014) and our incision rate data could be compatible with the migrating knick hypothesis, both data sets cannot be simultaneously correct when one examines the time of river occupation claimed by the two studies for terraces older than 500 ka. For example, Crow et al. (2014) placed the paleoriver at the 70 m terrace at Palisades (RM 65.2) at 623 _{+162 –78} ka. The modern river there stands at 830 m, making the paleoriver elevation 900 m. Downstream, at RM 96, we place the river elevation at 949 m at 506 ± 33 ka. A similar situation exists for our respective central Grand Canyon sites. Clearly, these conclusions cannot all be correct; if they were, the paleo-Colorado would have flowed uphill! One or both studies must contain at least one error or incorrect assumption. It is important to note, though, that if episodes of incision at a 1–4 km/m.y. rate accompany passage of a knick, the river elevation can decrease by hundreds of meters at one location within the time represented by the age determination’s error bars.

Crow et al. (2014) provided robust constraints on various past Colorado River elevations thanks to the unambiguous presence of Colorado River gravels on the terraces they studied. Their U/Th age determinations for terraces 467 ka and younger are equally robust. We again emphasize that our incision rate data and Crow et al.’s (2014) are compatible for these younger terraces. The discrepancy arises only for older terraces, for which we find Crow et al.’s (2014) age data far less robust. Their conclusion hinges on >600 ka U/Th ages, cosmogenic burial ages, and ²³⁴U model ages, all of which have error bars so large as to permit faster rates than they favor. As discussed above (see Methods), their >600 ka U/Th ages (623 _{+162 –78} ka age at Palisades; 678 _{+147 –79} ka and 651 _{+151 –82} ka at Elves Chasm) must be treated with caution given the effects of even small perturbations by fluids. In addition, the potential for subtle diagenesis, such as that seen in several of our P1 samples, exists. Such alteration would likely shift isotopic ratios toward artificially older ages, again biasing the regression toward a low rate. Furthermore, their ²³⁴U model ages assume an unrealistic range of U_i (uranium initial ratio—(²³⁴U/²³⁸U)_i), using a maximum U_i of 8.0. Although U_i ratios can vary widely, 8.0 is more than double that of any calculated U_i found for 79 dated travertine samples in studies by us (see Table 1), Szabo (1990), and Pederson et al. (2002, 2006) (highest observed = 3.9). It is also much higher than found in any modern Grand Canyon groundwater (4.76; Stewart et al. [1988]). Selection of higher maximum U_i produces an older maximum model age, forcing Crow et al.’s (2014) regression to calculate an unrealistically low incision rate.

By choosing to fit their data with a linear regression, Crow et al. (2014) presuppose that the incision rate remained steady. They argue that “low” mean square of weighted deviation (MSWD) values indicate that linear regression of their data is appropriate. Although we agree that the MSWD of 0.9 for their central Grand Canyon regression permits the observed deviations to be explained solely by analytical error, an MSWD near 1.0 does not confirm that analytical error alone is responsible. The MSWD test for a linear fit to data is quite permissive for a small data set with large analytical errors, such as that necessarily used by Crow et al. (2014). This permissiveness is revealed by the fact that MSWD values between 0.21 and 2.4 will satisfy the linearity test at the 95% confidence interval for their central Grand Canyon data (see their supplementary table 4). The eastern Grand Canyon data (MSWD of 2.7) fail even this permissive test of a linear fit (95% confidence for MSWDs of 0.21–2.1). It is also unclear why they excluded sample 13 (their Table 1) from their regression; its inclusion would increase incision rate and make the MSWD even larger.

Gardner et al. (1987) pointed out that calculated geomorphic rates measured over short time scales are typically faster than those measured over long time scales. This is because longer duration rates for episodic processes like incision inherently average in more periods of quiescence. For this same reason, two seemingly equal rates measured over different time intervals likely imply, in actuality, a faster rate in the distant past. Therefore, Crow et al.’s (2014) conclusion that incision rates have been constant on million-year time scales quite likely reflects an actual slowing of incision rate over time.

Crow et al.’s (2014) central and eastern Grand Canyon data (their figs. 5 and 6) could also be fit using regression lines with their favored slopes for terraces <467 ka combined with steeper slopes (i.e., faster incision rates) for the older terraces. In fact, when they regressed a combination of their ca. 600 ka eastern Canyon terrace data with proxy data from six caves selected precisely because they yield the lowest incision rates, the result was a 600 ka–4 Ma incision rate of 236 ± 31 m/m.y., which is faster than their <600 ka rate of 160 ± 11 m/m.y. (see their figs. 6 and S1). Similarly, they concluded from their U/Th age data that central Grand Canyon incision rates have been a constant 100–120 m/m.y. since 650 ka. But when they included ²³⁴U model ages so as to extend the history back to ca. 1.5 Ma, their regression returned a potentially higher incision rate of 87–246 m/m.y. They also acknowledged the possibility of a change in western Grand Canyon incision rate at 2 Ma given the large analytical age uncertainty in the Dry Canyon Cave proxy data.

Crow et al. (2014) considered the fact that the y-intercept for each regression reproduced the independently determined depth to modern bedrock as a successful test of the “geologic validity of the regression.” We do not, however, consider this a robust test of their conclusion that incision has been steady on the million-year time scale because the same y-intercept would be produced by fitting only the post–467 ka data with their favored slopes and using a steeper slope (i.e., faster incision rate) to fit the older data.

Unlike Crow et al.’s (2014) study, our conclusions for eastern Grand Canyon rely on data from a single terrace (P1) and those for central Grand Canyon are not based on terrace data at all. What if our interpretation that the Colorado River contributed to deposition of P1 is wrong? What if the P1 strath age isn’t 506 ka but is instead 600–1200 ka? We consider our interpretations in both cases to be robust, but it is instructive to examine whether or not our primary conclusion (that incision rate slowed toward the present) can withstand invalidation of either. If outcrop P1 was deposited solely by Hermit Creek, the Colorado River was no more than 1.2 km away, as that is the distance to the Redwall cliff north of the river. Today Hermit Creek stands ∼76 m higher than the river 1.2 km above the confluence. If we assume the gradient of ancestral Hermit Creek was equal to today’s gradient and the river lay 1.2 km away, the minimum incision rate since 506 ka is 343 m/m.y. This rate is still faster than the maximum post–400 ka rate, leaving our primary conclusion unchanged.

If, alternatively, we assume that the Colorado River stood at the P1 elevation at 1.2 Ma (the oldest possible age of the slightly altered P1 samples), the minimum incision rate is 206 m/m.y., identical to the maximum post–400 ka rate. Clearly, our primary conclusion is not sensitive to the details of our stratigraphic interpretation, but it is sensitive to whether or not the U/Th ages of samples P1-1 and P1-9 truly record the depositional age of P1’s basal fill.

It is easy to envision the simultaneous activity of several springs scattered across the actively growing Hermit debris fan producing the ca. 500 ka travertine found at the base of outcrops P1, P2, and P3 contemporaneous with clastic deposition. That said, travertine is susceptible to dissolution and re-precipitation, so the possibility that P1’s 500 ka samples record such an event must be admitted. Crow et al.’s (2014) U/Th ages from Elves Chasm’s 250-m-high wall of travertine reveal that such re-precipitation events have occurred there. However, our Perched Outcrops’ different hydrologic context makes it unlikely that later re-precipitation is a viable explanation for simultaneous 500 ka travertine formation in three separate outcrops. If we assume Crow et al.’s (2014) long-term eastern Grand Canyon incision rate of 160 m/m.y. is correct, the Colorado River would have stood at the elevation of outcrops P1–P3 ca. 1.6 Ma. By 500 ka, when travertine was precipitating in the basal fill of these outcrops, 1.1 m.y. would have elapsed, and the outcrops would have stood ∼175 m above the river. It is likely that the canyons and gullies that today isolate the outcrops hydrologically from one another had already formed. It is unlikely that a re-precipitation event would simultaneously affect all three outcrops under those circumstances.

It is clear from the above discussion that the primary obstacle to determining >500 k.y. duration incision rates for eastern and central Grand Canyon (and whether that rate is steady or variable) is the difficulty in obtaining robust, high-precision age data. Both our study and that of Crow et al. (2014) have pushed travertine U/Th dating to its age limit. The large error bars Crow et al. (2014) placed on burial cosmogenic ages of terraces reveal that this technique, too, has significant limitations for longer-duration incision rate studies. One potentially promising technique is to directly date the basal fill of a strath terrace using optically stimulated luminescence (OSL). Optically stimulated luminescence has been successfully applied to the dating of Grand Canyon river terraces younger than 70 ka (Anders et al., 2005; Pederson et al., 2006) but has not been considered suitable to studies of older deposits. Recent advances in OSL dating (e.g., Li and Li, 2013) hold promise that in the near future terraces as old as 1 Ma might be successfully dated using this technique.

The knickzone we observe migrating through eastern and central Grand Canyon ca. 500 ka could be the one formed at the Grand Wash Cliffs in response to Colorado River integration at 5–6 Ma. Pelletier’s (2010) computer model predicted upstream migration of that knick at ∼100 km/m.y., placing it somewhere between Lees Ferry and central Glen Canyon (Fig. 1) at 500 ka. That scenario suggests the knick was well upstream of both RM 96 and RM 159 at the time we document rapid incision in both locations; so we might be seeing a different knick. That said, Cook et al. (2009) predicted that the eastern Grand Canyon incision rate would decrease simultaneously with arrival of the knick at Lees Ferry, which they hypothesized occurred at ca. 500 ka. The ca. 400 ka slowing of incision we document at RM 96 fits that hypothesis, as does Darling et al.’s (2012) observation that incision rate increased sixfold in Glen Canyon ca. 300 ka.

Alternatively, the transient knick we observe formed more recently. Whipple and Tucker’s (1999) numerical modeling showed that a river will respond to either a base-level fall, rock uplift, or an increase in discharge via formation of a transient knickzone. This is true even if the perturbation is spatially uniform (for example, due to regional epeirogenic surface uplift or flexural rebound in response to regional denudation). Several potential triggers exist in the Grand Canyon region for production of such a knick. Pelletier (2010) concluded that retreat of Grand Canyon scarps triggered flexural-isostatic rebound that drove up to 350 m of Plio-Quaternary incision. Karlstrom et al. (2008, 2012b), Roberts et al. (2012), and Crow et al. (2014) proposed that incision is due to Neogene mantle-derived surface uplift. Karlstrom et al. (2008, 2012b) and Crow et al. (2014) found support for this mechanism in their conclusion that Grand Canyon incision rates have been steady on million-year time scales. Although we disagree that incision rates have been steady, their hypothesis that enhanced mantle buoyancy could be driving Grand Canyon incision is tenable. The river will first respond to such surface uplift via upstream migration of a transient knick (Whipple and Tucker, 1999) before settling into a uniform incision rate mode after knickzone passage (Cook et al., 2009). Becker et al. (2014) found evidence that topography along the Colorado Plateau’s southwestern edge, where Grand Canyon is located, is dynamically supported by shallow, upper mantle convection. If true, the Colorado River would likely respond to this topography via headward propagation of a knick such as the one we document. Yet another potential trigger for geologically recent knickzone propagation is an abrupt change to a more erosive climate, such as the one ca. 2.7 Ma associated with onset of northern hemisphere glaciation (e.g., Molnar, 2004).

Because incision rates vary in a complex way during the passage of a knickzone and because there are multiple mechanisms that can produce a transient knick, we conclude that more Grand Canyon incision rate data are needed before that history can be used to confidently discriminate between current hypotheses regarding the mechanism(s) that triggered recent incision.

We find that the average incision rate at RM 96 in Grand Canyon has been 519 _{+55 –58} m/m.y. since 506 ± 33 ka and the maximum rate since 394 ± 32 ka has been 210 _{+42 –49} m/m.y. These average rates require that a pulse of rapid incision (∼1–4 km/m.y) occurred between 500 and 400 ka, after which incision slowed to <210 m/m.y. The Redwall/Muav escarpment at RM 96 has been retreating at ∼600–800 m/m.y. since 500 ka. We attribute the pulse of high incision to upstream migration of a transient knickzone past RM 96 during this time interval. The average incision rate at RM 159 since ca. 520 ka has been ∼763 m/m.y. We conclude that this high average rate is due to passage of the same knickzone past RM 159 at approximately the same time. Numerical modeling of knickzone propagation (Cook et al., 2009) reveals that rapid incision can be recorded over similar durations simultaneously across a wide reach, meaning that our finding does not require an unreasonably fast rate of upstream knickzone propagation. This knickzone might be the one that migrated upstream from the Grand Wash escarpment in response to Colorado River integration at 5–6 Ma. Alternatively, it might be associated with rock uplift in response to erosion-triggered isostatic rebound, with surface uplift produced by the encroachment of anomalously buoyant mantle, or with change at 2.7 Ma to a cooler, more erosive climate at the onset of the Pleistocene ice ages.

We thank Emma Benenati of the National Park Service for helping us to secure a sample collection permit, Zhaofeng Zhang for assistance with U/Th work, and Blake Lowrey, Sam Coggeshall, and Terri Cook for their hard work in the field. We have benefited greatly from discussions with Bob Anderson, David Budd, Ryan Crow, Lang Farmer, Steve Martel, Charles Stern, and Greg Tucker. Ryan Crow shared his data and interpretations. We are grateful for the helpful reviews provided by Joel Pederson and Ryan Crow on earlier versions of the manuscript.