Kelin X. Whipple

Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs

The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the elevation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We review and explore the stream-power erosion model in an effort to (1) elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationship for system response time to tectonic perturbations, (3) determine the sensitivity of model behavior to various model parameters, and (4) integrate the above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the streampower erosion law. Dimensional analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift-erosion number, greatly reducing the number of variables that need to be considered in the sensitivity analysis. The degree of nonlinearity in the relationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion processes directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream channel gradient, and the total fluvial relief of mountain ranges. Similarly, the predicted response time to changes in rock uplift rate is shown to depend on climate, rock strength, and the magnitude of tectonic perturbation, with the slope exponent n controlling the degree of dependence on these various factors. For typical drainage basin geometries the response time is relatively insensitive to the size of the system. Work on the physics of bedrock erosion processes, their sensitivity to extreme floods, their transient responses to sudden changes in climate or uplift rate, and the scaling of local rock erosion studies to reach-scale modeling studies are most sorely needed.

Landscape response to tectonic forcing: Digital elevation model analysis of stream profiles in the Mendocino triple junction region, northern California

The topographic evolution of orogens is fundamentally dictated by rates and patterns of bedrock-channel incision. Quantitative field assessments of process-based laws are needed to accurately describe landscape uplift and denudation in response to tectonics and climate. We evaluate and calibrate the shear stress (or similar unit stream-power) bedrock-incision model by studying stream profiles in a tectonically active mountain range. Previous work on emergent marine terraces in the Mendocino triple junction region of northern California provides spatial and temporal control on rock-uplift rates. Digital elevation models and field data are used to quantify differences in landscape morphology associated with along-strike northwest to southeast changes in tectonic and climatic conditions. Analysis of longitudinal profiles supports the hypothesis that the study-area channels are in equilibrium with current uplift and climatic conditions, consistent with theoretical calculations of system response time based on the shear-stress model. Within uncertainty, the profile concavity (𝛉) of the trunk streams is constant throughout the study area (𝛉 ≈ 0.43), as predicted by the model. Channel steepness correlates with uplift rate. These data help constrain the two key unknown model parameters, the coefficient of erosion ( K ) and the exponent associated with channel gradient ( n ). This analysis shows that K cannot be treated as a constant throughout the study area, despite generally homogeneous substrate properties. For a reasonable range of slope-exponent values ( n ), best-fit values of K are positively correlated with uplift rate. This correlation has important implications for landscape-evolution models and likely reflects dynamic adjustment of K to tectonic changes, due to variations in orographic precipitation, and perhaps channel width, sediment load, and frequency of debris flows. The apparent variation in K makes a unique value of n impossible to constrain with present data.

River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation

Improved formulation of bedrock erosion laws requires knowledge of the actual processes operative at the bed. We present qualitative field evidence from a wide range of settings that the relative efficacy of the various processes of fluvial erosion (e.g., plucking, abrasion, cavitation, solution) is a strong function of substrate lithology, and that joint spacing, fractures, and bedding planes exert the most direct control. The relative importance of the various processes and the nature of the interplay between them are inferred from detailed observations of the morphology of erosional forms on channel bed and banks, and their spatial distributions. We find that plucking dominates wherever rocks are well jointed on a submeter scale. Hydraulic wedging of small clasts into cracks, bashing and abrasion by bedload, and chemical and physical weathering all contribute to the loosening and removal of joint blocks. In more massive rocks, abrasion by suspended sand appears to be rate limiting in the systems studied here. Concentration of erosion on downstream sides of obstacles and tight coupling between fluid-flow patterns and fine-scale morphology of erosion forms testify to the importance of abrasion by suspended-load, rather than bedload, particles. Mechanical analyses indicate that erosion by suspended-load abrasion is considerably more nonlinear in shear stress than erosion by plucking. In addition, a new analysis indicates that cavitation is more likely to occur in natural systems than previously argued. Cavitation must be considered a viable process in many actively incising bedrock channels and may contribute to the fluting and potholing of massive, unjointed rocks that is otherwise attributed to suspended-load abrasion. Direct field evidence of cavitation erosion is, however, lacking. In terms of the well-known shear-stress (or stream-power) erosion law, erosion by plucking is consistent with a slope exponent ( n ) of ∼2/3 to 1, whereas erosion by suspended-load abrasion is more consistent with a slope exponent of ∼5/3. Given that substrate lithology appears to dictate the dominant erosion process, this finding has important implications for long-term landscape evolution and the models used to study it.

Quantifying differential rock-uplift rates via stream profile analysis

Despite intensive research into the coupling between tectonics and surface processes, our ability to obtain quantitative information on the rates of tectonic processes from topography remains limited due primarily to a dearth of data with which to test and calibrate process rate laws. Here we develop a simple theory for the impact of spatially variable rock-uplift rate on the concavity of bedrock river profiles. Application of the analysis to the Siwalik Hills of central Nepal demonstrates that systematic differences in the concavity of channels in this region match the predictions of a stream power incision model and depend on the position and direction of the channel relative to gradients in the vertical component of deformation rate across an active fault-bend fold. Furthermore, calibration of model parameters from channel profiles argued to be in steady state with the current climatic and tectonic regime indicates that (1) the ratio of exponents on channel drainage area and slope ( m / n ) is ∼0.46, consistent with theoretical predictions; (2) the slope exponent is consistent with incision either linearly proportional to shear stress or unit stream power ( n = 0.66 or n = 1, respectively); and (3) the coefficient of erosion is within the range of previously published estimates (mean K = 4.3 × 10 −4 m 0.2 /yr). Application of these model parameters to other channels in the Siwalik Hills yields estimates of spatially variable erosion rates that mimic expected variations in rock-uplift rate across a fault-bend fold. Thus, the sensitivity of channel gradient to rock- uplift rate in this landscape allows us to derive quantitative estimates of spatial variations in erosion rate directly from topographic data.

Late Cenozoic uplift of southeastern Tibet

The age of surface uplift in southeastern Tibet is currently unknown, but the initiation of major river incision can be used as a proxy for the timing of initial uplift. The topographically high eastern plateau and gently dipping southeastern plateau margin are mantled by an elevated, low-relief relict landscape that formed at a time of slow erosion at low elevation and low tectonic uplift rates prior to uplift of the eastern Tibetan Plateau. Thermochronology from deep river gorges that are cut into the relict landscape shows slow cooling between ca. 100 and ca. 10–20 Ma and a change to rapid cooling after ca. 13 Ma with initiation of rapid river incision at 0.25–0.5 mm/yr between 9 and 13 Ma. A rapid increase in mean elevation of eastern Tibet beginning at this time supports tectonic-climate models that correlate the lateral (eastern) expansion of high topography in Tibet with the late Miocene intensification of the Indian and east Asian monsoons.

Late Cenozoic evolution of the eastern margin of the Tibetan Plateau: Inferences from 40Ar/39Ar and (U‐Th)/He thermochronology

High topography in central Asia is perhaps the most fundamental expression of the Cenozoic Indo-Asian collision, yet an understanding of the timing and rates of development of the Tibetan Plateau remains elusive. Here we investigate the Cenozoic thermal histories of rocks along the eastern margin of the plateau adjacent to the Sichuan Basin in an effort to determine when the steep topographic escarpment that characterizes this margin developed. Temperature-time paths inferred from ^(40)Ar/^(39)Ar thermochronology of biotite, multiple diffusion domain modeling of alkali feldspar ^(40)Ar release spectra, and (U-Th)/He thermochronology of zircon and apatite imply that rocks at the present-day topographic front of the plateau underwent slow cooling ( 30°–50°C/m.y.) coincident with exhumation from inferred depths of ∼8–10 km, at denudation rates of 1–2 mm/yr. Samples from the interior of the plateau continued to cool relatively slowly during the same time period (∼3°C/m.y.), suggesting limited exhumation (1–2 km). However, these samples record a slight increase in cooling rate (from <1 to ∼3°C/m.y.) at some time during the middle Tertiary; the tectonic significance of this change remains uncertain. Regardless, late Cenozoic denudation in this region appears to have been markedly heterogeneous, with the highest rates of exhumation focused at the topographic front of the plateau margin. We infer that the onset of rapid cooling at the plateau margin reflects the erosional response to the development of regionally significant topographic gradients between the plateau and the stable Sichuan Basin and thus marks the onset of deformation related to the development of the Tibetan Plateau in this region. The present margin of the plateau adjacent to and north of the Sichuan Basin is apparently no older than the late Miocene or early Pliocene (∼5–12 Ma).

Geomorphic limits to climate-induced increases in topographic relief

Recognition of the potential for strong dynamic coupling between atmospheric and tectonic processes has sparked intense cross-disciplinary investigation and debate on the question of whether tectonics have driven long-term climate change or vice versa. It has been proposed that climate change might have driven the uplift of mountain summits through an isostatic response to valley incision. Because isostasy acts to compensate mean elevations, the debate hinges on the question of whether climate change can significantly increase topographic relief or, more precisely, increase the volume of ‘missing mass’ between summits and ridges. Here we show that, in tectonically active mountain ranges, geomorphic constraints allow only a relatively small increase in topographic relief in response to climate change. Thus, although climate change may cause significant increases in denudation rates, potentially establishing an important feedback between surficial and crustal processes, neither fluvial nor glacial erosion is likely to induce significant isostatic peak uplift.

Beyond threshold hillslopes: Channel adjustment to base-level fall in tectonically active mountain ranges

Numerous empirical and model-based studies argue that, in general, hillslopes and river channels increase their gradients to accommodate high rates of base-level fall. To date, however, few data sets show the dynamic range of both these relationships needed to test theoretical models of hillslope evolution and river incision. Here, we utilize concentrations of 10 Be in quartz extracted from river sand on the eastern margin of the Tibetan Plateau to explore relationships among short-term (10 2 –10 5 a) erosion rate, hillslope gradient, and channel steepness. Our data illustrate nonlinear behavior and a threshold in the relationship between erosion rate and mean hillslope gradient, confi rming the generalization that hillslopes around the world are limited by slope stability and cease to provide a metric for erosion at high rates (>~0.2 mm/a). The relationship between channel steepness index and erosion rate is also nonlinear, but channels continue to steepen beyond the point where threshold hillslopes emerge up to at least 0.6 mm/a, demonstrating that channel steepness is a more reliable topographic metric than mean hillslope gradient for erosion rate and that channels ultimately drive landscape adjustment to increasing rates of base-level fall in tectonically active settings.

Has focused denudation sustained active thrusting at the Himalayan topographic front

The geomorphic character of major river drainages in the Himalayan foothills of central Nepal suggests the existence of a discrete, west-northwest‐trending break in rock uplift rates that does not correspond to previously mapped faults. The 40 Ar/ 39 Ar thermochronologic data from detrital muscovites with provenance from both sides of the discontinuity indicate that this geomorphic break also corresponds to a major discontinuity in cooling ages: samples to the south are Proterozoic to Paleozoic, whereas those to the north are Miocene and younger. Combined, these observations virtually require recent (Pliocene‐ Holocene) motion on a thrust-sense shear zone in the central Nepal Himalaya, ;20‐30 km south of the Main Central thrust. Field observations are consistent with motion on a broad shear zone subparallel to the fabric of the Lesser Himalayan lithotectonic sequence. The results suggest that motion on thrusts in the toe of the Himalayan wedge may be synchronous with deeper exhumation on more hinterland structures in central Nepal. We speculate that this continued exhumation in the hinterland may be related to intense, sustained erosion driven by focused orographic precipitation at the foot of the High Himalaya.

Hydroplaning of subaqueous debris flows

We report laboratory experiments that demonstrate that the fronts of subaqueous debris flows can hydroplane on thin layers of water. The hydroplaning dramatically reduces the bed drag, thus increasing head velocity. These high velocities promote sediment suspension and turbidity-current formation. Hydroplaning causes the fronts of debris flows to accelerate away from their bodies to the point of completely detaching from the bodies, producing surging. Instigation of hydroplaning is controlled by the balance of gravity and inertia forces at the debris front and is suitably characterized by the densimetric Froude number. The laboratory flows constrain hydroplaning to cases where the calculated densimetric Froude number is greater than 0.4. The presence of a basal lubricating layer of water underneath hydroplaning debris flows and slides offers a possible explanation for the long run-out distances of many subaqueous flows and slides on very low slopes.