Stream power

About: Stream power is a research topic. Over the lifetime, 1135 publications have been published within this topic receiving 51324 citations.

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

Abstract: 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.

Sediment and rock strength controls on river incision into bedrock

Abstract: Recent theoretical investigations suggest that the rate of river incision into bedrock depends nonlinearly on sediment supply, challenging the common assumption that incision rate is simply proportional to stream power. Our measurements from laboratory abrasion mills support the hypothesis that sediment promotes erosion at low supply rates by providing tools for abrasion, but inhibits erosion at high supply rates by burying underlying bedrock beneath transient deposits. Maximum erosion rates occur at a critical level of coarse-grained sediment supply where the bedrock is only partially exposed. Fine-grained sediments provide poor abrasive tools for lowering bedrock river beds because they tend to travel in suspension. Experiments also reveal that rock resistance to fluvial erosion scales with the square of rock tensile strength. Our results suggest that spatial and temporal variations in the extent of bedrock exposure provide incising rivers with a previously unrecognized degree of freedom in adjusting to changes in rock uplift rate and climate. Furthermore, we conclude that the grain size distribution of sediment supplied by hillslopes to the channel network is a fundamental control on bedrock channel gradients and topographic relief.

Quantifying differential rock-uplift rates via stream profile analysis

Abstract: 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.

River Longitudinal Profiles and Bedrock Incision Models: Stream Power and the Influence of Sediment Supply

Abstract: The simplicity and apparent mechanistic basis of the stream power river incision law have led to its wide use in empirical and theoretical studies. Here we identify constraints on its calibration and application, and present a mechanistic theory for the effects of sediment supply on incision rates which spotlights additional limitations on the applicability of the stream power law. On channels steeper than about 20%, incision is probably dominated by episodic debris flows, and on sufficiently gentle slopes, sediment may bury the bedrock and prevent erosion. These two limits bound the application of the stream power law and strongly constrain the possible combination of parameters in the law. In order to avoid infinite slopes at the drainage divide in numerical models of river profiles using the stream power law it is commonly assumed that the first grid cell is unchanneled. We show, however, that the size of the grid may strongly influence the calculated equilibrium relief. Analysis of slope-drainage area relationships for a river network in a Northern California watershed using digital elevation data and review of data previously reported by Hack reveal that non-equilibrium profiles may produce well defined slope-area relationships (as expected in equilibrium channels), but large differences between tributaries may point to disequilibrium conditions. To explore the role of variations in sediment supply and transport capacity in bedrock incision we introduce a mechanistic model for abrasion of bedrock by saltating bedload. The model predicts that incision rates reach a maximum at intermediate levels of sediment supply and transport capacity. Incision rates decline away from the maximum with either decreasing supply (due to a shortage of tools) or increasing supply (due to gradual bed alluviation), and with either decreasing transport capacity (due to less energetic particle movement) or increasing transport capacity (due less frequent particle impacts per unit bed area). We use this model to predict longitudinal profiles under varying boundary conditions and sediment supply rates and find that even in actively downcutting rivers, the river slope needed to maintain incision may be only slightly greater than the slope required to transport the imposed load. Hence, the channel slope-drainage area relationships of rivers actively cutting through bedrock may predominately reflect the grain size and supply rate of sediment and only secondarily the influence of bedrock resistance to erosion.