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2008 |
Sklar, L S; Dietrich, W E Implications of the saltation-abrasion bedrock incision model for steady-state river longitudinal profile relief and concavity Journal Article Earth Surface Processes and Landforms, 33 (7), pp. 1129-1151, 2008. Abstract | Links | BibTeX | Tags: bedrock channels, bedrock channels;erosion, erosion, geomorphology, laser altimetry @article{DOI:10.1002/esp.1689, title = { Implications of the saltation-abrasion bedrock incision model for steady-state river longitudinal profile relief and concavity}, author = {Sklar, L. S. and Dietrich, W. E.}, url = {http://angelo.berkeley.edu/wp-content/uploads/Sklar_2008_EarthSurProc.pdf}, doi = {DOI:10.1002/esp.1689}, year = {2008}, date = {2008-05-22}, journal = {Earth Surface Processes and Landforms}, volume = {33}, number = {7}, pages = {1129-1151}, abstract = {The saltation–abrasion model predicts rates of river incision into bedrock as an explicit function of sediment supply, grain size, boundary shear stress and rock strength. Here we use this experimentally calibrated model to explore the controls on river longitudinal profile concavity and relief for the simple but illustrative case of steady-state topography. Over a wide range of rock uplift rates we find a characteristic downstream trend, in which upstream reaches are close to the threshold of sediment motion with large extents of bedrock exposure in the channel bed, while downstream reaches have higher excess shear stresses and lesser extents of bedrock exposure. Profile concavity is most sensitive to spatial gradients in runoff and the rate of downstream sediment fining. Concavity is also sensitive to the supply rate of coarse sediment, which varies with rock uplift rate and with the fraction of the total sediment load in the bedload size class. Variations in rock strength have little influence on profile concavity. Profile relief is most sensitive to grain size and amount of runoff. Rock uplift rate and rock strength influence relief most strongly for high rates of rock uplift. Analysis of potential covariation of grain size with rock uplift rate and rock strength suggests that the influence of these variables on profile form could occur in large part through their influence on grain size. Similarly, covariation between grain size and the fraction of sediment load in the bedload size class provides another indirect avenue for rock uplift and strength to influence profile form.}, keywords = {bedrock channels, bedrock channels;erosion, erosion, geomorphology, laser altimetry}, pubstate = {published}, tppubtype = {article} } The saltation–abrasion model predicts rates of river incision into bedrock as an explicit function of sediment supply, grain size, boundary shear stress and rock strength. Here we use this experimentally calibrated model to explore the controls on river longitudinal profile concavity and relief for the simple but illustrative case of steady-state topography. Over a wide range of rock uplift rates we find a characteristic downstream trend, in which upstream reaches are close to the threshold of sediment motion with large extents of bedrock exposure in the channel bed, while downstream reaches have higher excess shear stresses and lesser extents of bedrock exposure. Profile concavity is most sensitive to spatial gradients in runoff and the rate of downstream sediment fining. Concavity is also sensitive to the supply rate of coarse sediment, which varies with rock uplift rate and with the fraction of the total sediment load in the bedload size class. Variations in rock strength have little influence on profile concavity. Profile relief is most sensitive to grain size and amount of runoff. Rock uplift rate and rock strength influence relief most strongly for high rates of rock uplift. Analysis of potential covariation of grain size with rock uplift rate and rock strength suggests that the influence of these variables on profile form could occur in large part through their influence on grain size. Similarly, covariation between grain size and the fraction of sediment load in the bedload size class provides another indirect avenue for rock uplift and strength to influence profile form. |
2006 |
Sklar, Leonard S; Dietrich, William E The role of sediment in controlling bedrock channel slope: Implications of the saltation-abrasion incision model Journal Article Geomorphology, 82 (1-2), pp. 58-83, 2006. Abstract | Links | BibTeX | Tags: erosion, Grain size, landscape evolution, Magnitude–frequency, rivers, sediment supply @article{Sklar2006, title = {The role of sediment in controlling bedrock channel slope: Implications of the saltation-abrasion incision model}, author = {Leonard S. Sklar and William E. Dietrich}, url = {http://angelo.berkeley.edu/wp-content/uploads/Sklar_2006_Geomorpho.pdf}, doi = {10.1016/j.geomorph.2005.08.019}, year = {2006}, date = {2006-12-06}, journal = {Geomorphology}, volume = {82}, number = {1-2}, pages = {58-83}, abstract = {The saltation–abrasion model is a mechanistic model for river incision into bedrock by saltating bedload, which we have previously derived and used experimental data to constrain all parameter values. Here we develop a method for applying the saltation–abrasion model at a landscape scale, and use the model as a reference for evaluating the behavior of a wide range of alternative incision models, in order to consider the implications of the saltation–abrasion model, as well as other models, for predicting topographic steady-state channel slope. To determine the single-valued discharge that best represents the effects of the full discharge distribution in transporting sediment and wearing bedrock, we assume all runoff can be partitioned between a low-flow and a high-flow discharge, in which all bedload sediment transport occurs during high flow. We then use the gauged discharge record and measurements of channel characteristics at a reference field site and find that the optimum discharge has a moderate magnitude and frequency, due to the constraints of the threshold of grain motion and bed alluviation by high relative sediment supply. Incision models can be classified according to which of the effects of sediment on bedrock incision are accounted for. Using the predictions of the saltation–abrasion model as a reference, we find that the threshold of motion is the most important effect that should be represented explicitly, followed in order of decreasing importance by the cover effect, the tools effect and the threshold of suspension effect. Models that lack the threshold of motion over-predict incision rate for low shear stresses and under-predict the steady-state channel slope for low to moderate rock uplift rates and rock strengths. Models that lack the cover effect over-predict incision rate for high sediment supply rates, and fail to represent the degree of freedom in slope adjustment provided by partial bed coverage. Models that lack the tools effect over-predict incision rate for low sediment supply rates, and do not allow for the possibility that incision rate can decline for increases in shear stress above a peak value. Overall, the saltation–abrasion model predicts that steady-state channel slope is most sensitive to changes in grain size, such that the effect of variations in rock uplift rate and rock strength may affect slope indirectly through their possible, but as yet poorly understood, influence on the size distribution of sediments delivered to channel networks by hillslopes.}, keywords = {erosion, Grain size, landscape evolution, Magnitude–frequency, rivers, sediment supply}, pubstate = {published}, tppubtype = {article} } The saltation–abrasion model is a mechanistic model for river incision into bedrock by saltating bedload, which we have previously derived and used experimental data to constrain all parameter values. Here we develop a method for applying the saltation–abrasion model at a landscape scale, and use the model as a reference for evaluating the behavior of a wide range of alternative incision models, in order to consider the implications of the saltation–abrasion model, as well as other models, for predicting topographic steady-state channel slope. To determine the single-valued discharge that best represents the effects of the full discharge distribution in transporting sediment and wearing bedrock, we assume all runoff can be partitioned between a low-flow and a high-flow discharge, in which all bedload sediment transport occurs during high flow. We then use the gauged discharge record and measurements of channel characteristics at a reference field site and find that the optimum discharge has a moderate magnitude and frequency, due to the constraints of the threshold of grain motion and bed alluviation by high relative sediment supply. Incision models can be classified according to which of the effects of sediment on bedrock incision are accounted for. Using the predictions of the saltation–abrasion model as a reference, we find that the threshold of motion is the most important effect that should be represented explicitly, followed in order of decreasing importance by the cover effect, the tools effect and the threshold of suspension effect. Models that lack the threshold of motion over-predict incision rate for low shear stresses and under-predict the steady-state channel slope for low to moderate rock uplift rates and rock strengths. Models that lack the cover effect over-predict incision rate for high sediment supply rates, and fail to represent the degree of freedom in slope adjustment provided by partial bed coverage. Models that lack the tools effect over-predict incision rate for low sediment supply rates, and do not allow for the possibility that incision rate can decline for increases in shear stress above a peak value. Overall, the saltation–abrasion model predicts that steady-state channel slope is most sensitive to changes in grain size, such that the effect of variations in rock uplift rate and rock strength may affect slope indirectly through their possible, but as yet poorly understood, influence on the size distribution of sediments delivered to channel networks by hillslopes. |
2005 |
Stock, J D; Montgomery, D R; Collins, B D; Dietrich, W E GSA Bulletin, 117 (1-2), pp. 174-194, 2005. Abstract | Links | BibTeX | Tags: erosion, geomorphology, neotectonics, rivers, Weathering @article{Stock2005, title = {Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by rivers and debris flows}, author = {J.D. Stock and D.R. Montgomery and B.D. Collins and W.E. Dietrich}, url = {http://angelo.berkeley.edu/wp-content/uploads/Stock_2005_GSABulletin.pdf}, doi = {10.1130/B25560.1}, year = {2005}, date = {2005-01-01}, journal = {GSA Bulletin}, volume = {117}, number = {1-2}, pages = {174-194}, abstract = {Until recently, published rates of incision of bedrock valleys came from indirect dating of incised surfaces. A small but growing literature based on direct measurement reports short-term bedrock lowering at geologically unsustainable rates. We report observations of bedrock lowering from erosion pins monitored over 1–7 yr in 10 valleys that cut indurated volcanic and sedimentary rocks in Washington, Oregon, California, and Taiwan. Most of these channels have historically been stripped of sediment. Their bedrock is exposed to bed-load abrasion, plucking, and seasonal wetting and drying that comminutes hard, intact rock into plates or equant fragments that are removed by higher flows. Consequent incision rates are proportional to the square of rock tensile strength, in agreement with experimental results of others. Measured rates up to centimeters per year far exceed regional long-term erosion-rate estimates, even for apparently minor sediment-transport rates. Cultural artifacts on adjoining strath terraces in Washington and Taiwan indicate at least several decades of lowering at these extreme rates. Lacking sediment cover, lithologies at these sites lower at rates that far exceed long-term rock-uplift rates. This rate disparity makes it unlikely that the long profiles of these rivers are directly adjusted to either bedrock hardness or rock-uplift rate in the manner predicted by the stream power law, despite the observation that their profiles are well fit by power-law plots of drainage area vs. slope. We hypothesize that the threshold of motion of a thin sediment mantle, rather than bedrock hardness or rock-uplift rate, controls channel slope in weak bedrock lithologies with tensile strengths below ∼3–5 MPa. To illustrate this hypothesis and to provide an alternative interpretation for power-law plots of area vs. slope, we combine Shields' threshold transport concept with measured hydraulic relationships and downstream fining rates. In contrast to fluvial reaches, none of the hundreds of erosion pins we installed in steep valleys recently scoured to bedrock by debris flows indicate any postevent fluvial lowering. These results are consistent with episodic debris flows as the primary agent of bedrock lowering in the steepest parts of the channel network above ∼0.03–0.10 slope.}, keywords = {erosion, geomorphology, neotectonics, rivers, Weathering}, pubstate = {published}, tppubtype = {article} } Until recently, published rates of incision of bedrock valleys came from indirect dating of incised surfaces. A small but growing literature based on direct measurement reports short-term bedrock lowering at geologically unsustainable rates. We report observations of bedrock lowering from erosion pins monitored over 1–7 yr in 10 valleys that cut indurated volcanic and sedimentary rocks in Washington, Oregon, California, and Taiwan. Most of these channels have historically been stripped of sediment. Their bedrock is exposed to bed-load abrasion, plucking, and seasonal wetting and drying that comminutes hard, intact rock into plates or equant fragments that are removed by higher flows. Consequent incision rates are proportional to the square of rock tensile strength, in agreement with experimental results of others. Measured rates up to centimeters per year far exceed regional long-term erosion-rate estimates, even for apparently minor sediment-transport rates. Cultural artifacts on adjoining strath terraces in Washington and Taiwan indicate at least several decades of lowering at these extreme rates. Lacking sediment cover, lithologies at these sites lower at rates that far exceed long-term rock-uplift rates. This rate disparity makes it unlikely that the long profiles of these rivers are directly adjusted to either bedrock hardness or rock-uplift rate in the manner predicted by the stream power law, despite the observation that their profiles are well fit by power-law plots of drainage area vs. slope. We hypothesize that the threshold of motion of a thin sediment mantle, rather than bedrock hardness or rock-uplift rate, controls channel slope in weak bedrock lithologies with tensile strengths below ∼3–5 MPa. To illustrate this hypothesis and to provide an alternative interpretation for power-law plots of area vs. slope, we combine Shields' threshold transport concept with measured hydraulic relationships and downstream fining rates. In contrast to fluvial reaches, none of the hundreds of erosion pins we installed in steep valleys recently scoured to bedrock by debris flows indicate any postevent fluvial lowering. These results are consistent with episodic debris flows as the primary agent of bedrock lowering in the steepest parts of the channel network above ∼0.03–0.10 slope. |
2004 |
Sklar, Leonard S; Dietrich, William E A mechanistic model for river incision into bedrock by saltating bed load Journal Article Water Resources Research, 40 (6), pp. W06301, 2004. Abstract | Links | BibTeX | Tags: abrasion, bedrock incision, erosion, landscape evolution, saltation @article{Sklar2004, title = {A mechanistic model for river incision into bedrock by saltating bed load}, author = {Leonard S. Sklar and William E. Dietrich}, url = {http://angelo.berkeley.edu/wp-content/uploads/A-mechanistic-model-for-river-incision-into-bedrock-by-saltating-bed-load_Sklar.pdf}, doi = {doi:10.1029/2003WR002496}, year = {2004}, date = {2004-06-18}, journal = {Water Resources Research}, volume = {40}, number = {6}, pages = {W06301}, abstract = {[1] Abrasion by bed load is a ubiquitous and sometimes dominant erosional mechanism for fluvial incision into bedrock. Here we develop a model for bedrock abrasion by saltating bed load wherein the wear rate depends linearly on the flux of impact kinetic energy normal to the bed and on the fraction of the bed that is not armored by transient deposits of alluvium. We assume that the extent of alluvial bed cover depends on the ratio of coarse sediment supply to bed load transport capacity. Particle impact velocity and impact frequency depend on saltation trajectories, which can be predicted using empirical functions of excess shear stress. The model predicts a nonlinear dependence of bedrock abrasion rate on both sediment supply and transport capacity. Maximum wear rates occur at moderate relative supply rates due to the tradeoff between the availability of abrasive tools and the partial alluviation of the bedrock bed. Maximum wear rates also occur at intermediate levels of excess shear stress due to the reduction in impact frequency as grain motion approaches the threshold of suspension. Measurements of bedrock wear in a laboratory abrasion mill agree well with model predictions and allow calibration of the one free model parameter, which relates rock strength to rock resistance to abrasive wear. The model results suggest that grain size and sediment supply are fundamental controls on bedrock incision rates, not only by bed load abrasion but also by all other mechanisms that require bedrock to be exposed in the channel bed.}, keywords = {abrasion, bedrock incision, erosion, landscape evolution, saltation}, pubstate = {published}, tppubtype = {article} } [1] Abrasion by bed load is a ubiquitous and sometimes dominant erosional mechanism for fluvial incision into bedrock. Here we develop a model for bedrock abrasion by saltating bed load wherein the wear rate depends linearly on the flux of impact kinetic energy normal to the bed and on the fraction of the bed that is not armored by transient deposits of alluvium. We assume that the extent of alluvial bed cover depends on the ratio of coarse sediment supply to bed load transport capacity. Particle impact velocity and impact frequency depend on saltation trajectories, which can be predicted using empirical functions of excess shear stress. The model predicts a nonlinear dependence of bedrock abrasion rate on both sediment supply and transport capacity. Maximum wear rates occur at moderate relative supply rates due to the tradeoff between the availability of abrasive tools and the partial alluviation of the bedrock bed. Maximum wear rates also occur at intermediate levels of excess shear stress due to the reduction in impact frequency as grain motion approaches the threshold of suspension. Measurements of bedrock wear in a laboratory abrasion mill agree well with model predictions and allow calibration of the one free model parameter, which relates rock strength to rock resistance to abrasive wear. The model results suggest that grain size and sediment supply are fundamental controls on bedrock incision rates, not only by bed load abrasion but also by all other mechanisms that require bedrock to be exposed in the channel bed. |