scholarly journals Mass balance, grade, and adjustment timescales in bedrock channels

2020 ◽  
Vol 8 (1) ◽  
pp. 103-122 ◽  
Author(s):  
Jens Martin Turowski
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Mechanistic Model ◽  
Channel Width ◽  
Bedrock Rivers ◽  
Channel Incision ◽  
Bedrock Channel ◽  
Lateral Incision ◽  
Lateral Erosion ◽  
Bedrock Channels

Abstract. Rivers are dynamical systems that are thought to evolve towards a steady-state configuration. Then, geomorphic parameters, such as channel width and slope, are constant over time. In the mathematical description of the system, the steady state corresponds to a fixed point in the dynamic equations in which all time derivatives are equal to zero. In alluvial rivers, steady state is characterized by grade. This can be expressed as a so-called order principle: an alluvial river evolves to achieve a state in which sediment transport is constant along the river channel and is equal to transport capacity everywhere. In bedrock rivers, steady state is thought to be achieved with a balance between channel incision and uplift. The corresponding order principle is the following: a bedrock river evolves to achieve a vertical bedrock incision rate that is equal to the uplift rate or base-level lowering rate. In the present work, considerations of process physics and of the mass balance of a bedrock channel are used to argue that bedrock rivers evolve to achieve both grade and a balance between channel incision and uplift. As such, bedrock channels are governed by two order principles. As a consequence, the recognition of a steady state with respect to one of them does not necessarily imply an overall steady state. For further discussion of the bedrock channel evolution towards a steady state, expressions for adjustment timescales are sought. For this, a mechanistic model for lateral erosion of bedrock channels is developed, which allows one to obtain analytical solutions for the adjustment timescales for the morphological variables of channel width, channel bed slope, and alluvial bed cover. The adjustment timescale to achieve steady cover is of the order of minutes to days, while the adjustment timescales for width and slope are of the order of thousands of years. Thus, cover is adjusted quickly in response to a change in boundary conditions to achieve a graded state. The resulting change in vertical and lateral incision rates triggers a slow adjustment of width and slope, which in turn affects bed cover. As a result of these feedbacks, it can be expected that a bedrock channel is close to a graded state most of the time, even when it is transiently adjusting its bedrock channel morphology.

scholarly journals Mass balance, grade, and adjustment timescales in bedrock channels

2019 ◽  
Author(s):  
Jens Martin Turowski
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Mechanistic Model ◽  
Channel Width ◽  
Bedrock Rivers ◽  
Bedrock Channel ◽  
Lateral Incision ◽  
Lateral Erosion ◽  
Bed Slope ◽  
Bedrock Channels

Abstract. Rivers are dynamical systems that are thought to evolve towards a steady state configuration. Then, geomorphic parameters, such as channel width and slope, are constant over time. In the mathematical description of the system, the steady state corresponds to a fixed point in the dynamic equations in which all time derivatives are equal to zero. In alluvial rivers, steady state is characterised by grade. This can be expressed as a so-called order principle: An alluvial river evolves to achieve a state in which sediment transport is constant along the river channel, and is equal to transport capacity everywhere. In bedrock rivers, steady state is thought to be achieved with a balance between erosion and uplift. The corresponding order principle is: A bedrock river evolves to achieve a vertical bedrock incision rate that is equal to the uplift rate or baselevel lowering rate. Within the present paper, considerations of process physics and of the mass balance of a bedrock channel are used to argue that bedrock rivers evolve to achieve both grade and a balance between erosion and uplift. As such, bedrock channels are governed by two order principles. As a consequence, the recognition of a steady state with respect to one of them does not necessarily imply an overall steady state. For further discussion of the bedrock channel evolution towards a steady state, expressions for adjustment timescales are sought. For this, a mechanistic model for lateral erosion of bedrock channels is developed, which allows to obtain analytical solutions for the adjustment timescales for the morphological variables of channel width, channel bed slope and alluvial bed cover. The adjustment timescale to achieve steady cover is of the order of minutes to days, while the adjustment timescales for width and slope are of the order of thousands of years. Thus, cover is adjusted quickly in response to a change in boundary conditions to achieve a graded state. The resulting change in vertical and lateral incision rates triggers a slow adjustment of width and slope, which in turn affects bed cover. As a result of these feedbacks, it can be expected that a bedrock channel is close to a graded state most of the time, even when it is transiently adjusting its bedrock channel morphology.

scholarly journals Developing and evaluating a theory for the lateral erosion of bedrock channels for use in landscape evolution models

2017 ◽  
Author(s):  
Abigail L. Langston ◽  
Gregory E. Tucker
Keyword(s):  
Landscape Evolution ◽  
Water Discharge ◽  
Evolution Model ◽  
Sediment Flux ◽  
Lateral Migration ◽  
Catchment Scale ◽  
Bedrock Channel ◽  
Vertical Incision ◽  
Lateral Erosion ◽  
Bedrock Channels

Abstract. Understanding how a bedrock river erodes its banks laterally is a frontier in geomorphology. Theory for the vertical incision of bedrock channels is widely implemented in the current generation of landscape evolution models. However, in general existing models do not seek to implement the lateral migration of bedrock channel walls. This is problematic, as modeling geomorphic processes such as terrace formation and hillslope-channel coupling depends on accurate simulation of valley widening. We have developed and implemented a theory for the lateral migration of bedrock channel walls in a catchment-scale landscape evolution model. Two model formulations are presented, one representing the slow process of widening a bedrock canyon, the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Model experiments were run with a range of values for bedrock erodibility and tendency towards transport- or detachment-limited behavior and varying magnitudes of sediment flux and water discharge in order to determine the role each plays in the development of wide bedrock valleys. Results show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are many times wider than the grid discretization scale. This theory for the lateral erosion of bedrock channel walls and the numerical implementation of the theory in a catchment-scale landscape evolution model is a significant first step towards understanding the factors that control the rates and spatial extent of wide bedrock valleys.

scholarly journals A mechanistic model for lateral erosion of bedrock channel banks by bedload particle impacts

2020 ◽  
Author(s):  
Tingan Li ◽  
Theodore K. Fuller ◽  
Leonard S. Sklar ◽  
Karen B. Gran ◽  
Jeremy G. Venditti
Keyword(s):  
Mechanistic Model ◽  
Bedrock Channel ◽  
Lateral Erosion

scholarly journals The role of lateral erosion in the evolution of nondendritic drainage networks to dendricity and the persistence of dynamic networks

2021 ◽  
Vol 118 (16) ◽  
pp. e2015770118
Author(s):  
Jeffrey S. Kwang ◽  
Abigail L. Langston ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Dynamic Networks ◽  
River Networks ◽  
Stable Configuration ◽  
Lateral Incision ◽  
Drainage Networks ◽  
Physically Based ◽  
Physically Based Models ◽  
Lateral Erosion ◽  
Two Parameters

Dendritic, i.e., tree-like, river networks are ubiquitous features on Earth’s landscapes; however, how and why river networks organize themselves into this form are incompletely understood. A branching pattern has been argued to be an optimal state. Therefore, we should expect models of river evolution to drastically reorganize (suboptimal) purely nondendritic networks into (more optimal) dendritic networks. To date, current physically based models of river basin evolution are incapable of achieving this result without substantial allogenic forcing. Here, we present a model that does indeed accomplish massive drainage reorganization. The key feature in our model is basin-wide lateral incision of bedrock channels. The addition of this submodel allows for channels to laterally migrate, which generates river capture events and drainage migration. An important factor in the model that dictates the rate and frequency of drainage network reorganization is the ratio of two parameters, the lateral and vertical rock erodibility constants. In addition, our model is unique from others because its simulations approach a dynamic steady state. At a dynamic steady state, drainage networks persistently reorganize instead of approaching a stable configuration. Our model results suggest that lateral bedrock incision processes can drive major drainage reorganization and explain apparent long-lived transience in landscapes on Earth.

scholarly journals A Mechanistic Model for Lateral Erosion of Bedrock Channel Banks by Bedload Particle Impacts

2020 ◽  
Vol 125 (6) ◽  
Author(s):  
Tingan Li ◽  
Theodore K. Fuller ◽  
Leonard S. Sklar ◽  
Karen B. Gran ◽  
Jeremy G. Venditti
Keyword(s):  
Mechanistic Model ◽  
Bedrock Channel ◽  
Lateral Erosion

scholarly journals Alluvial cover controlling the width, slope and sinuosity of bedrock channels

2017 ◽  
Author(s):  
Jens Martin Turowski
Keyword(s):  
Theoretical Explanation ◽  
Rate Of Change ◽  
Sediment Supply ◽  
Sediment Flux ◽  
Channel Width ◽  
Bedrock Channel ◽  
The Pacific ◽  
Storm Frequency ◽  
Bed Slope ◽  
Bedrock Channels

Abstract. The problem of bedrock channel meandering is closely related to the problems of channel width and slope. Active meandering occurs when the channel walls are eroded, which also drives channel widening. Further, for a given drop in elevation, the more sinuous a channel is, the lower is its channel bed slope in comparison to a straight channel. It can thus be expected that studies of bedrock channel meandering give insights into width and slope adjustment and vice versa. The mechanisms by which bedrock channels actively meander have been debated since the beginning of modern geomorphic research in the 19th century, but a final consensus has not been reached. Remote sensing studies of the Pacific Arc islands show that regional channel sinuosity scales with storm frequency and inversely with the erodibility of the substrate. However, no mechanisms are known that effectively reduce sinuosity and keep it at a constant value, and a coherent theoretical explanation for the field observations is lacking. It has long been argued that whether a bedrock channel meanders actively or not is determined by the availability of sediment relative to transport capacity, a notion that has also been demonstrated in laboratory experiments. Here, this idea is taken up by postulating that the rate of change of both width and sinuosity over time is dependent on bed cover only. Based on the physics of erosion by bedload impacts, a scaling argument is developed to link bedrock channel width, slope and sinuosity to sediment supply, discharge and erodibility. It is shown that this simple model built on sediment-flux driven bedrock erosion yields the observed scaling relationships of channel width and slope with discharge and erosion rate, can explain why sinuosity evolves to a steady state value and predict the observed relations between sinuosity, erodibility and storm frequency.

scholarly journals Alluvial cover controlling the width, slope and sinuosity of bedrock channels

2018 ◽  
Vol 6 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Jens Martin Turowski
Keyword(s):  
Bedload Transport ◽  
Rate Of Change ◽  
Sediment Supply ◽  
Sediment Flux ◽  
Channel Width ◽  
Transport Capacity ◽  
Bedrock Channel ◽  
Bed Slope ◽  
The 19Th Century ◽  
Bedrock Channels

Abstract. Bedrock channel slope and width are important parameters for setting bedload transport capacity and for stream-profile inversion to obtain tectonics information. Channel width and slope development are closely related to the problem of bedrock channel sinuosity. It is therefore likely that observations on bedrock channel meandering yields insights into the development of channel width and slope. Active meandering occurs when the bedrock channel walls are eroded, which also drives channel widening. Further, for a given drop in elevation, the more sinuous a channel is, the lower is its channel bed slope in comparison to a straight channel. It can thus be expected that studies of bedrock channel meandering give insights into width and slope adjustment and vice versa. The mechanisms by which bedrock channels actively meander have been debated since the beginning of modern geomorphic research in the 19th century, but a final consensus has not been reached. It has long been argued that whether a bedrock channel meanders actively or not is determined by the availability of sediment relative to transport capacity, a notion that has also been demonstrated in laboratory experiments. Here, this idea is taken up by postulating that the rate of change of both width and sinuosity over time is dependent on bed cover only. Based on the physics of erosion by bedload impacts, a scaling argument is developed to link bedrock channel width, slope and sinuosity to sediment supply, discharge and erodibility. This simple model built on sediment-flux-driven bedrock erosion concepts yields the observed scaling relationships of channel width and slope with discharge and erosion rate. Further, it explains why sinuosity evolves to a steady-state value and predicts the observed relations between sinuosity, erodibility and storm frequency, as has been observed for meandering bedrock rivers on Pacific Arc islands.

scholarly journals Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models

2018 ◽  
Vol 6 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Abigail L. Langston ◽  
Gregory E. Tucker
Keyword(s):  
Landscape Evolution ◽  
Water Discharge ◽  
Evolution Model ◽  
Sediment Flux ◽  
Lateral Migration ◽  
Catchment Scale ◽  
Bedrock Channel ◽  
Vertical Incision ◽  
Lateral Erosion ◽  
Bedrock Channels

Abstract. Understanding how a bedrock river erodes its banks laterally is a frontier in geomorphology. Theories for the vertical incision of bedrock channels are widely implemented in the current generation of landscape evolution models. However, in general existing models do not seek to implement the lateral migration of bedrock channel walls. This is problematic, as modeling geomorphic processes such as terrace formation and hillslope–channel coupling depends on the accurate simulation of valley widening. We have developed and implemented a theory for the lateral migration of bedrock channel walls in a catchment-scale landscape evolution model. Two model formulations are presented, one representing the slow process of widening a bedrock canyon and the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Model experiments were run with a range of values for bedrock erodibility and tendency towards transport- or detachment-limited behavior and varying magnitudes of sediment flux and water discharge in order to determine the role that each plays in the development of wide bedrock valleys. The results show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are many times wider than the grid discretization scale. This theory for the lateral erosion of bedrock channel walls and the numerical implementation of the theory in a catchment-scale landscape evolution model is a significant first step towards understanding the factors that control the rates and spatial extent of wide bedrock valleys.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

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