scholarly journals Bedload transport controls bedrock erosion under sediment-starved conditions

2015 ◽  
Vol 3 (3) ◽  
pp. 291-309 ◽  
Author(s):  
A. R. Beer ◽  
J. M. Turowski
Keyword(s):  
Erosion Rate ◽  
Landscape Evolution ◽  
Bedload Transport ◽  
Minor Importance ◽  
Stream Power ◽  
Catchment Scale ◽  
Data Set ◽  
Erosion Processes ◽  
Bedrock Erosion ◽  
Mountainous Landscape

Abstract. Fluvial bedrock incision constrains the pace of mountainous landscape evolution. Bedrock erosion processes have been described with incision models that are widely applied in river-reach and catchment-scale studies. However, so far no linked field data set at the process scale had been published that permits the assessment of model plausibility and accuracy. Here, we evaluate the predictive power of various incision models using independent data on hydraulics, bedload transport and erosion recorded on an artificial bedrock slab installed in a steep bedrock stream section for a single bedload transport event. The influence of transported bedload on the erosion rate (the "tools effect") is shown to be dominant, while other sediment effects are of minor importance. Hence, a simple temporally distributed incision model, in which erosion rate is proportional to bedload transport rate, is proposed for transient local studies under detachment-limited conditions. This model can be site-calibrated with temporally lumped bedload and erosion data and its applicability can be assessed by visual inspection of the study site. For the event at hand, basic discharge-based models, such as derivatives of the stream power model family, are adequate to reproduce the overall trend of the observed erosion rate. This may be relevant for long-term studies of landscape evolution without specific interest in transient local behavior. However, it remains to be seen whether the same model calibration can reliably predict erosion in future events.

scholarly journals Bedload transport controls intra-event bedrock erosion

2015 ◽  
Vol 3 (1) ◽  
pp. 53-82 ◽  
Author(s):  
A. R. Beer ◽  
J. M. Turowski
Keyword(s):  
Erosion Rate ◽  
Landscape Evolution ◽  
Bedload Transport ◽  
Mountain Stream ◽  
Minor Importance ◽  
Stream Power ◽  
Catchment Scale ◽  
Data Set ◽  
Erosion Processes ◽  
Mountainous Landscape

Abstract. Fluvial bedrock incision constrains the pace of mountainous landscape evolution. Fluvial erosion processes have been described with incision models that are widely applied in river reach and catchment scale studies. However, so far, no linked field data set at the process scale had been published that allows to assess model requirements and adequacy. Here, we evaluate the predictive power of various incision models on data on hydraulics, bedload transport and erosion recorded on an artificial bedrock slab installed in a steep mountain stream for a single bedload transport event. The influence of transported bedload on erosion rate (the "tools effect") is shown to be dominant while other effects are of minor importance. Hence, a simple temporal distributed incision model in which erosion rate is proportional to bedload transport rate is proposed for transient local studies. This model can be site-calibrated with temporally lumped bedload and erosion data and its applicability can be assessed by visual inspection of the study site. Basic discharge-based models like derivatives of the stream power model family however, are adequate to reproduce the overall trend of the observed erosion rate, at least for the event on hand. This is relevant for long-term studies of e.g. landscape evolution with no interest in transient local behaviour.

TLS-recorded massive bedrock erosion of a hyperconcentrated flow in an Alpine Gorge: approaches to modelling the event (Höllentalklamm, Germany)

2021 ◽  
Author(s):  
Verena Stammberger ◽  
Benjamin Jacobs ◽  
Michael Krautblatter
Keyword(s):  
Morphological Changes ◽  
Precipitation Event ◽  
Rheological Parameters ◽  
Data Set ◽  
Erosion Rates ◽  
Erosion Processes ◽  
Bedrock Erosion ◽  
Hyperconcentrated Flow ◽  
The Impact ◽  
Modelling Approaches

<p>High-intensity precipitation events and the resulting extreme discharges in mountain torrents are immensely dangerous and destructive hazards that can put lives in danger and cause expensive damages to infrastructure. There is a high probability that further changes in climate will favour the genesis and therefore increase the frequency of such extreme events. Nevertheless, there is a pronounced desire to experience breathtaking mountainous landscapes, especially when easy accessible. An example is the Höllental gorge (between 1032 and 1062 m a.s.l., Wetterstein mountains, Germany), a key touristic attraction in the region with up to 100k visitors per year. Especially for such highly frequented places, the knowledge and comprehension of possible risks from hydrological and geomorphic hazards is crucial. With this in mind, we are reconstructing and discussing possible modelling approaches of a recent event of a hyperconcentrated flow through the gorge.</p><p>In June 2020 a local extreme precipitation event between 50 and 60 mm/h caused a rapid accumulation of the surface runoff due to the steep slopes of the Höllental (inclination of ø 110%). Secondary sediment storages were mobilized and transported to the main channel where a hyperconcentrated flow developed at the beginning of the gorge. Depending on the percentage of transported sediment in the flow, temporary transitions to a debris flow were possible. Throughout the ravine, massive forces reshaped the rock walls and the channel bed by particle erosion, shearing and relocation of boulders up to 20 m<sup>3</sup>.</p><p>In this study we present a comparison of two terrestrial laser scan campaigns, the first two weeks prior to the event and the second just five days after. We were able to accurately calculate the morphological changes along the sides of the channel and obtained a unique data set for bedrock erosion rates due to the impact of a hyperconcentrated flow. We mapped the flow height throughout the whole gorge by identifying the visible transition of undisturbed to roughened rock surfaces. DEM difference calculation upstream allows to determine the erosion and deposition heights as well as the corresponding volumes. Additionally, electrical resistivity tomographies reveal the thickness of (still) available sediment upstream.</p><p>Here we discuss possible numerical and analytical modelling approaches and analyse preliminary results. We aim at coupling the observed erosion rates to calculated velocities of a model that integrates the complex topography as well as the rheological parameters of the flow. A calibration of the model will be achieved with the mapped flow height in the gorge. Due to the complexity of the gorge, a frequently used numerical simulation as well as a analytical open-channel flow model will be analyzed and compared.</p><p>This study presents a unique dataset of effective erosion rates with records collected pre- and post-event. The results contribute to strongly improve the understanding of the flow dynamics in hyperconcentrated flows and give unparalleled information about erosion processes in narrow bedrock channels.</p>

scholarly journals The SPACE 1.0 model: A Landlab component for 2-D calculation of sediment transport, bedrock erosion, and landscape evolution

2017 ◽  
Author(s):  
Charles M. Shobe ◽  
Gregory E. Tucker ◽  
Katherine R. Barnhart
Keyword(s):  
Sediment Transport ◽  
Analytical Solutions ◽  
Landscape Evolution ◽  
Sediment Flux ◽  
Surface Processes ◽  
Stream Power ◽  
Space Model ◽  
Lithospheric Flexure ◽  
Hillslope Evolution ◽  
Bedrock Erosion

Abstract. Models of landscape evolution by river erosion are often either transport-limited (sediment is always available, but may or may not be transportable) or detachment-limited (sediment must be detached from the bed, but is then always transportable). While several models incorporate elements of, or transition between, transport-limited and detachment-limited behavior, most require that either sediment or bedrock, but not both, are eroded at any given time. We present SPACE (Stream Power with Alluvium Conservation and Entrainment) 1.0, a new model for simultaneous evolution of an alluvium layer and a bedrock bed based on conservation of sediment mass both on the bed and in the water column. The model treats sediment transport and bedrock erosion simultaneously, embracing the reality that many rivers (even those commonly defined as "bedrock" rivers) flow over a partially alluviated bed. The SPACE model is a component of the Landlab modeling toolkit, a Python-language library used to create models of earth surface processes. Landlab allows efficient coupling between the SPACE model and components simulating basin hydrology, hillslope evolution, weathering, lithospheric flexure, and other surface processes. Here, we first derive the governing equations of the SPACE model from existing sediment transport and bedrock erosion formulations and explore the behavior of local analytical solutions for sediment flux and alluvium thickness. We derive steady-state analytical solutions for channel slope, alluvium thickness, and sediment flux, and show that SPACE matches predicted behavior in detachment-limited, transport-limited, and mixed conditions. We provide an example of landscape evolution modeling in which SPACE is coupled with hillslope diffusion, and demonstrate that SPACE provides an effective framework for simultaneously modeling 2-D sediment transport and bedrock erosion.

scholarly journals Constraining the Stream Power Law: a novel approach combining a Landscape Evolution Model and an inversion method

2013 ◽  
Vol 1 (1) ◽  
pp. 891-921
Author(s):  
T. Croissant ◽  
J. Braun
Keyword(s):  
Power Law ◽  
Erosion Rate ◽  
Landscape Evolution ◽  
Evolution Model ◽  
Drainage Area ◽  
Inversion Method ◽  
Stream Power ◽  
Time Step ◽  
Novel Approach ◽  
River Profiles

Abstract. In the past few decades, many studies have been dedicated to our understanding of the interactions between tectonic and erosion and, in many instances, using numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the Stream Power Law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the Stream Power Law remain poorly constrained. In this study, we present a novel approach to constrain the Stream Power Law coefficients under the detachment limited mode by combining a highly efficient Landscape Evolution Model, FastScape, which solves the Stream Power Law under arbitrary geometries and boundary conditions and an inversion algorithm, the Neighborhood Algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provide well resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

scholarly journals Constraining the stream power law: a novel approach combining a landscape evolution model and an inversion method

2014 ◽  
Vol 2 (1) ◽  
pp. 155-166 ◽  
Author(s):  
T. Croissant ◽  
J. Braun
Keyword(s):  
Power Law ◽  
Erosion Rate ◽  
Landscape Evolution ◽  
Evolution Model ◽  
Drainage Area ◽  
Inversion Method ◽  
Stream Power ◽  
Time Step ◽  
Novel Approach ◽  
River Profiles

Abstract. In the past few decades, many studies have been dedicated to the understanding of the interactions between tectonics and erosion, in many instances through the use of numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the stream power law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the stream power law remain poorly constrained. In this study, we present a novel approach to constrain the stream power law coefficients under the detachment-limited mode by combining a highly efficient landscape evolution model, FastScape, which solves the stream power law under arbitrary geometries and boundary conditions and an inversion algorithm, the neighborhood algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provides well-resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

scholarly journals Determinants of prepaid systems of healthcare financing: a worldwide country-level perspective

2021 ◽  
Author(s):  
Andrea M. Leiter ◽  
Engelbert Theurl
Keyword(s):  
Health Care ◽  
Panel Data ◽  
Health Care Financing ◽  
Value Added ◽  
The Elderly ◽  
Dynamic Panel Data ◽  
Individual Characteristics ◽  
Minor Importance ◽  
Data Set ◽  
Country Level

AbstractIn this paper we examine determinants of prepaid modes of health care financing in a worldwide cross-country perspective. We use three different indicators to capture the role of prepaid modes in health care financing: (i) the share of total prepaid financing as percent of total current health expenditures, (ii) the share of voluntary prepaid financing as percent of total prepaid financing, and (iii) the share of compulsory health insurance as percent of total compulsory prepaid financing. In the econometric analysis, we refer to a panel data set comprising 154 countries and covering the time period 2000–2015. We apply a static as well as a dynamic panel data model. We find that the current structure of prepaid financing is significantly determined by its different forms in the past. The significant influence of GDP per capita, governmental revenues, the agricultural value added, development assistance for health, degree of urbanization and regulatory quality varies depending on the financing structure we look at. The share of the elderly and the education level are only of minor importance for explaining the variation in a country’s share of prepaid health care financing. The importance of the mentioned variables as determinants for prepaid health care financing also varies depending on the countries’ socio-economic development. From our analysis we conclude that more detailed information on indicators which reflect the distribution of individual characteristics (such as income, family size and structure and health risks) within a country’s population would be needed to gain deeper insight into the decisive determinants for prepaid health care financing.

scholarly journals Macro-roughness model of bedrock–alluvial river morphodynamics

2015 ◽  
Vol 3 (1) ◽  
pp. 113-138 ◽  
Author(s):  
L. Zhang ◽  
G. Parker ◽  
C. P. Stark ◽  
T. Inoue ◽  
E. Viparelli ◽  
...  
Keyword(s):  
Fixed Bed ◽  
River Mouth ◽  
Steady State Solution ◽  
Bedload Transport ◽  
Spatiotemporal Variation ◽  
Sediment Supply ◽  
Complex Case ◽  
Upstream Migration ◽  
Major Advance ◽  
Bedrock Erosion

Abstract. The 1-D saltation–abrasion model of channel bedrock incision of Sklar and Dietrich (2004), in which the erosion rate is buffered by the surface area fraction of bedrock covered by alluvium, was a major advance over models that treat river erosion as a function of bed slope and drainage area. Their model is, however, limited because it calculates bed cover in terms of bedload sediment supply rather than local bedload transport. It implicitly assumes that as sediment supply from upstream changes, the transport rate adjusts instantaneously everywhere downstream to match. This assumption is not valid in general, and thus can give rise to unphysical consequences. Here we present a unified morphodynamic formulation of both channel incision and alluviation that specifically tracks the spatiotemporal variation in both bedload transport and alluvial thickness. It does so by relating the bedrock cover fraction to the ratio of alluvium thickness to bedrock macro-roughness, rather than to the ratio of bedload supply rate to capacity bedload transport. The new formulation (MRSAA) predicts waves of alluviation and rarification, in addition to bedrock erosion. Embedded in it are three physical processes: alluvial diffusion, fast downstream advection of alluvial disturbances, and slow upstream migration of incisional disturbances. Solutions of this formulation over a fixed bed are used to demonstrate the stripping of an initial alluvial cover, the emplacement of alluvial cover over an initially bare bed and the advection–diffusion of a sediment pulse over an alluvial bed. A solution for alluvial–incisional interaction in a channel with a basement undergoing net rock uplift shows how an impulsive increase in sediment supply can quickly and completely bury the bedrock under thick alluvium, thus blocking bedrock erosion. As the river responds to rock uplift or base level fall, the transition point separating an alluvial reach upstream from an alluvial–bedrock reach downstream migrates upstream in the form of a "hidden knickpoint". A tectonically more complex case of rock uplift subject to a localized zone of subsidence (graben) yields a steady-state solution that is not attainable with the original saltation–abrasion model. A solution for the case of bedrock–alluvial coevolution upstream of an alluviated river mouth illustrates how the bedrock surface can be progressively buried not far below the alluvium. Because the model tracks the spatiotemporal variation in both bedload transport and alluvial thickness, it is applicable to the study of the incisional response of a river subject to temporally varying sediment supply. It thus has the potential to capture the response of an alluvial–bedrock river to massive impulsive sediment inputs associated with landslides or debris flows.

Temporal variations in bedload transport rates and sediment storage in gravel-bed rivers

1992 ◽  
Vol 16 (3) ◽  
pp. 319-338 ◽  
Author(s):  
Trevor Hoey
Keyword(s):  
Three Dimensional ◽  
Temporal Variations ◽  
Sampling Interval ◽  
Bedload Transport ◽  
Sediment Storage ◽  
Data Set ◽  
Gravel Bed ◽  
Wide Range ◽  
Gravel Bed Rivers ◽  
Bed Waves

Temporal variability in bedload transport rates and spatial variability in sediment storage have been reported with increasing frequency in recent years. A spatial and temporal classification for these features is suggested based on the gravel bedform classification of Church and Jones (1982). The identified scales, meso-, macro-, and mega- are each broad, and within each there is a wide range of processes acting to produce bedload fluctuations. Sampling the same data set with different sampling intervals yields a near linear relationship between sampling interval and pulse period. A range of modelling strategies has been applied to bed waves. The most successful have been those which allow for the three-dimensional nature of sediment storage processes, and which allow changes in the width and depth of stored sediment. The existence of bed waves makes equilibrium in gravel-bed rivers necessarily dynamic. Bedload pulses and bed waves can be regarded as equilibrium forms at sufficiently long timescales.

scholarly journals Landscape evolution models using the stream power incision model show unrealistic behavior when <i>m</i> ∕ <i>n</i> equals 0.5

2017 ◽  
Vol 5 (4) ◽  
pp. 807-820 ◽  
Author(s):  
Jeffrey S. Kwang ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Landscape Evolution ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
River Incision ◽  
Vertical Incision ◽  
Small Scales ◽  
Insight Into

Abstract. Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KAmSn, where E is the vertical incision rate, K is the erodibility constant, A is the upstream drainage area, S is the channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m ∕ n = 0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only on small scales) is neglected, the choice m ∕ n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10 km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000 km2 domain.

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