3D lithological structure in a steady state model drives divide migration

2021 ◽  
Author(s):  
Emma Graf ◽  
Simon Mudd ◽  
Florian Kober ◽  
Angela Landgraf ◽  
Andreas Ludwig
Keyword(s):  
Steady State ◽  
Landscape Evolution ◽  
Geophysical Methods ◽  
Drainage Area ◽  
Stream Power ◽  
K Value ◽  
Model Simulations ◽  
Rock Structure ◽  
The Difference ◽  
Future Landscape

<p>Predicting future relief is a longstanding challenge in the field of geomorphology. Past denudation and incision rates can be reconstructed and modelled from field data such as thermochronometers, cosmogenic nuclides or optically stimulated luminescence, whereas future rates are then, by definition, fully unknown. Predicting future landscape evolution is further complicated by the dynamic nature of drainage networks, as well as the necessity of constraining properties such as erodibility in order to make sensible predictions. One of the few constraints available for future landscape properties is the underground stratigraphy imaged by wells or geophysical methods. The 3D rock structure will eventually be exhumed and can be utilised to constrain the future states of model simulations.</p><p>In this contribution, we present a landscape evolution model capable of ingesting 3D lithologic information and adapting to alternative channel networks, and demonstrate it using a study area in the Swiss Jura Mountains. The model calculates local relief using steady state solutions of the stream power incision model, and also quantifies hillslope relief using a very simple critical slope gradient where hillslope angles are set to a critical value on pixels that have a small drainage area. Further, drainage divides are allowed to migrate to minimize sharp breaks in relief across drainage divides.</p><p>We calibrate the values of erodibility, K, for each lithological unit by extracting ranges of apparent K value from the present-day landscape based on drainage area and gradient along the drainage network. This is then further refined by i) using a Monte Carlo approach to create combinations of K based on these ranges, and ii) comparing the real and model landscape for each combination with the aim to minimise the difference between the two. We then run selected model simulations of future base level fall and potential drainage reorganisation events, highlighting the effects of i.) spatially variable erodibility and ii.) lateral changes of the main channel axis on divide migration.</p>

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.

A morphologically-consistent expression for the transition from stream-power-law regime to a debris-flow regime

2020 ◽  
Author(s):  
Odin Marc ◽  
Hussain Alqattan ◽  
Sean Willett
Keyword(s):  
Steady State ◽  
Debris Flow ◽  
Landscape Evolution ◽  
Drainage Area ◽  
Slope Gradient ◽  
Stream Power ◽  
Denudation Rates ◽  
Fluvial Incision ◽  
Critical Slope

&lt;p&gt;&amp;#160;Many long-term landscape evolution models are currently combining equations describing the evolution of the surface under fluvial incision (using the so-called stream-power incision model) and hillslope transport (often modeled as linear diffusion). Some models combine these two terms (e.g., Fastscape) and implicitly contain a transition from hillslope to fluvial processes dependent on the ratio of the diffusive and fluvial erosional parameters, D and K respectively (Perron et al., 2009). Other models require as input a hillslope-fluvial transition length (e.g., DAC) and apply hillslope erosion from the ridge-top to this lengthscale and fluvial incision only downstream of it. Still, in both cases the influence of non-linear processes such as landslide and debris-flow on this transition are not accounted.&lt;/p&gt;&lt;p&gt;We have analyzed the scaling between slope gradient and drainage areas in LIDAR-derived high-resolution DEM for &gt;30 catchments, with apparent steady-state morphology, and where long-term denudation estimates, E, were estimated from cosmogenic nuclides . The catchments span different lithology, climate and denudation rates from ~0.05 to ~3 mm/yr but show a consistent pattern where substantial portion of upstream channels exhibit slope gradient roughly constant with drainage area, and transition towards a negative scaling between slope and area (characteristic of fluvial processes) after a critical drainage area, A&lt;sub&gt;c.&lt;/sub&gt; Previous work (Stock and Dietrich, 2003) suggested the portion with constant slope may be dominated by erosion due to debris-flow processes, maintaining the channel at a critical slope, S&lt;sub&gt;df&lt;/sub&gt;.&lt;/p&gt;&lt;p&gt;Here we show that both S&lt;sub&gt;df&lt;/sub&gt;, and A&lt;sub&gt;c&lt;/sub&gt;, are strongly correlated to the long-term denudation, E. Further, we find that S&lt;sub&gt;df&lt;/sub&gt; seems to saturate at a critical slope angle, S&lt;sub&gt;c&lt;/sub&gt; , near 40&amp;#176; when denudation rates reach about 1mm/yr consistent with predictions for the slope of a non-linear diffusive hillsllopes (Roering et al., 2007). Combining this expression with the empirical model for the steady-state slope of Stock and Dietrich, 2003, and enforcing the consistency with a stream-power-law downstream we find that the steady state values for S&lt;sub&gt;df&lt;/sub&gt; and A&lt;sub&gt;c&lt;/sub&gt; can be fully expressed as analytical functions of E, K, D and S&lt;sub&gt;c&lt;/sub&gt;. We assess the validity of these expressions with independent estimate of K and D extracted from local channel steepness and hilltop curvature.&amp;#160;&lt;/p&gt;&lt;p&gt;As the impact of debris flow on landscape morphology seems ubiquitous on landscape with more than 0.1 mm/yr of erosion, the classical landscape evolution formulation may need to be upgraded to correctly represent steady-state morphology of the upstream part of catchment (&lt;span&gt;i.e.&lt;/span&gt;, &lt;1km&lt;sup&gt;2&lt;/sup&gt;). Even if it still lack physical basis, we propose a formulation that adequately represent the steady state morphology from ridge to large drainage area. We show that it yield a new definition of Chi that may be better match the morphology of channel approaching ridges and we also discuss how to implement this new-steady state formulation in landscape evolution models.&lt;/p&gt;

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

2017 ◽  
Author(s):  
Jeffrey S. Kwang ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Landscape Evolution ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
Channel Network ◽  
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 = vertical incision rate, K = erodibility constant, A =  upstream drainage area, S = 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; indeed, this ratio has been deemed to yield the “optimal channel network.” Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only at 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 1 m2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 100 km2 domain.

scholarly journals Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model

2018 ◽  
Vol 6 (3) ◽  
pp. 779-808 ◽  
Author(s):  
Nikos Theodoratos ◽  
Hansjörg Seybold ◽  
James W. Kirchner
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Degrees Of Freedom ◽  
Landscape Evolution ◽  
Initial Conditions ◽  
Evolution Model ◽  
Model Parameters ◽  
Stream Power ◽  
Linear Diffusion ◽  
Characteristic Scales

Abstract. The scaling and similarity of fluvial landscapes can reveal fundamental aspects of the physics driving their evolution. Here, we perform a dimensional analysis of the governing equation of a widely used landscape evolution model (LEM) that combines stream-power incision and linear diffusion laws. Our analysis assumes that length and height are conceptually distinct dimensions and uses characteristic scales that depend only on the model parameters (incision coefficient, diffusion coefficient, and uplift rate) rather than on the size of the domain or of landscape features. We use previously defined characteristic scales of length, height, and time, but, for the first time, we combine all three in a single analysis. Using these characteristic scales, we non-dimensionalize the LEM such that it includes only dimensionless variables and no parameters. This significantly simplifies the LEM by removing all parameter-related degrees of freedom. The only remaining degrees of freedom are in the boundary and initial conditions. Thus, for any given set of dimensionless boundary and initial conditions, all simulations, regardless of parameters, are just rescaled copies of each other, both in steady state and throughout their evolution. Therefore, the entire model parameter space can be explored by temporally and spatially rescaling a single simulation. This is orders of magnitude faster than performing multiple simulations to span multidimensional parameter spaces. The characteristic scales of length, height and time are geomorphologically interpretable; they define relationships between topography and the relative strengths of landscape-forming processes. The characteristic height scale specifies how drainage areas and slopes must be related to curvatures for a landscape to be in steady state and leads to methods for defining valleys, estimating model parameters, and testing whether real topography follows the LEM. The characteristic length scale is roughly equal to the scale of the transition from diffusion-dominated to advection-dominated propagation of topographic perturbations (e.g., knickpoints). We introduce a modified definition of the landscape Péclet number, which quantifies the relative influence of advective versus diffusive propagation of perturbations. Our Péclet number definition can account for the scaling of basin length with basin area, which depends on topographic convergence versus divergence.

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.

Orographic precipitation patterns, stream power, and river longitudinal profiles: Predictions and implications for detecting climate’s influence in mountain landscapes

2021 ◽  
Author(s):  
Joel Leonard ◽  
Kelin Whipple
Keyword(s):  
Climate Change ◽  
Steady State ◽  
Landscape Evolution ◽  
Orographic Precipitation ◽  
Power Model ◽  
Quasi Steady State ◽  
Stream Power ◽  
Spatial Gradients ◽  
Channel Steepness

&lt;p&gt;Dynamic climates featuring spatially and temporally variable precipitation patterns are ubiquitous in mountain settings. To understand the role of climate on landscape evolution in such settings, and how climate change-related signals might be translated into the sedimentary realm, this variability must be addressed. Here, we present an analysis of how spatial gradients and temporal changes in rainfall combine to affect both the steady state form and transient evolution of river profiles of large transverse river basins as predicted by the stream power model. Where rainfall is uniform, the stream power model predicts that topographic metrics, like fluvial relief and normalized channel steepness index (k&lt;sub&gt;sn&lt;/sub&gt;), vary inversely and monotonically with rainfall at steady state. In contrast, we find that these relationships are more complex and can be inverted in many circumstances, even at steady state, in the presence of orographic rainfall gradients. An important consequence of this is that correlations between average rainfall (climate) and topography are always weaker in catchments that experience rainfall gradients relative to expectations based on uniformly distributed rainfall. Moreover, dispersion caused by rainfall gradients is systematic, varying both with the polarity (i.e., generally increasing vs. decreasing downstream) and intensity of the gradient. Therefore, even in quasi-steady-state, rainfall gradients have the potential to obscure or distort the influence of climate on landscapes if they are not accounted for. In addition, we find that temporal changes in spatially variable rainfall patterns can produce complex erosional and morphological responses that can be contrary to expectations based on the change in mean rainfall. Specifically, enhanced incision and surface uplift may occur simultaneously in different parts of a landscape in a pattern that evolves during the transient response to climate change, complicating prediction of the net erosional and topographic response to climate change. Thus, transient responses to the orographic distribution of rainfall may misleadingly appear inconsistent with erosional or morphological responses expected for a relative change in average climate. Additionally, topographic indications of transient adjustment, even to a dramatic change in orographic precipitation, can be subtle enough that a landscape can appear to be in quasi-steady-state. In such cases, spatial gradients in erosion rate driven by a change in orographic precipitation pattern may be mistakenly interpreted as recording spatial gradients in rock uplift rate, potentially at once obscuring an important influence of climate and misinterpreting tectonic drivers of landscape evolution. Finally, we explore the use of a variant of normalized channel steepness index (k&lt;sub&gt;sn-q&lt;/sub&gt;) that is able to incorporate the influence of spatially variable in rainfall based on the stream power model. Importantly, we find that k&lt;sub&gt;sn-q&lt;/sub&gt; preforms well to help diagnose and quantify the role of climate acting in a landscape, in particular during transient adjustment to changes in rainfall patterns where the standard channel steepness metric (k&lt;sub&gt;sn&lt;/sub&gt;) may be misleading.&lt;/p&gt;

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 Characterization of a Shallow Coastal Aquifer in the Framework of a Subsurface Storage and Soil Aquifer Treatment Project Using Electrical Resistivity Tomography (Port de la Selva, Spain)

2021 ◽  
Vol 11 (6) ◽  
pp. 2448
Author(s):  
Alex Sendrós ◽  
Aritz Urruela ◽  
Mahjoub Himi ◽  
Carlos Alonso ◽  
Raúl Lovera ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Water Reuse ◽  
Electrical Resistivity Tomography ◽  
Groundwater Modeling ◽  
Geophysical Methods ◽  
Soil Aquifer Treatment ◽  
Modeling Tools ◽  
Resistivity Tomography ◽  
Implicit Modeling ◽  
The Difference

Water percolation through infiltration ponds is creating significant synergies for the broad adoption of water reuse as an additional non-conventional water supply. Despite the apparent simplicity of the soil aquifer treatment (SAT) approaches, the complexity of site-specific hydrogeological conditions and the processes occurring at various scales require an exhaustive understanding of the system’s response. The non-saturated zone and underlying aquifers cannot be considered as a black box, nor accept its characterization from few boreholes not well distributed over the area to be investigated. Electrical resistivity tomography (ERT) is a non-invasive technology, highly responsive to geological heterogeneities that has demonstrated useful to provide the detailed subsurface information required for groundwater modeling. The relationships between the electrical resistivity of the alluvial sediments and the bedrock and the difference in salinity of groundwater highlight the potential of geophysical methods over other more costly subsurface exploration techniques. The results of our research show that ERT coupled with implicit modeling tools provides information that can significantly help to identify aquifer geometry and characterize the saltwater intrusion of shallow alluvial aquifers. The proposed approaches could improve the reliability of groundwater models and the commitment of stakeholders to the benefits of SAT procedures.

scholarly journals Effects of Genotypes and Treatment on Oxygenscan Parameters in Sickle Cell Disease

Cells ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 811
Author(s):  
Camille Boisson ◽  
Minke A. E. Rab ◽  
Elie Nader ◽  
Céline Renoux ◽  
Celeste Kanne ◽  
...  
Keyword(s):  
Steady State ◽  
Sickle Cell Disease ◽  
Blood Cell ◽  
Sickle Cell ◽  
Red Blood Cell ◽  
Cell Disease ◽  
Oxygen Gradient ◽  
Acute Complication ◽  
Adults And Children ◽  
The Difference

(1) Background: The aim of the present study was to compare oxygen gradient ektacytometry parameters between sickle cell patients of different genotypes (SS, SC, and S/β+) or under different treatments (hydroxyurea or chronic red blood cell exchange). (2) Methods: Oxygen gradient ektacytometry was performed in 167 adults and children at steady state. In addition, five SS patients had oxygenscan measurements at steady state and during an acute complication requiring hospitalization. (3) Results: Red blood cell (RBC) deformability upon deoxygenation (EImin) and in normoxia (EImax) was increased, and the susceptibility of RBC to sickle upon deoxygenation was decreased in SC patients when compared to untreated SS patients older than 5 years old. SS patients under chronic red blood cell exchange had higher EImin and EImax and lower susceptibility of RBC to sickle upon deoxygenation compared to untreated SS patients, SS patients younger than 5 years old, and hydroxyurea-treated SS and SC patients. The susceptibility of RBC to sickle upon deoxygenation was increased in the five SS patients during acute complication compared to steady state, although the difference between steady state and acute complication was variable from one patient to another. (4) Conclusions: The present study demonstrates that oxygen gradient ektacytometry parameters are affected by sickle cell disease (SCD) genotype and treatment.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

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