African Epeirogeny in the Geomorphic Record

2021 ◽  
Author(s):  
Conor O'Malley ◽  
Nicky White ◽  
Gareth Roberts ◽  
Simon Stephenson
Keyword(s):  
Inverse Modeling ◽  
Landscape Evolution ◽  
Power Spectral Analysis ◽  
Forward Model ◽  
Uplift Rate ◽  
Geological Evidence ◽  
Sedimentary Flux ◽  
Self Similar ◽  
River Profiles ◽  
Tectonic Forcing

<p>A range of geological evidence documents the growth of African topography as a result of sub-plate support throughout Cenozoic times. Recent studies used inverse modeling of drainage networks governed by the linear stream power law to quantify the spatio-temporal history of uplift and erosion across the continent. Here, we test predictions of this uplift rate history by applying it as tectonic forcing to naturalistic landscape evolution simulations. These simulations parameterise dynamic drainage reorganisation, track sedimentary flux, and permit variable erodibility, none of which are feasible in inverse models. Modelled topography, river profiles, drainage planforms and sedimentary flux patterns broadly match observations. We test the sensitivity of forward model prediction to variations in erodilibity by employing spatio-temporally variable precipitation rate. Forward model predictions are relatively robust to even large excursions, suggesting landscapes contain internal feedbacks which modulate these effects and permit close recovery of the geomorphic record of uplift. Wavelet power spectral analysis reveals observed African river profiles are self-similar at wavelengths >~ 100 km, meaning longest-wavelength features have the highest amplitudes. At shorter wavelengths, spectral slopes increase, implying sharper features are generated only at wavelengths <~ 100km. Synthetic fluvial profiles recovered from simple landscape evolution models driven by uplift forcing obtained from inverse modeling of observed river profiles are self-similar across all wavelengths. This self-similarity solely reflects the tectonic forcing applied. When noise in erodibility or uplift rate forcing is added to forward simulations, power spectra of resulting fluvial profiles more closely approximate spectra of observed profiles. Thus sharp signals in observed river profiles arise from factors which do not correlate between neighbouring tributaries, e.g. lithological constrasts, self-forming hydraulic shocks, or human alteration. The recoverability of regional uplift from observed fluvial profiles is made possible by the fact that most topographic power is generated by regional uplift and resides at long-wavelengths.</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.

scholarly journals Dimensional analysis of a landscape evolution model with incision threshold

2020 ◽  
Vol 8 (2) ◽  
pp. 505-526
Author(s):  
Nikos Theodoratos ◽  
James W. Kirchner
Keyword(s):  
Dimensional Analysis ◽  
Governing Equation ◽  
Dimensionless Parameter ◽  
Landscape Evolution ◽  
Initial Conditions ◽  
Uplift Rate ◽  
Stream Power ◽  
Linear Diffusion ◽  
Scaling Properties

Abstract. The ability of erosional processes to incise into a topographic surface can be limited by a threshold. Incision thresholds affect the topography of landscapes and their scaling properties and can introduce nonlinear relations between climate and erosion with notable implications for long-term landscape evolution. Despite their potential importance, incision thresholds are often omitted from the incision terms of landscape evolution models (LEMs) to simplify analyses. Here, we present theoretical and numerical results from a dimensional analysis of an LEM that includes terms for threshold-limited stream-power incision, linear diffusion, and uplift. The LEM is parameterized by four parameters (incision coefficient and incision threshold, diffusion coefficient, and uplift rate). The LEM's governing equation can be greatly simplified by recasting it in a dimensionless form that depends on only one dimensionless parameter, the incision-threshold number Nθ. This dimensionless parameter is defined in terms of the incision threshold, the incision coefficient, and the uplift rate, and it quantifies the reduction in the rate of incision due to the incision threshold relative to the uplift rate. Being the only parameter in the dimensionless governing equation, Nθ is the only parameter controlling the evolution of landscapes in this LEM. Thus, landscapes with the same Nθ will evolve geometrically similarly, provided that their boundary and initial conditions are normalized according to appropriate scaling relationships, as we demonstrate using a numerical experiment. In contrast, landscapes with different Nθ values will be influenced to different degrees by their incision thresholds. Using results from a second set of numerical simulations, each with a different incision-threshold number, we qualitatively illustrate how the value of Nθ influences the topography, and we show that relief scales with the quantity Nθ+1 (except where the incision threshold reduces the rate of incision to zero).

The interaction between uplift and landscape evolution in central and northern Qilian Shan: Insights from numerical modeling

2020 ◽  
Author(s):  
Yifei Li ◽  
Huai Zhang ◽  
Zhen Zhang
Keyword(s):  
Tibetan Plateau ◽  
Landscape Evolution ◽  
Great Influence ◽  
Arid Climate ◽  
Structural Deformation ◽  
The Tibetan Plateau ◽  
Lateral Growth ◽  
Uplift Rate ◽  
Fault Propagation

&lt;p&gt;The Qilian Shan, located in the northeastern margin of the Tibetan Plateau, is characterized by intensive Cenozoic structural deformation with rapid lateral growth due to the continuous Indo-Asian continental collision. Both low-temperature thermochronological dating and geological mapping suggest that the major emergence of Cenozoic Qilian Shan occurred in the Miocene. The central and northern Qilian Shan uplift successively, and deformation has passed away from the adjacent Hexi Corridor Basin into the Gobi-Alashan. The regional landform shows a low-relief surface in the Qilian Shan hinterland and high steep relief in the northern range front.&lt;/p&gt;&lt;p&gt;The rivers rising in the hinterland of the Qilian Shan, i.e., the Shule River (SL), Beda River (BD), and Hei River (HE), are flowing across the northern range front. It is noteworthy that the development of these rivers is within the context of the in-sequence fault propagation pattern with the lifespan of ~3 Ma. When combined with the differential topographies between hinterland and range front, this kind of river drainage pattern inevitably has abundant geodynamical significances, mainly in terms of the long-term coupling between tectonic and surficial processes. To date, the dynamic conditions in shaping the aforementioned tectonic landscape features remain unknown and are critical in revealing the lateral growth of the NE Tibetan Plateau. A series of landscape evolution models are conducted based on thick-skinned Qilian Shan structural wedge. The wavelength of mountains is constrained by the critical wedge theory.&lt;/p&gt;&lt;p&gt;Our results show that the in-sequence fault propagation together with the arid climate since the Miocene contributes to the low-relief topography in the hinterland of Qilian Shan. The front regions with rapid uplifting rates cut off rivers. Thus, sediments from the hinterlands cannot be directly carried out by rivers. The intermountain areas receive sediments from the adjacent uplift regions, resulting in an increased elevation. Because of the long-term average arid climate, the river incision is limited. For most areas, it is difficult to form transversal rivers immediately that cut through mountains and carry sediment out of the plateau. With the northeastward in-sequence fault propagation, the transversal rivers finally formed with headwaters within the hinterland of Qilian Shan, such as the SL, BD and HE. The broad consistency of landforms, in turn, strongly favors the geological conclusion that faults in the central and northern Qilian Shan were activated sequentially. The rapid uplift rate in the active range front is tested in the range of 0.6-1.0 mm/a. It is found that this rate is insensitivity to the drainage and landscape evolution pattern. However, the background uplift rate has a great influence on the elevation of the plateau and is positively correlated. The current topography of &gt;4000 m in the hinterland of Qilian Shan is controlled by a background uplift rate of ~0.2mm /a.&lt;/p&gt;

scholarly journals River profile response to normal fault growth and linkage: an example from the Hellenic forearc of south-central Crete, Greece

2017 ◽  
Vol 5 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Sean F. Gallen ◽  
Karl W. Wegmann
Keyword(s):  
Profile Analysis ◽  
Normal Fault ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
River Incision ◽  
South Central ◽  
History Of ◽  
River Profiles ◽  
Fault Growth

Abstract. Topography is a reflection of the tectonic and geodynamic processes that act to uplift the Earth's surface and the erosional processes that work to return it to base level. Numerous studies have shown that topography is a sensitive recorder of tectonic signals. A quasi-physical understanding of the relationship between river incision and rock uplift has made the analysis of fluvial topography a popular technique for deciphering relative, and some argue absolute, histories of rock uplift. Here we present results from a study of the fluvial topography from south-central Crete, demonstrating that river longitudinal profiles indeed record the relative history of uplift, but several other processes make it difficult to recover quantitative uplift histories. Prior research demonstrates that the south-central coastline of Crete is bound by a large ( ∼  100 km long) E–W striking composite normal fault system. Marine terraces reveal that it is uplifting between 0.1 and 1.0 mm yr−1. These studies suggest that two normal fault systems, the offshore Ptolemy and onshore South-Central Crete faults, linked together in the recent geologic past (ca. 0.4–1 My BP). Fault mechanics predict that when adjacent faults link into a single fault the uplift rate in footwalls of the linkage zone will increase rapidly. We use this natural experiment to assess the response of river profiles to a temporal jump in uplift rate and to assess the applicability of the stream power incision model to this setting. Using river profile analysis we show that rivers in south-central Crete record the relative uplift history of fault growth and linkage as theory predicts that they should. Calibration of the commonly used stream power incision model shows that the slope exponent, n, is  ∼  0.5, contrary to most studies that find n  ≥  1. Analysis of fluvial knickpoints shows that migration distances are not proportional to upstream contributing drainage area, as predicted by the stream power incision model. Maps of the transformed stream distance variable, χ, indicate that drainage basin instability, drainage divide migration, and river capture events complicate river profile analysis in south-central Crete. Waterfalls are observed in southern Crete and appear to operate under less efficient and different incision mechanics than assumed by the stream power incision model. Drainage area exchange and waterfall formation are argued to obscure linkages between empirically derived metrics and quasi-physical descriptions of river incision, making it difficult to quantitatively interpret rock uplift histories from river profiles in this setting. Karst hydrology, break down of assumed drainage area discharge scaling, and chemical weathering might also contribute to the failure of the stream power incision model to adequately predict the behavior of the fluvial system in south-central Crete.

scholarly journals PAMTRA 1.0: A Passive and Active Microwave radiative TRAnsfer tool for simulating radiometer and radar measurements of the cloudy atmosphere

2020 ◽  
Author(s):  
Mario Mech ◽  
Maximilian Maahn ◽  
Stefan Kneifel ◽  
Davide Ori ◽  
Emiliano Orlandi ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Forward Model ◽  
Doppler Spectrum ◽  
Brightness Temperatures ◽  
Cloudy Atmosphere ◽  
Radar Measurements ◽  
Self Similar ◽  
Atmospheric State ◽  
Simulation Results

Abstract. Forward models are a key tool to generate synthetic observations given the knowledge of the atmospheric state. In this way they are an integral part of inversion algorithms that aim to retrieve geophysical variables from observations or in data assimilation. Their application for the exploitation of the full information content of remote sensing observations becomes increasingly important when these are used to evaluate the performance of cloud resolving models (CRMs). Herein, CRMs profiles or fields provide the input to the forward model whose simulation results are subsequently compared to the observations. This paper introduces the freely available comprehensive microwave forward model PAMTRA (Passive and Active Microwave TRAnsfer), demonstrates its capabilities to simulate passive and active measurements across the microwave spectral region for up- and downward looking geometries, and illustrates how the forward simulations can be used to evaluate CRMs and to interpret measurements to improve our understanding of cloud processes. PAMTRA is unique as it treats passive and active radiative transfer (RT) in a consistent way with the passive forward model providing up- and down-welling polarized brightness temperatures and radiances for arbitrary observation angles. The active part is capable of simulating the full radar Doppler spectrum and its moments. PAMTRA is designed to be flexible with respect to instrument specifications, interfaces to many different formats of in- and output type, especially CRMs, spanning the range from bin-resolved microphysical output to one- and two-moment schemes, and to in situ measured hydrometeor properties. A specific highlight is the incorporation of the self-similar Rayleigh--Gans Approximation (SSRGA) both for active and passive applications which becomes especially important for the investigation of frozen hydrometeors.

scholarly journals PAMTRA 1.0: the Passive and Active Microwave radiative TRAnsfer tool for simulating radiometer and radar measurements of the cloudy atmosphere

2020 ◽  
Vol 13 (9) ◽  
pp. 4229-4251 ◽  
Author(s):  
Mario Mech ◽  
Maximilian Maahn ◽  
Stefan Kneifel ◽  
Davide Ori ◽  
Emiliano Orlandi ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Forward Model ◽  
Doppler Spectrum ◽  
Brightness Temperatures ◽  
Input And Output ◽  
Cloudy Atmosphere ◽  
Radar Measurements ◽  
Self Similar ◽  
Atmospheric State

Abstract. Forward models are a key tool to generate synthetic observations given knowledge of the atmospheric state. In this way, they are an integral part of inversion algorithms that aim to retrieve geophysical variables from observations or in data assimilation. Their application for the exploitation of the full information content of remote sensing observations becomes increasingly important when these are used to evaluate the performance of cloud-resolving models (CRMs). Herein, CRM profiles or fields provide the input to the forward model whose simulation results are subsequently compared to the observations. This paper introduces the freely available comprehensive microwave forward model PAMTRA (Passive and Active Microwave TRAnsfer), demonstrates its capabilities to simulate passive and active measurements across the microwave spectral region for upward- and downward-looking geometries, and illustrates how the forward simulations can be used to evaluate CRMs and to interpret measurements to improve our understanding of cloud processes. PAMTRA is unique as it treats passive and active radiative transfer (RT) in a consistent way with the passive forward model providing upwelling and downwelling polarized brightness temperatures and radiances for arbitrary observation angles. The active part is capable of simulating the full radar Doppler spectrum and its moments. PAMTRA is designed to be flexible with respect to instrument specifications and interfaces to many different formats of input and output, especially CRMs, spanning the range from bin-resolved microphysical output to one- and two-moment schemes, and to in situ measured hydrometeor properties. A specific highlight is the incorporation of the self-similar Rayleigh–Gans approximation (SSRGA) for both active and passive applications, which becomes especially important for the investigation of frozen hydrometeors.

Importance of concavity for interpreting rates and patterns of landscape evolution from river profiles

2020 ◽  
Author(s):  
Boris Gailleton ◽  
Simon Mudd ◽  
Fiona Clubb ◽  
Martin Hurst ◽  
Stuart Grieve
Keyword(s):  
Landscape Evolution ◽  
Spatial Scales ◽  
Reference Value ◽  
High Sensitivity ◽  
Drainage Area ◽  
Relative Distribution ◽  
Sea Level Changes ◽  
Widespread Application ◽  
River Profiles ◽  
Channel Steepness

&lt;p&gt;The analysis of river profiles is a fundamental tool in modern quantitative geomorphology. Since the 1960's, workers have demonstrated a systematic power-law relationship between river gradient and discharge, or its proxy drainage area, predicting a steepening of rivers towards the headwaters. This relationship provides means of quantitatively describing river profiles by extracting a concavity index (&lt;em&gt;&amp;#952;&lt;/em&gt;), the rate at which slope decreases as a function of drainage area, and steepness index (&lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;), the steepness of river reaches independent of changes in drainage area. Recent developments have provided an alternative representation of the slope-area relationship, aiming to circumvent its high sensitivity to topographic noise and to the branching nature of fluvial networks by directly integrating drainage area normalised to a concavity index into a transformed coordinate (&lt;em&gt;&amp;#967;&lt;/em&gt;). These parameters can be easily extracted from digital elevation models, resulting in their widespread application to detect tectonic, climatic, and autogenic signals from landscape morphology, such as active faulting, stream piracy, drainage divide migration or sea-level changes.&lt;/p&gt;&lt;p&gt;River profile concavity, or &lt;em&gt;&amp;#952;&lt;/em&gt;, is an essential metric to constrain, as it is necessary to fix a reference value &lt;em&gt;&amp;#952;&lt;sup&gt;ref&lt;/sup&gt;&lt;/em&gt; in order to compare &lt;em&gt;&amp;#967;&lt;/em&gt; or &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; values between different drainage basins. This exposes a key problem with the slope-area relationship: the watersheds within a study area do not necessarily all have the same optimal &lt;em&gt;&amp;#952;&lt;/em&gt;, potentially leading to incorrect interpretations of the relative distribution of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; within a landscape. This problem is enhanced over large spatial scales, such as over the width of an orogen, where the probability of &lt;em&gt;&amp;#952;&lt;/em&gt; heterogeneity increases drastically. However, the distortion of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt; linked to a &lt;em&gt;&amp;#952;&lt;sup&gt;ref&lt;/sup&gt;&lt;/em&gt; being different than the local best-fit has been poorly explored: we currently do not know how much these concavity variations influence channel steepness interpretations.&lt;/p&gt;&lt;p&gt;In this contribution, we explore the extent of the effect of varying concavity on channel steepness using analytical and numerical methods both on landscape evolution models and real landscapes. We show that (i) relative values of &lt;em&gt;&amp;#967;&lt;/em&gt; and &lt;em&gt;k&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;, i.e location of local maxima, minima and variations, can be significantly and non-linearly impacted as a function of their &lt;em&gt;&amp;#916;&amp;#952;&lt;/em&gt; from optimal &lt;em&gt;&amp;#952;&lt;/em&gt; and drainage area; (ii) we identify cases where asymmetries in &lt;em&gt;&amp;#952;&lt;/em&gt; can cause incorrect interpretations of changes in channel steepness (iii) present tools to quantify the extent and therefore the risk of misinterpretation.&lt;/p&gt;

Inverse modeling of dog airway and respiratory system impedances

1987 ◽  
Vol 62 (6) ◽  
pp. 2273-2282 ◽  
Author(s):  
A. C. Jackson ◽  
K. R. Lutchen ◽  
H. L. Dorkin
Keyword(s):  
Respiratory System ◽  
Inverse Modeling ◽  
Element Model ◽  
Forward Model ◽  
Tube Model ◽  
Tube Radius ◽  
Lumped Element ◽  
Inverse Models ◽  
Gas Compression ◽  
Frequency Independent

Mechanical parameters of the respiratory system are often estimated from respiratory impedances using lumped-element inverse models. One such six-element model is composed of an airway branch [with a resistance (Raw) and inertance (Iaw)] separated from a tissue branch [with a resistance (Rt), inertance (It), and compliance (Ct)] by a shunt compliance representing alveolar gas compression (Cg). Even though the airways are known to have frequency-dependent resistance and inertance, these inverse models have been composed of linear frequency-independent elements. In this study we investigated the use of inverse models where the airway branch was represented by a frequency-independent Raw and Iaw, a Raw that is linearly related to frequency and an Iaw that is independent of frequency, and a system of identical parallel tubes the impedance of which was computed from the tube radius and length. These inverse models were used to analyze airway and respiratory impedances between 2 and 1,024 Hz that were predicted from an anatomically detailed forward model. The forward model represented the airways by an asymmetrically branched network with a terminal impedance representative of known Cg, Rt, It, and Ct. For respiratory impedances between 2 and 128 Hz, all models fit the data reasonably well, and reasonably accurate estimates of Cg, Rt, It, and Ct were extracted from these data. For data above 200 Hz, however, only the multiple-tube model accurately fitted respiratory impedances (Zrs). This model fitted the Zrs data best when composed of 27 tubes, each having a radius of 0.148 cm and a length of 16.5 cm.

scholarly journals A segmentation approach for the reproducible extraction and quantification of knickpoints from river long profiles

2018 ◽  
Author(s):  
Boris Gailleton ◽  
Simon M. Mudd ◽  
Fiona J. Clubb ◽  
Daniel Peifer ◽  
Martin D. Hurst
Keyword(s):  
Landscape Evolution ◽  
Channel Length ◽  
Negative Slope ◽  
Erosion Rates ◽  
Quadrilátero Ferrífero ◽  
Extraction Algorithm ◽  
Tectonically Active ◽  
Segmentation Approach ◽  
Reproducible Method ◽  
River Profiles

Abstract. Changes in the steepness of river profiles or abrupt vertical steps (i.e. waterfalls) are thought to be indicative of changes in erosion rates, lithology, or other factors that affect landscape evolution. These changes are referred to as knickpoints or knickzones and are pervasive in bedrock river systems. Such features are thought to reveal information about landscape evolution and patterns of erosion, and therefore their locations are often reported in the geomorphic literature. It is imperative that studies reporting knickpoints and knickzones use a reproducible method of quantifying their locations, as their number and spatial distribution play an important role in interpreting tectonically active landscapes. In this contribution we introduce a reproducible knickpoint and knickzone extraction algorithm that uses river profiles transformed by integrating drainage area along channel length (the so-called integral or χ method). The profile is then statistically segmented and the differing slopes and step changes in elevations of these segments are used to identify knickpoints and knickzones, and their relative magnitudes. The output locations of identified knickpoints and knickzones compare favourably with human mapping: we test the method on Santa Cruz Island, CA, using previously reported knickzones and also test the method against a new dataset from the Quadrilátero Ferrífero in Brazil. The algorithm allows extraction of varying knickpoint morphologies, including stepped, positive slope-breaks (concave upward) and negative slope-break knickpoints. We identify parameters that most affect the resulting knickpoint and knickzone locations, and provide guidance for both usage and outputs of the method to produce reproducible knickpoint datasets.

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