Scales of Similarity and Disparity Between Drainage Networks

Roberts, Gareth G.

doi:10.1029/2019gl082446

Cited by 18 publications

(18 citation statements)

References 45 publications

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“…To determine scales at which river profiles are generated, their longitudinal profiles are transformed from the spatial domain, z ( x ), into the space‐wave number domain, z ( x , k ). Perhaps more conceptually simple is to first consider converting rivers into the wave number (i.e., spatial frequency) domain using, for example, a Fourier transform (e.g., Roberts, 2019). Transformation of rivers into the Fourier wave number domain, Z ( k ), should result in no change in total spectral power, P T , since

P_{T} = \int_{- \infty}^{\infty} {false| z (x) false|}^{2} normald x = \int_{- \infty}^{\infty} {false| Z (k) false|}^{2} normald f .

…”

Section: Observations and Methodologymentioning

confidence: 99%

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Scale‐Dependent Contributors to River Profile Geometry

et al. 2021

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A range of complex hydraulic and geomorphic processes shape terrestrial landscapes. It remains unclear how these processes act to generate observed drainage networks across scales of interest. To address this issue, we transform observed and synthetic longitudinal river profiles into the spectral domain with a view to interrogating the different scales at which fluvial landscapes are generated. North American river profiles are characterized by red noise (i.e., spectral power, ϕ ∝ k−2, where k is wave number) at wavelengths >100 km and pink noise (ϕ ∝ k−1) at shorter wavelengths. This observation suggests that river profile geometries are scale‐dependent and using small‐scale observations to develop a general understanding of large‐scale landscape evolution is not straightforward. At wavelengths >100 km, river profile geometries appear to be controlled by smoothly varying patterns of regional uplift and slope‐dependent incision. Landscape simulations, based upon stream power that are externally forced by regional uplift do not exhibit a spectral transition from red to pink noise because these simulations do not incorporate heterogeneous erodibility. Spectral analysis of erodibility extracted from patterns of lithologic variation along river profiles suggests that the missing spectral transition is accounted for by heterogeneous substrates, which are characterized by white or blue noise (ϕ ∝ k0 or k1). Our results have implications for the way by which rivers record large‐scale tectonic forcing while incising through complex lithologic patterns.

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P_{T} = \int_{- \infty}^{\infty} {false| z (x) false|}^{2} normald x = \int_{- \infty}^{\infty} {false| Z (k) false|}^{2} normald f .

…”

Section: Observations and Methodologymentioning

confidence: 99%

“…If both wavelet transforms are real valued, the cross‐wavelet spectrum is obtained by multiplying the two transformed signals. The resultant cross‐wavelet power spectrum, | W AB |, is highest where large amplitude signals on both rivers occupy the same distance‐wave number space (Grinsted et al., 2004; Roberts, 2019).…”

Section: Observations and Methodologymentioning

confidence: 99%

Scale‐Dependent Contributors to River Profile Geometry

et al. 2021

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“…Journal of Geophysical Research: Earth Surface generated by regional uplift Roberts, 2019). Nevertheless, there is a substantial body of work which demonstrates that at smaller scales these processes determine the efficacy of fluvial erosion and the geometry of river profiles (e.g.…”

Section: 1029/2018jf004979mentioning

confidence: 99%

Continental‐Scale Landscape Evolution: A History of North American Topography

2019

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The generation and evolution of continental topography are fundamental geologic and geomorphic concerns. In particular, the history of landscape development might contain useful information about the spatiotemporal evolution of deep Earth processes, such as mantle convection. A significant challenge is to generate observations and theoretical predictions of sufficient fidelity to enable landscape evolution to be constrained at scales of interest. Here, we combine substantial inventories of stratigraphic and geomorphic observations with inverse and forward modeling approaches to determine how the North American landscape evolved. First, stratigraphic markers are used to estimate postdepositional regional uplift. Present‐day elevations of these deposits demonstrate that >2 km of long‐wavelength surface uplift centered on the Colorado‐Rocky‐Mountain plateaus occurred in Cenozoic times. Second, to bridge the gaps between these measurements, an inverse modeling scheme is used to calculate the smoothest spatiotemporal pattern of rock uplift rate that yields the smallest misfit between 4,161 observed and calculated longitudinal river profiles. Our results suggest that Cenozoic regional uplift occurred in a series of stages, in agreement with independent stratigraphic observations. Finally, a landscape evolution model driven by this calculated rock uplift history is used to determine drainage patterns, denudation, and sedimentary flux from Late Cretaceous times until the present day. These patterns are broadly consistent with stratigraphic and thermochronologic observations. We conclude that a calibrated inverse modeling strategy can be used to reliably extract the temporal and spatial evolution of the North American landscape at geodynamically useful scales.

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“…Drainage networks are a ubiquitous feature of terrestrial landscapes, and the elevation of river profiles along their lengths has long been known to record the interplay of uplift and erosion (Howard et al, 1994). Recent spectral analyses of African drainage patterns indicates that river elevation changes are dominanted by power at wavelengths 100 km, suggesting that large coherent signals, such as regional uplift caused by dynamic topography, are potentially recoverable despite overprinting by shorter wavelength complexities, such as variations in lithology, precipitation and biota (Roberts, 2019;Roberts et al, 2019).…”

Section: Drainage Analysismentioning

confidence: 99%

Observational estimates of dynamic topography through space and time

Hoggard¹,

Austermann²,

Randel³

et al. 2023

Preprint

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Earth's mantle undergoes convection on million-year timescales as heat is transferred from depth to the surface. Whilst this flow has long been linked to the large-scale horizontal forces that drive plate tectonics and supercontinent cycles, geologists are increasingly recognising the signature of convection through transient vertical motions in the rock record, known as "dynamic topography". A significant component of topography is supported by lithospheric isostasy, and changes in lithospheric thermal structure are sometimes included in the definition of dynamic topography. An additional component arises from active flow within the underlying convecting mantle, and this process causes dynamic topography that has lengthscales varying from 10,000 km down to 500 km and typical amplitudes of ±1 km. Transient uplift and subsidence events are often slow, but might evolve at rates as fast as 500 m/Myr over cycles as short as ~3 Myr, leading to periodic overwriting of the geological record that results in complex interpretational challenges. Despite these difficulties, a growing number of observational and computational studies have highlighted the important role of dynamic topography in fields as diverse as intraplate magmatism, sedimentary stratigraphy, landscape evolution, paleo-shorelines, oceanic circulation patterns, and ice sheet stability. This review provides a brief overview of our current understanding of the topic and explores some basic insights that can be gained from simple three-dimensional numerical simulations of mantle convection under different convective regimes. We summarise a suite of observational techniques used to estimate dynamic topography, and finish by laying out some key unanswered questions to stimulate debate and inspire future studies.

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Scales of Similarity and Disparity Between Drainage Networks

Cited by 18 publications

References 45 publications

Scale‐Dependent Contributors to River Profile Geometry

Scale‐Dependent Contributors to River Profile Geometry

Continental‐Scale Landscape Evolution: A History of North American Topography

Observational estimates of dynamic topography through space and time

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